Finite Group Databasebeta

← C137×#23580 #46872966

Subgroups — C137×#23580 #46872966

Order 35072.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C137C211yesmaximal, characteristic, complemented
2C2×#442×C137C211yesmaximal, characteristic, complemented
3C2×C4×D8×C137C211yesmaximal, characteristic, complemented
4#2324×C137C211yesmaximal, characteristic, complemented
5#2059×C137C211yesmaximal, characteristic, complemented
6#2041×C137C211yesmaximal, characteristic, complemented
7#2034×C137C211yesmaximal, characteristic, complemented
8#2033×C137C211yesmaximal, characteristic, complemented
9#2025×C137C211yesmaximal, characteristic, complemented
10#2011×C137C211yesmaximal, characteristic, complemented
11#1999×C137C211yesmaximal, characteristic, complemented
12#1999×C137C211yesmaximal, characteristic, complemented
13#1762×C137C211yesmaximal, characteristic, complemented
14C4×#102×C137C211yesmaximal, characteristic, complemented
15#1750×C137C211yesmaximal, characteristic, complemented
16C22×D8×C137C2211yescharacteristic
17C22×D8×C137C2211yescharacteristic
18#540×C137—24no—
19#540×C137—24no—
20C2×#127×C137C2211yescharacteristic
21C2×#125×C137C2211yescharacteristic
22C2×#123×C137—21no—
23C2×#123×C137—21no—
24C2×#121×C137—21no—
25C2×#121×C137—21no—
26C2×#121×C137C2211yescharacteristic
27C2×#121×C137C2211yescharacteristic
28C2×#121×C137C2211yescharacteristic
29C2×C4×D4×C137C2211yescharacteristic
30C2×C4×D4×C137C2211yescharacteristic
31C2×C4×D4×C137C2211yescharacteristic
32C2×#117×C137C2211yescharacteristic
33#442×C137—24no—
34C4×D8×C137—24no—
35C2×#107×C137C2211yescharacteristic
36C2×#106×C137C2211yescharacteristic
37C2×#102×C137C2211yescharacteristic
38C2×#102×C137C2211yescharacteristic
39C2×#102×C137C2211yescharacteristic
40C2×#102×C137C2211yescharacteristic
41C2×#102×C137C2211yescharacteristic
42C2×#102×C137C2211yescharacteristic
43C2×#102×C137C2211yescharacteristic
44C2×#102×C137C2211yescharacteristic
45C2×C22⋊C8×C137C2211yescharacteristic
46C2×C22⋊C8×C137C2211yescharacteristic
47C2×#97×C137C2211yescharacteristic
48C2×C4×C8×C137C2211yescharacteristic
49#390×C137—21no—
50#390×C137C2211yescharacteristic
51#389×C137C2211yescharacteristic
52#388×C137—21no—
53#386×C137—21no—
54#385×C137—21no—
55#380×C137C2211yescharacteristic
56C4×C4⋊C4×C137C2211yescharacteristic
57#340×C137C2211yescharacteristic
58#340×C137C2211yescharacteristic
59#340×C137C2211yescharacteristic
60#340×C137C2211yescharacteristic
61#336×C137C2211yescharacteristic
62#336×C137C2211yescharacteristic
63C22×D4×C137—21no—
64C22×D4×C137—21no—
65C22×D4×C137—21no—
66C22×D4×C137—21no—
67C22×D4×C137—21no—
68C22×D4×C137C2311yescharacteristic
69C22×D4×C137C2311yescharacteristic
70C22×D4×C137C2311yescharacteristic
71C23×C4×C137—21no—
72C23×C4×C137—21no—
73C23×C4×C137—21no—
74C23×C4×C137C2311yescharacteristic
75C2×D8×C137—22no—
76C2×D8×C137—22no—
77C2×D8×C137—22no—
78C2×D8×C137—22no—
79C2×D8×C137—22no—
80C2×D8×C137—22no—
81C22×C8×C137C2311yescharacteristic
82C22×C8×C137C2311yescharacteristic
83C22×C8×C137C2311yescharacteristic
84C22×C8×C137C2311yescharacteristic
85#127×C137—22no—
86#127×C137—22no—
87#125×C137—22no—
88#125×C137—22no—
89#123×C137—28no—
90#123×C137—28no—
91#121×C137—28no—
92#121×C137—28no—
93#121×C137—22no—
94#121×C137—22no—
95#121×C137—22no—
96#121×C137—22no—
97#121×C137—22no—
