Finite Group Databasebeta

← C137×#16526 #46865912

Subgroups — C137×#16526 #46865912

Order 35072.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C137C211yesmaximal, characteristic, complemented
2C2×#394×C137C211yesmaximal, characteristic, complemented
3C2×#394×C137C211yesmaximal, characteristic, complemented
4C2×#394×C137C211yesmaximal, characteristic, complemented
5C2×#392×C137C211yesmaximal, characteristic
6C2×#390×C137C211yesmaximal, characteristic, complemented
7#1444×C137C211yesmaximal, characteristic, complemented
8#1440×C137C211yesmaximal, characteristic, complemented
9#1439×C137C211yesmaximal, characteristic, complemented
10#1439×C137C211yesmaximal, characteristic, complemented
11#1439×C137C211yesmaximal, characteristic, complemented
12#1438×C137C211yesmaximal, characteristic, complemented
13#1438×C137C211yesmaximal, characteristic, complemented
14#1437×C137C211yesmaximal, characteristic, complemented
15#1436×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C23×D4×C137C2211yescharacteristic
19C22×C4⋊C4×C137C2211yescharacteristic
20C22×C4⋊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×C22⋊C4×C137C2211yescharacteristic
37C22×C22⋊C4×C137C2211yescharacteristic
38C22×C42×C137C2211yescharacteristic
39#397×C137—24no—
40#394×C137—24no—
41#394×C137—24no—
42#394×C137—24no—
43#392×C137—24no—
44#390×C137—24no—
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
57C25×C137C2311yescharacteristic
58C25×C137C2311yescharacteristic
59C25×C137C2311yescharacteristic
60C22×D4×C137—22no—
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—41no—
69C22×D4×C137—41no—
70C22×D4×C137—41no—
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×C137—41no—
80C22×D4×C137D414yes—
81C23×C4×C137C2311yescharacteristic
82C23×C4×C137C2311yescharacteristic
83C23×C4×C137C2311yescharacteristic
84C23×C4×C137C2311yescharacteristic
85C23×C4×C137C2311yescharacteristic
86C23×C4×C137C2311yescharacteristic
87C23×C4×C137C2311yescharacteristic
88C23×C4×C137C2311yescharacteristic
89C23×C4×C137C2311yescharacteristic
90C23×C4×C137C2311yescharacteristic
91C23×C4×C137C2311yescharacteristic
92C23×C4×C137C2311yescharacteristic
93C2×C4⋊C4×C137—22no—
94C2×C4⋊C4×C137—22no—
95C2×C4⋊C4×C137—22no—
96C2×C4⋊C4×C137—22no—
97C2×C4⋊C4×C137—22no—
98C2×C4⋊C4×C137—22no—
99C2×C4⋊C4×C137—41no—
100C2×C4⋊C4×C137—41no—
101C2×C4⋊C4×C137—41no—
102C2×C4⋊C4×C137—41no—
103C2×C4⋊C4×C137—41no—
104C2×C4⋊C4×C137—41no—
105C2×C22⋊C4×C137—22no—
106C2×C22⋊C4×C137—22no—
107C2×C22⋊C4×C137—22no—
108C2×C22⋊C4×C137—22no—
109C2×C22⋊C4×C137—22no—
110C2×C22⋊C4×C137—22no—
111C2×C22⋊C4×C137—22no—
112C2×C22⋊C4×C137—22no—
113C2×C22⋊C4×C137—22no—
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—22no—
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×C137—41no—
149C2×C22⋊C4×C137D414yescomplemented
150C2×C42×C137—22no—
151C2×C42×C137—41no—
152C2×C42×C137—41no—
153#95×C137—22no—
154#95×C137—22no—
155#95×C137—22no—
156#95×C137—22no—
157#95×C137—22no—
158#95×C137—22no—
159#95×C137—22no—
160#95×C137—41no—
161#95×C137—41no—
162#95×C137—41no—
163#95×C137—41no—
164#95×C137D414yescomplemented
165C24×C137—21no—
166C24×C137—21no—
167C24×C137—21no—
168C24×C137—21no—
169C24×C137—21no—
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×C137C2×D412yes—
208C24×C137C2×D412yes—
209C24×C137C2×D412yes—
210C24×C137C2411yescharacteristic
211C2×D4×C137—28no—
212C2×D4×C137—44no—
213C2×D4×C137—44no—
214C2×D4×C137—44no—
215C2×D4×C137—44no—
216C2×D4×C137—44no—
217C2×D4×C137—44no—
218C2×D4×C137—44no—
219C2×D4×C137—44no—
220C2×D4×C137—44no—
