Finite Group Databasebeta

← #34034648

Subgroups — #34034648

Order 18688.

756 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22627080C211yesmaximal, characteristic, complemented
2#22627079C211yesmaximal, characteristic
3#22627079C211yesmaximal, characteristic
4#22627079C211yesmaximal, characteristic
5#22627078C211yesmaximal, characteristic, complemented
6#22627078C211yesmaximal, characteristic, complemented
7#22627078C211yesmaximal, characteristic, complemented
8#22627076C211yesmaximal, characteristic
9C4⋊C4×#10596842C211yesmaximal, characteristic, complemented
10C4⋊C4×#10596842C211yesmaximal, characteristic, complemented
11C4×C4⋊#10596842C211yesmaximal, characteristic, complemented
12C22⋊C4×#10596842C211yesmaximal, characteristic
13C22⋊C4×#10596842C211yesmaximal, characteristic
14#22627065C211yesmaximal, characteristic, complemented
15#126×#64408C211yesmaximal, characteristic
16C23×#10596842C2211yescharacteristic
17C2×C4⋊#10596842C2211yescharacteristic
18C2×C4⋊#10596842C2211yescharacteristic
19C2×C4⋊#10596842C2211yescharacteristic
20C2×C4⋊#10596842C2211yescharacteristic
21C2×C4⋊#10596842C2211yescharacteristic
22C2×C22⋊#10596842C2211yescharacteristic
23C2×C22⋊#10596842C2211yescharacteristic
24C2×C22⋊#10596842C2211yescharacteristic
25C2×C4×#10596842C2211yescharacteristic
26C2×C4×#10596842C2211yescharacteristic
27C2×C4×#10596842C2211yescharacteristic
28C2×C4×#10596842C2211yescharacteristic
29C2×C4×#10596842C2211yescharacteristic
30C2×C4×#10596842C2211yescharacteristic
31C2×C4×#10596842C2211yescharacteristic
32(C2×#10596842)⋊C4C2211yescharacteristic
33(C2×#10596842)⋊C4C2211yescharacteristic
34(C2×#10596842)⋊C4C2211yescharacteristic
35(C2×#10596842)⋊C4C2211yescharacteristic
36(C2×#10596842)⋊C4C2211yescharacteristic
37(C2×#10596842)⋊C4C2211yescharacteristic
38(C2×#10596842)⋊C4C2211yescharacteristic
39(C2×#10596842)⋊C4C2211yescharacteristic
40(C2×#10596842)⋊C4C2211yescharacteristic
41(C2×#10596842)⋊C4C2211yescharacteristic
42(C2×#10596842)⋊C4C2211yescharacteristic
43(C2×#10596842)⋊C4C2211yescharacteristic
44#17989537C411yescharacteristic
45#17989537C411yescharacteristic
46#17989537C411yescharacteristic
47#17989536C411yescharacteristic
48#17989536C411yescharacteristic
49#17989536C411yescharacteristic
50#17989532C411yescharacteristic
51C4⋊C4×#64408C2211yescharacteristic
52C4⋊C4×#64408C2211yescharacteristic
53C4⋊C4×#64408C2211yescharacteristic
54C22⋊C4×#64408C2211yescharacteristic
55C22⋊C4×#64408C2211yescharacteristic
56C22⋊C4×#64408C2211yescharacteristic
57C42×#64408C2211yescharacteristic
58#126×D73C411yescharacteristic
59C22×#10596842—22no—
60C22×#10596842—22no—
61C22×#10596842—41no—
62C22×#10596842C2311yescharacteristic