98#121×C137—22no—
99C4×D4×C137—22no—
100C4×D4×C137—22no—
101C4×D4×C137—22no—
102C4×D4×C137—22no—
103C4×D4×C137D414yescomplemented
104C4×D4×C137D414yescomplemented
105#117×C137—22no—
106#117×C137—22no—
107C2×C4⋊C4×C137—21no—
108C2×C4⋊C4×C137—21no—
109C2×C4⋊C4×C137—21no—
110C2×C4⋊C4×C137D411yescharacteristic
111C2×C4⋊C4×C137D411yescharacteristic
112C2×C4⋊C4×C137C2311yescharacteristic
113C2×C4⋊C4×C137C2311yescharacteristic
114C2×C4⋊C4×C137C2311yescharacteristic
115C2×C4⋊C4×C137C2311yescharacteristic
116C2×C4⋊C4×C137C2311yescharacteristic
117C2×C22⋊C4×C137—21no—
118C2×C22⋊C4×C137—21no—
119C2×C22⋊C4×C137—21no—
120C2×C22⋊C4×C137—21no—
121C2×C22⋊C4×C137—21no—
122C2×C22⋊C4×C137—21no—
123C2×C22⋊C4×C137—21no—
124C2×C22⋊C4×C137—21no—
125C2×C22⋊C4×C137—21no—
126C2×C22⋊C4×C137D411yescharacteristic
127C2×C22⋊C4×C137D411yescharacteristic
128C2×C42×C137—21no—
129C2×C42×C137C2311yescharacteristic
130C2×C42×C137C2311yescharacteristic
131#107×C137—22no—
132#106×C137—22no—
133#102×C137—22no—
134#102×C137—22no—
135#102×C137—22no—
136#102×C137—22no—
137#102×C137—22no—
138#102×C137—22no—
139#102×C137—22no—
140#102×C137—22no—
141C22⋊C8×C137—22no—
142C22⋊C8×C137—22no—
143#97×C137—22no—
144C4×C8×C137—22no—
145#95×C137—21no—
146#95×C137—21no—
147#95×C137—21no—
148C24×C137—21no—
149C24×C137—21no—
150C24×C137—21no—
151C24×C137C2×D411yescharacteristic
152C2×D4×C137—24no—
153C2×D4×C137—24no—
154C2×D4×C137—24no—
155C2×D4×C137—24no—
156C2×D4×C137—24no—
157C2×D4×C137—21no—
158C2×D4×C137—21no—
159C2×D4×C137—21no—
160C2×D4×C137—21no—
161C2×D4×C137—21no—
162C2×D4×C137—21no—
163C2×D4×C137—21no—
164C2×D4×C137—21no—
165C2×D4×C137—21no—
166C2×D4×C137—21no—
167C2×D4×C137—21no—
168C2×D4×C137—21no—
169C2×D4×C137—21no—
170C2×D4×C137—21no—
171C2×D4×C137—21no—
172C2×D4×C137—81no—
173C2×D4×C137—81no—
174C2×D4×C137—81no—
175C2×D4×C137—81no—
176C2×D4×C137—81no—
177C2×D4×C137—81no—
178C2×D4×C137—81no—
179C2×D4×C137—81no—
180C2×D4×C137—81no—
181C2×D4×C137—81no—
182C2×D4×C137C2×D412yes—
183C2×D4×C137C2×D412yes—
184C2×D4×C137#4112yes—
185C22×C4×C137—21no—
186C22×C4×C137—21no—
187C22×C4×C137—21no—
188C22×C4×C137—21no—
189C22×C4×C137—21no—
190C22×C4×C137—21no—
191C22×C4×C137—21no—
192C22×C4×C137—21no—
193C22×C4×C137—21no—
194C22×C4×C137—24no—
195C22×C4×C137—24no—
196C22×C4×C137—21no—
197C22×C4×C137—21no—
198C22×C4×C137—42no—
199C22×C4×C137—81no—
200C22×C4×C137—81no—
201C22×C4×C137—81no—
202C22×C4×C137—81no—
203C22×C4×C137—81no—
204C22×C4×C137—81no—
205C22×C4×C137C2×D411yescharacteristic
206C22×C4×C137C2×D411yescharacteristic
207C22×C4×C137C2×D411yescharacteristic
208C22×C4×C137C2×D411yescharacteristic
209C22×C4×C137C2×D411yescharacteristic
210C22×C4×C137C2411yescharacteristic
211D8×C137—28no—
212D8×C137—28no—
213C2×C8×C137—21no—
214C2×C8×C137—21no—
215C2×C8×C137—21no—
216C2×C8×C137—21no—
217C2×C8×C137—21no—
218C2×C8×C137—21no—
219C2×C8×C137—21no—
220C2×C8×C137—21no—
221C2×C8×C137—21no—
222C2×C8×C137—21no—
223C2×C8×C137#4112yes—
224C2×C8×C137#4112yes—
225C4⋊C4×C137—24no—
226C4⋊C4×C137—24no—
227C4⋊C4×C137—22no—
228C4⋊C4×C137—22no—
229C4⋊C4×C137—21no—
230C4⋊C4×C137—21no—
231C4⋊C4×C137—21no—
232C4⋊C4×C137—21no—
233C4⋊C4×C137—21no—
234C4⋊C4×C137—21no—
235C4⋊C4×C137—21no—
236C4⋊C4×C137—81no—
237C4⋊C4×C137C2×D412yes—
238C4⋊C4×C137C2×D412yes—
239C4⋊C4×C137#4112yes—
240C22⋊C4×C137—24no—
241C22⋊C4×C137—24no—