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—
232C22×C4×C137—21no—
233C22×C4×C137—21no—
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—21no—
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×C137C2×D412yes—
307C22×C4×C137C2×D412yes—
308C22×C4×C137C2×D412yes—
309C22×C4×C137C2×D412yes—
310C22×C4×C137C2×D412yes—
311C22×C4×C137C2×D412yes—
312C22×C4×C137#4112yes—
313C22×C4×C137#4112yes—
314C22×C4×C137#4112yes—
315C22×C4×C137#4112yes—
316C4⋊C4×C137—44no—
317C4⋊C4×C137—44no—
318C4⋊C4×C137—44no—
319C4⋊C4×C137—44no—
320C22⋊C4×C137—44no—
321C22⋊C4×C137—44no—
322C22⋊C4×C137—44no—
323C22⋊C4×C137—44no—
324C22⋊C4×C137—44no—
325C22⋊C4×C137—44no—
326C22⋊C4×C137—44no—
327C22⋊C4×C137—44no—
328C22⋊C4×C137—44no—
329C22⋊C4×C137—44no—
330C22⋊C4×C137—44no—
331C22⋊C4×C137—44no—
332C22⋊C4×C137—44no—
333C22⋊C4×C137—44no—
334C22⋊C4×C137—44no—
335C42×C137—44no—
336C23×C137—22no—
337C23×C137—22no—
338C23×C137—22no—
339C23×C137—22no—
340C23×C137—22no—
341C23×C137—22no—
342C23×C137—22no—
343C23×C137—22no—
344C23×C137—22no—
345C23×C137—22no—
346C23×C137—22no—
347C23×C137—22no—
348C23×C137—22no—
349C23×C137—22no—
350C23×C137—22no—
351C23×C137—22no—
352C23×C137—22no—
353C23×C137—22no—
354C23×C137—22no—
355C23×C137—22no—
356C23×C137—22no—
357C23×C137—41no—
358C23×C137—41no—
359C23×C137—41no—
360C23×C137—41no—
361C23×C137—41no—
362C23×C137—41no—
363C23×C137—41no—
364C23×C137—41no—
365C23×C137—41no—
366C23×C137—41no—
367C23×C137—41no—
368C23×C137—41no—
369C23×C137—41no—
370C23×C137—41no—
371C23×C137—41no—
372C23×C137—41no—
373C23×C137—41no—
374C23×C137—41no—
375C23×C137—41no—
376C23×C137—41no—
377C23×C137—41no—
378C23×C137—41no—
379C23×C137—41no—
380C23×C137—41no—
381C23×C137—41no—
382C23×C137—41no—
383C23×C137—41no—
384C23×C137—41no—
385C23×C137—41no—
386C23×C137—41no—
387C23×C137—41no—
388C23×C137—41no—
389C23×C137—41no—
390C23×C137—41no—
391C23×C137—41no—
392C23×C137—41no—
393C23×C137—41no—
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×C137C22×D411yescharacteristic
442C23×C137C22×D411yescharacteristic
443C23×C137C22×D411yescharacteristic
444C23×C137C2×#4111yescharacteristic
445C23×C137C2×#4111yescharacteristic
446C23×C137C2×#4111yescharacteristic
447C23×C137C2×#4111yescharacteristic
448C23×C137H(5,𝔽2)11yescharacteristic
449C23×C137H(5,𝔽2)11yescharacteristic
450C23×C137H(5,𝔽2)11yescharacteristic
451C23×C137H(5,𝔽2)11yescharacteristic
452C23×C137H(5,𝔽2)11yescharacteristic
453C23×C137H(5,𝔽2)11yescharacteristic
454C23×C137H(5,𝔽2)11yescharacteristic
455C23×C1372−1+411yescharacteristic
456D4×C137—416no—
457D4×C137—416no—
458D4×C137—416no—
459C2×C4×C137—22no—
460C2×C4×C137—22no—
461C2×C4×C137—22no—
462C2×C4×C137—22no—
463C2×C4×C137—22no—
464C2×C4×C137—22no—
465C2×C4×C137—22no—
466C2×C4×C137—22no—
467C2×C4×C137—22no—
468C2×C4×C137—22no—
469C2×C4×C137—22no—
470C2×C4×C137—22no—
471C2×C4×C137—22no—
472C2×C4×C137—22no—
473C2×C4×C137—22no—
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—41no—
487C2×C4×C137—41no—
488C2×C4×C137—41no—
489C2×C4×C137—41no—
490C2×C4×C137—41no—
491C2×C4×C137—41no—
492C2×C4×C137—41no—
493C2×C4×C137—41no—
494C2×C4×C137—41no—
495C2×C4×C137—41no—
496C2×C4×C137—41no—
497C2×C4×C137—41no—
498C2×C4×C137—41no—
499C2×C4×C137—41no—
500C2×C4×C137—41no—
501C2×C4×C137—41no—
502C2×C4×C137—41no—
503C2×C4×C137—41no—
504C2×C4×C137—41no—
505C2×C4×C137—41no—
506C2×C4×C137—41no—
507C2×C4×C137—41no—
508C2×C4×C137—41no—
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#12314yes—
543C22×C137—42no—
544C22×C137—42no—
545C22×C137—42no—
546C22×C137—42no—