63C22×#10596842C2311yescharacteristic
64C22×#10596842C2311yescharacteristic
65C22×#10596842C2311yescharacteristic
66C22×#10596842C2311yescharacteristic
67C22×#10596842C2311yescharacteristic
68C22×#10596842C2311yescharacteristic
69C22×#10596842C2311yescharacteristic
70C4⋊#10596842—22no—
71C4⋊#10596842—22no—
72C4⋊#10596842—22no—
73C4⋊#10596842—22no—
74C4⋊#10596842—41no—
75C22⋊#10596842—22no—
76C22⋊#10596842—22no—
77C22⋊#10596842—41no—
78C4×#10596842—22no—
79C4×#10596842—22no—
80C4×#10596842—22no—
81C4×#10596842—22no—
82C4×#10596842—41no—
83C4×#10596842—41no—
84C4×#10596842—41no—
85C23×#64408C2311yescharacteristic
86C2×C4⋊#64408C2×C411yescharacteristic
87C2×C4⋊#64408C2×C411yescharacteristic
88C2×C4⋊#64408C2×C411yescharacteristic
89C2×C22⋊#64408C2×C411yescharacteristic
90C2×C22⋊#64408C2×C411yescharacteristic
91C2×C22⋊#64408C2×C411yescharacteristic
92C2×C4×#64408C2×C411yescharacteristic
93C2×C4×#64408C2×C411yescharacteristic
94C2×C4×#64408C2×C411yescharacteristic
95C2×C4×#64408C2311yescharacteristic
96C2×C4×#64408C2311yescharacteristic
97C2×C4×#64408C2311yescharacteristic
98C2×C4×#64408C2311yescharacteristic
99C2×C4×#64408C2311yescharacteristic
100C2×C4×#64408C2311yescharacteristic
101(C2×#64408)⋊C4C2×C411yescharacteristic
102(C2×#64408)⋊C4C2×C411yescharacteristic
103(C2×#64408)⋊C4C2×C411yescharacteristic
104(C2×#64408)⋊C4C2×C411yescharacteristic
105(C2×#64408)⋊C4C2×C411yescharacteristic
106(C2×#64408)⋊C4C2×C411yescharacteristic
107(C2×#64408)⋊C4C2×C411yescharacteristic
108(C2×#64408)⋊C4C2×C411yescharacteristic
109(C2×#64408)⋊C4C2×C411yescharacteristic
110(C2×#64408)⋊C4C2×C411yescharacteristic
111(C2×#64408)⋊C4C2×C411yescharacteristic
112(C2×#64408)⋊C4C2×C411yescharacteristic
113#14556586C811yescharacteristic, complemented
114#14556586C811yescharacteristic, complemented
115#14556586C811yescharacteristic, complemented
116#14556585C811yescharacteristic, complemented
117#14556584C811yescharacteristic, complemented
118#14556584C811yescharacteristic, complemented
119#14556584C811yescharacteristic, complemented
120C4⋊C4×D73C2×C411yescharacteristic
121C4⋊C4×D73C2×C411yescharacteristic
122C4⋊C4×D73C2×C411yescharacteristic
123C22⋊C4×D73C2×C411yescharacteristic
124C22⋊C4×D73C2×C411yescharacteristic
125C22⋊C4×D73C2×C411yescharacteristic
126C42×D73C2×C411yescharacteristic
127#126×C73C811yescharacteristic, complemented
128C2×#10596842—21no—
129C2×#10596842—21no—
130C2×#10596842—21no—
131C2×#10596842—21no—
132C2×#10596842—21no—
133C2×#10596842—21no—
134C2×#10596842—21no—
135C2×#10596842—21no—
136C2×#10596842—21no—
137C2×#10596842—21no—
138C2×#10596842—21no—
139C2×#10596842—21no—
140C2×#10596842—21no—
