Finite Group Databasebeta

← C137×#14519 #46863905

Subgroups — C137×#14519 #46863905

Order 35072.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C137C211yesmaximal, characteristic
2C2×#390×C137C211yesmaximal, characteristic, complemented
3C2×#386×C137C211yesmaximal, characteristic, complemented
4C2×#386×C137C211yesmaximal, characteristic, complemented
5C2×#386×C137C211yesmaximal, characteristic, complemented
6C2×#386×C137C211yesmaximal, characteristic, complemented
7C2×#385×C137C211yesmaximal, characteristic, complemented
8#1442×C137C211yesmaximal, characteristic, complemented
9#1440×C137C211yesmaximal, characteristic, complemented
10#1439×C137C211yesmaximal, characteristic, complemented
11#1439×C137C211yesmaximal, characteristic, complemented
12#1438×C137C211yesmaximal, characteristic, complemented
13#1437×C137C211yesmaximal, characteristic, complemented
14#1434×C137C211yesmaximal, characteristic, complemented
15C22⋊#95×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C23×D4×C137C2211yescharacteristic
19C24×C4×C137C2211yescharacteristic
20C24×C4×C137C2211yescharacteristic
21C22×C4⋊C4×C137C2211yescharacteristic
22C22×C4⋊C4×C137C2211yescharacteristic
23C22×C22⋊C4×C137C2211yescharacteristic
24C22×C22⋊C4×C137C2211yescharacteristic
25C22×C22⋊C4×C137C2211yescharacteristic
26C22×C22⋊C4×C137C2211yescharacteristic
27C22×C22⋊C4×C137C2211yescharacteristic
28C22×C22⋊C4×C137C2211yescharacteristic
29C22×C22⋊C4×C137C2211yescharacteristic
30C22×C22⋊C4×C137C2211yescharacteristic
31C22×C22⋊C4×C137C2211yescharacteristic
32C22×C22⋊C4×C137C2211yescharacteristic
33C22×C22⋊C4×C137C2211yescharacteristic
34C22×C22⋊C4×C137C2211yescharacteristic
35C22×C22⋊C4×C137C2211yescharacteristic
36C22×C42×C137C2211yescharacteristic
37#392×C137C418yescomplemented
38#390×C137—24no—
39#386×C137—24no—
40#386×C137—24no—
41#386×C137—24no—
42#386×C137—24no—
43#385×C137—24no—
44C2×#95×C137C2211yescharacteristic
45C2×#95×C137C2211yescharacteristic
46C2×#95×C137C2211yescharacteristic
47C2×#95×C137C2211yescharacteristic
48C2×#95×C137C2211yescharacteristic
49C2×#95×C137C2211yescharacteristic
50C2×#95×C137C2211yescharacteristic
51C2×#95×C137C2211yescharacteristic
52C2×#95×C137C2211yescharacteristic
53C2×#95×C137C2211yescharacteristic
54C2×#95×C137C2211yescharacteristic
55C2×#95×C137C2211yescharacteristic
56C2×#95×C137C2211yescharacteristic
57C2×#95×C137C2211yescharacteristic
58C25×C137C2311yescharacteristic
59C25×C137C2311yescharacteristic
60C25×C137C2311yescharacteristic
61C22×D4×C137—22no—
62C22×D4×C137—22no—
63C22×D4×C137—22no—
64C22×D4×C137—22no—
65C22×D4×C137—22no—
66C22×D4×C137—22no—
67C22×D4×C137—22no—
68C22×D4×C137—22no—
69C22×D4×C137—22no—
70C22×D4×C137—22no—
71C22×D4×C137—41no—
72C22×D4×C137—41no—
73C22×D4×C137—41no—
74C22×D4×C137—41no—
75C22×D4×C137—41no—
76C22×D4×C137—41no—
77C22×D4×C137—41no—
78C22×D4×C137—41no—
79C22×D4×C137C2×C414yes—
80C22×D4×C137C2×C414yescomplemented
81C22×D4×C137C2×C414yescomplemented
82C23×C4×C137—22no—
83C23×C4×C137—22no—
84C23×C4×C137—22no—
85C23×C4×C137—22no—
86C23×C4×C137—22no—
87C23×C4×C137—22no—
88C23×C4×C137—41no—
89C23×C4×C137—41no—
90C23×C4×C137—41no—
91C23×C4×C137—41no—
