Finite Group Databasebeta

← C137×#18415 #46867801

Subgroups — C137×#18415 #46867801

Order 35072.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3534×C137C211yesmaximal, characteristic
2#3196×C137C211yesmaximal, characteristic, complemented
3#3187×C137C211yesmaximal, characteristic, complemented
4#2663×C137C211yesmaximal, characteristic, complemented
5#1618×C137C211yesmaximal, characteristic, complemented
6#1616×C137C211yesmaximal, characteristic, complemented
7#1615×C137C211yesmaximal, characteristic, complemented
8#1613×C137C211yesmaximal, characteristic, complemented
9#1606×C137C211yesmaximal, characteristic, complemented
10#1604×C137C211yesmaximal, characteristic, complemented
11#1603×C137C211yesmaximal, characteristic, complemented
12#1601×C137C211yesmaximal, characteristic, complemented
13#1507×C137C211yesmaximal, characteristic, complemented
14#1501×C137C211yesmaximal, characteristic, complemented
15#1468×C137C211yesmaximal, characteristic, complemented
16#562×C137—21no—
17#560×C137—21no—
18#553×C137—21no—
19#551×C137—21no—
20#546×C137—21no—
21#546×C137—21no—
22#546×C137—21no—
23D42×C137—21no—
24#540×C137—21no—
25#539×C137—21no—
26#539×C137C2211yescharacteristic
27#538×C137—21no—
28#538×C137C2211yescharacteristic
29#537×C137C2211yescharacteristic
30#534×C137—21no—
31#534×C137C2211yescharacteristic
32#525×C137C2211yescharacteristic
33C2×#123×C137C2211yescharacteristic
34C2×C22⋊Q8×C137C2211yescharacteristic, complemented
35C2×#121×C137C2211yescharacteristic
36#485×C137—21no—
37#484×C137C2211yescharacteristic, complemented
38#483×C137—21no—
39#481×C137C2211yescharacteristic
40#481×C137C2211yescharacteristic, complemented
41#481×C137C2211yescharacteristic, complemented
42#470×C137—21no—
43#468×C137—21no—
44#465×C137—21no—
45#465×C137—21no—
46#452×C137—21no—
47#451×C137C2211yescharacteristic, complemented
48#450×C137—21no—
49#448×C137C2211yescharacteristic
50#448×C137C2211yescharacteristic, complemented
51#448×C137C2211yescharacteristic, complemented
52#407×C137C2211yescharacteristic, complemented
53C2×C22⋊C8×C137C2211yescharacteristic, complemented
54#400×C137C2211yescharacteristic, complemented
55#399×C137C2211yescharacteristic, complemented
56#397×C137—21no—
57#395×C137C2211yescharacteristic, complemented
58#394×C137—21no—
59#393×C137C2211yescharacteristic, complemented
60#389×C137—21no—
61#388×C137—21no—
62C4×C22⋊C4×C137C2211yescharacteristic, complemented
63#328×C137C2211yescharacteristic, complemented
64#328×C137C2211yescharacteristic, complemented
65#327×C137C2211yescharacteristic
66#327×C137C2211yescharacteristic
67#327×C137C2211yescharacteristic, complemented
68#327×C137C2211yescharacteristic, complemented
69#327×C137C2211yescharacteristic, complemented
70#327×C137C2211yescharacteristic, complemented
71#324×C137C2211yescharacteristic, complemented
72#324×C137C2211yescharacteristic, complemented
73#323×C137C2211yescharacteristic, complemented
74#323×C137C2211yescharacteristic, complemented
75C2×#41×C137—21no—
76C2×#41×C137D411yescharacteristic
77C22×Q8×C137C2311yescharacteristic
78C22×D4×C137—21no—
79C22×D4×C137—21no—
80C22×D4×C137—21no—
81C22×D4×C137D411yescharacteristic
82C22×D4×C137D411yescharacteristic
83C23×C4×C137C2311yescharacteristic
84C2×Q16×C137—21no—
