Finite Group Databasebeta

← C137×#25131 #46874517

Subgroups — C137×#25131 #46874517

Order 35072.

1158 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C137C211yesmaximal, characteristic, complemented
2C2×#449×C137C211yesmaximal, characteristic, complemented
3C2×#435×C137C211yesmaximal, characteristic, complemented
4C2×#416×C137C211yesmaximal, characteristic, complemented
5#2414×C137C211yesmaximal, characteristic, complemented
6#2407×C137C211yesmaximal, characteristic, complemented
7#2067×C137C211yesmaximal, characteristic, complemented
8#2055×C137C211yesmaximal, characteristic, complemented
9#2035×C137C211yesmaximal, characteristic, complemented
10#1999×C137C211yesmaximal, characteristic, complemented
11#1972×C137C211yesmaximal, characteristic, complemented
12#1935×C137C211yesmaximal, characteristic, complemented
13#1895×C137C211yesmaximal, characteristic, complemented
14#1893×C137C211yesmaximal, characteristic, complemented
15#1854×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C22×SD16×C137C2211yescharacteristic
18C22×D8×C137C2211yescharacteristic
19C22×M16×C137C2211yescharacteristic
20C23×C8×C137C2211yescharacteristic
21C2×C22⋊Q8×C137C2211yescharacteristic
22C2×#121×C137C2211yescharacteristic
23C2×#121×C137C2211yescharacteristic
24C2×#121×C137C2211yescharacteristic
25C2×C4×D4×C137C2211yescharacteristic
26C2×#117×C137C2211yescharacteristic
27#468×C137—24no—
28#449×C137—24no—
29#435×C137—24no—
30C2×#107×C137C2211yescharacteristic
31C2×#106×C137C2211yescharacteristic
32C2×C4⋊C8×C137C2211yescharacteristic
33#416×C137—24no—
34C2×#103×C137C2211yescharacteristic
35C2×#103×C137C2211yescharacteristic
36C2×#103×C137C2211yescharacteristic
37C2×#102×C137C2211yescharacteristic
38C2×#102×C137C2211yescharacteristic
39C2×#102×C137C2211yescharacteristic
40C2×#102×C137C2211yescharacteristic
41C2×#102×C137C2211yescharacteristic
42C2×C22⋊C8×C137C2211yescharacteristic
43C2×C22⋊C8×C137C2211yescharacteristic
44C2×#97×C137C2211yescharacteristic
45#394×C137—21no—
46#394×C137—21no—
47#392×C137—21no—
48#392×C137—21no—
49#391×C137C2211yescharacteristic
50#390×C137—21no—
51#390×C137C2211yescharacteristic
52#390×C137C2211yescharacteristic
53#389×C137C2211yescharacteristic
54#388×C137—21no—
55#386×C137—21no—
56#385×C137—21no—
57#380×C137C2211yescharacteristic
58#380×C137C2211yescharacteristic
59#340×C137C2211yescharacteristic
60#340×C137C2211yescharacteristic
61#340×C137C2211yescharacteristic
62#340×C137C2211yescharacteristic
63C2×#41×C137—22no—
64C2×#41×C137—22no—
65C2×#41×C137—22no—
66C2×#41×C137—22no—
67C2×#41×C137—41no—
68C2×#41×C137—41no—
69C22×Q8×C137C2311yescharacteristic
70C22×D4×C137—21no—
71C22×D4×C137—21no—
72C22×D4×C137—21no—
73C22×D4×C137—21no—
74C22×D4×C137D411yescharacteristic
75C22×D4×C137C2311yescharacteristic
76C22×D4×C137C2311yescharacteristic
77C23×C4×C137—21no—
78C23×C4×C137C2311yescharacteristic
79C23×C4×C137C2311yescharacteristic
80C2×SD16×C137—22no—
81C2×SD16×C137—22no—
82C2×SD16×C137—41no—
83C2×D8×C137—22no—
84C2×D8×C137—22no—
85C2×D8×C137—41no—
86C2×M16×C137—22no—
87C2×M16×C137—22no—
88C2×M16×C137—41no—
89C22×C8×C137—22no—
90C22×C8×C137—22no—
91C22×C8×C137—41no—
92C22×C8×C137C2311yescharacteristic
93C22×C8×C137C2311yescharacteristic
94C22×C8×C137C2311yescharacteristic
95C22×C8×C137C2311yescharacteristic
96C22⋊Q8×C137—22no—
97C22⋊Q8×C137—41no—
98#121×C137—22no—
