Finite Group Databasebeta

← C137×#18253 #46867639

Subgroups — C137×#18253 #46867639

Order 35072.

1196 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3535×C137C211yesmaximal, characteristic, complemented
2#3007×C137C211yesmaximal, characteristic, complemented
3#3002×C137C211yesmaximal, characteristic, complemented
4#2430×C137C211yesmaximal, characteristic, complemented
5#1606×C137C211yesmaximal, characteristic, complemented
6#1605×C137C211yesmaximal, characteristic, complemented
7#1603×C137C211yesmaximal, characteristic, complemented
8#1602×C137C211yesmaximal, characteristic, complemented
9#1600×C137C211yesmaximal, characteristic, complemented
10#1599×C137C211yesmaximal, characteristic, complemented
11#1597×C137C211yesmaximal, characteristic, complemented
12#1596×C137C211yesmaximal, characteristic, complemented
13#1504×C137C211yesmaximal, characteristic, complemented
14C2×#328×C137C211yesmaximal, characteristic, complemented
15#1468×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C2×#137×C137—21no—
18C2×#135×C137—21no—
19#563×C137—21no—
20#562×C137—21no—
21#554×C137—21no—
22#552×C137—21no—
23#551×C137—21no—
24#551×C137—21no—
25#547×C137—21no—
26#546×C137—21no—
27#544×C137C2211yescharacteristic
28#543×C137C2211yescharacteristic
29#542×C137—21no—
30#539×C137—21no—
31#539×C137—21no—
32#539×C137C2211yescharacteristic
33#538×C137C2211yescharacteristic
34#536×C137—21no—
35#525×C137C2211yescharacteristic
36C2×#123×C137C2211yescharacteristic
37C2×C22⋊Q8×C137C2211yescharacteristic
38C2×#121×C137—21no—
39#452×C137—21no—
40#452×C137—21no—
41#452×C137—21no—
42#451×C137C2211yescharacteristic
43#451×C137C2211yescharacteristic
44#451×C137C2211yescharacteristic
45#450×C137C2211yescharacteristic
46#450×C137C2211yescharacteristic
47#450×C137C2211yescharacteristic
48#449×C137—21no—
49#448×C137C2211yescharacteristic
50#447×C137C2211yescharacteristic
51#417×C137—21no—
52#416×C137—21no—
53#407×C137C2211yescharacteristic
54C2×C22⋊C8×C137C2211yescharacteristic
55#395×C137C2211yescharacteristic
56#394×C137C2211yescharacteristic
57#393×C137C2211yescharacteristic
58#392×C137C2211yescharacteristic
59#386×C137—21no—
60#386×C137—21no—
61#385×C137—21no—
62C2×#95×C137C2211yescharacteristic
63#328×C137C2211yescharacteristic
64#328×C137C2211yescharacteristic
65#328×C137C2211yescharacteristic
66#328×C137C2211yescharacteristic
67#328×C137C2211yescharacteristic
68#328×C137C2211yescharacteristic
69#327×C137C2211yescharacteristic
70#327×C137C2211yescharacteristic
71#324×C137C2211yescharacteristic
72#324×C137C2211yescharacteristic
73#323×C137C2211yescharacteristic
74#323×C137C2211yescharacteristic
75C2×#41×C137—21no—
76C2×#41×C137—21no—
77C2×#41×C137—21no—
78C2×#41×C137—21no—
79C2×#41×C137—21no—
80C2×#41×C137—44no—
81C2×#41×C137D411yescharacteristic, complemented
82C22×Q8×C137D411yescharacteristic, complemented
83C22×Q8×C137C2311yescharacteristic
84C22×D4×C137—21no—
85C22×D4×C137—21no—
86C22×D4×C137D411yescharacteristic
87C22×D4×C137C2311yescharacteristic
88C23×C4×C137—21no—
