Finite Group Databasebeta

← C137×#25153 #46874539

Subgroups — C137×#25153 #46874539

Order 35072.

1186 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C137C211yesmaximal, characteristic, complemented
2C2×#448×C137C211yesmaximal, characteristic, complemented
3C2×#448×C137C211yesmaximal, characteristic, complemented
4C2×C4×SD16×C137C211yesmaximal, characteristic, complemented
5#2428×C137C211yesmaximal, characteristic
6Q8×C22⋊C4×C137C211yesmaximal, characteristic, complemented
7#2066×C137C211yesmaximal, characteristic, complemented
8#2034×C137C211yesmaximal, characteristic, complemented
9#2034×C137C211yesmaximal, characteristic, complemented
10#2014×C137C211yesmaximal, characteristic, complemented
11#1968×C137C211yesmaximal, characteristic, complemented
12#1923×C137C211yesmaximal, characteristic, complemented
13#1880×C137C211yesmaximal, characteristic, complemented
14#1877×C137C211yesmaximal, characteristic, complemented
15#1865×C137C211yesmaximal, characteristic, complemented
16C23×Q8×C137C2211yescharacteristic
17C22×SD16×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic
19C22×SD16×C137C2211yescharacteristic
20C22×SD16×C137C2211yescharacteristic
21C2×#127×C137C2211yescharacteristic
22C2×#121×C137—21no—
23C2×#121×C137C2211yescharacteristic
24C2×#121×C137C2211yescharacteristic
25C2×C4×Q8×C137C2211yescharacteristic
26C2×C4×Q8×C137C2211yescharacteristic
27C2×C4×D4×C137C2211yescharacteristic
28#460×C137—24no—
29#448×C137—24no—
30#448×C137—24no—
31C4×SD16×C137—24no—
32C2×#106×C137C2211yescharacteristic
33C2×#106×C137C2211yescharacteristic
34C2×C4⋊C8×C137C2211yescharacteristic
35C2×#103×C137C2211yescharacteristic
36C2×#103×C137C2211yescharacteristic
37C2×#103×C137C2211yescharacteristic
38C2×#103×C137C2211yescharacteristic
39C2×#102×C137C2211yescharacteristic
40C2×#102×C137C2211yescharacteristic
41C2×#102×C137C2211yescharacteristic
42C2×#102×C137C2211yescharacteristic
43C2×C22⋊C8×C137C2211yescharacteristic
44C2×C22⋊C8×C137C2211yescharacteristic
45C2×C4×C8×C137C2211yescharacteristic
46#394×C137—21no—
47#392×C137—21no—
48#391×C137—21no—
49#391×C137—21no—
50#391×C137C2211yescharacteristic
51#391×C137C2211yescharacteristic
52#390×C137C2211yescharacteristic
53#389×C137C2211yescharacteristic
54#386×C137—21no—
55#380×C137—21no—
56#380×C137C2211yescharacteristic
57C4×C22⋊C4×C137—21no—
58C4×C22⋊C4×C137C2211yescharacteristic
59#340×C137C2211yescharacteristic
60#340×C137C2211yescharacteristic
61#336×C137C2211yescharacteristic
62#336×C137C2211yescharacteristic
63C22×Q8×C137—22no—
64C22×Q8×C137—22no—
65C22×Q8×C137—21no—
66C22×Q8×C137—22no—
67C22×Q8×C137—22no—
68C22×Q8×C137—41no—
69C22×Q8×C137—41no—
70C22×Q8×C137C2311yescharacteristic
71C22×Q8×C137C2311yescharacteristic
72C22×D4×C137—21no—
73C22×D4×C137—21no—
74C22×D4×C137—21no—
75C22×D4×C137—21no—
76C22×D4×C137C2311yescharacteristic
77C22×D4×C137C2311yescharacteristic
78C23×C4×C137—21no—
79C23×C4×C137—21no—
80C23×C4×C137C2311yescharacteristic
81C2×SD16×C137—22no—
82C2×SD16×C137—22no—
83C2×SD16×C137—22no—
84C2×SD16×C137—22no—
85C2×SD16×C137—22no—
86C2×SD16×C137—22no—
87C2×SD16×C137—22no—
88C2×SD16×C137—22no—
89C2×SD16×C137—22no—
90C2×SD16×C137—41no—
91C2×SD16×C137—41no—
92C2×SD16×C137D414yescomplemented
93C22×C8×C137C2311yescharacteristic
94C22×C8×C137C2311yescharacteristic
95C22×C8×C137C2311yescharacteristic
96C22×C8×C137C2311yescharacteristic
97#127×C137—22no—
98#127×C137—41no—
99#121×C137—22no—
100#121×C137—22no—
101#121×C137—41no—
102#121×C137—41no—
103#121×C137—44no—
