Finite Group Databasebeta

← C137×#14095 #46863481

Subgroups — C137×#14095 #46863481

Order 35072.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C137C211yesmaximal, characteristic
2C2×#390×C137C211yesmaximal, characteristic
3C2×#387×C137C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊C4×C137C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C137C211yesmaximal, characteristic, complemented
6#1441×C137C211yesmaximal, characteristic, complemented
7#1439×C137C211yesmaximal, characteristic, complemented
8#1439×C137C211yesmaximal, characteristic, complemented
9#1438×C137C211yesmaximal, characteristic
10#1437×C137C211yesmaximal, characteristic, complemented
11#1437×C137C211yesmaximal, characteristic, complemented
12#1437×C137C211yesmaximal, characteristic, complemented
13#1437×C137C211yesmaximal, characteristic, complemented
14#1436×C137C211yesmaximal, characteristic, complemented
15C22⋊#95×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137C2211yescharacteristic
17C24×C4×C137C2211yescharacteristic
18C2×#123×C137—24no—
19C2×#123×C137—24no—
20C2×#123×C137C418yescomplemented
21C22×C4⋊C4×C137C2211yescharacteristic
22C22×C4⋊C4×C137C2211yescharacteristic
23C22×C4⋊C4×C137C2211yescharacteristic
24C22×C4⋊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
37C22×C42×C137C2211yescharacteristic
38C22×C42×C137C2211yescharacteristic
39C22×C42×C137C2211yescharacteristic
40#390×C137—24no—
41#387×C137—24no—
42C4×C4⋊C4×C137—24no—
43C4×C22⋊C4×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
60C22×D4×C137—22no—
61C22×D4×C137—22no—
62C22×D4×C137—22no—
63C22×D4×C137—22no—
64C22×D4×C137—41no—
65C22×D4×C137—41no—
66C22×D4×C137C2×C414yes—
67C23×C4×C137—22no—
68C23×C4×C137—22no—
69C23×C4×C137—22no—
70C23×C4×C137—22no—
71C23×C4×C137—41no—
72C23×C4×C137—41no—
73C23×C4×C137C2×C414yes—
74C23×C4×C137C2311yescharacteristic
75C23×C4×C137C2311yescharacteristic
76C23×C4×C137C2311yescharacteristic
77C23×C4×C137C2311yescharacteristic
78C23×C4×C137C2311yescharacteristic
79C23×C4×C137C2311yescharacteristic
80C23×C4×C137C2311yescharacteristic
81C23×C4×C137C2311yescharacteristic
82C23×C4×C137C2311yescharacteristic
83C23×C4×C137C2311yescharacteristic
84C23×C4×C137C2311yescharacteristic
85C23×C4×C137C2311yescharacteristic
86C23×C4×C137C2311yescharacteristic
87#123×C137—232no—
88C2×C4⋊C4×C137—22no—
89C2×C4⋊C4×C137—22no—
90C2×C4⋊C4×C137—22no—
91C2×C4⋊C4×C137—22no—
92C2×C4⋊C4×C137—22no—
93C2×C4⋊C4×C137—22no—
94C2×C4⋊C4×C137—22no—
95C2×C4⋊C4×C137—41no—
96C2×C4⋊C4×C137C2×C414yes—
97C2×C4⋊C4×C137C2×C414yes—
98C2×C4⋊C4×C137D414yes—
99C2×C4⋊C4×C137D414yes—
100C2×C22⋊C4×C137—22no—
101C2×C22⋊C4×C137—22no—
102C2×C22⋊C4×C137—22no—
103C2×C22⋊C4×C137—22no—
104C2×C22⋊C4×C137—22no—
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—41no—
124C2×C22⋊C4×C137—41no—
125C2×C22⋊C4×C137—41no—
126C2×C22⋊C4×C137—41no—
127C2×C22⋊C4×C137—41no—