92C23×C4×C137—41no—
93C23×C4×C137—41no—
94C23×C4×C137—41no—
95C23×C4×C137—41no—
96C23×C4×C137C2311yescharacteristic
97C23×C4×C137C2311yescharacteristic
98C23×C4×C137C2311yescharacteristic
99C23×C4×C137C2311yescharacteristic
100C23×C4×C137C2311yescharacteristic
101C23×C4×C137C2311yescharacteristic
102C23×C4×C137C2311yescharacteristic
103C23×C4×C137C2311yescharacteristic
104C23×C4×C137C2311yescharacteristic
105C23×C4×C137C2311yescharacteristic
106C23×C4×C137C2311yescharacteristic
107C23×C4×C137C2311yescharacteristic
108C2×C4⋊C4×C137—22no—
109C2×C4⋊C4×C137—22no—
110C2×C4⋊C4×C137—22no—
111C2×C4⋊C4×C137—41no—
112C2×C4⋊C4×C137—41no—
113C2×C4⋊C4×C137—41no—
114C2×C22⋊C4×C137—22no—
115C2×C22⋊C4×C137—22no—
116C2×C22⋊C4×C137—22no—
117C2×C22⋊C4×C137—22no—
118C2×C22⋊C4×C137—22no—
119C2×C22⋊C4×C137—22no—
120C2×C22⋊C4×C137—22no—
121C2×C22⋊C4×C137—22no—
122C2×C22⋊C4×C137—22no—
123C2×C22⋊C4×C137—22no—
124C2×C22⋊C4×C137—22no—
125C2×C22⋊C4×C137—22no—
126C2×C22⋊C4×C137—22no—
127C2×C22⋊C4×C137—22no—
128C2×C22⋊C4×C137—22no—
129C2×C22⋊C4×C137—22no—
130C2×C22⋊C4×C137—41no—
131C2×C22⋊C4×C137—41no—
132C2×C22⋊C4×C137—41no—
133C2×C22⋊C4×C137—41no—
134C2×C22⋊C4×C137—41no—
135C2×C22⋊C4×C137—41no—
136C2×C22⋊C4×C137—41no—
137C2×C22⋊C4×C137—41no—
138C2×C22⋊C4×C137—41no—
139C2×C22⋊C4×C137—41no—
140C2×C22⋊C4×C137—41no—
141C2×C22⋊C4×C137—41no—
142C2×C22⋊C4×C137—41no—
143C2×C22⋊C4×C137—41no—
144C2×C22⋊C4×C137—41no—
145C2×C22⋊C4×C137—41no—
146C2×C22⋊C4×C137—41no—
147C2×C22⋊C4×C137—41no—
148C2×C22⋊C4×C137C2×C414yescomplemented
149C2×C22⋊C4×C137C2×C414yescomplemented
150C2×C22⋊C4×C137C2×C414yescomplemented
151C2×C22⋊C4×C137D414yescomplemented
152C2×C22⋊C4×C137D414yescomplemented
153C2×C42×C137—22no—
154C2×C42×C137—22no—
155C2×C42×C137—41no—
156#95×C137—22no—
157#95×C137—22no—
158#95×C137—22no—
159#95×C137—22no—
160#95×C137—22no—
161#95×C137—22no—
162#95×C137—22no—
163#95×C137—22no—
164#95×C137—41no—
165#95×C137—41no—
166#95×C137—41no—
167#95×C137—41no—
168#95×C137C2×C414yescomplemented
169#95×C137D414yescomplemented
170C24×C137—21no—
171C24×C137—21no—
172C24×C137—21no—
173C24×C137—21no—
174C24×C137—21no—
175C24×C137—21no—
176C24×C137—21no—
177C24×C137—21no—
178C24×C137—21no—
179C24×C137—21no—
180C24×C137—21no—
181C24×C137—21no—
182C24×C137—21no—
183C24×C137—21no—
184C24×C137—21no—
185C24×C137—21no—
186C24×C137—21no—
187C24×C137—21no—
188C24×C137—21no—
189C24×C137—21no—
190C24×C137—21no—
191C24×C137—21no—
192C24×C137—21no—
193C24×C137—21no—
194C24×C137—21no—
195C24×C137—21no—
196C24×C137—21no—
197C24×C137—21no—
198C24×C137—21no—
199C24×C137—21no—
200C24×C137—21no—
201C24×C137—21no—
202C24×C137—21no—
203C24×C137—21no—
204C24×C137—21no—
205C24×C137—21no—
206C24×C137—21no—
207C24×C137—21no—
208C24×C137C22×C412yes—
209C24×C137C22×C412yes—
210C24×C137C22×C412yes—
211C24×C137C2×D412yes—
212C24×C137C2×D412yes—
213C24×C137#4112yes—
214C24×C137#4112yes—
215C24×C137C2411yescharacteristic
216C2×D4×C137—28no—
217C2×D4×C137—28no—
218C2×D4×C137—28no—
219C2×D4×C137—28no—
220C2×D4×C137—28no—
221C2×D4×C137—44no—
222C2×D4×C137—44no—
223C2×D4×C137—44no—
224C2×D4×C137—44no—
225C2×D4×C137—44no—
226C2×D4×C137—44no—