141C2×#10596842—21no—
142C2×#10596842—21no—
143C2×#10596842—21no—
144C2×#10596842—21no—
145C2×#10596842—21no—
146C2×#10596842—21no—
147C2×#10596842—21no—
148C2×#10596842—44no—
149C2×#10596842#4112yes—
150C2×#10596842#4112yes—
151C2×#10596842#4112yes—
152C2×#10596842#4112yes—
153C22×#64408—21no—
154C22×#64408—21no—
155C22×#64408—21no—
156C22×#64408—21no—
157C22×#64408—21no—
158C22×#64408—21no—
159C22×#64408C22×C411yescharacteristic
160C22×#64408C22×C411yescharacteristic
161C22×#64408C22×C411yescharacteristic
162C22×#64408C22×C411yescharacteristic
163C22×#64408C22×C411yescharacteristic
164C22×#64408C22×C411yescharacteristic
165C22×#64408C22×C411yescharacteristic
166C22×#64408C2411yescharacteristic
167C4⋊#64408—22no—
168C4⋊#64408—22no—
169C4⋊#64408—41no—
170C22⋊#64408—22no—
171C22⋊#64408—22no—
172C22⋊#64408—41no—
173C4×#64408—22no—
174C4×#64408—22no—
175C4×#64408—21no—
176C4×#64408—21no—
177C4×#64408—21no—
178C4×#64408—21no—
179C4×#64408—21no—
180C4×#64408—21no—
181C4×#64408—21no—
182C4×#64408—21no—
183C4×#64408—21no—
184C4×#64408—21no—
185C4×#64408—21no—
186C4×#64408—21no—
187C4×#64408—41no—
188C23×D73C22×C411yescharacteristic
189C2×C4×D73C22×C411yescharacteristic
190C2×C4×D73C22×C411yescharacteristic
191C2×C4×D73C22×C411yescharacteristic
192C2×C4×D73C22×C411yescharacteristic
193C2×C4×D73C22×C411yescharacteristic
194C2×C4×D73C22×C411yescharacteristic
195C4⋊Dic73C2×C811yescharacteristic, complemented
196C4⋊Dic73C2×C811yescharacteristic, complemented
197C4⋊Dic73C2×C811yescharacteristic, complemented
198#11924007C2×C811yescharacteristic, complemented
199#11924007C2×C811yescharacteristic, complemented
200#11924007C2×C811yescharacteristic, complemented
201#11924007C2×C811yescharacteristic, complemented
202#11924007C2×C811yescharacteristic, complemented
203#11924007C2×C811yescharacteristic, complemented
204C22⋊Dic73C2×C811yescharacteristic
205C22⋊Dic73C2×C811yescharacteristic
206C22⋊Dic73C2×C811yescharacteristic
207#11924005C2×C811yescharacteristic
208#11924005C2×C811yescharacteristic
209#11924005C2×C811yescharacteristic
210#11924005C2×C811yescharacteristic
211#11924005C2×C811yescharacteristic
212#11924005C2×C811yescharacteristic
213C4×Dic73C2×C811yescharacteristic, complemented
214C4×Dic73C2×C811yescharacteristic, complemented
215C4×Dic73C2×C811yescharacteristic, complemented
216C4⋊C4×C73C2×C811yescharacteristic, complemented
217C4⋊C4×C73C2×C811yescharacteristic, complemented
218C4⋊C4×C73C2×C811yescharacteristic, complemented
219C22⋊C4×C73C2×C811yescharacteristic
220C22⋊C4×C73C2×C811yescharacteristic
221C22⋊C4×C73C2×C811yescharacteristic
222C42×C73C2×C811yescharacteristic, complemented
223C23×C73C22×C811yescharacteristic