128C2×C22⋊C4×C137—41no—
129C2×C22⋊C4×C137C2×C414yes—
130C2×C22⋊C4×C137C2×C414yes—
131C2×C22⋊C4×C137C2×C414yes—
132C2×C22⋊C4×C137D414yes—
133C2×C42×C137—22no—
134C2×C42×C137—22no—
135C2×C42×C137—22no—
136C2×C42×C137—22no—
137C2×C42×C137—22no—
138C2×C42×C137—22no—
139C2×C42×C137—22no—
140C2×C42×C137—22no—
141C2×C42×C137—22no—
142C2×C42×C137—41no—
143C2×C42×C137—41no—
144C2×C42×C137—41no—
145#95×C137—22no—
146#95×C137—22no—
147#95×C137—22no—
148#95×C137—22no—
149#95×C137—22no—
150#95×C137—22no—
151#95×C137—22no—
152#95×C137—22no—
153#95×C137—22no—
154#95×C137—22no—
155#95×C137—41no—
156#95×C137—41no—
157#95×C137—41no—
158#95×C137—41no—
159C24×C137—21no—
160C24×C137—21no—
161C24×C137—21no—
162C24×C137—21no—
163C24×C137—21no—
164C24×C137—21no—
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×C137C22×C412yes—
186C24×C137C22×C412yes—
187C24×C137C2×D412yes—
188C24×C137#4112yes—
189C24×C137C2411yescharacteristic
190C2×D4×C137—28no—
191C2×D4×C137—28no—
192C2×D4×C137—44no—
193C2×D4×C137—44no—
194C2×D4×C137—44no—
195C2×D4×C137—44no—
196C2×D4×C137—44no—
197C22×C4×C137—21no—
198C22×C4×C137—21no—
199C22×C4×C137—21no—
200C22×C4×C137—21no—
201C22×C4×C137—21no—
202C22×C4×C137—21no—
203C22×C4×C137—21no—
204C22×C4×C137—21no—
205C22×C4×C137—21no—
206C22×C4×C137—21no—
207C22×C4×C137—21no—
208C22×C4×C137—21no—
209C22×C4×C137—21no—
210C22×C4×C137—21no—
211C22×C4×C137—21no—
212C22×C4×C137—21no—
213C22×C4×C137—28no—
214C22×C4×C137—21no—
215C22×C4×C137—21no—
216C22×C4×C137—21no—
217C22×C4×C137—21no—
218C22×C4×C137—21no—
219C22×C4×C137—21no—
220C22×C4×C137—21no—
221C22×C4×C137—21no—
222C22×C4×C137—21no—
223C22×C4×C137—21no—
224C22×C4×C137—21no—
225C22×C4×C137—21no—
226C22×C4×C137—21no—
227C22×C4×C137—21no—
228C22×C4×C137—21no—
229C22×C4×C137—21no—
230C22×C4×C137—21no—
231C22×C4×C137—21no—
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—28no—
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—44no—
272C22×C4×C137—44no—
273C22×C4×C137—44no—
274C22×C4×C137—44no—
275C22×C4×C137—44no—
276C22×C4×C137C22×C412yes—
277C22×C4×C137C22×C412yes—
278C22×C4×C137C22×C412yes—
279C22×C4×C137C22×C412yes—
280C22×C4×C137C22×C412yes—
281C22×C4×C137C2×D412yes—
282C22×C4×C137C2×D412yes—
283C22×C4×C137C2×D412yes—
284C22×C4×C137C2×D412yes—
285C22×C4×C137C2×D412yes—
286C22×C4×C137C2×D412yes—
287C22×C4×C137C2×D412yes—
288C22×C4×C137C2×D412yes—
289C22×C4×C137#4112yes—
290C22×C4×C137#4112yes—
291C22×C4×C137#4112yes—
292C22×C4×C137#4112yes—
293C22×C4×C137#4112yes—
294C22×C4×C137#4112yes—
295C4⋊C4×C137—28no—
296C4⋊C4×C137—28no—
297C4⋊C4×C137—44no—
298C4⋊C4×C137C22⋊C4116yescomplemented
299C22⋊C4×C137—28no—
300C22⋊C4×C137—28no—
301C22⋊C4×C137—28no—
302C22⋊C4×C137—28no—
303C22⋊C4×C137—28no—
304C22⋊C4×C137—44no—
305C22⋊C4×C137—44no—
306C22⋊C4×C137—44no—
307C22⋊C4×C137—44no—
308C22⋊C4×C137—44no—
309C22⋊C4×C137—44no—
310C42×C137—28no—
311C42×C137—44no—
312C42×C137—44no—