227C2×D4×C137—44no—
228C2×D4×C137—44no—
229C2×D4×C137—44no—
230C2×D4×C137—44no—
231C2×D4×C137—44no—
232C2×D4×C137—44no—
233C2×D4×C137—44no—
234C2×D4×C137—44no—
235C2×D4×C137—44no—
236C2×D4×C137—44no—
237C22×C4×C137—21no—
238C22×C4×C137—21no—
239C22×C4×C137—21no—
240C22×C4×C137—21no—
241C22×C4×C137—21no—
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—21no—
245C22×C4×C137—21no—
246C22×C4×C137—21no—
247C22×C4×C137—21no—
248C22×C4×C137—21no—
249C22×C4×C137—21no—
250C22×C4×C137—21no—
251C22×C4×C137—21no—
252C22×C4×C137—21no—
253C22×C4×C137—21no—
254C22×C4×C137—21no—
255C22×C4×C137—21no—
256C22×C4×C137—21no—
257C22×C4×C137—21no—
258C22×C4×C137—21no—
259C22×C4×C137—21no—
260C22×C4×C137—21no—
261C22×C4×C137—21no—
262C22×C4×C137—21no—
263C22×C4×C137—21no—
264C22×C4×C137—21no—
265C22×C4×C137—21no—
266C22×C4×C137—21no—
267C22×C4×C137—21no—
268C22×C4×C137—21no—
269C22×C4×C137—21no—
270C22×C4×C137—21no—
271C22×C4×C137—21no—
272C22×C4×C137—21no—
273C22×C4×C137—21no—
274C22×C4×C137—21no—
275C22×C4×C137—21no—
276C22×C4×C137—21no—
277C22×C4×C137—21no—
278C22×C4×C137—21no—
279C22×C4×C137—21no—
280C22×C4×C137—21no—
281C22×C4×C137—21no—
282C22×C4×C137—21no—
283C22×C4×C137—21no—
284C22×C4×C137—21no—
285C22×C4×C137—21no—
286C22×C4×C137—21no—
287C22×C4×C137—21no—
288C22×C4×C137—21no—
289C22×C4×C137—21no—
290C22×C4×C137—21no—
291C22×C4×C137—21no—
292C22×C4×C137—21no—
293C22×C4×C137—21no—
294C22×C4×C137—21no—
295C22×C4×C137—21no—
296C22×C4×C137—21no—
297C22×C4×C137—21no—
298C22×C4×C137—21no—
299C22×C4×C137—21no—
300C22×C4×C137—21no—
301C22×C4×C137—21no—
302C22×C4×C137—21no—
303C22×C4×C137—21no—
304C22×C4×C137—21no—
305C22×C4×C137—21no—
306C22×C4×C137—21no—
307C22×C4×C137—21no—
308C22×C4×C137—21no—
309C22×C4×C137—44no—
310C22×C4×C137—44no—
311C22×C4×C137—44no—
312C22×C4×C137—44no—
313C22×C4×C137—44no—
314C22×C4×C137—44no—
315C22×C4×C137—44no—
316C22×C4×C137—44no—
317C22×C4×C137—44no—
318C22×C4×C137—44no—
319C22×C4×C137—44no—
320C22×C4×C137—44no—
321C22×C4×C137—44no—
322C22×C4×C137—44no—
323C22×C4×C137C22×C412yes—
324C22×C4×C137C22×C412yes—
325C22×C4×C137C22×C412yes—
326C22×C4×C137C22×C412yes—
327C22×C4×C137C2×D412yes—
328C22×C4×C137C2×D412yes—
329C22×C4×C137C2×D412yes—
330C22×C4×C137C2×D412yes—
331C22×C4×C137C2×D412yes—
332C22×C4×C137C2×D412yes—
333C22×C4×C137C2×D412yes—
334C22×C4×C137#4112yes—
335C4⋊C4×C137—44no—
336C4⋊C4×C137—44no—
337C22⋊C4×C137—28no—
338C22⋊C4×C137—44no—
339C22⋊C4×C137—44no—
340C22⋊C4×C137—44no—
341C22⋊C4×C137—44no—
342C22⋊C4×C137—44no—
343C22⋊C4×C137—44no—
344C22⋊C4×C137—44no—
345C22⋊C4×C137—44no—
346C22⋊C4×C137—44no—
347C22⋊C4×C137—44no—
348C22⋊C4×C137—44no—
349C22⋊C4×C137—44no—
350C42×C137—44no—
351C23×C137—22no—
352C23×C137—22no—
353C23×C137—22no—
354C23×C137—22no—
355C23×C137—22no—
356C23×C137—22no—
357C23×C137—22no—
358C23×C137—22no—
359C23×C137—22no—
360C23×C137—22no—
361C23×C137—22no—
362C23×C137—22no—
363C23×C137—22no—
364C23×C137—22no—
365C23×C137—22no—
366C23×C137—22no—
367C23×C137—22no—
368C23×C137—22no—
369C23×C137—22no—
370C23×C137—22no—
371C23×C137—22no—
372C23×C137—22no—
373C23×C137—22no—
374C23×C137—22no—
375C23×C137—22no—
376C23×C137—22no—
377C23×C137—22no—
