Finite Group Databasebeta

← C137×#22427 #46871813

Subgroups — C137×#22427 #46871813

Order 35072.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C137C211yesmaximal, characteristic
2C2×#436×C137C211yesmaximal, characteristic, complemented
3C2×#417×C137C211yesmaximal, characteristic, complemented
4C2×#418×C137C211yesmaximal, characteristic, complemented
5#2352×C137C211yesmaximal, characteristic, complemented
6#1983×C137C211yesmaximal, characteristic, complemented
7#1958×C137C211yesmaximal, characteristic, complemented
8#1895×C137C211yesmaximal, characteristic, complemented
9#1894×C137C211yesmaximal, characteristic, complemented
10#1874×C137C211yesmaximal, characteristic, complemented
11#1873×C137C211yesmaximal, characteristic, complemented
12#1804×C137C211yesmaximal, characteristic, complemented
13#1788×C137C211yesmaximal, characteristic, complemented
14#1786×C137C211yesmaximal, characteristic, complemented
15C4×#102×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C22×M16×C137C2211yescharacteristic
19C22×M16×C137C2211yescharacteristic, complemented
20#546×C137—24no—
21#546×C137C418yescomplemented
22C2×#124×C137C2211yescharacteristic
23C2×#123×C137—21no—
24C2×C22⋊Q8×C137C2211yescharacteristic
25C2×#121×C137—21no—
26C2×#121×C137C2211yescharacteristic
27C2×#120×C137—21no—
28C2×C4×D4×C137C2211yescharacteristic
29C2×C4×D4×C137C2211yescharacteristic
30C2×#117×C137C2211yescharacteristic
31C22×C4⋊C4×C137C2211yescharacteristic, complemented
32C22×C22⋊C4×C137—21no—
33#436×C137—24no—
34C2×C4⋊C8×C137C2211yescharacteristic, complemented
35#418×C137—24no—
36#417×C137—24no—
37C2×#103×C137C2211yescharacteristic, complemented
38C2×#103×C137C2211yescharacteristic, complemented
39C2×#103×C137C2211yescharacteristic, complemented
40C2×#103×C137C2211yescharacteristic, complemented
41C2×#102×C137C2211yescharacteristic
42C2×#102×C137C2211yescharacteristic
43C2×#102×C137C2211yescharacteristic
44C2×#102×C137C2211yescharacteristic
45C2×#102×C137C2211yescharacteristic
46C2×#102×C137C2211yescharacteristic
47C2×#102×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×C22⋊C8×C137C2211yescharacteristic
50C2×C22⋊C8×C137C2211yescharacteristic, complemented
51C2×C4×C8×C137C2211yescharacteristic, complemented
52#388×C137—21no—
53#387×C137—21no—
54#386×C137—21no—
55#382×C137C2211yescharacteristic, complemented
56#380×C137C2211yescharacteristic
57#380×C137C2211yescharacteristic, complemented
58C4×C4⋊C4×C137C2211yescharacteristic, complemented
59C4×C22⋊C4×C137—21no—
60#340×C137C2211yescharacteristic, complemented
61#340×C137C2211yescharacteristic, complemented
62#340×C137C2211yescharacteristic, complemented
63#340×C137C2211yescharacteristic, complemented
64C25×C137—21no—
65C2×#41×C137—22no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—41no—
69C2×#41×C137—41no—
70C2×#41×C137C2×C414yes—
71C22×Q8×C137C2311yescharacteristic
72C22×D4×C137—22no—
73C22×D4×C137—22no—
