Finite Group Databasebeta

← C137×#25174 #46874560

Subgroups — C137×#25174 #46874560

Order 35072.

1234 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C137C211yesmaximal, characteristic, complemented
2C2×#449×C137C211yesmaximal, characteristic, complemented
3C2×#449×C137C211yesmaximal, characteristic, complemented
4C2×#442×C137C211yesmaximal, characteristic, complemented
5#2428×C137C211yesmaximal, characteristic, complemented
6#2339×C137C211yesmaximal, characteristic, complemented
7#2066×C137C211yesmaximal, characteristic, complemented
8#2034×C137C211yesmaximal, characteristic, complemented
9#2033×C137C211yesmaximal, characteristic, complemented
10#2014×C137C211yesmaximal, characteristic, complemented
11#1973×C137C211yesmaximal, characteristic, complemented
12#1924×C137C211yesmaximal, characteristic, complemented
13#1879×C137C211yesmaximal, characteristic, complemented
14#1877×C137C211yesmaximal, characteristic, complemented
15#1862×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C22×SD16×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic
19C22×D8×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic
21C2×#127×C137C2211yescharacteristic
22C2×#121×C137—21no—
23C2×#121×C137C2211yescharacteristic
24C2×#121×C137C2211yescharacteristic
25C2×C4×D4×C137C2211yescharacteristic
26C2×C4×D4×C137C2211yescharacteristic
27C2×C4×D4×C137C2211yescharacteristic
28#459×C137—24no—
29#449×C137—24no—
30#449×C137—24no—
31#442×C137—24no—
32C2×#107×C137C2211yescharacteristic
33C2×#106×C137C2211yescharacteristic
34C2×C4⋊C8×C137C2211yescharacteristic
35C2×#103×C137C2211yescharacteristic
36C2×#103×C137C2211yescharacteristic
37C2×#102×C137C2211yescharacteristic
38C2×#102×C137C2211yescharacteristic
39C2×#102×C137C2211yescharacteristic
40C2×#102×C137C2211yescharacteristic
41C2×#102×C137C2211yescharacteristic
42C2×#102×C137C2211yescharacteristic
43C2×C22⋊C8×C137C2211yescharacteristic
44C2×C22⋊C8×C137C2211yescharacteristic
45C2×#97×C137C2211yescharacteristic
46#394×C137—21no—
47#392×C137—21no—
48#391×C137C2211yescharacteristic
49#391×C137C2211yescharacteristic
50#390×C137C2211yescharacteristic
51#389×C137C2211yescharacteristic
52#386×C137—21no—
53#386×C137—21no—
54#386×C137—21no—
55#381×C137—21no—
56#380×C137C2211yescharacteristic
57C4×C22⋊C4×C137C2211yescharacteristic
58C2×#95×C137—21no—
59#340×C137C2211yescharacteristic
60#340×C137C2211yescharacteristic
61#336×C137C2211yescharacteristic
62#336×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×C137—21no—
75C22×D4×C137C2311yescharacteristic
76C22×D4×C137C2311yescharacteristic
77C22×D4×C137C2311yescharacteristic
78C23×C4×C137—21no—
79C23×C4×C137—21no—
80C23×C4×C137—21no—
81C23×C4×C137—21no—
82C23×C4×C137C2311yescharacteristic
83C2×SD16×C137—22no—
84C2×SD16×C137—22no—
85C2×SD16×C137—22no—
86C2×SD16×C137—22no—
87C2×SD16×C137—41no—
88C2×SD16×C137—41no—
89C2×D8×C137—22no—
90C2×D8×C137—22no—
91C2×D8×C137—22no—
92C2×D8×C137—22no—
93C2×D8×C137—22no—
94C2×D8×C137D414yescomplemented
95C22×C8×C137C2311yescharacteristic
96C22×C8×C137C2311yescharacteristic
97C22×C8×C137C2311yescharacteristic
98C22×C8×C137C2311yescharacteristic