547C22×C137—42no—
548C22×C137—42no—
549C22×C137—42no—
550C22×C137—42no—
551C22×C137—42no—
552C22×C137—42no—
553C22×C137—42no—
554C22×C137—42no—
555C22×C137—42no—
556C22×C137—42no—
557C22×C137—42no—
558C22×C137—42no—
559C22×C137—42no—
560C22×C137—42no—
561C22×C137—42no—
562C22×C137—42no—
563C22×C137—42no—
564C22×C137—81no—
565C22×C137—81no—
566C22×C137—81no—
567C22×C137—81no—
568C22×C137—81no—
569C22×C137—81no—
570C22×C137—81no—
571C22×C137—81no—
572C22×C137—81no—
573C22×C137—81no—
574C22×C137—81no—
575C22×C137—81no—
576C22×C137—81no—
577C22×C137—81no—
578C22×C137—81no—
579C22×C137—81no—
580C22×C137—81no—
581C22×C137—81no—
582C22×C137—81no—
583C22×C137—81no—
584C22×C137—81no—
585C22×C137—81no—
586C22×C137—81no—
587C22×C137—81no—
588C22×C137C2×#12311yescharacteristic
589C22×C137#53211yescharacteristic
590C22×C137#53211yescharacteristic
591C22×C137#53411yescharacteristic
592C22×C137#53411yescharacteristic
593C22×C137#53411yescharacteristic
594C22×C137#53511yescharacteristic
595C22×C137#53511yescharacteristic
596C22×C137#53711yescharacteristic
597C22×C137#53811yescharacteristic
598C22×C137#53811yescharacteristic
599C22×C137#53811yescharacteristic
600C22×C137#53811yescharacteristic
601C22×C137#53811yescharacteristic
602C22×C137#53811yescharacteristic
603C22×C137#54011yescharacteristic
604C22×C137#54011yescharacteristic
605C22×C137#54211yescharacteristic
606C22×C137#54211yescharacteristic
607C22×C137D4211yescharacteristic
608C22×C137D4211yescharacteristic
609C22×C137D4211yescharacteristic
610C22×C137#54611yescharacteristic
611C22×C137#54611yescharacteristic
612C22×C137#54611yescharacteristic
613C22×C137#54711yescharacteristic
614C22×C137#54711yescharacteristic
615C22×C137#55011yescharacteristic
616C22×C137#55311yescharacteristic
617C22×C137#55511yescharacteristic
618C22×C137#55911yescharacteristic
619C22×C137#56011yescharacteristic
620C22×C137#56011yescharacteristic
621C22×C137#56211yescharacteristic
622C22×C137#56211yescharacteristic
623C4×C137—24no—
624C4×C137—42no—
625C4×C137—42no—
626C4×C137—42no—
627C4×C137—42no—
628C4×C137—42no—
629C4×C137—42no—
630C4×C137—42no—
631C4×C137—81no—
632C4×C137—81no—
633C4×C137—81no—
634C4×C137—81no—
635C2×C137—82no—
636C2×C137—82no—
637C2×C137—82no—
638C2×C137#242211yescharacteristic
639C2×C137#244511yescharacteristic
640C2×C137#255511yescharacteristic
641C2×C137#262211yescharacteristic
642C2×C137#266111yescharacteristic
643C2×C137#266211yescharacteristic
644C2×C137#266811yescharacteristic
645C2×C137#266911yescharacteristic
646C2×C137#267111yescharacteristic
647C2×C137#268211yescharacteristic
648C2×C137#268611yescharacteristic
649C2×C137#271011yescharacteristic
650C2×C137#271411yescharacteristic
651C2×C137#280311yescharacteristic
652C2×C137#282911yescharacteristic
653#16526C13711yesmaximal, characteristic, direct product factor, Sylow
654C137#1652611yescharacteristic, direct product factor, Sylow
655C2×#397C2×C13711yescharacteristic, complemented
656C2×#394C2×C13711yescharacteristic, complemented
657C2×#394C2×C13711yescharacteristic, complemented
658C2×#394C2×C13711yescharacteristic, complemented
659C2×#392C2×C13711yescharacteristic
660C2×#390C2×C13711yescharacteristic, complemented
661#1444C2×C13711yescharacteristic, complemented
662#1440C2×C13711yescharacteristic, complemented
663#1439C2×C13711yescharacteristic, complemented
664#1439C2×C13711yescharacteristic, complemented
665#1439C2×C13711yescharacteristic, complemented
666#1438C2×C13711yescharacteristic, complemented
667#1438C2×C13711yescharacteristic, complemented