378C23×C137—22no—
379C23×C137—22no—
380C23×C137—22no—
381C23×C137—22no—
382C23×C137—22no—
383C23×C137—22no—
384C23×C137—22no—
385C23×C137—22no—
386C23×C137—22no—
387C23×C137—22no—
388C23×C137—22no—
389C23×C137—22no—
390C23×C137—22no—
391C23×C137—22no—
392C23×C137—22no—
393C23×C137—22no—
394C23×C137—41no—
395C23×C137—41no—
396C23×C137—41no—
397C23×C137—41no—
398C23×C137—41no—
399C23×C137—41no—
400C23×C137—41no—
401C23×C137—41no—
402C23×C137—41no—
403C23×C137—41no—
404C23×C137—41no—
405C23×C137—41no—
406C23×C137—41no—
407C23×C137—41no—
408C23×C137—41no—
409C23×C137—41no—
410C23×C137—41no—
411C23×C137—41no—
412C23×C137—41no—
413C23×C137—41no—
414C23×C137—41no—
415C23×C137—41no—
416C23×C137—41no—
417C23×C137—41no—
418C23×C137—41no—
419C23×C137—41no—
420C23×C137—41no—
421C23×C137—41no—
422C23×C137—41no—
423C23×C137—41no—
424C23×C137—41no—
425C23×C137—41no—
426C23×C137—41no—
427C23×C137—41no—
428C23×C137—41no—
429C23×C137—41no—
430C23×C137—41no—
431C23×C137—41no—
432C23×C137—41no—
433C23×C137—41no—
434C23×C137—41no—
435C23×C137—41no—
436C23×C137—41no—
437C23×C137—41no—
438C23×C137—41no—
439C23×C137—41no—
440C23×C137—41no—
441C23×C137—41no—
442C23×C137—41no—
443C23×C137—41no—
444C23×C137—41no—
445C23×C137—41no—
446C23×C137—41no—
447C23×C137—41no—
448C23×C137—41no—
449C23×C137—41no—
450C23×C137—41no—
451C23×C137—41no—
452C23×C137—41no—
453C23×C137—41no—
454C23×C137C4×D414yes—
455C23×C137C4×D414yes—
456C23×C137C23×C411yescharacteristic
457C23×C137C22×D411yescharacteristic
458C23×C137C22×D411yescharacteristic
459C23×C137C22×D411yescharacteristic
460C23×C137C2×#4111yescharacteristic
461C23×C137C2×#4111yescharacteristic
462C23×C137C2×#4111yescharacteristic
463C23×C137H(5,𝔽2)11yescharacteristic
464C23×C137H(5,𝔽2)11yescharacteristic
465C23×C137H(5,𝔽2)11yescharacteristic
466C23×C137H(5,𝔽2)11yescharacteristic
467C23×C137H(5,𝔽2)11yescharacteristic
468C23×C137H(5,𝔽2)11yescharacteristic
469C23×C137H(5,𝔽2)11yescharacteristic
470C23×C1372−1+411yescharacteristic
471D4×C137—416no—
472D4×C137—416no—
473D4×C137—416no—
474C2×C4×C137—22no—
475C2×C4×C137—22no—
476C2×C4×C137—22no—
477C2×C4×C137—22no—
478C2×C4×C137—22no—
479C2×C4×C137—22no—
480C2×C4×C137—22no—
481C2×C4×C137—22no—
482C2×C4×C137—22no—
483C2×C4×C137—22no—
484C2×C4×C137—22no—
485C2×C4×C137—22no—
486C2×C4×C137—22no—
487C2×C4×C137—22no—
488C2×C4×C137—22no—
489C2×C4×C137—22no—
490C2×C4×C137—22no—
491C2×C4×C137—22no—
492C2×C4×C137—22no—
493C2×C4×C137—22no—
494C2×C4×C137—22no—
495C2×C4×C137—22no—
496C2×C4×C137—22no—
497C2×C4×C137—22no—
498C2×C4×C137—22no—
499C2×C4×C137—22no—
500C2×C4×C137—22no—
501C2×C4×C137—22no—
502C2×C4×C137—22no—
503C2×C4×C137—22no—
504C2×C4×C137—22no—
505C2×C4×C137—22no—
506C2×C4×C137—22no—
507C2×C4×C137—416no—
508C2×C4×C137—416no—
509C2×C4×C137—41no—
510C2×C4×C137—41no—
511C2×C4×C137—41no—
512C2×C4×C137—41no—
513C2×C4×C137—41no—
514C2×C4×C137—41no—
515C2×C4×C137—41no—
516C2×C4×C137—41no—
517C2×C4×C137—41no—
518C2×C4×C137—41no—
519C2×C4×C137—41no—
520C2×C4×C137—41no—
521C2×C4×C137—41no—
522C2×C4×C137—41no—
523C2×C4×C137—41no—
524C2×C4×C137—41no—
525C2×C4×C137—41no—
526C2×C4×C137—41no—
527C2×C4×C137—41no—
528C2×C4×C137—41no—