99#121×C137—22no—
100#121×C137—22no—
101#121×C137—22no—
102#121×C137—41no—
103#121×C137—41no—
104C4×D4×C137—22no—
105C4×D4×C137—22no—
106#117×C137—22no—
107#117×C137—41no—
108C2×C4⋊C4×C137—21no—
109C2×C4⋊C4×C137—21no—
110C2×C4⋊C4×C137D411yescharacteristic
111C2×C4⋊C4×C137C2311yescharacteristic
112C2×C4⋊C4×C137C2311yescharacteristic
113C2×C4⋊C4×C137C2311yescharacteristic
114C2×C4⋊C4×C137C2311yescharacteristic
115C2×C4⋊C4×C137C2311yescharacteristic
116C2×C22⋊C4×C137—21no—
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×C137—21no—
127C2×C22⋊C4×C137D411yescharacteristic
128C2×C22⋊C4×C137D411yescharacteristic
129C2×C42×C137—21no—
130C2×C42×C137C2311yescharacteristic
131#107×C137—22no—
132#106×C137—41no—
133C4⋊C8×C137—22no—
134#103×C137—22no—
135#103×C137—22no—
136#103×C137D414yescomplemented
137#102×C137—22no—
138#102×C137—22no—
139#102×C137—22no—
140#102×C137—22no—
141#102×C137—41no—
142C22⋊C8×C137—22no—
143C22⋊C8×C137D414yescomplemented
144#97×C137—22no—
145#95×C137—21no—
146#95×C137—21no—
147#95×C137—21no—
148#95×C137—21no—
149#95×C137—21no—
150C24×C137—21no—
151C24×C137—21no—
152C24×C137C2×D411yescharacteristic
153C24×C137C2×D411yescharacteristic
154#41×C137—28no—
155#41×C137—44no—
156#41×C137—44no—
157#41×C137—44no—
158C2×Q8×C137—21no—
159C2×Q8×C137—21no—
160C2×Q8×C137—21no—
161C2×Q8×C137—21no—
162C2×Q8×C137—21no—
163C2×Q8×C137C2×D412yes—
164C2×D4×C137—22no—
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—21no—
173C2×D4×C137—21no—
174C2×D4×C137—21no—
175C2×D4×C137—21no—
176C2×D4×C137—41no—
177C2×D4×C137—41no—
178C2×D4×C137—42no—
179C2×D4×C137—42no—
180C2×D4×C137—42no—
181C2×D4×C137—42no—
182C2×D4×C137—42no—
183C2×D4×C137—42no—
184C2×D4×C137—42no—
185C2×D4×C137—42no—
186C2×D4×C137—81no—
187C2×D4×C137—81no—
188C2×D4×C137—81no—
189C2×D4×C137—81no—
190C2×D4×C137#4112yes—
191C22×C4×C137—21no—
192C22×C4×C137—21no—
193C22×C4×C137—21no—
194C22×C4×C137—21no—
195C22×C4×C137—21no—
196C22×C4×C137—21no—
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—42no—
208C22×C4×C137—42no—
209C22×C4×C137—42no—
210C22×C4×C137C2×D411yescharacteristic
211C22×C4×C137C2×D411yescharacteristic
212C22×C4×C137C2×D411yescharacteristic
213C22×C4×C137C2×D411yescharacteristic
214C22×C4×C137C2×D412yes—
215C22×C4×C137#4112yes—
216C22×C4×C137C2411yescharacteristic
217SD16×C137—44no—
218D8×C137—44no—
219M16×C137—44no—
220C2×C8×C137—21no—
221C2×C8×C137—21no—
222C2×C8×C137—21no—
223C2×C8×C137—21no—
224C2×C8×C137—21no—
225C2×C8×C137—21no—
226C2×C8×C137—21no—
227C2×C8×C137—21no—
228C2×C8×C137—21no—
229C2×C8×C137—44no—
230C2×C8×C137C2×D412yes—
231C2×C8×C137C2×D412yes—
232C2×C8×C137C2×D412yes—
233C4⋊C4×C137—22no—
234C4⋊C4×C137—21no—
235C4⋊C4×C137—21no—
236C4⋊C4×C137—21no—
237C4⋊C4×C137—21no—
238C4⋊C4×C137—21no—
239C4⋊C4×C137—21no—
240C4⋊C4×C137—21no—
241C4⋊C4×C137—21no—
242C4⋊C4×C137—21no—
243C4⋊C4×C137—42no—
244C4⋊C4×C137—81no—
245C4⋊C4×C137C2×D412yes—
246C22⋊C4×C137—22no—
247C22⋊C4×C137—22no—
248C22⋊C4×C137—42no—
249C22⋊C4×C137—42no—
250C22⋊C4×C137—42no—
251C22⋊C4×C137—42no—
252C22⋊C4×C137—42no—
253C22⋊C4×C137—42no—
254C22⋊C4×C137—42no—
255C22⋊C4×C137—81no—
256C22⋊C4×C137—81no—
257C22⋊C4×C137—81no—
258C22⋊C4×C137—81no—
259C42×C137—21no—
260C42×C137—21no—
261C42×C137—42no—
262C23×C137—21no—
263C23×C137—21no—
264C23×C137—21no—
265C23×C137—21no—
266C23×C137—21no—
267C23×C137—21no—
268C23×C137—21no—