85C2×SD16×C137—21no—
86C2×SD16×C137—21no—
87C2×SD16×C137—21no—
88C2×M16×C137—21no—
89C22×C8×C137—21no—
90#127×C137—21no—
91#126×C137—21no—
92#126×C137—21no—
93#126×C137—21no—
94#126×C137—21no—
95#125×C137—21no—
96#125×C137—21no—
97#124×C137—21no—
98#124×C137—21no—
99#124×C137—21no—
100#123×C137—21no—
101#123×C137—21no—
102#123×C137—21no—
103#123×C137—21no—
104#123×C137—21no—
105#123×C137—21no—
106#123×C137—21no—
107#123×C137—21no—
108#123×C137—21no—
109#123×C137—21no—
110#123×C137—21no—
111#123×C137—21no—
112#123×C137—21no—
113#123×C137—21no—
114C22⋊Q8×C137—21no—
115C22⋊Q8×C137—21no—
116C22⋊Q8×C137—21no—
117C22⋊Q8×C137—21no—
118C22⋊Q8×C137—21no—
119C22⋊Q8×C137—21no—
120C22⋊Q8×C137—21no—
121C22⋊Q8×C137—21no—
122C22⋊Q8×C137—21no—
123C22⋊Q8×C137D411yescharacteristic
124C22⋊Q8×C137C2311yescharacteristic
125#121×C137—21no—
126#121×C137—21no—
127#121×C137—21no—
128#121×C137—21no—
129#121×C137—21no—
130#121×C137—21no—
131#121×C137—21no—
132#121×C137—21no—
133#121×C137—21no—
134#121×C137—21no—
135#121×C137—21no—
136#121×C137—21no—
137#121×C137—21no—
138#121×C137—21no—
139#121×C137—21no—
140#121×C137D411yescharacteristic
141#121×C137D411yescharacteristic
142#121×C137D411yescharacteristic
143#121×C137C2311yescharacteristic
144#121×C137C2311yescharacteristic
145#121×C137C2311yescharacteristic
146#120×C137—21no—
147#120×C137—21no—
148#120×C137—21no—
149#120×C137—21no—
150#120×C137—21no—
151#120×C137—21no—
152#120×C137—21no—
153#120×C137—21no—
154C4×D4×C137—21no—
155C4×D4×C137—21no—
156C4×D4×C137—21no—
157C4×D4×C137—21no—
158C4×D4×C137—21no—
159C4×D4×C137—21no—
160C4×D4×C137—21no—
161C4×D4×C137—21no—
162#117×C137—21no—
163#117×C137D411yescharacteristic
164C2×C4⋊C4×C137—21no—
165C2×C4⋊C4×C137—21no—
166C2×C4⋊C4×C137—21no—
167C2×C4⋊C4×C137D411yescharacteristic
168C2×C4⋊C4×C137D411yescharacteristic
169C2×C4⋊C4×C137C2311yescharacteristic
170C2×C4⋊C4×C137C2311yescharacteristic
171C2×C22⋊C4×C137—21no—
172C2×C22⋊C4×C137—21no—
173C2×C22⋊C4×C137—21no—
174C2×C22⋊C4×C137—21no—
175C2×C22⋊C4×C137—21no—
176C2×C22⋊C4×C137—21no—
177C2×C22⋊C4×C137—21no—
178C2×C22⋊C4×C137D411yescharacteristic
179C2×C22⋊C4×C137D411yescharacteristic
180C2×C22⋊C4×C137C2311yescharacteristic
181C2×C42×C137—21no—
182#107×C137—21no—
183#106×C137—21no—
184#106×C137—21no—
185#106×C137—21no—
186#103×C137—21no—
187#103×C137—21no—
188#103×C137—21no—
189#103×C137—21no—
190#103×C137—21no—
191#102×C137—21no—
192#102×C137—21no—
193#102×C137—21no—
194C22⋊C8×C137—21no—
195C22⋊C8×C137—21no—
196C22⋊C8×C137C2311yescharacteristic
197C22⋊C8×C137C2311yescharacteristic
198C22⋊C8×C137C2311yescharacteristic
199C22⋊C8×C137C2311yescharacteristic
200#95×C137—21no—
201#95×C137—21no—
202#95×C137—21no—
203#95×C137—21no—
204#95×C137C2311yescharacteristic
205#95×C137C2311yescharacteristic
206C24×C137—21no—
207C24×C137—21no—
208C24×C137C2×D411yescharacteristic
209C24×C137C2×D411yescharacteristic
210#41×C137—81no—
211#41×C137—81no—
212#41×C137—81no—
213C2×Q8×C137—21no—
214C2×Q8×C137—21no—
215C2×Q8×C137—21no—
216C2×Q8×C137—81no—
217C2×Q8×C137C2×D411yescharacteristic
218C2×D4×C137—21no—
219C2×D4×C137—21no—
220C2×D4×C137—21no—
221C2×D4×C137—21no—
222C2×D4×C137—21no—
223C2×D4×C137—21no—
224C2×D4×C137—21no—
225C2×D4×C137—21no—
226C2×D4×C137—21no—
227C2×D4×C137—21no—