313C42×C137—44no—
314C23×C137—22no—
315C23×C137—22no—
316C23×C137—22no—
317C23×C137—22no—
318C23×C137—22no—
319C23×C137—22no—
320C23×C137—22no—
321C23×C137—22no—
322C23×C137—22no—
323C23×C137—22no—
324C23×C137—22no—
325C23×C137—22no—
326C23×C137—22no—
327C23×C137—22no—
328C23×C137—22no—
329C23×C137—22no—
330C23×C137—22no—
331C23×C137—22no—
332C23×C137—22no—
333C23×C137—22no—
334C23×C137—22no—
335C23×C137—22no—
336C23×C137—22no—
337C23×C137—22no—
338C23×C137—22no—
339C23×C137—41no—
340C23×C137—41no—
341C23×C137—41no—
342C23×C137—41no—
343C23×C137—41no—
344C23×C137—41no—
345C23×C137—41no—
346C23×C137—41no—
347C23×C137—41no—
348C23×C137—41no—
349C23×C137—41no—
350C23×C137—41no—
351C23×C137—41no—
352C23×C137—41no—
353C23×C137—41no—
354C23×C137—41no—
355C23×C137—41no—
356C23×C137—41no—
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×C137C4×D414yes—
384C23×C137C23×C411yescharacteristic
385C23×C137C22×D411yescharacteristic
386C23×C137C22×D411yescharacteristic
387C23×C137C22×D411yescharacteristic
388C23×C137C2×#4111yescharacteristic
389C23×C137C2×#4111yescharacteristic
390C23×C137C2×#4111yescharacteristic
391C23×C137C2×#4111yescharacteristic
392C23×C137C2×#4111yescharacteristic
393C23×C137C2×#4111yescharacteristic
394C23×C137C2×#4111yescharacteristic
395C23×C137H(5,𝔽2)11yescharacteristic
396C23×C137H(5,𝔽2)11yescharacteristic
397C23×C137H(5,𝔽2)11yescharacteristic
398C23×C1372−1+411yescharacteristic
399D4×C137—416no—
400C2×C4×C137—22no—
401C2×C4×C137—22no—
402C2×C4×C137—22no—
403C2×C4×C137—22no—
404C2×C4×C137—22no—
405C2×C4×C137—22no—
406C2×C4×C137—22no—
407C2×C4×C137—22no—
408C2×C4×C137—22no—
409C2×C4×C137—22no—
410C2×C4×C137—22no—
411C2×C4×C137—22no—
412C2×C4×C137—22no—
413C2×C4×C137—22no—
414C2×C4×C137—22no—
415C2×C4×C137—22no—
416C2×C4×C137—22no—
417C2×C4×C137—22no—
418C2×C4×C137—22no—
419C2×C4×C137—22no—
420C2×C4×C137—22no—
421C2×C4×C137—22no—
422C2×C4×C137—22no—
423C2×C4×C137—22no—
424C2×C4×C137—22no—
425C2×C4×C137—22no—
426C2×C4×C137—22no—
427C2×C4×C137—22no—
428C2×C4×C137—22no—
429C2×C4×C137—22no—
430C2×C4×C137—22no—
431C2×C4×C137—22no—
432C2×C4×C137—22no—
433C2×C4×C137—22no—
434C2×C4×C137—22no—
435C2×C4×C137—22no—
436C2×C4×C137—22no—
437C2×C4×C137—22no—
438C2×C4×C137—22no—
439C2×C4×C137—22no—
440C2×C4×C137—22no—
441C2×C4×C137—22no—
442C2×C4×C137—22no—
443C2×C4×C137—22no—
444C2×C4×C137—22no—
445C2×C4×C137—416no—
446C2×C4×C137—41no—
447C2×C4×C137—41no—
448C2×C4×C137—41no—
449C2×C4×C137—41no—
450C2×C4×C137—41no—
451C2×C4×C137—41no—
452C2×C4×C137—41no—
453C2×C4×C137—41no—
454C2×C4×C137—41no—
455C2×C4×C137—41no—
456C2×C4×C137—41no—
457C2×C4×C137—41no—
458C2×C4×C137—41no—
459C2×C4×C137—41no—
460C2×C4×C137—41no—
461C2×C4×C137—41no—
462C2×C4×C137—41no—
463C2×C4×C137—41no—
464C2×C4×C137—41no—
465C2×C4×C137—41no—
466C2×C4×C137—41no—
467C2×C4×C137—41no—
468C2×C4×C137—41no—
469C2×C4×C137—41no—
470C2×C4×C137—41no—