529C2×C4×C137—41no—
530C2×C4×C137—41no—
531C2×C4×C137—41no—
532C2×C4×C137—41no—
533C2×C4×C137—41no—
534C2×C4×C137—41no—
535C2×C4×C137—41no—
536C2×C4×C137—41no—
537C2×C4×C137—41no—
538C2×C4×C137—41no—
539C2×C4×C137—41no—
540C2×C4×C137—41no—
541C2×C4×C137—41no—
542C2×C4×C137—41no—
543C2×C4×C137—41no—
544C2×C4×C137—41no—
545C2×C4×C137—41no—
546C2×C4×C137—41no—
547C2×C4×C137—41no—
548C2×C4×C137—41no—
549C2×C4×C137—41no—
550C2×C4×C137—41no—
551C2×C4×C137—41no—
552C2×C4×C137—41no—
553C2×C4×C137—41no—
554C2×C4×C137—41no—
555C2×C4×C137—41no—
556C2×C4×C137—41no—
557C2×C4×C137—41no—
558C2×C4×C137—41no—
559C2×C4×C137C4×D414yes—
560C22×C137—24no—
561C22×C137—24no—
562C22×C137—24no—
563C22×C137—24no—
564C22×C137—24no—
565C22×C137—24no—
566C22×C137—42no—
567C22×C137—42no—
568C22×C137—42no—
569C22×C137—42no—
570C22×C137—42no—
571C22×C137—42no—
572C22×C137—42no—
573C22×C137—42no—
574C22×C137—42no—
575C22×C137—42no—
576C22×C137—42no—
577C22×C137—42no—
578C22×C137—42no—
579C22×C137—42no—
580C22×C137—42no—
581C22×C137—42no—
582C22×C137—42no—
583C22×C137—42no—
584C22×C137—42no—
585C22×C137—42no—
586C22×C137—42no—
587C22×C137—42no—
588C22×C137—42no—
589C22×C137—42no—
590C22×C137—42no—
591C22×C137—42no—
592C22×C137—42no—
593C22×C137—42no—
594C22×C137—42no—
595C22×C137—42no—
596C22×C137—42no—
597C22×C137—81no—
598C22×C137—81no—
599C22×C137—81no—
600C22×C137—81no—
601C22×C137—81no—
602C22×C137—81no—
603C22×C137—81no—
604C22×C137—81no—
605C22×C137C2×C4×D411yescharacteristic
606C22×C137C2×C4×D411yescharacteristic
607C22×C137C2×C4×D411yescharacteristic
608C22×C137#51811yescharacteristic
609C22×C137#51811yescharacteristic
610C22×C137#51811yescharacteristic
611C22×C137#52011yescharacteristic
612C22×C137#53411yescharacteristic
613C22×C137#53411yescharacteristic
614C22×C137#53511yescharacteristic
615C22×C137#53511yescharacteristic
616C22×C137#53511yescharacteristic
617C22×C137#53711yescharacteristic
618C22×C137#53811yescharacteristic
619C22×C137#53811yescharacteristic
620C22×C137#53811yescharacteristic
621C22×C137#53911yescharacteristic
622C22×C137#54011yescharacteristic
623C22×C137#54011yescharacteristic
624C22×C137D4211yescharacteristic
625C22×C137D4211yescharacteristic
626C22×C137D4211yescharacteristic
627C22×C137#54611yescharacteristic
628C22×C137#54611yescharacteristic
629C22×C137#54611yescharacteristic
630C22×C137#54611yescharacteristic
631C22×C137#54711yescharacteristic
632C22×C137#54811yescharacteristic
633C22×C137#55111yescharacteristic
634C22×C137#55111yescharacteristic
635C22×C137#55311yescharacteristic
636C22×C137#56011yescharacteristic
637C22×C137#56011yescharacteristic
638C22×C137#56211yescharacteristic
639C22×C137#56211yescharacteristic
640C4×C137—24no—
641C4×C137—42no—
642C4×C137—42no—
643C4×C137—42no—
644C4×C137—42no—
645C4×C137—42no—
646C4×C137—42no—
647C4×C137—42no—
648C4×C137—42no—
649C4×C137—42no—
650C4×C137—81no—
651C4×C137—81no—
652C2×C137—44no—
653C2×C137—44no—
654C2×C137—82no—
655C2×C137#232111yescharacteristic
656C2×C137#232511yescharacteristic
657C2×C137#232811yescharacteristic
658C2×C137#235811yescharacteristic
659C2×C137#235811yescharacteristic
660C2×C137#236111yescharacteristic