74C22×D4×C137—21no—
75C22×D4×C137—21no—
76C22×D4×C137—21no—
77C22×D4×C137—22no—
78C22×D4×C137—41no—
79C22×D4×C137—41no—
80C22×D4×C137C2×C414yescomplemented
81C22×D4×C137D411yescharacteristic
82C22×D4×C137C2311yescharacteristic
83C22×D4×C137C2311yescharacteristic
84C23×C4×C137—21no—
85C23×C4×C137—21no—
86C23×C4×C137—21no—
87C23×C4×C137C2311yescharacteristic
88C23×C4×C137C2311yescharacteristic
89C2×M16×C137—22no—
90C2×M16×C137—22no—
91C2×M16×C137—22no—
92C2×M16×C137—22no—
93C2×M16×C137—41no—
94C2×M16×C137—41no—
95C22×C8×C137C2311yescharacteristic
96C22×C8×C137C2311yescharacteristic
97C22×C8×C137C2311yescharacteristic
98C22×C8×C137C2311yescharacteristic
99#124×C137—22no—
100#124×C137C2×C414yescomplemented
101#123×C137—28no—
102C22⋊Q8×C137—22no—
103C22⋊Q8×C137C2×C414yescomplemented
104#121×C137—22no—
105#121×C137—28no—
106#121×C137C2×C414yes—
107#120×C137—28no—
108C4×D4×C137—22no—
109C4×D4×C137C2×C414yes—
110C4×D4×C137C2×C414yescomplemented
111C4×D4×C137D414yes—
112#117×C137—22no—
113#117×C137—41no—
114C2×C4⋊C4×C137—21no—
115C2×C4⋊C4×C137—22no—
116C2×C4⋊C4×C137—21no—
117C2×C4⋊C4×C137—41no—
118C2×C4⋊C4×C137D411yescharacteristic
119C2×C4⋊C4×C137C2311yescharacteristic
120C2×C4⋊C4×C137C2311yescharacteristic
121C2×C4⋊C4×C137C2311yescharacteristic
122C2×C4⋊C4×C137C2311yescharacteristic
123C2×C4⋊C4×C137C2311yescharacteristic
124C2×C22⋊C4×C137—21no—
125C2×C22⋊C4×C137—21no—
126C2×C22⋊C4×C137—21no—
127C2×C22⋊C4×C137—21no—
128C2×C22⋊C4×C137—21no—
129C2×C22⋊C4×C137—28no—
130C2×C22⋊C4×C137—21no—
131C2×C22⋊C4×C137—21no—
132C2×C22⋊C4×C137—21no—
133C2×C22⋊C4×C137D411yescharacteristic
134C2×C22⋊C4×C137D411yescharacteristic
135C2×C42×C137—21no—
136C2×C42×C137—21no—
137C2×C42×C137C2311yescharacteristic
138C4⋊C8×C137—22no—
139#103×C137—22no—
140#103×C137—22no—
141#103×C137—41no—
142#103×C137—41no—
143#102×C137—22no—
144#102×C137—22no—
145#102×C137—22no—
146#102×C137—22no—
147#102×C137—22no—
148#102×C137—41no—
149#102×C137—41no—
150#102×C137D414yescomplemented
151C22⋊C8×C137—22no—
152C22⋊C8×C137—22no—
153C4×C8×C137—22no—
154#95×C137—21no—
155#95×C137—21no—
156#95×C137—21no—
157#95×C137—21no—
158#95×C137—21no—
159C24×C137—21no—
160C24×C137—21no—
161C24×C137—24no—
162C24×C137—42no—
163C24×C137—42no—
164C24×C137—42no—
165C24×C137—42no—
166C24×C137—81no—
167C24×C137—81no—
168C24×C137C2×D411yescharacteristic
169C24×C137C2×D411yescharacteristic
170#41×C137—28no—
171#41×C137—44no—
172#41×C137—44no—
173#41×C137—44no—
174C2×Q8×C137—21no—
175C2×Q8×C137—21no—
176C2×Q8×C137—21no—
177C2×Q8×C137—21no—
178C2×Q8×C137—21no—
179C2×Q8×C137C22×C412yes—
180C2×D4×C137—28no—
181C2×D4×C137—24no—
182C2×D4×C137—24no—
183C2×D4×C137—24no—
184C2×D4×C137—21no—
185C2×D4×C137—21no—
186C2×D4×C137—21no—
187C2×D4×C137—21no—
188C2×D4×C137—21no—
189C2×D4×C137—21no—
190C2×D4×C137—21no—
191C2×D4×C137—21no—
192C2×D4×C137—44no—
193C2×D4×C137—44no—
194C2×D4×C137—44no—
195C2×D4×C137—41no—
196C2×D4×C137—41no—