242C22⋊C4×C137—24no—
243C22⋊C4×C137—24no—
244C22⋊C4×C137—24no—
245C22⋊C4×C137—22no—
246C22⋊C4×C137—22no—
247C22⋊C4×C137—42no—
248C22⋊C4×C137—81no—
249C22⋊C4×C137—81no—
250C22⋊C4×C137—81no—
251C42×C137—21no—
252C42×C137—21no—
253C42×C137—81no—
254C42×C137C2×D412yes—
255C42×C137C2×D412yes—
256C23×C137—21no—
257C23×C137—22no—
258C23×C137—22no—
259C23×C137—22no—
260C23×C137—21no—
261C23×C137—21no—
262C23×C137—21no—
263C23×C137—21no—
264C23×C137—21no—
265C23×C137—21no—
266C23×C137—41no—
267C23×C137—41no—
268C23×C137—41no—
269C23×C137—41no—
270C23×C137—41no—
271C23×C137—41no—
272C23×C137—41no—
273C23×C137—41no—
274C23×C137—41no—
275C23×C137—41no—
276C23×C137—41no—
277C23×C137—41no—
278C23×C137—41no—
279C23×C137—41no—
280C23×C137—41no—
281C23×C137—41no—
282C23×C137—41no—
283C23×C137—41no—
284C23×C137C22×D411yescharacteristic
285D4×C137—22no—
286D4×C137—22no—
287D4×C137—22no—
288D4×C137—22no—
289D4×C137—22no—
290D4×C137—22no—
291D4×C137—41no—
292D4×C137—41no—
293D4×C137—41no—
294D4×C137—41no—
295D4×C137—41no—
296D4×C137—41no—
297D4×C137—84no—
298D4×C137—84no—
299D4×C137—84no—
300D4×C137—84no—
301D4×C137—84no—
302C2×C4×C137—21no—
303C2×C4×C137—21no—
304C2×C4×C137—21no—
305C2×C4×C137—21no—
306C2×C4×C137—21no—
307C2×C4×C137—21no—
308C2×C4×C137—21no—
309C2×C4×C137—22no—
310C2×C4×C137—22no—
311C2×C4×C137—21no—
312C2×C4×C137—22no—
313C2×C4×C137—21no—
314C2×C4×C137—21no—
315C2×C4×C137—21no—
316C2×C4×C137—21no—
317C2×C4×C137—21no—
318C2×C4×C137—41no—
319C2×C4×C137—41no—
320C2×C4×C137—41no—
321C2×C4×C137—41no—
322C2×C4×C137—41no—
323C2×C4×C137—41no—
324C2×C4×C137—41no—
325C2×C4×C137—41no—
326C2×C4×C137—41no—
327C2×C4×C137—41no—
328C2×C4×C137—41no—
329C2×C4×C137—41no—
330C2×C4×C137—41no—
331C2×C4×C137—41no—
332C2×C4×C137—41no—
333C2×C4×C137—41no—
334C2×C4×C137—84no—
335C2×C4×C137—84no—
336C2×C4×C137—84no—
337C2×C4×C137#12012yes—
338C2×C4×C137#12012yes—
339C2×C4×C137C22×D411yescharacteristic
340C2×C4×C137C22×D411yescharacteristic
341C2×C4×C137C2×#4111yescharacteristic
342C2×C4×C137C2×#4111yescharacteristic
343C2×C4×C137C2×#4111yescharacteristic
344C2×C4×C137C2×#4111yescharacteristic
345C8×C137—22no—
346C8×C137—22no—
347C8×C137—41no—
348C8×C137—41no—
349C22×C137—41no—
350C22×C137—42no—
351C22×C137—41no—
352C22×C137—42no—
353C22×C137—41no—
354C22×C137—42no—
355C22×C137—42no—
356C22×C137—42no—
357C22×C137—41no—
358C22×C137—41no—
359C22×C137—42no—
360C22×C137—41no—
361C22×C137—42no—
362C22×C137—42no—
363C22×C137—41no—
364C22×C137—42no—
365C22×C137—81no—
366C22×C137—81no—
367C22×C137—81no—
368C22×C137—81no—
369C22×C137—81no—
370C22×C137—81no—
371C22×C137—81no—
372C22×C137—81no—
373C22×C137—81no—
374C22×C137—81no—
375C22×C137—81no—
376C22×C137—81no—
377C22×C137C2×#12011yescharacteristic
378C22×C137#52511yescharacteristic
379C22×C137#53211yescharacteristic
380C22×C137#57611yescharacteristic
381C22×C137#57611yescharacteristic
382C22×C137#57611yescharacteristic
383C22×C137#57711yescharacteristic
384C4×C137—22no—
385C4×C137—22no—
386C4×C137—42no—
387C4×C137—41no—
388C4×C137—41no—
389C4×C137—42no—
390C4×C137—41no—
391C4×C137—42no—
392C4×C137—81no—
393C4×C137—81no—
394C4×C137#52511yescharacteristic
395C4×C137#52511yescharacteristic
396C4×C137#53211yescharacteristic
397C4×C137#53211yescharacteristic
398C2×C137—81no—
399C2×C137—82no—
400C2×C137—82no—
401C2×C137—82no—