661C2×C137#237711yescharacteristic
662C2×C137#266911yescharacteristic
663C2×C137#267111yescharacteristic
664C2×C137#267611yescharacteristic
665C2×C137#267811yescharacteristic
666C2×C137#268811yescharacteristic
667C2×C137#269611yescharacteristic
668C2×C137#270611yescharacteristic
669C2×C137#274911yescharacteristic
670#14519C13711yesmaximal, characteristic, direct product factor, Sylow
671C137#1451911yescharacteristic, direct product factor, Sylow
672C2×#392C2×C13711yescharacteristic
673C2×#390C2×C13711yescharacteristic, complemented
674C2×#386C2×C13711yescharacteristic, complemented
675C2×#386C2×C13711yescharacteristic, complemented
676C2×#386C2×C13711yescharacteristic, complemented
677C2×#386C2×C13711yescharacteristic, complemented
678C2×#385C2×C13711yescharacteristic, complemented
679#1442C2×C13711yescharacteristic, complemented
680#1440C2×C13711yescharacteristic, complemented
681#1439C2×C13711yescharacteristic, complemented
682#1439C2×C13711yescharacteristic, complemented
683#1438C2×C13711yescharacteristic, complemented
684#1437C2×C13711yescharacteristic, complemented
685#1434C2×C13711yescharacteristic, complemented
686C22⋊#95C2×C13711yescharacteristic, complemented
687C23×D4C22×C13711yescharacteristic
688C23×D4C22×C13711yescharacteristic
689C23×D4C22×C13711yescharacteristic
690C24×C4C22×C13711yescharacteristic
691C24×C4C22×C13711yescharacteristic
692C22×C4⋊C4C22×C13711yescharacteristic
693C22×C4⋊C4C22×C13711yescharacteristic
694C22×C22⋊C4C22×C13711yescharacteristic
695C22×C22⋊C4C22×C13711yescharacteristic
696C22×C22⋊C4C22×C13711yescharacteristic
697C22×C22⋊C4C22×C13711yescharacteristic
698C22×C22⋊C4C22×C13711yescharacteristic
699C22×C22⋊C4C22×C13711yescharacteristic
700C22×C22⋊C4C22×C13711yescharacteristic
701C22×C22⋊C4C22×C13711yescharacteristic
702C22×C22⋊C4C22×C13711yescharacteristic
703C22×C22⋊C4C22×C13711yescharacteristic
704C22×C22⋊C4C22×C13711yescharacteristic
705C22×C22⋊C4C22×C13711yescharacteristic
706C22×C22⋊C4C22×C13711yescharacteristic
707C22×C42C22×C13711yescharacteristic
708#392C4×C13718yescomplemented
709#390—24no—
710#386—24no—
711#386—24no—
712#386—24no—
713#386—24no—
714#385—24no—
715C2×#95C22×C13711yescharacteristic
716C2×#95C22×C13711yescharacteristic
717C2×#95C22×C13711yescharacteristic
718C2×#95C22×C13711yescharacteristic
719C2×#95C22×C13711yescharacteristic
720C2×#95C22×C13711yescharacteristic
721C2×#95C22×C13711yescharacteristic
722C2×#95C22×C13711yescharacteristic
723C2×#95C22×C13711yescharacteristic
724C2×#95C22×C13711yescharacteristic
725C2×#95C22×C13711yescharacteristic
726C2×#95C22×C13711yescharacteristic
727C2×#95C22×C13711yescharacteristic
728C2×#95C22×C13711yescharacteristic
729C25C23×C13711yescharacteristic
730C25C23×C13711yescharacteristic
731C25C23×C13711yescharacteristic
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4C2×C4×C13714yes—
751C22×D4C2×C4×C13714yescomplemented
752C22×D4C2×C4×C13714yescomplemented
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—41no—
760C23×C4—41no—
761C23×C4—41no—
762C23×C4—41no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4C23×C13711yescharacteristic
768C23×C4C23×C13711yescharacteristic