228C2×D4×C137—21no—
229C2×D4×C137—21no—
230C2×D4×C137—21no—
231C2×D4×C137—21no—
232C2×D4×C137—21no—
233C2×D4×C137—21no—
234C2×D4×C137—21no—
235C2×D4×C137—81no—
236C2×D4×C137—81no—
237C2×D4×C137—81no—
238C2×D4×C137—81no—
239C2×D4×C137—81no—
240C2×D4×C137—81no—
241C2×D4×C137—82no—
242C2×D4×C137C2×D411yescharacteristic
243C2×D4×C137C2×D411yescharacteristic
244C2×D4×C137C2×D411yescharacteristic
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—81no—
257C22×C4×C137C2×D411yescharacteristic
258C22×C4×C137C2×D411yescharacteristic
259C22×C4×C137C2×D411yescharacteristic
260C22×C4×C137C2×D411yescharacteristic
261C22×C4×C137C2×D411yescharacteristic
262C22×C4×C137C2×D411yescharacteristic
263C22×C4×C137C2×D411yescharacteristic
264C22×C4×C137C2×D411yescharacteristic
265C22×C4×C137C2411yescharacteristic
266Q16×C137—81no—
267SD16×C137—81no—
268SD16×C137—81no—
269SD16×C137—81no—
270M16×C137—81no—
271C2×C8×C137—21no—
272C2×C8×C137—21no—
273C2×C8×C137—21no—
274C2×C8×C137—21no—
275C2×C8×C137—81no—
276C4⋊C4×C137—21no—
277C4⋊C4×C137—21no—
278C4⋊C4×C137—21no—
279C4⋊C4×C137—21no—
280C4⋊C4×C137—21no—
281C4⋊C4×C137—21no—
282C4⋊C4×C137—21no—
283C4⋊C4×C137—21no—
284C4⋊C4×C137—21no—
285C4⋊C4×C137—21no—
286C4⋊C4×C137—21no—
287C4⋊C4×C137—21no—
288C4⋊C4×C137—21no—
289C4⋊C4×C137—21no—
290C4⋊C4×C137—21no—
291C4⋊C4×C137—42no—
292C4⋊C4×C137—41no—
293C4⋊C4×C137—41no—
294C4⋊C4×C137—81no—
295C4⋊C4×C137C2×D411yescharacteristic
296C4⋊C4×C137C2×D411yescharacteristic
297C4⋊C4×C137C2×D411yescharacteristic
298C4⋊C4×C137C2×D411yescharacteristic
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—21no—
310C22⋊C4×C137—21no—
311C22⋊C4×C137—21no—
312C22⋊C4×C137—21no—
313C22⋊C4×C137—21no—
314C22⋊C4×C137—21no—
315C22⋊C4×C137—21no—
316C22⋊C4×C137—21no—
317C22⋊C4×C137—21no—
318C22⋊C4×C137—21no—
319C22⋊C4×C137—21no—
320C22⋊C4×C137—21no—
321C22⋊C4×C137—21no—
322C22⋊C4×C137—21no—
323C22⋊C4×C137—21no—
324C22⋊C4×C137—42no—
325C22⋊C4×C137—42no—
326C22⋊C4×C137—41no—
327C22⋊C4×C137—41no—
328C22⋊C4×C137—81no—
329C42×C137—21no—
330C42×C137—21no—
331C42×C137—21no—
332C42×C137—81no—
333C23×C137—21no—
334C23×C137—21no—
335C23×C137—21no—
336C23×C137—21no—
337C23×C137—21no—
338C23×C137—21no—
339C23×C137—21no—
340C23×C137—21no—
341C23×C137—41no—
342C23×C137—41no—
343C23×C137—42no—
344C23×C137—41no—
345C23×C137—41no—
346C23×C137—81no—
347C23×C137—81no—
348C23×C137—81no—
349C23×C137—81no—
350C23×C137—81no—
351C23×C137#12011yescharacteristic
352C23×C137#12011yescharacteristic
353C23×C137C22×D411yescharacteristic
354Q8×C137—41no—
355Q8×C137—41no—
356Q8×C137—41no—
357Q8×C137—41no—
358Q8×C137—41no—
359Q8×C137—81no—
360D4×C137—41no—
361D4×C137—41no—
362D4×C137—41no—
363D4×C137—42no—
364D4×C137—42no—
365D4×C137—41no—
366D4×C137—41no—
367D4×C137—41no—
368D4×C137—41no—
369D4×C137—41no—
370D4×C137—41no—
371D4×C137—81no—
372D4×C137—81no—
373D4×C137—81no—
374D4×C137—81no—
375D4×C137—81no—
376D4×C137—81no—
377D4×C137—81no—
378D4×C137—81no—
379D4×C137—81no—
380D4×C137—81no—
381D4×C137—81no—
382D4×C137—81no—
383C2×C4×C137—22no—
384C2×C4×C137—21no—
385C2×C4×C137—21no—
386C2×C4×C137—21no—
387C2×C4×C137—21no—
388C2×C4×C137—21no—
389C2×C4×C137—21no—
390C2×C4×C137—21no—
391C2×C4×C137—21no—
392C2×C4×C137—21no—
393C2×C4×C137—21no—
394C2×C4×C137—41no—