197C2×D4×C137—42no—
198C2×D4×C137—42no—
199C2×D4×C137—42no—
200C2×D4×C137—42no—
201C2×D4×C137—81no—
202C2×D4×C137—81no—
203C2×D4×C137C22⋊C414yes—
204C2×D4×C137C22×C412yes—
205C2×D4×C137C22×C412yes—
206C2×D4×C137C2×D412yes—
207C2×D4×C137#4112yes—
208C22×C4×C137—21no—
209C22×C4×C137—21no—
210C22×C4×C137—21no—
211C22×C4×C137—21no—
212C22×C4×C137—21no—
213C22×C4×C137—21no—
214C22×C4×C137—21no—
215C22×C4×C137—21no—
216C22×C4×C137—21no—
217C22×C4×C137—21no—
218C22×C4×C137—21no—
219C22×C4×C137—24no—
220C22×C4×C137—24no—
221C22×C4×C137—21no—
222C22×C4×C137—21no—
223C22×C4×C137—21no—
224C22×C4×C137—42no—
225C22×C4×C137—42no—
226C22×C4×C137—42no—
227C22×C4×C137—42no—
228C22×C4×C137—81no—
229C22×C4×C137—81no—
230C22×C4×C137—81no—
231C22×C4×C137C22×C412yes—
232C22×C4×C137C22×C412yes—
233C22×C4×C137C2×D411yescharacteristic
234C22×C4×C137C2×D411yescharacteristic
235C22×C4×C137C2×D411yescharacteristic
236C22×C4×C137C2×D411yescharacteristic
237C22×C4×C137C2×D412yes—
238C22×C4×C137C2×D412yes—
239C22×C4×C137C2411yescharacteristic
240M16×C137—44no—
241M16×C137—44no—
242C2×C8×C137—21no—
243C2×C8×C137—21no—
244C2×C8×C137—21no—
245C2×C8×C137—21no—
246C2×C8×C137—21no—
247C2×C8×C137—21no—
248C2×C8×C137—21no—
249C2×C8×C137—21no—
250C2×C8×C137—21no—
251C2×C8×C137—21no—
252C2×C8×C137—21no—
253C2×C8×C137C2×D412yes—
254C4⋊C4×C137—24no—
255C4⋊C4×C137—21no—
256C4⋊C4×C137—21no—
257C4⋊C4×C137—21no—
258C4⋊C4×C137—21no—
259C4⋊C4×C137—21no—
260C4⋊C4×C137—21no—
261C4⋊C4×C137—21no—
262C4⋊C4×C137—21no—
263C4⋊C4×C137—42no—
264C4⋊C4×C137C22⋊C414yes—
265C4⋊C4×C137C22×C412yes—
266C4⋊C4×C137C2×D412yes—
267C22⋊C4×C137—24no—
268C22⋊C4×C137—24no—
269C22⋊C4×C137—24no—
270C22⋊C4×C137—24no—
271C22⋊C4×C137—24no—
272C22⋊C4×C137—42no—
273C22⋊C4×C137—42no—
274C22⋊C4×C137—81no—
275C22⋊C4×C137C22⋊C414yes—
276C22⋊C4×C137C22⋊C414yes—
277C42×C137—42no—
278C42×C137—81no—
279C42×C137C22×C412yes—
280C42×C137C2×D412yes—
281C23×C137—22no—
282C23×C137—21no—
283C23×C137—21no—
284C23×C137—22no—
285C23×C137—21no—
286C23×C137—21no—
287C23×C137—22no—
288C23×C137—21no—
289C23×C137—21no—
290C23×C137—21no—
291C23×C137—21no—
292C23×C137—21no—
293C23×C137—21no—
294C23×C137—21no—
295C23×C137—21no—
296C23×C137—22no—
297C23×C137—48no—
298C23×C137—48no—
299C23×C137—41no—
300C23×C137—41no—
301C23×C137—41no—
302C23×C137—41no—
303C23×C137—41no—
304C23×C137—41no—
305C23×C137—41no—
306C23×C137—41no—
307C23×C137—41no—
308C23×C137—41no—
309C23×C137—84no—
310C23×C137—84no—
311C23×C137—84no—
312C23×C137—84no—
313C23×C137—84no—
314C23×C137C2×C22⋊C412yes—
315C23×C137C2×C22⋊C412yes—
316C23×C137C22×D411yescharacteristic
317Q8×C137—22no—
318Q8×C137—22no—
319Q8×C137—41no—
320Q8×C137—41no—
321D4×C137—22no—
322D4×C137—22no—
323D4×C137—22no—
324D4×C137—22no—
325D4×C137—22no—
326D4×C137—44no—
327D4×C137—48no—
328D4×C137—48no—
329D4×C137—41no—
330D4×C137—41no—
331D4×C137—84no—
332D4×C137C4×D414yes—
333C2×C4×C137—21no—