471C2×C4×C137—41no—
472C2×C4×C137—41no—
473C2×C4×C137—41no—
474C2×C4×C137—41no—
475C2×C4×C137—41no—
476C2×C4×C137—41no—
477C2×C4×C137—41no—
478C2×C4×C137—41no—
479C2×C4×C137—41no—
480C2×C4×C137—41no—
481C2×C4×C137—41no—
482C2×C4×C137—41no—
483C2×C4×C137—41no—
484C2×C4×C137—41no—
485C2×C4×C137—41no—
486C2×C4×C137—41no—
487C2×C4×C137—41no—
488C2×C4×C137C2×C22⋊C414yes—
489C2×C4×C137C2×C22⋊C414yes—
490C2×C4×C137C2×C22⋊C414yes—
491C2×C4×C137#12314yescomplemented
492C22×C137—24no—
493C22×C137—24no—
494C22×C137—24no—
495C22×C137—42no—
496C22×C137—42no—
497C22×C137—42no—
498C22×C137—42no—
499C22×C137—42no—
500C22×C137—42no—
501C22×C137—42no—
502C22×C137—42no—
503C22×C137—42no—
504C22×C137—42no—
505C22×C137—42no—
506C22×C137—42no—
507C22×C137—42no—
508C22×C137—42no—
509C22×C137—42no—
510C22×C137—42no—
511C22×C137—42no—
512C22×C137—42no—
513C22×C137—42no—
514C22×C137—81no—
515C22×C137—81no—
516C22×C137—81no—
517C22×C137—81no—
518C22×C137—81no—
519C22×C137—81no—
520C22×C137—81no—
521C22×C137—81no—
522C22×C137C22×C22⋊C411yescharacteristic
523C22×C137C2×C4×D411yescharacteristic
524C22×C137C4×#4111yescharacteristic
525C22×C137C4×#4111yescharacteristic
526C22×C137C4×#4111yescharacteristic
527C22×C137#51811yescharacteristic
528C22×C137#52011yescharacteristic
529C22×C137C2×#12311yescharacteristic
530C22×C137#52511yescharacteristic
531C22×C137#52511yescharacteristic
532C22×C137#52511yescharacteristic
533C22×C137#52911yescharacteristic
534C22×C137#52911yescharacteristic
535C22×C137#53211yescharacteristic
536C22×C137#53211yescharacteristic
537C22×C137#53811yescharacteristic
538C22×C137#53911yescharacteristic
539C22×C137#54011yescharacteristic
540C22×C137#54211yescharacteristic
541C22×C137D4211yescharacteristic
542C22×C137D4211yescharacteristic
543C22×C137#54611yescharacteristic
544C22×C137#54611yescharacteristic
545C22×C137#54611yescharacteristic
546C22×C137#54711yescharacteristic
547C22×C137#54811yescharacteristic
548C22×C137#54811yescharacteristic
549C22×C137#55011yescharacteristic
550C22×C137#55011yescharacteristic
551C22×C137#55111yescharacteristic
552C22×C137#55111yescharacteristic
553C22×C137#55211yescharacteristic
554C22×C137#55311yescharacteristic
555C22×C137#55311yescharacteristic
556C22×C137#55911yescharacteristic
557C4×C137—24no—
558C4×C137—24no—
559C4×C137—24no—
560C4×C137—24no—
561C4×C137—42no—
562C4×C137—42no—
563C4×C137—42no—
564C4×C137—42no—
565C4×C137—42no—
566C4×C137—42no—
567C4×C137—42no—
568C4×C137—81no—
569C4×C137—81no—
570C2×C137—44no—
571C2×C137—82no—
572C2×C137#229711yescharacteristic
573C2×C137C4×#12311yescharacteristic
574C2×C137#233511yescharacteristic
575C2×C137D4×C22⋊C411yescharacteristic
576C2×C137#234111yescharacteristic
577C2×C137#235911yescharacteristic
578C2×C137#237411yescharacteristic
579C2×C137#244311yescharacteristic
580C2×C137#244511yescharacteristic
581C2×C137#245611yescharacteristic