395C2×C4×C137—41no—
396C2×C4×C137—41no—
397C2×C4×C137—41no—
398C2×C4×C137—41no—
399C2×C4×C137—41no—
400C2×C4×C137—41no—
401C2×C4×C137—41no—
402C2×C4×C137—41no—
403C2×C4×C137—41no—
404C2×C4×C137—41no—
405C2×C4×C137—41no—
406C2×C4×C137—41no—
407C2×C4×C137—41no—
408C2×C4×C137—41no—
409C2×C4×C137—41no—
410C2×C4×C137—41no—
411C2×C4×C137—41no—
412C2×C4×C137—41no—
413C2×C4×C137—81no—
414C2×C4×C137—81no—
415C2×C4×C137—81no—
416C2×C4×C137—81no—
417C2×C4×C137—81no—
418C2×C4×C137—81no—
419C2×C4×C137—81no—
420C2×C4×C137#12011yescharacteristic
421C2×C4×C137#12011yescharacteristic
422C2×C4×C137C22×D411yescharacteristic
423C2×C4×C137C22×D411yescharacteristic
424C8×C137—41no—
425C8×C137—41no—
426C8×C137—41no—
427C8×C137—41no—
428C22×C137—21no—
429C22×C137—21no—
430C22×C137—21no—
431C22×C137—21no—
432C22×C137—21no—
433C22×C137—21no—
434C22×C137—21no—
435C22×C137—21no—
436C22×C137—41no—
437C22×C137—41no—
438C22×C137—41no—
439C22×C137—41no—
440C22×C137—41no—
441C22×C137—41no—
442C22×C137—41no—
443C22×C137—41no—
444C22×C137—41no—
445C22×C137—41no—
446C22×C137—41no—
447C22×C137—41no—
448C22×C137—81no—
449C22×C137—81no—
450C22×C137—81no—
451C22×C137—81no—
452C22×C137—162no—
453C22×C137—162no—
454C22×C137C2×#12011yescharacteristic
455C22×C137#57711yescharacteristic
456C22×C137#57711yescharacteristic
457C4×C137—21no—
458C4×C137—21no—
459C4×C137—21no—
460C4×C137—21no—
461C4×C137—42no—
462C4×C137—41no—
463C4×C137—41no—
464C4×C137—41no—
465C4×C137—41no—
466C4×C137—41no—
467C4×C137—41no—
468C4×C137—41no—
469C4×C137—41no—
470C4×C137—81no—
471C4×C137—81no—
472C4×C137—81no—
473C2×C137—21no—
474C2×C137—21no—
475C2×C137—41no—
476C2×C137—41no—
477C2×C137—81no—
478C2×C137—81no—
479C2×C137—81no—
480C2×C137—81no—
481C2×C137#300911yescharacteristic
482C2×C137#301811yescharacteristic
483C2×C137#302611yescharacteristic
484#18415C13711yesmaximal, characteristic, direct product factor, Sylow
485C137#1841511yescharacteristic, direct product factor, Sylow
486#3534C2×C13711yescharacteristic
487#3196C2×C13711yescharacteristic, complemented
488#3187C2×C13711yescharacteristic, complemented
489#2663C2×C13711yescharacteristic, complemented
490#1618C2×C13711yescharacteristic, complemented
491#1616C2×C13711yescharacteristic, complemented
492#1615C2×C13711yescharacteristic, complemented
493#1613C2×C13711yescharacteristic, complemented
494#1606C2×C13711yescharacteristic, complemented
495#1604C2×C13711yescharacteristic, complemented
496#1603C2×C13711yescharacteristic, complemented
497#1601C2×C13711yescharacteristic, complemented
498#1507C2×C13711yescharacteristic, complemented
499#1501C2×C13711yescharacteristic, complemented
500#1468C2×C13711yescharacteristic, complemented
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C13711yescharacteristic
512#538—21no—
513#538C22×C13711yescharacteristic
514#537C22×C13711yescharacteristic
515#534—21no—
516#534C22×C13711yescharacteristic
517#525C22×C13711yescharacteristic
518C2×#123C22×C13711yescharacteristic
519C2×C22⋊Q8C22×C13711yescharacteristic, complemented
520C2×#121C22×C13711yescharacteristic
521#485—21no—
522#484C22×C13711yescharacteristic, complemented
523#483—21no—
524#481C22×C13711yescharacteristic
525#481C22×C13711yescharacteristic, complemented
526#481C22×C13711yescharacteristic, complemented