99#127×C137—22no—
100#127×C137—41no—
101#121×C137—22no—
102#121×C137—22no—
103#121×C137—44no—
104#121×C137—41no—
105#121×C137—41no—
106C4×D4×C137—22no—
107C4×D4×C137—22no—
108C4×D4×C137—22no—
109C4×D4×C137—41no—
110C4×D4×C137—41no—
111C4×D4×C137—41no—
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×C137—21no—
124C2×C22⋊C4×C137—21no—
125C2×C22⋊C4×C137D411yescharacteristic
126C2×C22⋊C4×C137D411yescharacteristic
127C2×C42×C137C2311yescharacteristic
128C2×C42×C137C2311yescharacteristic
129#107×C137—41no—
130#106×C137—22no—
131C4⋊C8×C137—22no—
132#103×C137—22no—
133#103×C137—22no—
134#102×C137—22no—
135#102×C137—22no—
136#102×C137—22no—
137#102×C137—22no—
138#102×C137—41no—
139#102×C137D414yescomplemented
140C22⋊C8×C137—22no—
141C22⋊C8×C137—22no—
142#97×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×C137—21no—
154C24×C137C2×D411yescharacteristic
155#41×C137—44no—
156#41×C137—44no—
157#41×C137—44no—
158#41×C137—44no—
159C2×Q8×C137—21no—
160C2×Q8×C137—21no—
161C2×Q8×C137—21no—
162C2×Q8×C137—21no—
163C2×Q8×C137—21no—
164C2×Q8×C137#4112yes—
165C2×D4×C137—24no—
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—21no—
177C2×D4×C137—21no—
178C2×D4×C137—21no—
179C2×D4×C137—21no—
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—42no—
187C2×D4×C137—42no—
188C2×D4×C137—42no—
189C2×D4×C137—42no—
190C2×D4×C137—81no—
191C2×D4×C137—81no—
192C2×D4×C137—81no—
193C2×D4×C137—81no—
194C2×D4×C137C2×D412yes—
195C2×D4×C137C2×D412yes—
196C2×D4×C137C2×D412yes—
197C2×D4×C137#4112yes—
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—42no—
215C22×C4×C137—42no—
216C22×C4×C137—42no—
217C22×C4×C137—42no—
218C22×C4×C137—81no—
219C22×C4×C137—81no—
220C22×C4×C137—81no—
221C22×C4×C137C2×D411yescharacteristic
222C22×C4×C137C2×D411yescharacteristic
223C22×C4×C137C2×D411yescharacteristic
224C22×C4×C137C2×D411yescharacteristic
225C22×C4×C137C2×D411yescharacteristic
226C22×C4×C137C2411yescharacteristic
227SD16×C137—44no—
228SD16×C137—44no—
229D8×C137—28no—
230D8×C137—44no—
231C2×C8×C137—21no—
232C2×C8×C137—21no—
233C2×C8×C137—21no—
234C2×C8×C137—21no—
235C2×C8×C137—21no—
236C2×C8×C137—21no—
237C2×C8×C137—21no—
238C2×C8×C137—21no—
239C2×C8×C137—21no—
240C2×C8×C137—21no—
241C2×C8×C137C2×D412yes—
242C2×C8×C137C2×D412yes—
243C4⋊C4×C137—21no—
244C4⋊C4×C137—21no—
245C4⋊C4×C137—21no—
246C4⋊C4×C137—21no—
247C4⋊C4×C137—21no—
248C4⋊C4×C137—21no—
249C4⋊C4×C137—21no—
250C4⋊C4×C137—42no—
251C4⋊C4×C137C2×D412yes—
252C22⋊C4×C137—22no—
253C22⋊C4×C137—41no—
254C22⋊C4×C137—42no—
255C22⋊C4×C137—42no—
256C22⋊C4×C137—42no—
257C22⋊C4×C137—42no—
258C22⋊C4×C137—42no—
259C22⋊C4×C137—42no—
260C22⋊C4×C137—81no—
261C22⋊C4×C137—81no—
262C42×C137—21no—
263C42×C137—21no—
264C42×C137—21no—
265C42×C137—21no—
266C23×C137—22no—
267C23×C137—22no—
268C23×C137—22no—
269C23×C137—21no—
270C23×C137—22no—
271C23×C137—21no—
272C23×C137—21no—
273C23×C137—21no—
274C23×C137—21no—
275C23×C137—21no—
276C23×C137—21no—
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—41no—
290C23×C137—41no—
291C23×C137—41no—
292C23×C137—41no—
293C23×C137—41no—
294C23×C137C22×D411yescharacteristic
295Q8×C137—22no—
296Q8×C137—22no—
297Q8×C137—41no—