104C4×Q8×C137—22no—
105C4×Q8×C137—22no—
106C4×Q8×C137—41no—
107C4×Q8×C137—41no—
108C4×D4×C137—22no—
109C4×D4×C137—41no—
110C2×C4⋊C4×C137—21no—
111C2×C4⋊C4×C137—21no—
112C2×C4⋊C4×C137—21no—
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×C137D411yescharacteristic
124C2×C22⋊C4×C137D411yescharacteristic
125C2×C42×C137—21no—
126C2×C42×C137—21no—
127C2×C42×C137C2311yescharacteristic
128C2×C42×C137C2311yescharacteristic
129#106×C137—22no—
130#106×C137—41no—
131C4⋊C8×C137—22no—
132#103×C137—22no—
133#103×C137—22no—
134#103×C137—22no—
135#103×C137D414yescomplemented
136#102×C137—22no—
137#102×C137—22no—
138#102×C137—22no—
139#102×C137—41no—
140C22⋊C8×C137—22no—
141C22⋊C8×C137—22no—
142C4×C8×C137—22no—
143#95×C137—21no—
144#95×C137—21no—
145#95×C137—21no—
146#95×C137—21no—
147#95×C137—21no—
148#95×C137—21no—
149#95×C137D411yescharacteristic
150#95×C137D411yescharacteristic
151C24×C137—21no—
152C24×C137—21no—
153C24×C137C2×D411yescharacteristic
154C2×Q8×C137—24no—
155C2×Q8×C137—21no—
156C2×Q8×C137—21no—
157C2×Q8×C137—21no—
158C2×Q8×C137—21no—
159C2×Q8×C137—21no—
160C2×Q8×C137—21no—
161C2×Q8×C137—21no—
162C2×Q8×C137—21no—
163C2×Q8×C137—42no—
164C2×Q8×C137—42no—
165C2×Q8×C137—44no—
166C2×Q8×C137—44no—
167C2×Q8×C137—44no—
168C2×Q8×C137—44no—
169C2×Q8×C137C2×D412yes—
170C2×Q8×C137C2×D412yes—
171C2×Q8×C137#4112yes—
172C2×Q8×C137#4112yes—
173C2×D4×C137—21no—
174C2×D4×C137—21no—
175C2×D4×C137—21no—
176C2×D4×C137—21no—
177C2×D4×C137—21no—
178C2×D4×C137—21no—
179C2×D4×C137—21no—
180C2×D4×C137—21no—
181C2×D4×C137—21no—
182C2×D4×C137—21no—
183C2×D4×C137—21no—
184C2×D4×C137—42no—
185C2×D4×C137—42no—
186C2×D4×C137—42no—
187C2×D4×C137—42no—
188C2×D4×C137—42no—
189C2×D4×C137—42no—
190C2×D4×C137—42no—
191C2×D4×C137—42no—
192C2×D4×C137—81no—
193C2×D4×C137—81no—
194C2×D4×C137—81no—
195C2×D4×C137—81no—
196C2×D4×C137C2×D412yes—
197C22×C4×C137—21no—
198C22×C4×C137—24no—
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—42no—
211C22×C4×C137—42no—
212C22×C4×C137—42no—
213C22×C4×C137—42no—
214C22×C4×C137—81no—
215C22×C4×C137C2×D411yescharacteristic
216C22×C4×C137C2×D411yescharacteristic
217C22×C4×C137C2×D411yescharacteristic
218C22×C4×C137C2×D411yescharacteristic
219C22×C4×C137C2×D411yescharacteristic
220C22×C4×C137C2411yescharacteristic
221SD16×C137—28no—
222SD16×C137—44no—
223SD16×C137—44no—
224SD16×C137—44no—
225C2×C8×C137—21no—
226C2×C8×C137—21no—
227C2×C8×C137—21no—
228C2×C8×C137—21no—
229C2×C8×C137—21no—
230C2×C8×C137—21no—
231C2×C8×C137—21no—
232C2×C8×C137—21no—
233C2×C8×C137—21no—
234C2×C8×C137—21no—
235C2×C8×C137C2×D412yes—
236C2×C8×C137C2×D412yes—
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—21no—
244C4⋊C4×C137—42no—
245C4⋊C4×C137—42no—
246C4⋊C4×C137—42no—
247C4⋊C4×C137C2×D412yes—
248C22⋊C4×C137—41no—
249C22⋊C4×C137—42no—
250C22⋊C4×C137—42no—
251C22⋊C4×C137—42no—
252C22⋊C4×C137—42no—
253C22⋊C4×C137—42no—
254C22⋊C4×C137—81no—
255C22⋊C4×C137SD1614yescomplemented
256C42×C137—21no—
257C42×C137—21no—
258C42×C137—21no—
259C42×C137—21no—
260C42×C137—42no—
261C42×C137—42no—
262C23×C137—21no—
263C23×C137—21no—
264C23×C137—21no—
265C23×C137—21no—
266C23×C137—21no—
267C23×C137—21no—
268C23×C137—22no—
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×C137C2×SD1612yes—
283C23×C137C22×D411yescharacteristic
284Q8×C137—22no—
285Q8×C137—22no—
286Q8×C137—22no—
287Q8×C137—22no—
288Q8×C137—22no—
289Q8×C137—48no—
290Q8×C137—41no—
291Q8×C137—41no—
292Q8×C137#12114yescomplemented
293D4×C137—22no—
294D4×C137—22no—
295D4×C137—41no—