582C2×C137#245811yescharacteristic
583C2×C137#246111yescharacteristic
584C2×C137#247111yescharacteristic
585C2×C137#255411yescharacteristic
586C2×C137#255811yescharacteristic
587#14095C13711yesmaximal, characteristic, direct product factor, Sylow
588C137#1409511yescharacteristic, direct product factor, Sylow
589C22×#123C2×C13711yescharacteristic
590C2×#390C2×C13711yescharacteristic
591C2×#387C2×C13711yescharacteristic, complemented
592C2×C4×C4⋊C4C2×C13711yescharacteristic, complemented
593C2×C4×C22⋊C4C2×C13711yescharacteristic, complemented
594#1441C2×C13711yescharacteristic, complemented
595#1439C2×C13711yescharacteristic, complemented
596#1439C2×C13711yescharacteristic, complemented
597#1438C2×C13711yescharacteristic
598#1437C2×C13711yescharacteristic, complemented
599#1437C2×C13711yescharacteristic, complemented
600#1437C2×C13711yescharacteristic, complemented
601#1437C2×C13711yescharacteristic, complemented
602#1436C2×C13711yescharacteristic, complemented
603C22⋊#95C2×C13711yescharacteristic, complemented
604C23×D4C22×C13711yescharacteristic
605C24×C4C22×C13711yescharacteristic
606C2×#123—24no—
607C2×#123—24no—
608C2×#123C4×C13718yescomplemented
609C22×C4⋊C4C22×C13711yescharacteristic
610C22×C4⋊C4C22×C13711yescharacteristic
611C22×C4⋊C4C22×C13711yescharacteristic
612C22×C4⋊C4C22×C13711yescharacteristic
613C22×C22⋊C4C22×C13711yescharacteristic
614C22×C22⋊C4C22×C13711yescharacteristic
615C22×C22⋊C4C22×C13711yescharacteristic
616C22×C22⋊C4C22×C13711yescharacteristic
617C22×C22⋊C4C22×C13711yescharacteristic
618C22×C22⋊C4C22×C13711yescharacteristic
619C22×C22⋊C4C22×C13711yescharacteristic
620C22×C22⋊C4C22×C13711yescharacteristic
621C22×C22⋊C4C22×C13711yescharacteristic
622C22×C22⋊C4C22×C13711yescharacteristic
623C22×C22⋊C4C22×C13711yescharacteristic
624C22×C42C22×C13711yescharacteristic
625C22×C42C22×C13711yescharacteristic
626C22×C42C22×C13711yescharacteristic
627C22×C42C22×C13711yescharacteristic
628#390—24no—
629#387—24no—
630C4×C4⋊C4—24no—
631C4×C22⋊C4—24no—
632C2×#95C22×C13711yescharacteristic
633C2×#95C22×C13711yescharacteristic
634C2×#95C22×C13711yescharacteristic
635C2×#95C22×C13711yescharacteristic
636C2×#95C22×C13711yescharacteristic
637C2×#95C22×C13711yescharacteristic
638C2×#95C22×C13711yescharacteristic
639C2×#95C22×C13711yescharacteristic
640C2×#95C22×C13711yescharacteristic
641C2×#95C22×C13711yescharacteristic
642C2×#95C22×C13711yescharacteristic
643C2×#95C22×C13711yescharacteristic
644C2×#95C22×C13711yescharacteristic
645C2×#95C22×C13711yescharacteristic
646C25C23×C13711yescharacteristic
647C25C23×C13711yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C2×C4×C13714yes—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4C2×C4×C13714yes—
662C23×C4C23×C13711yescharacteristic
663C23×C4C23×C13711yescharacteristic
664C23×C4C23×C13711yescharacteristic
665C23×C4C23×C13711yescharacteristic