269C23×C137—21no—
270C23×C137—22no—
271C23×C137—21no—
272C23×C137—21no—
273C23×C137—21no—
274C23×C137—21no—
275C23×C137—21no—
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×C137—41no—
285C23×C137—41no—
286C23×C137—41no—
287C23×C137—41no—
288C23×C137—41no—
289C23×C137#12112yes—
290C23×C137C22×D411yescharacteristic
291Q8×C137—22no—
292Q8×C137—22no—
293Q8×C137—41no—
294Q8×C137—41no—
295D4×C137—22no—
296D4×C137—22no—
297D4×C137—44no—
298D4×C137—48no—
299D4×C137—41no—
300D4×C137—41no—
301D4×C137—41no—
302D4×C137—41no—
303D4×C137—41no—
304D4×C137—41no—
305D4×C137—84no—
306D4×C137—84no—
307D4×C137—84no—
308C2×C4×C137—21no—
309C2×C4×C137—21no—
310C2×C4×C137—22no—
311C2×C4×C137—22no—
312C2×C4×C137—22no—
313C2×C4×C137—22no—
314C2×C4×C137—21no—
315C2×C4×C137—21no—
316C2×C4×C137—21no—
317C2×C4×C137—22no—
318C2×C4×C137—21no—
319C2×C4×C137—22no—
320C2×C4×C137—21no—
321C2×C4×C137—21no—
322C2×C4×C137—21no—
323C2×C4×C137—21no—
324C2×C4×C137—21no—
325C2×C4×C137—48no—
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—41no—
335C2×C4×C137—41no—
336C2×C4×C137—41no—
337C2×C4×C137—41no—
338C2×C4×C137—41no—
339C2×C4×C137—41no—
340C2×C4×C137—41no—
341C2×C4×C137—41no—
342C2×C4×C137—41no—
343C2×C4×C137—41no—
344C2×C4×C137—41no—
345C2×C4×C137—41no—
346C2×C4×C137#12112yes—
347C2×C4×C137C22×D411yescharacteristic
348C2×C4×C137C22×D411yescharacteristic
349C2×C4×C137C2×#4111yescharacteristic
350C2×C4×C137C2×#4111yescharacteristic
351C2×C4×C137H(5,𝔽2)11yescharacteristic
352C2×C4×C137H(5,𝔽2)11yescharacteristic
353C8×C137—22no—
354C8×C137—22no—
355C8×C137—22no—
356C8×C137—41no—
357C22×C137—22no—
358C22×C137—22no—
359C22×C137—22no—
360C22×C137—41no—
361C22×C137—41no—
362C22×C137—41no—
363C22×C137—41no—
364C22×C137—42no—
365C22×C137—41no—
366C22×C137—41no—
367C22×C137—41no—
368C22×C137—41no—
369C22×C137—42no—
370C22×C137—41no—
371C22×C137—41no—
372C22×C137—41no—
373C22×C137—42no—
374C22×C137—81no—
375C22×C137—81no—
376C22×C137—81no—
377C22×C137—81no—
378C22×C137—81no—
379C22×C137—81no—
380C22×C137—81no—
381C22×C137—81no—
382C22×C137—81no—
383C22×C137—81no—
384C22×C137—81no—
385C22×C137C2×#12111yescharacteristic
386C22×C137D4211yescharacteristic
387C22×C137#54611yescharacteristic
388C22×C137#57511yescharacteristic
389C22×C137#57511yescharacteristic
390C22×C137#57611yescharacteristic
391C22×C137#57711yescharacteristic
392C4×C137—22no—
393C4×C137—41no—
394C4×C137—42no—
395C4×C137—42no—
396C4×C137—41no—
397C4×C137—41no—
398C4×C137—81no—
399C4×C137—81no—
400C4×C137—81no—
401C4×C137—81no—
402C4×C137#52511yescharacteristic
403C4×C137#53811yescharacteristic
404C4×C137D4211yescharacteristic
405C4×C137#54611yescharacteristic
406C2×C137—42no—
407C2×C137—81no—
408C2×C137—82no—
409C2×C137—161no—
410C2×C137#242411yescharacteristic
411C2×C137#305411yescharacteristic
412C2×C137#306211yescharacteristic
413C2×C137#326811yescharacteristic
414C2×C137#327111yescharacteristic
415C2×C137#330711yescharacteristic
416C2×C137#331911yescharacteristic
417#25131C13711yesmaximal, characteristic, direct product factor, Sylow
418C137#2513111yescharacteristic, direct product factor, Sylow
419C2×#468C2×C13711yescharacteristic, complemented
420C2×#449C2×C13711yescharacteristic, complemented
421C2×#435C2×C13711yescharacteristic, complemented
422C2×#416C2×C13711yescharacteristic, complemented
423#2414C2×C13711yescharacteristic, complemented