89C23×C4×C137—21no—
90C23×C4×C137C2311yescharacteristic
91#137×C137—44no—
92#135×C137—44no—
93C2×Q16×C137—21no—
94C2×Q16×C137—21no—
95C2×Q16×C137—21no—
96C2×SD16×C137—21no—
97C2×SD16×C137—21no—
98C2×SD16×C137—21no—
99C2×SD16×C137—21no—
100C2×D8×C137—21no—
101C2×M16×C137—21no—
102C22×C8×C137—21no—
103C4⋊Q8×C137—21no—
104C4⋊Q8×C137—21no—
105C4⋊Q8×C137—21no—
106#126×C137—21no—
107#126×C137—21no—
108#126×C137—21no—
109#126×C137—21no—
110#126×C137—21no—
111#126×C137—21no—
112#125×C137—21no—
113#125×C137—21no—
114#125×C137—21no—
115#125×C137—21no—
116#125×C137—21no—
117#124×C137—21no—
118#124×C137—21no—
119#124×C137—21no—
120#124×C137—21no—
121#123×C137—21no—
122#123×C137—21no—
123#123×C137—21no—
124#123×C137—21no—
125#123×C137—21no—
126#123×C137—21no—
127#123×C137—21no—
128#123×C137—21no—
129#123×C137—21no—
130#123×C137—21no—
131#123×C137—21no—
132#123×C137—21no—
133#123×C137—21no—
134#123×C137—21no—
135C22⋊Q8×C137—21no—
136C22⋊Q8×C137—21no—
137C22⋊Q8×C137—21no—
138C22⋊Q8×C137—21no—
139C22⋊Q8×C137—21no—
140C22⋊Q8×C137—21no—
141C22⋊Q8×C137—21no—
142C22⋊Q8×C137—21no—
143C22⋊Q8×C137—21no—
144C22⋊Q8×C137—21no—
145C22⋊Q8×C137—21no—
146C22⋊Q8×C137—21no—
147C22⋊Q8×C137—21no—
148C22⋊Q8×C137—21no—
149C22⋊Q8×C137D411yescharacteristic, complemented
150C22⋊Q8×C137D411yescharacteristic, complemented
151C22⋊Q8×C137D411yescharacteristic, complemented
152C22⋊Q8×C137C2311yescharacteristic
153C22⋊Q8×C137C2311yescharacteristic
154C22⋊Q8×C137C2311yescharacteristic
155#121×C137—21no—
156#121×C137—21no—
157#121×C137—21no—
158#121×C137—21no—
159#121×C137—44no—
160#121×C137D411yescharacteristic, complemented
161#121×C137C2311yescharacteristic
162#120×C137—21no—
163#120×C137—21no—
164C4×Q8×C137—21no—
165C4×D4×C137—21no—
166C4×D4×C137—21no—
167C4×D4×C137—21no—
168C4×D4×C137—21no—
169C4×D4×C137—21no—
170C4×D4×C137—21no—
171C4×D4×C137—21no—
172#117×C137—21no—
173#117×C137—21no—
174#117×C137—21no—
175#117×C137D411yescharacteristic, complemented
176C2×C4⋊C4×C137—21no—
177C2×C4⋊C4×C137—21no—
178C2×C4⋊C4×C137—21no—
179C2×C4⋊C4×C137D411yescharacteristic
180C2×C4⋊C4×C137D411yescharacteristic, complemented
181C2×C4⋊C4×C137C2311yescharacteristic
182C2×C22⋊C4×C137—21no—
183C2×C22⋊C4×C137—21no—
184C2×C22⋊C4×C137—21no—
185C2×C22⋊C4×C137—21no—
186C2×C22⋊C4×C137—21no—
187C2×C22⋊C4×C137—21no—
188C2×C22⋊C4×C137D411yescharacteristic
189C2×C22⋊C4×C137D411yescharacteristic
190C2×C22⋊C4×C137C2311yescharacteristic
191#103×C137—21no—
192#103×C137—21no—
193#103×C137—21no—
194#103×C137—21no—
195#102×C137—21no—
196#102×C137—21no—
197#102×C137—21no—
198#102×C137—21no—
199C22⋊C8×C137—21no—
200C22⋊C8×C137—21no—
201C22⋊C8×C137C2311yescharacteristic
202C22⋊C8×C137C2311yescharacteristic
203C22⋊C8×C137C2311yescharacteristic
204C22⋊C8×C137C2311yescharacteristic
205#95×C137—21no—
206#95×C137—21no—
207#95×C137—21no—
208#95×C137C2311yescharacteristic
209#95×C137C2311yescharacteristic
210C24×C137—21no—
211C24×C137C2×D411yescharacteristic
212C24×C137C2×D411yescharacteristic
213#41×C137—24no—
214#41×C137—24no—
215#41×C137—42no—