298Q8×C137—41no—
299D4×C137—22no—
300D4×C137—22no—
301D4×C137—22no—
302D4×C137—22no—
303D4×C137—22no—
304D4×C137—48no—
305D4×C137—41no—
306D4×C137—41no—
307D4×C137—41no—
308D4×C137—41no—
309D4×C137—41no—
310D4×C137—41no—
311D4×C137—84no—
312D4×C137—84no—
313D4×C137—84no—
314D4×C137—84no—
315D4×C137#12114yescomplemented
316C2×C4×C137—21no—
317C2×C4×C137—21no—
318C2×C4×C137—21no—
319C2×C4×C137—22no—
320C2×C4×C137—21no—
321C2×C4×C137—21no—
322C2×C4×C137—21no—
323C2×C4×C137—22no—
324C2×C4×C137—21no—
325C2×C4×C137—21no—
326C2×C4×C137—21no—
327C2×C4×C137—21no—
328C2×C4×C137—21no—
329C2×C4×C137—21no—
330C2×C4×C137—21no—
331C2×C4×C137—21no—
332C2×C4×C137—48no—
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—41no—
347C2×C4×C137—41no—
348C2×C4×C137—41no—
349C2×C4×C137—41no—
350C2×C4×C137—84no—
351C2×C4×C137—84no—
352C2×C4×C137—84no—
353C2×C4×C137AGL(1,ℤ/8)12yes—
354C2×C4×C137C22×D411yescharacteristic
355C2×C4×C137C22×D411yescharacteristic
356C2×C4×C137C2×#4111yescharacteristic
357C2×C4×C137C2×#4111yescharacteristic
358C2×C4×C137H(5,𝔽2)11yescharacteristic
359C2×C4×C137H(5,𝔽2)11yescharacteristic
360C8×C137—22no—
361C8×C137—22no—
362C8×C137—41no—
363C8×C137—41no—
364C22×C137—24no—
365C22×C137—42no—
366C22×C137—42no—
367C22×C137—42no—
368C22×C137—42no—
369C22×C137—42no—
370C22×C137—42no—
371C22×C137—41no—
372C22×C137—41no—
373C22×C137—41no—
374C22×C137—42no—
375C22×C137—41no—
376C22×C137—42no—
377C22×C137—42no—
378C22×C137—41no—
379C22×C137—41no—
380C22×C137—41no—
381C22×C137—81no—
382C22×C137—81no—
383C22×C137—81no—
384C22×C137—81no—
385C22×C137—81no—
386C22×C137—81no—
387C22×C137—81no—
388C22×C137—81no—
389C22×C137—81no—
390C22×C137—81no—
391C22×C137—81no—
392C22×C137#52511yescharacteristic
393C22×C137D4211yescharacteristic
394C22×C137D4211yescharacteristic
395C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C137#57511yescharacteristic
397C22×C137#57611yescharacteristic
398C22×C137#57711yescharacteristic
399C4×C137—22no—
400C4×C137—41no—
401C4×C137—42no—
402C4×C137—41no—
403C4×C137—41no—
404C4×C137—41no—
405C4×C137—42no—
406C4×C137—81no—
407C4×C137—81no—
408C4×C137—81no—
409C4×C137C2×#12111yescharacteristic
410C4×C137#53811yescharacteristic
411C4×C137#54611yescharacteristic
412C4×C137#54611yescharacteristic
413C2×C137—44no—
414C2×C137—81no—
415C2×C137—82no—
416C2×C137—161no—
417C2×C137#242411yescharacteristic
418C2×C137#311511yescharacteristic
419C2×C137#311911yescharacteristic
420C2×C137#326411yescharacteristic
421C2×C137#326711yescharacteristic
422C2×C137#326811yescharacteristic
423C2×C137#327211yescharacteristic
424#25174C13711yesmaximal, characteristic, direct product factor, Sylow
425C137#2517411yescharacteristic, direct product factor, Sylow
426C2×#459C2×C13711yescharacteristic, complemented
427C2×#449C2×C13711yescharacteristic, complemented
428C2×#449C2×C13711yescharacteristic, complemented
429C2×#442C2×C13711yescharacteristic, complemented
430#2428C2×C13711yescharacteristic, complemented
431#2339C2×C13711yescharacteristic, complemented
432#2066C2×C13711yescharacteristic, complemented
433#2034C2×C13711yescharacteristic, complemented