334C2×C4×C137—21no—
335C2×C4×C137—21no—
336C2×C4×C137—21no—
337C2×C4×C137—21no—
338C2×C4×C137—21no—
339C2×C4×C137—21no—
340C2×C4×C137—21no—
341C2×C4×C137—22no—
342C2×C4×C137—22no—
343C2×C4×C137—22no—
344C2×C4×C137—22no—
345C2×C4×C137—22no—
346C2×C4×C137—22no—
347C2×C4×C137—22no—
348C2×C4×C137—22no—
349C2×C4×C137—22no—
350C2×C4×C137—22no—
351C2×C4×C137—22no—
352C2×C4×C137—48no—
353C2×C4×C137—41no—
354C2×C4×C137—41no—
355C2×C4×C137—41no—
356C2×C4×C137—41no—
357C2×C4×C137—41no—
358C2×C4×C137—41no—
359C2×C4×C137—41no—
360C2×C4×C137—41no—
361C2×C4×C137—41no—
362C2×C4×C137—41no—
363C2×C4×C137—41no—
364C2×C4×C137—41no—
365C2×C4×C137—41no—
366C2×C4×C137—41no—
367C2×C4×C137—41no—
368C2×C4×C137—84no—
369C2×C4×C137—84no—
370C2×C4×C137C2×C22⋊C412yes—
371C2×C4×C137C2×C22⋊C412yes—
372C2×C4×C137C2×C22⋊C412yes—
373C2×C4×C137C2×C22⋊C412yes—
374C2×C4×C137C23×C411yescharacteristic
375C2×C4×C137C22×D411yescharacteristic
376C2×C4×C137C22×D411yescharacteristic
377C2×C4×C137C2×#4111yescharacteristic
378C2×C4×C137H(5,𝔽2)11yescharacteristic
379C2×C4×C137H(5,𝔽2)11yescharacteristic
380C8×C137—22no—
381C8×C137—41no—
382C8×C137—41no—
383C8×C137—41no—
384C22×C137—22no—
385C22×C137—22no—
386C22×C137—24no—
387C22×C137—22no—
388C22×C137—22no—
389C22×C137—22no—
390C22×C137—22no—
391C22×C137—42no—
392C22×C137—42no—
393C22×C137—41no—
394C22×C137—41no—
395C22×C137—42no—
396C22×C137—41no—
397C22×C137—41no—
398C22×C137—42no—
399C22×C137—41no—
400C22×C137—41no—
401C22×C137—42no—
402C22×C137—41no—
403C22×C137—41no—
404C22×C137—42no—
405C22×C137—42no—
406C22×C137—42no—
407C22×C137—42no—
408C22×C137—816no—
409C22×C137—81no—
410C22×C137—81no—
411C22×C137—81no—
412C22×C137—81no—
413C22×C137C22×C22⋊C411yescharacteristic
414C22×C137D4211yescharacteristic
415C22×C137#54611yescharacteristic
416C22×C137#57511yescharacteristic
417C22×C137#57511yescharacteristic
418C22×C137#57611yescharacteristic
419C22×C137#57711yescharacteristic
420C4×C137—22no—
421C4×C137—22no—
422C4×C137—22no—
423C4×C137—22no—
424C4×C137—42no—
425C4×C137—42no—
426C4×C137—42no—
427C4×C137—81no—
428C4×C137—81no—
429C4×C137—81no—
430C4×C137C2×C4×D411yescharacteristic
431C4×C137#51811yescharacteristic
432C4×C137D4211yescharacteristic
433C4×C137#54611yescharacteristic
434C2×C137—42no—
435C2×C137—42no—
436C2×C137—44no—
437C2×C137—82no—
438C2×C137D4×C22⋊C411yescharacteristic
439C2×C137#289611yescharacteristic
440C2×C137#289711yescharacteristic
441C2×C137#327311yescharacteristic
442C2×C137#327511yescharacteristic
443C2×C137#332211yescharacteristic
444C2×C137#332311yescharacteristic
445#22427C13711yesmaximal, characteristic, direct product factor, Sylow
446C137#2242711yescharacteristic, direct product factor, Sylow
447C2×#546C2×C13711yescharacteristic
448C2×#436C2×C13711yescharacteristic, complemented
449C2×#417C2×C13711yescharacteristic, complemented
450C2×#418C2×C13711yescharacteristic, complemented
451#2352C2×C13711yescharacteristic, complemented