527#470—21no—
528#468—21no—
529#465—21no—
530#465—21no—
531#452—21no—
532#451C22×C13711yescharacteristic, complemented
533#450—21no—
534#448C22×C13711yescharacteristic
535#448C22×C13711yescharacteristic, complemented
536#448C22×C13711yescharacteristic, complemented
537#407C22×C13711yescharacteristic, complemented
538C2×C22⋊C8C22×C13711yescharacteristic, complemented
539#400C22×C13711yescharacteristic, complemented
540#399C22×C13711yescharacteristic, complemented
541#397—21no—
542#395C22×C13711yescharacteristic, complemented
543#394—21no—
544#393C22×C13711yescharacteristic, complemented
545#389—21no—
546#388—21no—
547C4×C22⋊C4C22×C13711yescharacteristic, complemented
548#328C22×C13711yescharacteristic, complemented
549#328C22×C13711yescharacteristic, complemented
550#327C22×C13711yescharacteristic
551#327C22×C13711yescharacteristic
552#327C22×C13711yescharacteristic, complemented
553#327C22×C13711yescharacteristic, complemented
554#327C22×C13711yescharacteristic, complemented
555#327C22×C13711yescharacteristic, complemented
556#324C22×C13711yescharacteristic, complemented
557#324C22×C13711yescharacteristic, complemented
558#323C22×C13711yescharacteristic, complemented
559#323C22×C13711yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C13711yescharacteristic
562C22×Q8C23×C13711yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C13711yescharacteristic
567C22×D4D4×C13711yescharacteristic
568C23×C4C23×C13711yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C13711yescharacteristic
609C22⋊Q8C23×C13711yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C13711yescharacteristic
626#121D4×C13711yescharacteristic
627#121D4×C13711yescharacteristic
628#121C23×C13711yescharacteristic
629#121C23×C13711yescharacteristic
630#121C23×C13711yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C13711yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C13711yescharacteristic
653C2×C4⋊C4D4×C13711yescharacteristic
654C2×C4⋊C4C23×C13711yescharacteristic
655C2×C4⋊C4C23×C13711yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C13711yescharacteristic
664C2×C22⋊C4D4×C13711yescharacteristic
665C2×C22⋊C4C23×C13711yescharacteristic
666C2×C42—21no—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C13711yescharacteristic
682C22⋊C8C23×C13711yescharacteristic
683C22⋊C8C23×C13711yescharacteristic
684C22⋊C8C23×C13711yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C13711yescharacteristic
690#95C23×C13711yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C13711yescharacteristic
694C24C2×D4×C13711yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C13711yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C13711yescharacteristic
728C2×D4C2×D4×C13711yescharacteristic
729C2×D4C2×D4×C13711yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C13711yescharacteristic
743C22×C4C2×D4×C13711yescharacteristic
744C22×C4C2×D4×C13711yescharacteristic
745C22×C4C2×D4×C13711yescharacteristic
746C22×C4C2×D4×C13711yescharacteristic
747C22×C4C2×D4×C13711yescharacteristic
748C22×C4C2×D4×C13711yescharacteristic
749C22×C4C2×D4×C13711yescharacteristic
750C22×C4C24×C13711yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C13711yescharacteristic
781C4⋊C4C2×D4×C13711yescharacteristic