216#41×C137—42no—
217#41×C137—42no—
218#41×C137—42no—
219#41×C137—42no—
220#41×C137—42no—
221#41×C137—42no—
222#41×C137—82no—
223C2×Q8×C137—21no—
224C2×Q8×C137—21no—
225C2×Q8×C137—21no—
226C2×Q8×C137—21no—
227C2×Q8×C137—21no—
228C2×Q8×C137—42no—
229C2×Q8×C137—42no—
230C2×Q8×C137C2×D411yescharacteristic
231C2×Q8×C137C2×D411yescharacteristic
232C2×Q8×C137C2×D411yescharacteristic
233C2×D4×C137—24no—
234C2×D4×C137—21no—
235C2×D4×C137—21no—
236C2×D4×C137—21no—
237C2×D4×C137—21no—
238C2×D4×C137—21no—
239C2×D4×C137—21no—
240C2×D4×C137—21no—
241C2×D4×C137—21no—
242C2×D4×C137—21no—
243C2×D4×C137—42no—
244C2×D4×C137—42no—
245C2×D4×C137—42no—
246C2×D4×C137—41no—
247C2×D4×C137—41no—
248C2×D4×C137—42no—
249C2×D4×C137—42no—
250C2×D4×C137—81no—
251C2×D4×C137C2×D411yescharacteristic
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—42no—
263C22×C4×C137—42no—
264C22×C4×C137—42no—
265C22×C4×C137—42no—
266C22×C4×C137—41no—
267C22×C4×C137—41no—
268C22×C4×C137—42no—
269C22×C4×C137—81no—
270C22×C4×C137C2×D411yescharacteristic
271C22×C4×C137C2×D411yescharacteristic
272C22×C4×C137C2×D411yescharacteristic
273C22×C4×C137C2×D411yescharacteristic
274C22×C4×C137C2×D411yescharacteristic
275C22×C4×C137C2×D411yescharacteristic
276C22×C4×C137C2×D411yescharacteristic
277C22×C4×C137C2×D411yescharacteristic
278C22×C4×C137C2411yescharacteristic
279Q16×C137—42no—
280Q16×C137—42no—
281Q16×C137—42no—
282SD16×C137—42no—
283SD16×C137—42no—
284SD16×C137—42no—
285SD16×C137—42no—
286D8×C137—42no—
287M16×C137—42no—
288C2×C8×C137—21no—
289C2×C8×C137—21no—
290C2×C8×C137—21no—
291C2×C8×C137—21no—
292C2×C8×C137—42no—
293C4⋊C4×C137—21no—
294C4⋊C4×C137—21no—
295C4⋊C4×C137—21no—
296C4⋊C4×C137—21no—
297C4⋊C4×C137—21no—
298C4⋊C4×C137—21no—
299C4⋊C4×C137—21no—
300C4⋊C4×C137—21no—
301C4⋊C4×C137—21no—
302C4⋊C4×C137—21no—
303C4⋊C4×C137—21no—
304C4⋊C4×C137—21no—
305C4⋊C4×C137—21no—
306C4⋊C4×C137—21no—
307C4⋊C4×C137—21no—
308C4⋊C4×C137—21no—
309C4⋊C4×C137—21no—
310C4⋊C4×C137—21no—
311C4⋊C4×C137—21no—
312C4⋊C4×C137—21no—
313C4⋊C4×C137—21no—
314C4⋊C4×C137—21no—
315C4⋊C4×C137—21no—
316C4⋊C4×C137—42no—
317C4⋊C4×C137C2×D411yescharacteristic
318C4⋊C4×C137C2×D411yescharacteristic
319C4⋊C4×C137C2×D411yescharacteristic
320C4⋊C4×C137C2×D411yescharacteristic
321C22⋊C4×C137—21no—
322C22⋊C4×C137—21no—
323C22⋊C4×C137—21no—
324C22⋊C4×C137—21no—
325C22⋊C4×C137—21no—
326C22⋊C4×C137—21no—
327C22⋊C4×C137—21no—
328C22⋊C4×C137—21no—
329C22⋊C4×C137—21no—
330C22⋊C4×C137—21no—
331C22⋊C4×C137—21no—
332C22⋊C4×C137—21no—
333C22⋊C4×C137—21no—
334C22⋊C4×C137—21no—
335C22⋊C4×C137—21no—
336C22⋊C4×C137—21no—
337C22⋊C4×C137—21no—
338C22⋊C4×C137—21no—
339C22⋊C4×C137—21no—
340C22⋊C4×C137—21no—
341C22⋊C4×C137—21no—
342C22⋊C4×C137—21no—
343C22⋊C4×C137—21no—
344C22⋊C4×C137—42no—
345C22⋊C4×C137—42no—
346C22⋊C4×C137—42no—
347C22⋊C4×C137—81no—
348C42×C137—21no—
349C42×C137—21no—
350C42×C137—21no—
351C42×C137—21no—
352C42×C137—21no—
353C23×C137—21no—
354C23×C137—21no—
355C23×C137—22no—
356C23×C137—22no—
357C23×C137—21no—
358C23×C137—21no—
359C23×C137—21no—