769C23×C4C23×C13711yescharacteristic
770C23×C4C23×C13711yescharacteristic
771C23×C4C23×C13711yescharacteristic
772C23×C4C23×C13711yescharacteristic
773C23×C4C23×C13711yescharacteristic
774C23×C4C23×C13711yescharacteristic
775C23×C4C23×C13711yescharacteristic
776C23×C4C23×C13711yescharacteristic
777C23×C4C23×C13711yescharacteristic
778C23×C4C23×C13711yescharacteristic
779C2×C4⋊C4—22no—
780C2×C4⋊C4—22no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—41no—
783C2×C4⋊C4—41no—
784C2×C4⋊C4—41no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4C2×C4×C13714yescomplemented
820C2×C22⋊C4C2×C4×C13714yescomplemented
821C2×C22⋊C4C2×C4×C13714yescomplemented
822C2×C22⋊C4D4×C13714yescomplemented
823C2×C22⋊C4D4×C13714yescomplemented
824C2×C42—22no—
825C2×C42—22no—
826C2×C42—41no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—41no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95C2×C4×C13714yescomplemented
840#95D4×C13714yescomplemented
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24C22×C4×C13712yes—
880C24C22×C4×C13712yes—
881C24C22×C4×C13712yes—
882C24C2×D4×C13712yes—
883C24C2×D4×C13712yes—
884C24#41×C13712yes—
885C24#41×C13712yes—
886C24C24×C13711yescharacteristic
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4C22×C4×C13712yes—
995C22×C4C22×C4×C13712yes—
996C22×C4C22×C4×C13712yes—
997C22×C4C22×C4×C13712yes—
998C22×C4C2×D4×C13712yes—
999C22×C4C2×D4×C13712yes—
1000C22×C4C2×D4×C13712yes—
1001C22×C4C2×D4×C13712yes—
1002C22×C4C2×D4×C13712yes—
1003C22×C4C2×D4×C13712yes—
1004C22×C4C2×D4×C13712yes—
1005C22×C4#41×C13712yes—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C22⋊C4—28no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C42—44no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23C4×D4×C13714yes—
1126C23C4×D4×C13714yes—
1127C23C23×C4×C13711yescharacteristic
1128C23C22×D4×C13711yescharacteristic
1129C23C22×D4×C13711yescharacteristic
1130C23C22×D4×C13711yescharacteristic
1131C23C2×#41×C13711yescharacteristic
1132C23C2×#41×C13711yescharacteristic
1133C23C2×#41×C13711yescharacteristic
1134C23H(5,𝔽2)×C13711yescharacteristic
1135C23H(5,𝔽2)×C13711yescharacteristic
1136C23H(5,𝔽2)×C13711yescharacteristic
1137C23H(5,𝔽2)×C13711yescharacteristic
1138C23H(5,𝔽2)×C13711yescharacteristic
1139C23H(5,𝔽2)×C13711yescharacteristic
1140C23H(5,𝔽2)×C13711yescharacteristic
1141C232−1+4×C13711yescharacteristic
1142D4—416no—
1143D4—416no—
1144D4—416no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—416no—
1179C2×C4—416no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4C4×D4×C13714yes—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22C2×C4×D4×C13711yescharacteristic
1277C22C2×C4×D4×C13711yescharacteristic
1278C22C2×C4×D4×C13711yescharacteristic
1279C22#518×C13711yescharacteristic
1280C22#518×C13711yescharacteristic
1281C22#518×C13711yescharacteristic
1282C22#520×C13711yescharacteristic
1283C22#534×C13711yescharacteristic
1284C22#534×C13711yescharacteristic
1285C22#535×C13711yescharacteristic
1286C22#535×C13711yescharacteristic
1287C22#535×C13711yescharacteristic
1288C22#537×C13711yescharacteristic
1289C22#538×C13711yescharacteristic