296D4×C137—41no—
297D4×C137—41no—
298D4×C137—41no—
299D4×C137—41no—
300D4×C137—41no—
301D4×C137—84no—
302D4×C137—84no—
303D4×C137—84no—
304D4×C137—84no—
305C2×C4×C137—22no—
306C2×C4×C137—21no—
307C2×C4×C137—21no—
308C2×C4×C137—22no—
309C2×C4×C137—22no—
310C2×C4×C137—21no—
311C2×C4×C137—21no—
312C2×C4×C137—22no—
313C2×C4×C137—21no—
314C2×C4×C137—21no—
315C2×C4×C137—21no—
316C2×C4×C137—22no—
317C2×C4×C137—21no—
318C2×C4×C137—21no—
319C2×C4×C137—21no—
320C2×C4×C137—21no—
321C2×C4×C137—21no—
322C2×C4×C137—21no—
323C2×C4×C137—48no—
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—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—84no—
342C2×C4×C137C2×SD1612yes—
343C2×C4×C137C2×SD1612yes—
344C2×C4×C137C22×D411yescharacteristic
345C2×C4×C137C22×D411yescharacteristic
346C2×C4×C137C2×#4111yescharacteristic
347C2×C4×C137C2×#4111yescharacteristic
348C2×C4×C137H(5,𝔽2)11yescharacteristic
349C2×C4×C137H(5,𝔽2)11yescharacteristic
350C8×C137—22no—
351C8×C137—22no—
352C8×C137—41no—
353C8×C137—41no—
354C22×C137—22no—
355C22×C137—22no—
356C22×C137—22no—
357C22×C137—41no—
358C22×C137—41no—
359C22×C137—41no—
360C22×C137—41no—
361C22×C137—42no—
362C22×C137—42no—
363C22×C137—42no—
364C22×C137—81no—
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#52511yescharacteristic
376C22×C137D4211yescharacteristic
377C22×C137D4211yescharacteristic
378C22×C137C22×SD1611yescharacteristic
379C22×C137#57511yescharacteristic
380C22×C137#57711yescharacteristic
381C22×C137#57711yescharacteristic
382C4×C137—24no—
383C4×C137—22no—
384C4×C137—22no—
385C4×C137—41no—
386C4×C137—42no—
387C4×C137—41no—
388C4×C137—41no—
389C4×C137—42no—
390C4×C137—81no—
391C4×C137—81no—
392C4×C137—81no—
393C4×C137C2×#12111yescharacteristic
394C4×C137#53811yescharacteristic
395C4×C137#54611yescharacteristic
396C4×C137#54611yescharacteristic
397C2×C137—42no—
398C2×C137—82no—
399C2×C137—161no—
400C2×C137#242411yescharacteristic
401C2×C137#310311yescharacteristic
402C2×C137#312611yescharacteristic
403C2×C137#327111yescharacteristic
404C2×C137#327511yescharacteristic
405C2×C137D4×SD1611yescharacteristic
406C2×C137D4×SD1611yescharacteristic
407#25153C13711yesmaximal, characteristic, direct product factor, Sylow
408C137#2515311yescharacteristic, direct product factor, Sylow
409C2×#460C2×C13711yescharacteristic, complemented
410C2×#448C2×C13711yescharacteristic, complemented
411C2×#448C2×C13711yescharacteristic, complemented
412C2×C4×SD16C2×C13711yescharacteristic, complemented
413#2428C2×C13711yescharacteristic
414Q8×C22⋊C4C2×C13711yescharacteristic, complemented
415#2066C2×C13711yescharacteristic, complemented
416#2034C2×C13711yescharacteristic, complemented
417#2034C2×C13711yescharacteristic, complemented
418#2014C2×C13711yescharacteristic, complemented
419#1968C2×C13711yescharacteristic, complemented
420#1923C2×C13711yescharacteristic, complemented
421#1880C2×C13711yescharacteristic, complemented
422#1877C2×C13711yescharacteristic, complemented
423#1865C2×C13711yescharacteristic, complemented
424C23×Q8C22×C13711yescharacteristic
425C22×SD16C22×C13711yescharacteristic
426C22×SD16C22×C13711yescharacteristic
427C22×SD16C22×C13711yescharacteristic
428C22×SD16C22×C13711yescharacteristic
429C2×#127C22×C13711yescharacteristic
430C2×#121—21no—
431C2×#121C22×C13711yescharacteristic
432C2×#121C22×C13711yescharacteristic
433C2×C4×Q8C22×C13711yescharacteristic
434C2×C4×Q8C22×C13711yescharacteristic
435C2×C4×D4C22×C13711yescharacteristic
436#460—24no—
437#448—24no—
438#448—24no—