360C23×C137—21no—
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#12011yescharacteristic
371C23×C137#12011yescharacteristic
372C23×C137C22×D411yescharacteristic
373Q8×C137—22no—
374Q8×C137—22no—
375Q8×C137—41no—
376Q8×C137—41no—
377Q8×C137—41no—
378Q8×C137—41no—
379Q8×C137—41no—
380Q8×C137—81no—
381Q8×C137—81no—
382Q8×C137—81no—
383D4×C137—22no—
384D4×C137—22no—
385D4×C137—41no—
386D4×C137—41no—
387D4×C137—41no—
388D4×C137—44no—
389D4×C137—41no—
390D4×C137—41no—
391D4×C137—44no—
392D4×C137—42no—
393D4×C137—42no—
394D4×C137—81no—
395D4×C137—81no—
396D4×C137—81no—
397D4×C137—81no—
398D4×C137—84no—
399C2×C4×C137—22no—
400C2×C4×C137—22no—
401C2×C4×C137—22no—
402C2×C4×C137—22no—
403C2×C4×C137—21no—
404C2×C4×C137—21no—
405C2×C4×C137—21no—
406C2×C4×C137—21no—
407C2×C4×C137—21no—
408C2×C4×C137—21no—
409C2×C4×C137—21no—
410C2×C4×C137—21no—
411C2×C4×C137—21no—
412C2×C4×C137—21no—
413C2×C4×C137—21no—
414C2×C4×C137—21no—
415C2×C4×C137—41no—
416C2×C4×C137—41no—
417C2×C4×C137—41no—
418C2×C4×C137—41no—
419C2×C4×C137—44no—
420C2×C4×C137—44no—
421C2×C4×C137—41no—
422C2×C4×C137—41no—
423C2×C4×C137—41no—
424C2×C4×C137—41no—
425C2×C4×C137—42no—
426C2×C4×C137—41no—
427C2×C4×C137—41no—
428C2×C4×C137—41no—
429C2×C4×C137—41no—
430C2×C4×C137—41no—
431C2×C4×C137—81no—
432C2×C4×C137—81no—
433C2×C4×C137—81no—
434C2×C4×C137—81no—
435C2×C4×C137—81no—
436C2×C4×C137—81no—
437C2×C4×C137—84no—
438C2×C4×C137#12011yescharacteristic
439C2×C4×C137#12011yescharacteristic
440C2×C4×C137C22×D411yescharacteristic
441C2×C4×C137C22×D411yescharacteristic
442C8×C137—41no—
443C8×C137—41no—
444C8×C137—41no—
445C8×C137—41no—
446C22×C137—21no—
447C22×C137—21no—
448C22×C137—21no—
449C22×C137—21no—
450C22×C137—21no—
451C22×C137—21no—
452C22×C137—21no—
453C22×C137—42no—
454C22×C137—42no—
455C22×C137—42no—
456C22×C137—42no—
457C22×C137—41no—
458C22×C137—41no—
459C22×C137—41no—
460C22×C137—41no—
461C22×C137—42no—
462C22×C137—41no—
463C22×C137—41no—
464C22×C137—81no—
465C22×C137—81no—
466C22×C137—81no—
467C22×C137—81no—
468C22×C137—81no—
469C22×C137—81no—
470C22×C137B(4,𝔽2)12yes—
471C22×C137C2×#12011yescharacteristic
472C22×C137#57711yescharacteristic
473C22×C137#57811yescharacteristic
474C4×C137—21no—
475C4×C137—21no—
476C4×C137—21no—
477C4×C137—21no—
478C4×C137—42no—
479C4×C137—41no—
480C4×C137—41no—
481C4×C137—41no—
482C4×C137—41no—
483C4×C137—41no—
484C4×C137—41no—
485C4×C137—42no—
486C4×C137—41no—
487C4×C137—41no—
488C4×C137—41no—
489C4×C137—41no—
490C4×C137—81no—
491C2×C137—21no—
492C2×C137—21no—
493C2×C137—22no—
494C2×C137—41no—
495C2×C137—81no—
496C2×C137—81no—
497C2×C137—82no—
498C2×C137#301311yescharacteristic
499C2×C137#301811yescharacteristic
500C2×C137C2×B(4,𝔽2)11yescharacteristic
501#18253C13711yesmaximal, characteristic, direct product factor, Sylow
502C137#1825311yescharacteristic, direct product factor, Sylow
503#3535C2×C13711yescharacteristic, complemented
504#3007C2×C13711yescharacteristic, complemented
505#3002C2×C13711yescharacteristic, complemented
506#2430C2×C13711yescharacteristic, complemented