424#2407C2×C13711yescharacteristic, complemented
425#2067C2×C13711yescharacteristic, complemented
426#2055C2×C13711yescharacteristic, complemented
427#2035C2×C13711yescharacteristic, complemented
428#1999C2×C13711yescharacteristic, complemented
429#1972C2×C13711yescharacteristic, complemented
430#1935C2×C13711yescharacteristic, complemented
431#1895C2×C13711yescharacteristic, complemented
432#1893C2×C13711yescharacteristic, complemented
433#1854C2×C13711yescharacteristic, complemented
434C22×#41C22×C13711yescharacteristic
435C22×SD16C22×C13711yescharacteristic
436C22×D8C22×C13711yescharacteristic
437C22×M16C22×C13711yescharacteristic
438C23×C8C22×C13711yescharacteristic
439C2×C22⋊Q8C22×C13711yescharacteristic
440C2×#121C22×C13711yescharacteristic
441C2×#121C22×C13711yescharacteristic
442C2×#121C22×C13711yescharacteristic
443C2×C4×D4C22×C13711yescharacteristic
444C2×#117C22×C13711yescharacteristic
445#468—24no—
446#449—24no—
447#435—24no—
448C2×#107C22×C13711yescharacteristic
449C2×#106C22×C13711yescharacteristic
450C2×C4⋊C8C22×C13711yescharacteristic
451#416—24no—
452C2×#103C22×C13711yescharacteristic
453C2×#103C22×C13711yescharacteristic
454C2×#103C22×C13711yescharacteristic
455C2×#102C22×C13711yescharacteristic
456C2×#102C22×C13711yescharacteristic
457C2×#102C22×C13711yescharacteristic
458C2×#102C22×C13711yescharacteristic
459C2×#102C22×C13711yescharacteristic
460C2×C22⋊C8C22×C13711yescharacteristic
461C2×C22⋊C8C22×C13711yescharacteristic
462C2×#97C22×C13711yescharacteristic
463#394—21no—
464#394—21no—
465#392—21no—
466#392—21no—
467#391C22×C13711yescharacteristic
468#390—21no—
469#390C22×C13711yescharacteristic
470#390C22×C13711yescharacteristic
471#389C22×C13711yescharacteristic
472#388—21no—
473#386—21no—
474#385—21no—
475#380C22×C13711yescharacteristic
476#380C22×C13711yescharacteristic
477#340C22×C13711yescharacteristic
478#340C22×C13711yescharacteristic
479#340C22×C13711yescharacteristic
480#340C22×C13711yescharacteristic
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8C23×C13711yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C13711yescharacteristic
493C22×D4C23×C13711yescharacteristic
494C22×D4C23×C13711yescharacteristic
495C23×C4—21no—
496C23×C4C23×C13711yescharacteristic
497C23×C4C23×C13711yescharacteristic
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8C23×C13711yescharacteristic
511C22×C8C23×C13711yescharacteristic
512C22×C8C23×C13711yescharacteristic
513C22×C8C23×C13711yescharacteristic
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522C4×D4—22no—
523C4×D4—22no—
524#117—22no—
525#117—41no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4D4×C13711yescharacteristic
529C2×C4⋊C4C23×C13711yescharacteristic
530C2×C4⋊C4C23×C13711yescharacteristic
531C2×C4⋊C4C23×C13711yescharacteristic
532C2×C4⋊C4C23×C13711yescharacteristic
533C2×C4⋊C4C23×C13711yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C13711yescharacteristic
546C2×C22⋊C4D4×C13711yescharacteristic
547C2×C42—21no—
548C2×C42C23×C13711yescharacteristic
549#107—22no—
550#106—41no—
551C4⋊C8—22no—
552#103—22no—
553#103—22no—
554#103D4×C13714yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8D4×C13714yescomplemented
562#97—22no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C13711yescharacteristic