668#1437C2×C13711yescharacteristic, complemented
669#1436C2×C13711yescharacteristic, complemented
670C23×D4C22×C13711yescharacteristic
671C23×D4C22×C13711yescharacteristic
672C23×D4C22×C13711yescharacteristic
673C22×C4⋊C4C22×C13711yescharacteristic
674C22×C4⋊C4C22×C13711yescharacteristic
675C22×C4⋊C4C22×C13711yescharacteristic
676C22×C4⋊C4C22×C13711yescharacteristic
677C22×C22⋊C4C22×C13711yescharacteristic
678C22×C22⋊C4C22×C13711yescharacteristic
679C22×C22⋊C4C22×C13711yescharacteristic
680C22×C22⋊C4C22×C13711yescharacteristic
681C22×C22⋊C4C22×C13711yescharacteristic
682C22×C22⋊C4C22×C13711yescharacteristic
683C22×C22⋊C4C22×C13711yescharacteristic
684C22×C22⋊C4C22×C13711yescharacteristic
685C22×C22⋊C4C22×C13711yescharacteristic
686C22×C22⋊C4C22×C13711yescharacteristic
687C22×C22⋊C4C22×C13711yescharacteristic
688C22×C22⋊C4C22×C13711yescharacteristic
689C22×C22⋊C4C22×C13711yescharacteristic
690C22×C22⋊C4C22×C13711yescharacteristic
691C22×C22⋊C4C22×C13711yescharacteristic
692C22×C42C22×C13711yescharacteristic
693#397—24no—
694#394—24no—
695#394—24no—
696#394—24no—
697#392—24no—
698#390—24no—
699C2×#95C22×C13711yescharacteristic
700C2×#95C22×C13711yescharacteristic
701C2×#95C22×C13711yescharacteristic
702C2×#95C22×C13711yescharacteristic
703C2×#95C22×C13711yescharacteristic
704C2×#95C22×C13711yescharacteristic
705C2×#95C22×C13711yescharacteristic
706C2×#95C22×C13711yescharacteristic
707C2×#95C22×C13711yescharacteristic
708C2×#95C22×C13711yescharacteristic
709C2×#95C22×C13711yescharacteristic
710C2×#95C22×C13711yescharacteristic
711C25C23×C13711yescharacteristic
712C25C23×C13711yescharacteristic
713C25C23×C13711yescharacteristic
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4D4×C13714yes—
735C23×C4C23×C13711yescharacteristic
736C23×C4C23×C13711yescharacteristic
737C23×C4C23×C13711yescharacteristic
738C23×C4C23×C13711yescharacteristic
739C23×C4C23×C13711yescharacteristic
740C23×C4C23×C13711yescharacteristic
741C23×C4C23×C13711yescharacteristic
742C23×C4C23×C13711yescharacteristic
743C23×C4C23×C13711yescharacteristic
744C23×C4C23×C13711yescharacteristic
745C23×C4C23×C13711yescharacteristic
746C23×C4C23×C13711yescharacteristic
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—41no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C4⋊C4—41no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4D4×C13714yescomplemented
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95D4×C13714yescomplemented
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
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—
861C24C2×D4×C13712yes—
862C24C2×D4×C13712yes—
863C24C2×D4×C13712yes—
864C24C24×C13711yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
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×C4C2×D4×C13712yes—
961C22×C4C2×D4×C13712yes—
962C22×C4C2×D4×C13712yes—
963C22×C4C2×D4×C13712yes—
964C22×C4C2×D4×C13712yes—
965C22×C4C2×D4×C13712yes—
966C22×C4#41×C13712yes—
967C22×C4#41×C13712yes—
968C22×C4#41×C13712yes—
969C22×C4#41×C13712yes—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
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—
989C42—44no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
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—
1095C23C22×D4×C13711yescharacteristic
1096C23C22×D4×C13711yescharacteristic
1097C23C22×D4×C13711yescharacteristic
1098C23C2×#41×C13711yescharacteristic
1099C23C2×#41×C13711yescharacteristic
1100C23C2×#41×C13711yescharacteristic
1101C23C2×#41×C13711yescharacteristic
1102C23H(5,𝔽2)×C13711yescharacteristic