224C22×D73—21no—
225C22×D73—21no—
226C22×D73—21no—
227C22×D73—21no—
228C22×D73—21no—
229C22×D73—21no—
230C22×D73C22×C811yescharacteristic
231C22×D73C23×C411yescharacteristic
232C2×#64408—21no—
233C2×#64408—21no—
234C2×#64408—21no—
235C2×#64408—21no—
236C2×#64408—21no—
237C2×#64408—21no—
238C2×#64408—21no—
239C2×#64408—21no—
240C2×#64408—21no—
241C2×#64408—21no—
242C2×#64408—21no—
243C2×#64408—21no—
244C2×#64408—21no—
245C2×#64408—21no—
246C2×#64408—21no—
247C2×#64408—21no—
248C2×#64408—21no—
249C2×#64408—21no—
250C2×#64408—21no—
251C2×#64408—41no—
252C2×#64408—41no—
253C2×#64408—41no—
254C2×#64408—41no—
255C2×#64408#13112yes—
256C2×#64408#13112yes—
257C2×#64408C2×#4111yescharacteristic
258C2×#64408C2×#4111yescharacteristic
259C2×#64408C2×#4111yescharacteristic
260C2×#64408C2×#4111yescharacteristic
261C2×#64408H(5,𝔽2)11yescharacteristic
262C2×#644082−1+411yescharacteristic
263#10596842—22no—
264#10596842—22no—
265#10596842—22no—
266#10596842—22no—
267#10596842—41no—
268#10596842—41no—
269#10596842—41no—
270#10596842—41no—
271C2×C4×C73C22×C811yescharacteristic
272C2×C4×C73C22×C811yescharacteristic
273C2×C4×C73C22×C811yescharacteristic
274C2×C4×C73C22×C811yescharacteristic
275C2×C4×C73C22×C811yescharacteristic
276C2×C4×C73C22×C811yescharacteristic
277C2×Dic73C22×C811yescharacteristic
278C2×Dic73C22×C811yescharacteristic
279C2×Dic73C22×C811yescharacteristic
280C2×Dic73C22×C811yescharacteristic
281C2×Dic73C22×C811yescharacteristic
282C2×Dic73C22×C811yescharacteristic
283C4×D73—21no—
284C4×D73—21no—
285C4×D73—21no—
286C4×D73—21no—
287C4×D73—21no—
288C4×D73—21no—
289C4×D73—21no—
290C4×D73—21no—
291C4×D73—21no—
292C4×D73—21no—
293C4×D73—21no—
294C4×D73—21no—
295C22×C73—21no—
296C22×C73—21no—
297C22×C73—21no—
298C22×C73C23×C811yescharacteristic
299C2×D73—21no—
300C2×D73—21no—
301C2×D73—21no—
302C2×D73—41no—
303C2×D73—41no—
304C2×D73—41no—
305C2×D73—41no—
306C2×D73C4×#4111yescharacteristic
307C2×D73C4×#4111yescharacteristic
308C2×D73#52011yescharacteristic
309C2×D73C2×#13111yescharacteristic
310C2×D73C2×#13111yescharacteristic
311C2×D73#56811yescharacteristic
312#64408—22no—
313#64408—22no—
314#64408—41no—
315#64408—41no—
316#64408—41no—
317#64408—41no—
318#64408—41no—
319#64408#55111yescharacteristic
320#64408#55211yescharacteristic
321#64408#55311yescharacteristic
322#64408#55611yescharacteristic
323C4×C73—21no—
324C4×C73—21no—
325C4×C73—21no—
326C4×C73—21no—
327C4×C73—21no—
328C4×C73—21no—
329Dic73—21no—
330Dic73—21no—
331Dic73—21no—
332Dic73—21no—
333Dic73—21no—
334Dic73—21no—
335#23278—731nomaximal, Sylow
336C2×C73—41no—
337C2×C73C8×#4111yescharacteristic
338C2×C73C8×#4111yescharacteristic
339C2×C73#298811yescharacteristic