507#1606C2×C13711yescharacteristic, complemented
508#1605C2×C13711yescharacteristic, complemented
509#1603C2×C13711yescharacteristic, complemented
510#1602C2×C13711yescharacteristic, complemented
511#1600C2×C13711yescharacteristic, complemented
512#1599C2×C13711yescharacteristic, complemented
513#1597C2×C13711yescharacteristic, complemented
514#1596C2×C13711yescharacteristic, complemented
515#1504C2×C13711yescharacteristic, complemented
516C2×#328C2×C13711yescharacteristic, complemented
517#1468C2×C13711yescharacteristic, complemented
518C22×#41C22×C13711yescharacteristic
519C2×#137—21no—
520C2×#135—21no—
521#563—21no—
522#562—21no—
523#554—21no—
524#552—21no—
525#551—21no—
526#551—21no—
527#547—21no—
528#546—21no—
529#544C22×C13711yescharacteristic
530#543C22×C13711yescharacteristic
531#542—21no—
532#539—21no—
533#539—21no—
534#539C22×C13711yescharacteristic
535#538C22×C13711yescharacteristic
536#536—21no—
537#525C22×C13711yescharacteristic
538C2×#123C22×C13711yescharacteristic
539C2×C22⋊Q8C22×C13711yescharacteristic
540C2×#121—21no—
541#452—21no—
542#452—21no—
543#452—21no—
544#451C22×C13711yescharacteristic
545#451C22×C13711yescharacteristic
546#451C22×C13711yescharacteristic
547#450C22×C13711yescharacteristic
548#450C22×C13711yescharacteristic
549#450C22×C13711yescharacteristic
550#449—21no—
551#448C22×C13711yescharacteristic
552#447C22×C13711yescharacteristic
553#417—21no—
554#416—21no—
555#407C22×C13711yescharacteristic
556C2×C22⋊C8C22×C13711yescharacteristic
557#395C22×C13711yescharacteristic
558#394C22×C13711yescharacteristic
559#393C22×C13711yescharacteristic
560#392C22×C13711yescharacteristic
561#386—21no—
562#386—21no—
563#385—21no—
564C2×#95C22×C13711yescharacteristic
565#328C22×C13711yescharacteristic
566#328C22×C13711yescharacteristic
567#328C22×C13711yescharacteristic
568#328C22×C13711yescharacteristic
569#328C22×C13711yescharacteristic
570#328C22×C13711yescharacteristic
571#327C22×C13711yescharacteristic
572#327C22×C13711yescharacteristic
573#324C22×C13711yescharacteristic
574#324C22×C13711yescharacteristic
575#323C22×C13711yescharacteristic
576#323C22×C13711yescharacteristic
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—44no—
583C2×#41D4×C13711yescharacteristic, complemented
584C22×Q8D4×C13711yescharacteristic, complemented
585C22×Q8C23×C13711yescharacteristic
586C22×D4—21no—
587C22×D4—21no—
588C22×D4D4×C13711yescharacteristic
589C22×D4C23×C13711yescharacteristic
590C23×C4—21no—
591C23×C4—21no—
592C23×C4C23×C13711yescharacteristic
593#137—44no—
594#135—44no—
595C2×Q16—21no—
596C2×Q16—21no—
597C2×Q16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—21no—
601C2×SD16—21no—
602C2×D8—21no—
603C2×M16—21no—
604C22×C8—21no—
605C4⋊Q8—21no—
606C4⋊Q8—21no—
607C4⋊Q8—21no—
608#126—21no—
609#126—21no—
610#126—21no—
611#126—21no—
612#126—21no—
613#126—21no—
614#125—21no—
615#125—21no—
616#125—21no—
617#125—21no—
618#125—21no—
619#124—21no—
620#124—21no—
621#124—21no—
622#124—21no—
623#123—21no—
624#123—21no—
625#123—21no—