452#1983C2×C13711yescharacteristic, complemented
453#1958C2×C13711yescharacteristic, complemented
454#1895C2×C13711yescharacteristic, complemented
455#1894C2×C13711yescharacteristic, complemented
456#1874C2×C13711yescharacteristic, complemented
457#1873C2×C13711yescharacteristic, complemented
458#1804C2×C13711yescharacteristic, complemented
459#1788C2×C13711yescharacteristic, complemented
460#1786C2×C13711yescharacteristic, complemented
461C4×#102C2×C13711yescharacteristic, complemented
462C22×#41C22×C13711yescharacteristic
463C23×D4C22×C13711yescharacteristic
464C22×M16C22×C13711yescharacteristic
465C22×M16C22×C13711yescharacteristic, complemented
466#546—24no—
467#546C4×C13718yescomplemented
468C2×#124C22×C13711yescharacteristic
469C2×#123—21no—
470C2×C22⋊Q8C22×C13711yescharacteristic
471C2×#121—21no—
472C2×#121C22×C13711yescharacteristic
473C2×#120—21no—
474C2×C4×D4C22×C13711yescharacteristic
475C2×C4×D4C22×C13711yescharacteristic
476C2×#117C22×C13711yescharacteristic
477C22×C4⋊C4C22×C13711yescharacteristic, complemented
478C22×C22⋊C4—21no—
479#436—24no—
480C2×C4⋊C8C22×C13711yescharacteristic, complemented
481#418—24no—
482#417—24no—
483C2×#103C22×C13711yescharacteristic, complemented
484C2×#103C22×C13711yescharacteristic, complemented
485C2×#103C22×C13711yescharacteristic, complemented
486C2×#103C22×C13711yescharacteristic, complemented
487C2×#102C22×C13711yescharacteristic
488C2×#102C22×C13711yescharacteristic
489C2×#102C22×C13711yescharacteristic
490C2×#102C22×C13711yescharacteristic
491C2×#102C22×C13711yescharacteristic
492C2×#102C22×C13711yescharacteristic
493C2×#102C22×C13711yescharacteristic
494C2×#102C22×C13711yescharacteristic
495C2×C22⋊C8C22×C13711yescharacteristic
496C2×C22⋊C8C22×C13711yescharacteristic, complemented
497C2×C4×C8C22×C13711yescharacteristic, complemented
498#388—21no—
499#387—21no—
500#386—21no—
501#382C22×C13711yescharacteristic, complemented
502#380C22×C13711yescharacteristic
503#380C22×C13711yescharacteristic, complemented
504C4×C4⋊C4C22×C13711yescharacteristic, complemented
505C4×C22⋊C4—21no—
506#340C22×C13711yescharacteristic, complemented
507#340C22×C13711yescharacteristic, complemented
508#340C22×C13711yescharacteristic, complemented
509#340C22×C13711yescharacteristic, complemented
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×C4×C13714yes—
517C22×Q8C23×C13711yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×C4×C13714yescomplemented
527C22×D4D4×C13711yescharacteristic
528C22×D4C23×C13711yescharacteristic
529C22×D4C23×C13711yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C23×C13711yescharacteristic
534C23×C4C23×C13711yescharacteristic
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8C23×C13711yescharacteristic
542C22×C8C23×C13711yescharacteristic
543C22×C8C23×C13711yescharacteristic
544C22×C8C23×C13711yescharacteristic
545#124—22no—