666C23×C4C23×C13711yescharacteristic
667C23×C4C23×C13711yescharacteristic
668C23×C4C23×C13711yescharacteristic
669C23×C4C23×C13711yescharacteristic
670C23×C4C23×C13711yescharacteristic
671C23×C4C23×C13711yescharacteristic
672C23×C4C23×C13711yescharacteristic
673C23×C4C23×C13711yescharacteristic
674C23×C4C23×C13711yescharacteristic
675#123—232no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4C2×C4×C13714yes—
685C2×C4⋊C4C2×C4×C13714yes—
686C2×C4⋊C4D4×C13714yes—
687C2×C4⋊C4D4×C13714yes—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4C2×C4×C13714yes—
718C2×C22⋊C4C2×C4×C13714yes—
719C2×C22⋊C4C2×C4×C13714yes—
720C2×C22⋊C4D4×C13714yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—41no—
731C2×C42—41no—
732C2×C42—41no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95—41no—
746#95—41no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C22×C4×C13712yes—
774C24C22×C4×C13712yes—
775C24C2×D4×C13712yes—
776C24#41×C13712yes—
777C24C24×C13711yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—28no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—28no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4C22×C4×C13712yes—
865C22×C4C22×C4×C13712yes—
866C22×C4C22×C4×C13712yes—
867C22×C4C22×C4×C13712yes—
868C22×C4C22×C4×C13712yes—
869C22×C4C2×D4×C13712yes—
870C22×C4C2×D4×C13712yes—
871C22×C4C2×D4×C13712yes—
872C22×C4C2×D4×C13712yes—
873C22×C4C2×D4×C13712yes—
874C22×C4C2×D4×C13712yes—
875C22×C4C2×D4×C13712yes—
876C22×C4C2×D4×C13712yes—
877C22×C4#41×C13712yes—
878C22×C4#41×C13712yes—
879C22×C4#41×C13712yes—
880C22×C4#41×C13712yes—
881C22×C4#41×C13712yes—
882C22×C4#41×C13712yes—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—44no—
886C4⋊C4C22⋊C4×C137116yescomplemented
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—44no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C4×D4×C13714yes—
972C23C23×C4×C13711yescharacteristic
973C23C22×D4×C13711yescharacteristic
974C23C22×D4×C13711yescharacteristic
975C23C22×D4×C13711yescharacteristic
976C23C2×#41×C13711yescharacteristic
977C23C2×#41×C13711yescharacteristic
978C23C2×#41×C13711yescharacteristic
979C23C2×#41×C13711yescharacteristic
980C23C2×#41×C13711yescharacteristic
981C23C2×#41×C13711yescharacteristic
982C23C2×#41×C13711yescharacteristic
983C23H(5,𝔽2)×C13711yescharacteristic
984C23H(5,𝔽2)×C13711yescharacteristic
985C23H(5,𝔽2)×C13711yescharacteristic
986C232−1+4×C13711yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—416no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4C2×C22⋊C4×C13714yes—
1077C2×C4C2×C22⋊C4×C13714yes—
1078C2×C4C2×C22⋊C4×C13714yes—
1079C2×C4#123×C13714yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C22×C22⋊C4×C13711yescharacteristic
1111C22C2×C4×D4×C13711yescharacteristic
1112C22C4×#41×C13711yescharacteristic
1113C22C4×#41×C13711yescharacteristic
1114C22C4×#41×C13711yescharacteristic
1115C22#518×C13711yescharacteristic