626#123—21no—
627#123—21no—
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—21no—
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8—21no—
647C22⋊Q8—21no—
648C22⋊Q8—21no—
649C22⋊Q8—21no—
650C22⋊Q8—21no—
651C22⋊Q8D4×C13711yescharacteristic, complemented
652C22⋊Q8D4×C13711yescharacteristic, complemented
653C22⋊Q8D4×C13711yescharacteristic, complemented
654C22⋊Q8C23×C13711yescharacteristic
655C22⋊Q8C23×C13711yescharacteristic
656C22⋊Q8C23×C13711yescharacteristic
657#121—21no—
658#121—21no—
659#121—21no—
660#121—21no—
661#121—44no—
662#121D4×C13711yescharacteristic, complemented
663#121C23×C13711yescharacteristic
664#120—21no—
665#120—21no—
666C4×Q8—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4—21no—
673C4×D4—21no—
674#117—21no—
675#117—21no—
676#117—21no—
677#117D4×C13711yescharacteristic, complemented
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4D4×C13711yescharacteristic
682C2×C4⋊C4D4×C13711yescharacteristic, complemented
683C2×C4⋊C4C23×C13711yescharacteristic
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4D4×C13711yescharacteristic
691C2×C22⋊C4D4×C13711yescharacteristic
692C2×C22⋊C4C23×C13711yescharacteristic
693#103—21no—
694#103—21no—
695#103—21no—
696#103—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C13711yescharacteristic
704C22⋊C8C23×C13711yescharacteristic
705C22⋊C8C23×C13711yescharacteristic
706C22⋊C8C23×C13711yescharacteristic
707#95—21no—
708#95—21no—
709#95—21no—
710#95C23×C13711yescharacteristic
711#95C23×C13711yescharacteristic
712C24—21no—
713C24C2×D4×C13711yescharacteristic
714C24C2×D4×C13711yescharacteristic
715#41—24no—
716#41—24no—
717#41—42no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41—82no—
725C2×Q8—21no—
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—21no—
729C2×Q8—21no—
730C2×Q8—42no—
731C2×Q8—42no—
732C2×Q8C2×D4×C13711yescharacteristic
733C2×Q8C2×D4×C13711yescharacteristic
734C2×Q8C2×D4×C13711yescharacteristic
735C2×D4—24no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—41no—
749C2×D4—41no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4C2×D4×C13711yescharacteristic
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—42no—
771C22×C4—81no—
772C22×C4C2×D4×C13711yescharacteristic
773C22×C4C2×D4×C13711yescharacteristic
774C22×C4C2×D4×C13711yescharacteristic
775C22×C4C2×D4×C13711yescharacteristic
776C22×C4C2×D4×C13711yescharacteristic
777C22×C4C2×D4×C13711yescharacteristic
778C22×C4C2×D4×C13711yescharacteristic
779C22×C4C2×D4×C13711yescharacteristic
780C22×C4C24×C13711yescharacteristic
781Q16—42no—
782Q16—42no—
783Q16—42no—
784SD16—42no—
785SD16—42no—
786SD16—42no—
787SD16—42no—
788D8—42no—
789M16—42no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—42no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C13711yescharacteristic
820C4⋊C4C2×D4×C13711yescharacteristic
821C4⋊C4C2×D4×C13711yescharacteristic
822C4⋊C4C2×D4×C13711yescharacteristic
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—21no—
845C22⋊C4—21no—
846C22⋊C4—42no—
847C22⋊C4—42no—
848C22⋊C4—42no—