546#124C2×C4×C13714yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×C4×C13714yescomplemented
550#121—22no—
551#121—28no—
552#121C2×C4×C13714yes—
553#120—28no—
554C4×D4—22no—
555C4×D4C2×C4×C13714yes—
556C4×D4C2×C4×C13714yescomplemented
557C4×D4D4×C13714yes—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4D4×C13711yescharacteristic
565C2×C4⋊C4C23×C13711yescharacteristic
566C2×C4⋊C4C23×C13711yescharacteristic
567C2×C4⋊C4C23×C13711yescharacteristic
568C2×C4⋊C4C23×C13711yescharacteristic
569C2×C4⋊C4C23×C13711yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C13711yescharacteristic
580C2×C22⋊C4D4×C13711yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C23×C13711yescharacteristic
584C4⋊C8—22no—
585#103—22no—
586#103—22no—
587#103—41no—
588#103—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102—41no—
596#102D4×C13714yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×D4×C13711yescharacteristic
615C24C2×D4×C13711yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×C4×C13712yes—
626C2×D4—28no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊C4×C13714yes—
650C2×D4C22×C4×C13712yes—
651C2×D4C22×C4×C13712yes—
652C2×D4C2×D4×C13712yes—
653C2×D4#41×C13712yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—81no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4C22×C4×C13712yes—
678C22×C4C22×C4×C13712yes—
679C22×C4C2×D4×C13711yescharacteristic
680C22×C4C2×D4×C13711yescharacteristic
681C22×C4C2×D4×C13711yescharacteristic
682C22×C4C2×D4×C13711yescharacteristic
683C22×C4C2×D4×C13712yes—
684C22×C4C2×D4×C13712yes—
685C22×C4C24×C13711yescharacteristic
686M16—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C13712yes—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4C22⋊C4×C13714yes—
711C4⋊C4C22×C4×C13712yes—
712C4⋊C4C2×D4×C13712yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4C22⋊C4×C13714yes—
722C22⋊C4C22⋊C4×C13714yes—
723C42—42no—
724C42—81no—
725C42C22×C4×C13712yes—
726C42C2×D4×C13712yes—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊C4×C13712yes—
761C23C2×C22⋊C4×C13712yes—
762C23C22×D4×C13711yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4C4×D4×C13714yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C2×C22⋊C4×C13712yes—
817C2×C4C2×C22⋊C4×C13712yes—
818C2×C4C2×C22⋊C4×C13712yes—
819C2×C4C2×C22⋊C4×C13712yes—
820C2×C4C23×C4×C13711yescharacteristic
821C2×C4C22×D4×C13711yescharacteristic
822C2×C4C22×D4×C13711yescharacteristic
823C2×C4C2×#41×C13711yescharacteristic
824C2×C4H(5,𝔽2)×C13711yescharacteristic
825C2×C4H(5,𝔽2)×C13711yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C22×C22⋊C4×C13711yescharacteristic
860C22D42×C13711yescharacteristic
861C22#546×C13711yescharacteristic
862C22#575×C13711yescharacteristic
863C22#575×C13711yescharacteristic
864C22#576×C13711yescharacteristic
865C22#577×C13711yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4C2×C4×D4×C13711yescharacteristic
877C4#518×C13711yescharacteristic