1116C22#520×C13711yescharacteristic
1117C22C2×#123×C13711yescharacteristic
1118C22#525×C13711yescharacteristic
1119C22#525×C13711yescharacteristic
1120C22#525×C13711yescharacteristic
1121C22#529×C13711yescharacteristic
1122C22#529×C13711yescharacteristic
1123C22#532×C13711yescharacteristic
1124C22#532×C13711yescharacteristic
1125C22#538×C13711yescharacteristic
1126C22#539×C13711yescharacteristic
1127C22#540×C13711yescharacteristic
1128C22#542×C13711yescharacteristic
1129C22D42×C13711yescharacteristic
1130C22D42×C13711yescharacteristic
1131C22#546×C13711yescharacteristic
1132C22#546×C13711yescharacteristic
1133C22#546×C13711yescharacteristic
1134C22#547×C13711yescharacteristic
1135C22#548×C13711yescharacteristic
1136C22#548×C13711yescharacteristic
1137C22#550×C13711yescharacteristic
1138C22#550×C13711yescharacteristic
1139C22#551×C13711yescharacteristic
1140C22#551×C13711yescharacteristic
1141C22#552×C13711yescharacteristic
1142C22#553×C13711yescharacteristic
1143C22#553×C13711yescharacteristic
1144C22#559×C13711yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2#2297×C13711yescharacteristic
1161C2C4×#123×C13711yescharacteristic
1162C2#2335×C13711yescharacteristic
1163C2D4×C22⋊C4×C13711yescharacteristic
1164C2#2341×C13711yescharacteristic
1165C2#2359×C13711yescharacteristic
1166C2#2374×C13711yescharacteristic
1167C2#2443×C13711yescharacteristic
1168C2#2445×C13711yescharacteristic
1169C2#2456×C13711yescharacteristic
1170C2#2458×C13711yescharacteristic
1171C2#2461×C13711yescharacteristic
1172C2#2471×C13711yescharacteristic
1173C2#2554×C13711yescharacteristic
1174C2#2558×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
prime radicalC23×D4×C137C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#387×C137C2semidirect
4. C2×C4×C4⋊C4×C137C2semidirect
5. C2×C4×C22⋊C4×C137C2semidirect
6. #1441×C137C2semidirect
7. #1439×C137C2semidirect
8. #1439×C137C2semidirect
10. #1437×C137C2semidirect
11. #1437×C137C2semidirect
12. #1437×C137C2semidirect
13. #1437×C137C2semidirect
14. #1436×C137C2semidirect
15. C22⋊#95×C137C2semidirect
20. C2×#123×C137C4semidirect
298. C4⋊C4×C137C22⋊C4semidirect
491. C2×C4×C137#123semidirect
587. #14095C137direct (N × H)
588. C137#14095direct (N × H)
591. C2×#387C2×C137semidirect
592. C2×C4×C4⋊C4C2×C137semidirect
593. C2×C4×C22⋊C4C2×C137semidirect
594. #1441C2×C137semidirect
595. #1439C2×C137semidirect
596. #1439C2×C137semidirect
598. #1437C2×C137semidirect
599. #1437C2×C137semidirect
600. #1437C2×C137semidirect
601. #1437C2×C137semidirect
602. #1436C2×C137semidirect
603. C22⋊#95C2×C137semidirect
608. C2×#123C4×C137semidirect
886. C4⋊C4C22⋊C4×C137semidirect
1079. C2×C4#123×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1372
C2×#390×C1372
C2×#387×C1372
C2×C4×C4⋊C4×C1372
C2×C4×C22⋊C4×C1372
#1441×C1372
#1439×C1372
#1438×C1372
#1437×C1372
#1436×C1372
C22⋊#95×C1372
#14095137