571C24C2×D4×C13711yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×D4×C13712yes—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4#41×C13712yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4C2×D4×C13711yescharacteristic
629C22×C4C2×D4×C13711yescharacteristic
630C22×C4C2×D4×C13711yescharacteristic
631C22×C4C2×D4×C13711yescharacteristic
632C22×C4C2×D4×C13712yes—
633C22×C4#41×C13712yes—
634C22×C4C24×C13711yescharacteristic
635SD16—44no—
636D8—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C13712yes—
649C2×C8C2×D4×C13712yes—
650C2×C8C2×D4×C13712yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C13712yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—42no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23#121×C13712yes—
708C23C22×D4×C13711yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713D4—22no—
714D4—22no—
715D4—44no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—84no—
724D4—84no—
725D4—84no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—48no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4#121×C13712yes—
765C2×C4C22×D4×C13711yescharacteristic
766C2×C4C22×D4×C13711yescharacteristic
767C2×C4C2×#41×C13711yescharacteristic
768C2×C4C2×#41×C13711yescharacteristic
769C2×C4H(5,𝔽2)×C13711yescharacteristic
770C2×C4H(5,𝔽2)×C13711yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C13711yescharacteristic
804C22D42×C13711yescharacteristic
805C22#546×C13711yescharacteristic
806C22#575×C13711yescharacteristic
807C22#575×C13711yescharacteristic
808C22#576×C13711yescharacteristic
809C22#577×C13711yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—42no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4#525×C13711yescharacteristic
821C4#538×C13711yescharacteristic
822C4D42×C13711yescharacteristic
823C4#546×C13711yescharacteristic
824C2—42no—
825C2—81no—
826C2—82no—
827C2—161no—
828C2#2424×C13711yescharacteristic
829C2#3054×C13711yescharacteristic
830C2#3062×C13711yescharacteristic
831C2#3268×C13711yescharacteristic
832C2#3271×C13711yescharacteristic
833C2#3307×C13711yescharacteristic
834C2#3319×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C4×D4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C137C2semidirect
2. C2×#449×C137C2semidirect
3. C2×#435×C137C2semidirect
4. C2×#416×C137C2semidirect
5. #2414×C137C2semidirect
6. #2407×C137C2semidirect
7. #2067×C137C2semidirect
8. #2055×C137C2semidirect
9. #2035×C137C2semidirect
10. #1999×C137C2semidirect
11. #1972×C137C2semidirect
12. #1935×C137C2semidirect
13. #1895×C137C2semidirect
14. #1893×C137C2semidirect
15. #1854×C137C2semidirect
136. #103×C137D4semidirect
143. C22⋊C8×C137D4semidirect
417. #25131C137direct (N × H)
418. C137#25131direct (N × H)
419. C2×#468C2×C137semidirect
420. C2×#449C2×C137semidirect
421. C2×#435C2×C137semidirect
422. C2×#416C2×C137semidirect
423. #2414C2×C137semidirect
424. #2407C2×C137semidirect
425. #2067C2×C137semidirect
426. #2055C2×C137semidirect
427. #2035C2×C137semidirect
428. #1999C2×C137semidirect
429. #1972C2×C137semidirect
430. #1935C2×C137semidirect
431. #1895C2×C137semidirect
432. #1893C2×C137semidirect
433. #1854C2×C137semidirect
554. #103D4×C137semidirect
561. C22⋊C8D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1372
C2×#449×C1372
C2×#435×C1372
C2×#416×C1372
#2414×C1372
#2407×C1372
#2067×C1372
#2055×C1372
#2035×C1372
#1999×C1372
#1972×C1372
#1935×C1372
#1895×C1372
#1893×C1372
#1854×C1372
#25131137