878C4D42×C13711yescharacteristic
879C4#546×C13711yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊C4×C13711yescharacteristic
885C2#2896×C13711yescharacteristic
886C2#2897×C13711yescharacteristic
887C2#3273×C13711yescharacteristic
888C2#3275×C13711yescharacteristic
889C2#3322×C13711yescharacteristic
890C2#3323×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutatorC2×C4C23×C4×C137
Frattini, cosocleC22×C4C24×C137
prime radicalC2×#546×C137C2
LCSG ▷ C2×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
2. C2×#436×C137C2semidirect
3. C2×#417×C137C2semidirect
4. C2×#418×C137C2semidirect
5. #2352×C137C2semidirect
6. #1983×C137C2semidirect
7. #1958×C137C2semidirect
8. #1895×C137C2semidirect
9. #1894×C137C2semidirect
10. #1874×C137C2semidirect
11. #1873×C137C2semidirect
12. #1804×C137C2semidirect
13. #1788×C137C2semidirect
14. #1786×C137C2semidirect
15. C4×#102×C137C2semidirect
19. C22×M16×C137C22semidirect
21. #546×C137C4semidirect
31. C22×C4⋊C4×C137C22semidirect
34. C2×C4⋊C8×C137C22semidirect
37. C2×#103×C137C22semidirect
38. C2×#103×C137C22semidirect
39. C2×#103×C137C22semidirect
40. C2×#103×C137C22semidirect
50. C2×C22⋊C8×C137C22semidirect
51. C2×C4×C8×C137C22semidirect
55. #382×C137C22semidirect
57. #380×C137C22semidirect
58. C4×C4⋊C4×C137C22semidirect
60. #340×C137C22semidirect
61. #340×C137C22semidirect
62. #340×C137C22semidirect
63. #340×C137C22semidirect
80. C22×D4×C137C2×C4semidirect
100. #124×C137C2×C4semidirect
103. C22⋊Q8×C137C2×C4semidirect
110. C4×D4×C137C2×C4semidirect
150. #102×C137D4semidirect
445. #22427C137direct (N × H)
446. C137#22427direct (N × H)
448. C2×#436C2×C137semidirect
449. C2×#417C2×C137semidirect
450. C2×#418C2×C137semidirect
451. #2352C2×C137semidirect
452. #1983C2×C137semidirect
453. #1958C2×C137semidirect
454. #1895C2×C137semidirect
455. #1894C2×C137semidirect
456. #1874C2×C137semidirect
457. #1873C2×C137semidirect
458. #1804C2×C137semidirect
459. #1788C2×C137semidirect
460. #1786C2×C137semidirect
461. C4×#102C2×C137semidirect
465. C22×M16C22×C137semidirect
467. #546C4×C137semidirect
477. C22×C4⋊C4C22×C137semidirect
480. C2×C4⋊C8C22×C137semidirect
483. C2×#103C22×C137semidirect
484. C2×#103C22×C137semidirect
485. C2×#103C22×C137semidirect
486. C2×#103C22×C137semidirect
496. C2×C22⋊C8C22×C137semidirect
497. C2×C4×C8C22×C137semidirect
501. #382C22×C137semidirect
503. #380C22×C137semidirect
504. C4×C4⋊C4C22×C137semidirect
506. #340C22×C137semidirect
507. #340C22×C137semidirect
508. #340C22×C137semidirect
509. #340C22×C137semidirect
526. C22×D4C2×C4×C137semidirect
546. #124C2×C4×C137semidirect
549. C22⋊Q8C2×C4×C137semidirect
556. C4×D4C2×C4×C137semidirect
596. #102D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1372
C2×#436×C1372
C2×#417×C1372
C2×#418×C1372
#2352×C1372
#1983×C1372
#1958×C1372
#1895×C1372
#1894×C1372
#1874×C1372
#1873×C1372
#1804×C1372
#1788×C1372
#1786×C1372
C4×#102×C1372
#22427137