782C4⋊C4C2×D4×C13711yescharacteristic
783C4⋊C4C2×D4×C13711yescharacteristic
784C22⋊C4—21no—
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—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C13711yescharacteristic
837C23#120×C13711yescharacteristic
838C23C22×D4×C13711yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C13711yescharacteristic
906C2×C4#120×C13711yescharacteristic
907C2×C4C22×D4×C13711yescharacteristic
908C2×C4C22×D4×C13711yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C13711yescharacteristic
940C22#577×C13711yescharacteristic
941C22#577×C13711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2#3009×C13711yescharacteristic
967C2#3018×C13711yescharacteristic
968C2#3026×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
prime radical#3534×C137C2
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
2. #3196×C137C2semidirect
3. #3187×C137C2semidirect
4. #2663×C137C2semidirect
5. #1618×C137C2semidirect
6. #1616×C137C2semidirect
7. #1615×C137C2semidirect
8. #1613×C137C2semidirect
9. #1606×C137C2semidirect
10. #1604×C137C2semidirect
11. #1603×C137C2semidirect
12. #1601×C137C2semidirect
13. #1507×C137C2semidirect
14. #1501×C137C2semidirect
15. #1468×C137C2semidirect
34. C2×C22⋊Q8×C137C22semidirect
37. #484×C137C22semidirect
40. #481×C137C22semidirect
41. #481×C137C22semidirect
47. #451×C137C22semidirect
50. #448×C137C22semidirect
51. #448×C137C22semidirect
52. #407×C137C22semidirect
53. C2×C22⋊C8×C137C22semidirect
54. #400×C137C22semidirect
55. #399×C137C22semidirect
57. #395×C137C22semidirect
59. #393×C137C22semidirect
62. C4×C22⋊C4×C137C22semidirect
63. #328×C137C22semidirect
64. #328×C137C22semidirect
67. #327×C137C22semidirect
68. #327×C137C22semidirect
69. #327×C137C22semidirect
70. #327×C137C22semidirect
71. #324×C137C22semidirect
72. #324×C137C22semidirect
73. #323×C137C22semidirect
74. #323×C137C22semidirect
484. #18415C137direct (N × H)
485. C137#18415direct (N × H)
487. #3196C2×C137semidirect
488. #3187C2×C137semidirect
489. #2663C2×C137semidirect
490. #1618C2×C137semidirect
491. #1616C2×C137semidirect
492. #1615C2×C137semidirect
493. #1613C2×C137semidirect
494. #1606C2×C137semidirect
495. #1604C2×C137semidirect
496. #1603C2×C137semidirect
497. #1601C2×C137semidirect
498. #1507C2×C137semidirect
499. #1501C2×C137semidirect
500. #1468C2×C137semidirect
519. C2×C22⋊Q8C22×C137semidirect
522. #484C22×C137semidirect
525. #481C22×C137semidirect
526. #481C22×C137semidirect
532. #451C22×C137semidirect
535. #448C22×C137semidirect
536. #448C22×C137semidirect
537. #407C22×C137semidirect
538. C2×C22⋊C8C22×C137semidirect
539. #400C22×C137semidirect
540. #399C22×C137semidirect
542. #395C22×C137semidirect
544. #393C22×C137semidirect
547. C4×C22⋊C4C22×C137semidirect
548. #328C22×C137semidirect
549. #328C22×C137semidirect
552. #327C22×C137semidirect
553. #327C22×C137semidirect
554. #327C22×C137semidirect
555. #327C22×C137semidirect
556. #324C22×C137semidirect
557. #324C22×C137semidirect
558. #323C22×C137semidirect
559. #323C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3534×C1372
#3196×C1372
#3187×C1372
#2663×C1372
#1618×C1372
#1616×C1372
#1615×C1372
#1613×C1372
#1606×C1372
#1604×C1372
#1603×C1372
#1601×C1372
#1507×C1372
#1501×C1372
#1468×C1372
#18415137