439C4×SD16—24no—
440C2×#106C22×C13711yescharacteristic
441C2×#106C22×C13711yescharacteristic
442C2×C4⋊C8C22×C13711yescharacteristic
443C2×#103C22×C13711yescharacteristic
444C2×#103C22×C13711yescharacteristic
445C2×#103C22×C13711yescharacteristic
446C2×#103C22×C13711yescharacteristic
447C2×#102C22×C13711yescharacteristic
448C2×#102C22×C13711yescharacteristic
449C2×#102C22×C13711yescharacteristic
450C2×#102C22×C13711yescharacteristic
451C2×C22⋊C8C22×C13711yescharacteristic
452C2×C22⋊C8C22×C13711yescharacteristic
453C2×C4×C8C22×C13711yescharacteristic
454#394—21no—
455#392—21no—
456#391—21no—
457#391—21no—
458#391C22×C13711yescharacteristic
459#391C22×C13711yescharacteristic
460#390C22×C13711yescharacteristic
461#389C22×C13711yescharacteristic
462#386—21no—
463#380—21no—
464#380C22×C13711yescharacteristic
465C4×C22⋊C4—21no—
466C4×C22⋊C4C22×C13711yescharacteristic
467#340C22×C13711yescharacteristic
468#340C22×C13711yescharacteristic
469#336C22×C13711yescharacteristic
470#336C22×C13711yescharacteristic
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—21no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8—41no—
477C22×Q8—41no—
478C22×Q8C23×C13711yescharacteristic
479C22×Q8C23×C13711yescharacteristic
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C23×C13711yescharacteristic
485C22×D4C23×C13711yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C23×C13711yescharacteristic
489C2×SD16—22no—
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—41no—
499C2×SD16—41no—
500C2×SD16D4×C13714yescomplemented
501C22×C8C23×C13711yescharacteristic
502C22×C8C23×C13711yescharacteristic
503C22×C8C23×C13711yescharacteristic
504C22×C8C23×C13711yescharacteristic
505#127—22no—
506#127—41no—
507#121—22no—
508#121—22no—
509#121—41no—
510#121—41no—
511#121—44no—
512C4×Q8—22no—
513C4×Q8—22no—
514C4×Q8—41no—
515C4×Q8—41no—
516C4×D4—22no—
517C4×D4—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4C23×C13711yescharacteristic
522C2×C4⋊C4C23×C13711yescharacteristic
523C2×C4⋊C4C23×C13711yescharacteristic
524C2×C4⋊C4C23×C13711yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4D4×C13711yescharacteristic
532C2×C22⋊C4D4×C13711yescharacteristic
533C2×C42—21no—
534C2×C42—21no—
535C2×C42C23×C13711yescharacteristic
536C2×C42C23×C13711yescharacteristic
537#106—22no—
538#106—41no—
539C4⋊C8—22no—
540#103—22no—
541#103—22no—
542#103—22no—
543#103D4×C13714yescomplemented
544#102—22no—
545#102—22no—
546#102—22no—
547#102—41no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C4×C8—22no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95D4×C13711yescharacteristic
558#95D4×C13711yescharacteristic
559C24—21no—
560C24—21no—
561C24C2×D4×C13711yescharacteristic
562C2×Q8—24no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8C2×D4×C13712yes—
578C2×Q8C2×D4×C13712yes—
579C2×Q8#41×C13712yes—
580C2×Q8#41×C13712yes—
581C2×D4—21no—
582C2×D4—21no—
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—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4C2×D4×C13712yes—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—21no—
608C22×C4—21no—
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—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—81no—
623C22×C4C2×D4×C13711yescharacteristic
624C22×C4C2×D4×C13711yescharacteristic
625C22×C4C2×D4×C13711yescharacteristic
626C22×C4C2×D4×C13711yescharacteristic
627C22×C4C2×D4×C13711yescharacteristic
628C22×C4C24×C13711yescharacteristic
629SD16—28no—
630SD16—44no—
631SD16—44no—