402C2×C137#238811yescharacteristic
403C2×C137#300811yescharacteristic
404C2×C137#301211yescharacteristic
405C2×C137#311911yescharacteristic
406C2×C137#312211yescharacteristic
407C2×C137#317611yescharacteristic
408C2×C137#317911yescharacteristic
409#23580C13711yesmaximal, characteristic, direct product factor, Sylow
410C137#2358011yescharacteristic, direct product factor, Sylow
411C2×#540C2×C13711yescharacteristic, complemented
412C2×#442C2×C13711yescharacteristic, complemented
413C2×C4×D8C2×C13711yescharacteristic, complemented
414#2324C2×C13711yescharacteristic, complemented
415#2059C2×C13711yescharacteristic, complemented
416#2041C2×C13711yescharacteristic, complemented
417#2034C2×C13711yescharacteristic, complemented
418#2033C2×C13711yescharacteristic, complemented
419#2025C2×C13711yescharacteristic, complemented
420#2011C2×C13711yescharacteristic, complemented
421#1999C2×C13711yescharacteristic, complemented
422#1999C2×C13711yescharacteristic, complemented
423#1762C2×C13711yescharacteristic, complemented
424C4×#102C2×C13711yescharacteristic, complemented
425#1750C2×C13711yescharacteristic, complemented
426C22×D8C22×C13711yescharacteristic
427C22×D8C22×C13711yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C13711yescharacteristic
431C2×#125C22×C13711yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C13711yescharacteristic
437C2×#121C22×C13711yescharacteristic
438C2×#121C22×C13711yescharacteristic
439C2×C4×D4C22×C13711yescharacteristic
440C2×C4×D4C22×C13711yescharacteristic
441C2×C4×D4C22×C13711yescharacteristic
442C2×#117C22×C13711yescharacteristic
443#442—24no—
444C4×D8—24no—
445C2×#107C22×C13711yescharacteristic
446C2×#106C22×C13711yescharacteristic
447C2×#102C22×C13711yescharacteristic
448C2×#102C22×C13711yescharacteristic
449C2×#102C22×C13711yescharacteristic
450C2×#102C22×C13711yescharacteristic
451C2×#102C22×C13711yescharacteristic
452C2×#102C22×C13711yescharacteristic
453C2×#102C22×C13711yescharacteristic
454C2×#102C22×C13711yescharacteristic
455C2×C22⋊C8C22×C13711yescharacteristic
456C2×C22⋊C8C22×C13711yescharacteristic
457C2×#97C22×C13711yescharacteristic
458C2×C4×C8C22×C13711yescharacteristic
459#390—21no—
460#390C22×C13711yescharacteristic
461#389C22×C13711yescharacteristic
462#388—21no—
463#386—21no—
464#385—21no—
465#380C22×C13711yescharacteristic
466C4×C4⋊C4C22×C13711yescharacteristic
467#340C22×C13711yescharacteristic
468#340C22×C13711yescharacteristic
469#340C22×C13711yescharacteristic
470#340C22×C13711yescharacteristic
471#336C22×C13711yescharacteristic
472#336C22×C13711yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C13711yescharacteristic
479C22×D4C23×C13711yescharacteristic
480C22×D4C23×C13711yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C13711yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C13711yescharacteristic
492C22×C8C23×C13711yescharacteristic
493C22×C8C23×C13711yescharacteristic
494C22×C8C23×C13711yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C13714yescomplemented
514C4×D4D4×C13714yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C13711yescharacteristic
521C2×C4⋊C4D4×C13711yescharacteristic
522C2×C4⋊C4C23×C13711yescharacteristic
523C2×C4⋊C4C23×C13711yescharacteristic
524C2×C4⋊C4C23×C13711yescharacteristic
525C2×C4⋊C4C23×C13711yescharacteristic