1290C22#538×C13711yescharacteristic
1291C22#538×C13711yescharacteristic
1292C22#539×C13711yescharacteristic
1293C22#540×C13711yescharacteristic
1294C22#540×C13711yescharacteristic
1295C22D42×C13711yescharacteristic
1296C22D42×C13711yescharacteristic
1297C22D42×C13711yescharacteristic
1298C22#546×C13711yescharacteristic
1299C22#546×C13711yescharacteristic
1300C22#546×C13711yescharacteristic
1301C22#546×C13711yescharacteristic
1302C22#547×C13711yescharacteristic
1303C22#548×C13711yescharacteristic
1304C22#551×C13711yescharacteristic
1305C22#551×C13711yescharacteristic
1306C22#553×C13711yescharacteristic
1307C22#560×C13711yescharacteristic
1308C22#560×C13711yescharacteristic
1309C22#562×C13711yescharacteristic
1310C22#562×C13711yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C2—44no—
1324C2—44no—
1325C2—82no—
1326C2#2321×C13711yescharacteristic
1327C2#2325×C13711yescharacteristic
1328C2#2328×C13711yescharacteristic
1329C2#2358×C13711yescharacteristic
1330C2#2358×C13711yescharacteristic
1331C2#2361×C13711yescharacteristic
1332C2#2377×C13711yescharacteristic
1333C2#2669×C13711yescharacteristic
1334C2#2671×C13711yescharacteristic
1335C2#2676×C13711yescharacteristic
1336C2#2678×C13711yescharacteristic
1337C2#2688×C13711yescharacteristic
1338C2#2696×C13711yescharacteristic
1339C2#2706×C13711yescharacteristic
1340C2#2749×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
prime radicalC2×#392×C137C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#390×C137C2semidirect
3. C2×#386×C137C2semidirect
4. C2×#386×C137C2semidirect
5. C2×#386×C137C2semidirect
6. C2×#386×C137C2semidirect
7. C2×#385×C137C2semidirect
8. #1442×C137C2semidirect
9. #1440×C137C2semidirect
10. #1439×C137C2semidirect
11. #1439×C137C2semidirect
12. #1438×C137C2semidirect
13. #1437×C137C2semidirect
14. #1434×C137C2semidirect
15. C22⋊#95×C137C2semidirect
37. #392×C137C4semidirect
80. C22×D4×C137C2×C4semidirect
81. C22×D4×C137C2×C4semidirect
148. C2×C22⋊C4×C137C2×C4semidirect
149. C2×C22⋊C4×C137C2×C4semidirect
150. C2×C22⋊C4×C137C2×C4semidirect
151. C2×C22⋊C4×C137D4semidirect
152. C2×C22⋊C4×C137D4semidirect
168. #95×C137C2×C4semidirect
169. #95×C137D4semidirect
670. #14519C137direct (N × H)
671. C137#14519direct (N × H)
673. C2×#390C2×C137semidirect
674. C2×#386C2×C137semidirect
675. C2×#386C2×C137semidirect
676. C2×#386C2×C137semidirect
677. C2×#386C2×C137semidirect
678. C2×#385C2×C137semidirect
679. #1442C2×C137semidirect
680. #1440C2×C137semidirect
681. #1439C2×C137semidirect
682. #1439C2×C137semidirect
683. #1438C2×C137semidirect
684. #1437C2×C137semidirect
685. #1434C2×C137semidirect
686. C22⋊#95C2×C137semidirect
708. #392C4×C137semidirect
751. C22×D4C2×C4×C137semidirect
752. C22×D4C2×C4×C137semidirect
819. C2×C22⋊C4C2×C4×C137semidirect
820. C2×C22⋊C4C2×C4×C137semidirect
821. C2×C22⋊C4C2×C4×C137semidirect
822. C2×C22⋊C4D4×C137semidirect
823. C2×C22⋊C4D4×C137semidirect
839. #95C2×C4×C137semidirect
840. #95D4×C137semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#392×C1372
C2×#390×C1372
C2×#386×C1372
C2×#385×C1372
#1442×C1372
#1440×C1372
#1439×C1372
#1438×C1372
#1437×C1372
#1434×C1372
C22⋊#95×C1372
#14519137