1103C23H(5,𝔽2)×C13711yescharacteristic
1104C23H(5,𝔽2)×C13711yescharacteristic
1105C23H(5,𝔽2)×C13711yescharacteristic
1106C23H(5,𝔽2)×C13711yescharacteristic
1107C23H(5,𝔽2)×C13711yescharacteristic
1108C23H(5,𝔽2)×C13711yescharacteristic
1109C232−1+4×C13711yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
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#123×C13714yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×#123×C13711yescharacteristic
1243C22#532×C13711yescharacteristic
1244C22#532×C13711yescharacteristic
1245C22#534×C13711yescharacteristic
1246C22#534×C13711yescharacteristic
1247C22#534×C13711yescharacteristic
1248C22#535×C13711yescharacteristic
1249C22#535×C13711yescharacteristic
1250C22#537×C13711yescharacteristic
1251C22#538×C13711yescharacteristic
1252C22#538×C13711yescharacteristic
1253C22#538×C13711yescharacteristic
1254C22#538×C13711yescharacteristic
1255C22#538×C13711yescharacteristic
1256C22#538×C13711yescharacteristic
1257C22#540×C13711yescharacteristic
1258C22#540×C13711yescharacteristic
1259C22#542×C13711yescharacteristic
1260C22#542×C13711yescharacteristic
1261C22D42×C13711yescharacteristic
1262C22D42×C13711yescharacteristic
1263C22D42×C13711yescharacteristic
1264C22#546×C13711yescharacteristic
1265C22#546×C13711yescharacteristic
1266C22#546×C13711yescharacteristic
1267C22#547×C13711yescharacteristic
1268C22#547×C13711yescharacteristic
1269C22#550×C13711yescharacteristic
1270C22#553×C13711yescharacteristic
1271C22#555×C13711yescharacteristic
1272C22#559×C13711yescharacteristic
1273C22#560×C13711yescharacteristic
1274C22#560×C13711yescharacteristic
1275C22#562×C13711yescharacteristic
1276C22#562×C13711yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2#2422×C13711yescharacteristic
1293C2#2445×C13711yescharacteristic
1294C2#2555×C13711yescharacteristic
1295C2#2622×C13711yescharacteristic
1296C2#2661×C13711yescharacteristic
1297C2#2662×C13711yescharacteristic
1298C2#2668×C13711yescharacteristic
1299C2#2669×C13711yescharacteristic
1300C2#2671×C13711yescharacteristic
1301C2#2682×C13711yescharacteristic
1302C2#2686×C13711yescharacteristic
1303C2#2710×C13711yescharacteristic
1304C2#2714×C13711yescharacteristic
1305C2#2803×C13711yescharacteristic
1306C2#2829×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutator, Frattini, cosocleC24C24×C137
prime radicalC2×#392×C137C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#397×C137C2semidirect
2. C2×#394×C137C2semidirect
3. C2×#394×C137C2semidirect
4. C2×#394×C137C2semidirect
6. C2×#390×C137C2semidirect
7. #1444×C137C2semidirect
8. #1440×C137C2semidirect
9. #1439×C137C2semidirect
10. #1439×C137C2semidirect
11. #1439×C137C2semidirect
12. #1438×C137C2semidirect
13. #1438×C137C2semidirect
14. #1437×C137C2semidirect
15. #1436×C137C2semidirect
149. C2×C22⋊C4×C137D4semidirect
164. #95×C137D4semidirect
653. #16526C137direct (N × H)
654. C137#16526direct (N × H)
655. C2×#397C2×C137semidirect
656. C2×#394C2×C137semidirect
657. C2×#394C2×C137semidirect
658. C2×#394C2×C137semidirect
660. C2×#390C2×C137semidirect
661. #1444C2×C137semidirect
662. #1440C2×C137semidirect
663. #1439C2×C137semidirect
664. #1439C2×C137semidirect
665. #1439C2×C137semidirect
666. #1438C2×C137semidirect
667. #1438C2×C137semidirect
668. #1437C2×C137semidirect
669. #1436C2×C137semidirect
803. C2×C22⋊C4D4×C137semidirect
818. #95D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1372
C2×#394×C1372
C2×#392×C1372
C2×#390×C1372
#1444×C1372
#1440×C1372
#1439×C1372
#1438×C1372
#1437×C1372
#1436×C1372
#16526137