434#2033C2×C13711yescharacteristic, complemented
435#2014C2×C13711yescharacteristic, complemented
436#1973C2×C13711yescharacteristic, complemented
437#1924C2×C13711yescharacteristic, complemented
438#1879C2×C13711yescharacteristic, complemented
439#1877C2×C13711yescharacteristic, complemented
440#1862C2×C13711yescharacteristic, complemented
441C22×#41C22×C13711yescharacteristic
442C22×SD16C22×C13711yescharacteristic
443C22×SD16C22×C13711yescharacteristic
444C22×D8C22×C13711yescharacteristic
445C22×D8C22×C13711yescharacteristic
446C2×#127C22×C13711yescharacteristic
447C2×#121—21no—
448C2×#121C22×C13711yescharacteristic
449C2×#121C22×C13711yescharacteristic
450C2×C4×D4C22×C13711yescharacteristic
451C2×C4×D4C22×C13711yescharacteristic
452C2×C4×D4C22×C13711yescharacteristic
453#459—24no—
454#449—24no—
455#449—24no—
456#442—24no—
457C2×#107C22×C13711yescharacteristic
458C2×#106C22×C13711yescharacteristic
459C2×C4⋊C8C22×C13711yescharacteristic
460C2×#103C22×C13711yescharacteristic
461C2×#103C22×C13711yescharacteristic
462C2×#102C22×C13711yescharacteristic
463C2×#102C22×C13711yescharacteristic
464C2×#102C22×C13711yescharacteristic
465C2×#102C22×C13711yescharacteristic
466C2×#102C22×C13711yescharacteristic
467C2×#102C22×C13711yescharacteristic
468C2×C22⋊C8C22×C13711yescharacteristic
469C2×C22⋊C8C22×C13711yescharacteristic
470C2×#97C22×C13711yescharacteristic
471#394—21no—
472#392—21no—
473#391C22×C13711yescharacteristic
474#391C22×C13711yescharacteristic
475#390C22×C13711yescharacteristic
476#389C22×C13711yescharacteristic
477#386—21no—
478#386—21no—
479#386—21no—
480#381—21no—
481#380C22×C13711yescharacteristic
482C4×C22⋊C4C22×C13711yescharacteristic
483C2×#95—21no—
484#340C22×C13711yescharacteristic
485#340C22×C13711yescharacteristic
486#336C22×C13711yescharacteristic
487#336C22×C13711yescharacteristic
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C23×C13711yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C13711yescharacteristic
501C22×D4C23×C13711yescharacteristic
502C22×D4C23×C13711yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C13711yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8D4×C13714yescomplemented
520C22×C8C23×C13711yescharacteristic
521C22×C8C23×C13711yescharacteristic
522C22×C8C23×C13711yescharacteristic
523C22×C8C23×C13711yescharacteristic
524#127—22no—
525#127—41no—
526#121—22no—
527#121—22no—
528#121—44no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C13711yescharacteristic
539C2×C4⋊C4C23×C13711yescharacteristic
540C2×C4⋊C4C23×C13711yescharacteristic
541C2×C4⋊C4C23×C13711yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C13711yescharacteristic
551C2×C22⋊C4D4×C13711yescharacteristic
552C2×C42C23×C13711yescharacteristic
553C2×C42C23×C13711yescharacteristic
554#107—41no—
555#106—22no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C13714yescomplemented
565C22⋊C8—22no—
566C22⋊C8—22no—
567#97—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C13711yescharacteristic
575#95D4×C13711yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C13711yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C13712yes—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C13712yes—