849C22⋊C4—81no—
850C42—21no—
851C42—21no—
852C42—21no—
853C42—21no—
854C42—21no—
855C23—22no—
856C23—21no—
857C23—21no—
858C23—22no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23#120×C13711yescharacteristic
873C23#120×C13711yescharacteristic
874C23C22×D4×C13711yescharacteristic
875Q8—22no—
876Q8—22no—
877Q8—41no—
878Q8—41no—
879Q8—41no—
880Q8—41no—
881Q8—41no—
882Q8—81no—
883Q8—81no—
884Q8—81no—
885D4—22no—
886D4—22no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—44no—
891D4—44no—
892D4—42no—
893D4—42no—
894D4—41no—
895D4—41no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—84no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—42no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4—81no—
939C2×C4—84no—
940C2×C4#120×C13711yescharacteristic
941C2×C4#120×C13711yescharacteristic
942C2×C4C22×D4×C13711yescharacteristic
943C2×C4C22×D4×C13711yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22B(4,𝔽2)×C13712yes—
973C22C2×#120×C13711yescharacteristic
974C22#577×C13711yescharacteristic
975C22#578×C13711yescharacteristic
976C4—21no—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—42no—
981C4—41no—
982C4—41no—
983C4—41no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—81no—
993C2—21no—
994C2—21no—
995C2—22no—
996C2—41no—
997C2—82no—
998C2—81no—
999C2—81no—
1000C2#3013×C13711yescharacteristic
1001C2#3018×C13711yescharacteristic
1002C2C2×B(4,𝔽2)×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3535×C137C2semidirect
2. #3007×C137C2semidirect
3. #3002×C137C2semidirect
4. #2430×C137C2semidirect
5. #1606×C137C2semidirect
6. #1605×C137C2semidirect
7. #1603×C137C2semidirect
8. #1602×C137C2semidirect
9. #1600×C137C2semidirect
10. #1599×C137C2semidirect
11. #1597×C137C2semidirect
12. #1596×C137C2semidirect
13. #1504×C137C2semidirect
14. C2×#328×C137C2semidirect
15. #1468×C137C2semidirect
81. C2×#41×C137D4semidirect
82. C22×Q8×C137D4semidirect
149. C22⋊Q8×C137D4semidirect
150. C22⋊Q8×C137D4semidirect
151. C22⋊Q8×C137D4semidirect
160. #121×C137D4semidirect
175. #117×C137D4semidirect
180. C2×C4⋊C4×C137D4semidirect
501. #18253C137direct (N × H)
502. C137#18253direct (N × H)
503. #3535C2×C137semidirect
504. #3007C2×C137semidirect
505. #3002C2×C137semidirect
506. #2430C2×C137semidirect
507. #1606C2×C137semidirect
508. #1605C2×C137semidirect
509. #1603C2×C137semidirect
510. #1602C2×C137semidirect
511. #1600C2×C137semidirect
512. #1599C2×C137semidirect
513. #1597C2×C137semidirect
514. #1596C2×C137semidirect
515. #1504C2×C137semidirect
516. C2×#328C2×C137semidirect
517. #1468C2×C137semidirect
583. C2×#41D4×C137semidirect
584. C22×Q8D4×C137semidirect
651. C22⋊Q8D4×C137semidirect
652. C22⋊Q8D4×C137semidirect
653. C22⋊Q8D4×C137semidirect
662. #121D4×C137semidirect
677. #117D4×C137semidirect
682. C2×C4⋊C4D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3535×C1372
#3007×C1372
#3002×C1372
#2430×C1372
#1606×C1372
#1605×C1372
#1603×C1372
#1602×C1372
#1600×C1372
#1599×C1372
#1597×C1372
#1596×C1372
#1504×C1372
C2×#328×C1372
#1468×C1372
#18253137