632SD16—44no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8C2×D4×C13712yes—
644C2×C8C2×D4×C13712yes—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4C2×D4×C13712yes—
656C22⋊C4—41no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—81no—
663C22⋊C4SD16×C13714yescomplemented
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—42no—
669C42—42no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—22no—
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—
690C23C2×SD16×C13712yes—
691C23C22×D4×C13711yescharacteristic
692Q8—22no—
693Q8—22no—
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—48no—
698Q8—41no—
699Q8—41no—
700Q8#121×C13714yescomplemented
701D4—22no—
702D4—22no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
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—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—84no—
750C2×C4C2×SD16×C13712yes—
751C2×C4C2×SD16×C13712yes—
752C2×C4C22×D4×C13711yescharacteristic
753C2×C4C22×D4×C13711yescharacteristic
754C2×C4C2×#41×C13711yescharacteristic
755C2×C4C2×#41×C13711yescharacteristic
756C2×C4H(5,𝔽2)×C13711yescharacteristic
757C2×C4H(5,𝔽2)×C13711yescharacteristic
758C8—22no—
759C8—22no—
760C8—41no—
761C8—41no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22#525×C13711yescharacteristic
784C22D42×C13711yescharacteristic
785C22D42×C13711yescharacteristic
786C22C22×SD16×C13711yescharacteristic
787C22#575×C13711yescharacteristic
788C22#577×C13711yescharacteristic
789C22#577×C13711yescharacteristic
790C4—24no—
791C4—22no—
792C4—22no—
793C4—41no—
794C4—42no—
795C4—41no—
796C4—41no—
797C4—42no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4C2×#121×C13711yescharacteristic
802C4#538×C13711yescharacteristic
803C4#546×C13711yescharacteristic
804C4#546×C13711yescharacteristic
805C2—42no—
806C2—82no—
807C2—161no—
808C2#2424×C13711yescharacteristic
809C2#3103×C13711yescharacteristic
810C2#3126×C13711yescharacteristic
811C2#3271×C13711yescharacteristic
812C2#3275×C13711yescharacteristic
813C2D4×SD16×C13711yescharacteristic
814C2D4×SD16×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radical#2428×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C4×C22⋊C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#460×C137C2semidirect
2. C2×#448×C137C2semidirect
3. C2×#448×C137C2semidirect
4. C2×C4×SD16×C137C2semidirect
6. Q8×C22⋊C4×C137C2semidirect
7. #2066×C137C2semidirect
8. #2034×C137C2semidirect
9. #2034×C137C2semidirect
10. #2014×C137C2semidirect
11. #1968×C137C2semidirect
12. #1923×C137C2semidirect
13. #1880×C137C2semidirect
14. #1877×C137C2semidirect
15. #1865×C137C2semidirect
92. C2×SD16×C137D4semidirect
135. #103×C137D4semidirect
255. C22⋊C4×C137SD16semidirect
292. Q8×C137#121semidirect
407. #25153C137direct (N × H)
408. C137#25153direct (N × H)
409. C2×#460C2×C137semidirect
410. C2×#448C2×C137semidirect
411. C2×#448C2×C137semidirect
412. C2×C4×SD16C2×C137semidirect
414. Q8×C22⋊C4C2×C137semidirect
415. #2066C2×C137semidirect
416. #2034C2×C137semidirect
417. #2034C2×C137semidirect
418. #2014C2×C137semidirect
419. #1968C2×C137semidirect
420. #1923C2×C137semidirect
421. #1880C2×C137semidirect
422. #1877C2×C137semidirect
423. #1865C2×C137semidirect
500. C2×SD16D4×C137semidirect
543. #103D4×C137semidirect
663. C22⋊C4SD16×C137semidirect
700. Q8#121×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1372
C2×#448×C1372
C2×C4×SD16×C1372
#2428×C1372
Q8×C22⋊C4×C1372
#2066×C1372
#2034×C1372
#2014×C1372
#1968×C1372
#1923×C1372
#1880×C1372
#1877×C1372
#1865×C1372
#25153137