526C2×C4⋊C4C23×C13711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C13711yescharacteristic
537C2×C22⋊C4D4×C13711yescharacteristic
538C2×C42—21no—
539C2×C42C23×C13711yescharacteristic
540C2×C42C23×C13711yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C13711yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C13712yes—
593C2×D4C2×D4×C13712yes—
594C2×D4#41×C13712yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C13711yescharacteristic
616C22×C4C2×D4×C13711yescharacteristic
617C22×C4C2×D4×C13711yescharacteristic
618C22×C4C2×D4×C13711yescharacteristic
619C22×C4C2×D4×C13711yescharacteristic
620C22×C4C24×C13711yescharacteristic
621D8—28no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C13712yes—
634C2×C8#41×C13712yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C13712yes—
648C4⋊C4C2×D4×C13712yes—
649C4⋊C4#41×C13712yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C13712yes—
665C42C2×D4×C13712yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C13711yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C13712yes—
748C2×C4#120×C13712yes—
749C2×C4C22×D4×C13711yescharacteristic
750C2×C4C22×D4×C13711yescharacteristic
751C2×C4C2×#41×C13711yescharacteristic
752C2×C4C2×#41×C13711yescharacteristic
753C2×C4C2×#41×C13711yescharacteristic
754C2×C4C2×#41×C13711yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C13711yescharacteristic
788C22#525×C13711yescharacteristic
789C22#532×C13711yescharacteristic
790C22#576×C13711yescharacteristic
791C22#576×C13711yescharacteristic
792C22#576×C13711yescharacteristic
793C22#577×C13711yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4#525×C13711yescharacteristic
805C4#525×C13711yescharacteristic
806C4#532×C13711yescharacteristic
807C4#532×C13711yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2#2388×C13711yescharacteristic
813C2#3008×C13711yescharacteristic
814C2#3012×C13711yescharacteristic
815C2#3119×C13711yescharacteristic
816C2#3122×C13711yescharacteristic
817C2#3176×C13711yescharacteristic
818C2#3179×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×#117×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C137C2semidirect
2. C2×#442×C137C2semidirect
3. C2×C4×D8×C137C2semidirect
4. #2324×C137C2semidirect
5. #2059×C137C2semidirect
6. #2041×C137C2semidirect
7. #2034×C137C2semidirect
8. #2033×C137C2semidirect
9. #2025×C137C2semidirect
10. #2011×C137C2semidirect
11. #1999×C137C2semidirect
12. #1999×C137C2semidirect
13. #1762×C137C2semidirect
14. C4×#102×C137C2semidirect
15. #1750×C137C2semidirect
103. C4×D4×C137D4semidirect
104. C4×D4×C137D4semidirect
409. #23580C137direct (N × H)
410. C137#23580direct (N × H)
411. C2×#540C2×C137semidirect
412. C2×#442C2×C137semidirect
413. C2×C4×D8C2×C137semidirect
414. #2324C2×C137semidirect
415. #2059C2×C137semidirect
416. #2041C2×C137semidirect
417. #2034C2×C137semidirect
418. #2033C2×C137semidirect
419. #2025C2×C137semidirect
420. #2011C2×C137semidirect
421. #1999C2×C137semidirect
422. #1999C2×C137semidirect
423. #1762C2×C137semidirect
424. C4×#102C2×C137semidirect
425. #1750C2×C137semidirect
513. C4×D4D4×C137semidirect
514. C4×D4D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C1372
C2×#442×C1372
C2×C4×D8×C1372
#2324×C1372
#2059×C1372
#2041×C1372
#2034×C1372
#2033×C1372
#2025×C1372
#2011×C1372
#1999×C1372
#1762×C1372
C4×#102×C1372
#1750×C1372
#23580137