620C2×D4C2×D4×C13712yes—
621C2×D4C2×D4×C13712yes—
622C2×D4#41×C13712yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C13711yescharacteristic
647C22×C4C2×D4×C13711yescharacteristic
648C22×C4C2×D4×C13711yescharacteristic
649C22×C4C2×D4×C13711yescharacteristic
650C22×C4C2×D4×C13711yescharacteristic
651C22×C4C24×C13711yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C13712yes—
667C2×C8C2×D4×C13712yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C13712yes—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23C22×D4×C13711yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4#121×C13714yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4AGL(1,ℤ/8)×C13712yes—
779C2×C4C22×D4×C13711yescharacteristic
780C2×C4C22×D4×C13711yescharacteristic
781C2×C4C2×#41×C13711yescharacteristic
782C2×C4C2×#41×C13711yescharacteristic
783C2×C4H(5,𝔽2)×C13711yescharacteristic
784C2×C4H(5,𝔽2)×C13711yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—42no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22#525×C13711yescharacteristic
818C22D42×C13711yescharacteristic
819C22D42×C13711yescharacteristic
820C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
821C22#575×C13711yescharacteristic
822C22#576×C13711yescharacteristic
823C22#577×C13711yescharacteristic
824C4—22no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#121×C13711yescharacteristic
835C4#538×C13711yescharacteristic
836C4#546×C13711yescharacteristic
837C4#546×C13711yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2#2424×C13711yescharacteristic
843C2#3115×C13711yescharacteristic
844C2#3119×C13711yescharacteristic
845C2#3264×C13711yescharacteristic
846C2#3267×C13711yescharacteristic
847C2#3268×C13711yescharacteristic
848C2#3272×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
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×#459×C137C2semidirect
2. C2×#449×C137C2semidirect
3. C2×#449×C137C2semidirect
4. C2×#442×C137C2semidirect
5. #2428×C137C2semidirect
6. #2339×C137C2semidirect
7. #2066×C137C2semidirect
8. #2034×C137C2semidirect
9. #2033×C137C2semidirect
10. #2014×C137C2semidirect
11. #1973×C137C2semidirect
12. #1924×C137C2semidirect
13. #1879×C137C2semidirect
14. #1877×C137C2semidirect
15. #1862×C137C2semidirect
94. C2×D8×C137D4semidirect
139. #102×C137D4semidirect
315. D4×C137#121semidirect
424. #25174C137direct (N × H)
425. C137#25174direct (N × H)
426. C2×#459C2×C137semidirect
427. C2×#449C2×C137semidirect
428. C2×#449C2×C137semidirect
429. C2×#442C2×C137semidirect
430. #2428C2×C137semidirect
431. #2339C2×C137semidirect
432. #2066C2×C137semidirect
433. #2034C2×C137semidirect
434. #2033C2×C137semidirect
435. #2014C2×C137semidirect
436. #1973C2×C137semidirect
437. #1924C2×C137semidirect
438. #1879C2×C137semidirect
439. #1877C2×C137semidirect
440. #1862C2×C137semidirect
519. C2×D8D4×C137semidirect
564. #102D4×C137semidirect
740. D4#121×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1372
C2×#449×C1372
C2×#442×C1372
#2428×C1372
#2339×C1372
#2066×C1372
#2034×C1372
#2033×C1372
#2014×C1372
#1973×C1372
#1924×C1372
#1879×C1372
#1877×C1372
#1862×C1372
#25174137