340D73—41no—
341D73#237311yescharacteristic
342D73#296811yescharacteristic
343D73#296911yescharacteristic
344D73#299411yescharacteristic
345C4×#126—731no—
346#1939—731no—
347#1923—731no—
348#1923—731no—
349#1923—731no—
350#1916—731no—
351#1916—731no—
352#1916—731no—
353#1850—731no—
354C8×C4⋊C4—731no—
355C8×C4⋊C4—731no—
356C4×C4⋊C8—731no—
357C8×C22⋊C4—731no—
358C8×C22⋊C4—731no—
359#1744—731no—
360C73#2327811yescharacteristic, complemented, Sylow
361C23×C8—731no—
362C2×#126—731no—
363C2×C4⋊C8—731no—
364C2×C4⋊C8—731no—
365C2×C4⋊C8—731no—
366C2×C4⋊C8—731no—
367C2×C4⋊C8—731no—
368C2×C22⋊C8—731no—
369C2×C22⋊C8—731no—
370C2×C22⋊C8—731no—
371C2×C4×C8—731no—
372C2×C4×C8—731no—
373C2×C4×C8—731no—
374C2×C4×C8—731no—
375C2×C4×C8—731no—
376C2×C4×C8—731no—
377C2×C4×C8—731no—
378#388—731no—
379#388—731no—
380#388—731no—
381#387—731no—
382#387—731no—
383#387—731no—
384#383—731no—
385C4×C4⋊C4—731no—
386C4×C4⋊C4—731no—
387C4×C4⋊C4—731no—
388C4×C22⋊C4—731no—
389C4×C22⋊C4—731no—
390C4×C22⋊C4—731no—
391C43—731no—
392#336—731no—
393#336—731no—
394#336—731no—
395#336—731no—
396#336—731no—
397#336—731no—
398#336—731no—
399#336—731no—
400#336—731no—
401#336—731no—
402#336—731no—
403#336—731no—
404C23×C4—731no—
405C22×C8—2921no—
406C22×C8—731no—
407C22×C8—731no—
408C22×C8—731no—
409C22×C8—731no—
410C22×C8—731no—
411C22×C8—731no—
412C22×C8—731no—
413C22×C8—731no—
414C22×C8—1462no—
415C22×C8—1462no—
416#126—731no—
417#126—731no—
418#126—731no—
419#126—731no—
420#126—731no—
421#126—731no—
422#126—731no—
423#126#1059684211yescharacteristic, complemented
424C2×C4⋊C4—731no—
425C2×C4⋊C4—731no—
426C2×C4⋊C4—731no—
427C2×C4⋊C4—731no—
428C2×C4⋊C4—731no—
429C2×C4⋊C4—731no—
430C2×C22⋊C4—731no—
431C2×C22⋊C4—731no—
432C2×C22⋊C4—731no—
433C2×C22⋊C4—731no—
434C2×C22⋊C4—731no—
435C2×C22⋊C4—731no—
436C2×C42—731no—
437C2×C42—731no—
438C2×C42—731no—
439C2×C42—731no—
440C2×C42—731no—
441C2×C42—731no—
442C2×C42—731no—
443C2×C42—731no—
444C2×C42—731no—
445C2×C42—731no—
446C4⋊C8—2921no—
447C4⋊C8—1462no—
448C4⋊C8—1462no—
449C4⋊C8—1462no—
450C4⋊C8—1462no—
451C22⋊C8—2921no—
452C22⋊C8—1462no—
453C22⋊C8—1462no—
454C4×C8—2921no—
455C4×C8—2921no—
456C4×C8—2921no—
457C4×C8—1462no—
458C4×C8—1462no—
459C4×C8—1462no—
460C4×C8—1462no—
461#95—731no—
462#95—731no—
463#95—731no—
464#95—731no—
465#95—731no—
466#95—731no—
467#95—731no—
468#95—731no—
469#95—731no—
470#95—731no—
471#95—731no—
472#95—731no—
473C24—731no—
474C22×C4—731no—
475C22×C4—731no—
476C22×C4—731no—
477C22×C4—731no—
478C22×C4—731no—
479C22×C4—731no—
480C22×C4—731no—
481C22×C4—731no—
482C22×C4—731no—
483C22×C4—731no—
484C22×C4—731no—
485C22×C4—731no—
486C22×C4—731no—
487C22×C4—731no—
488C22×C4—1461no—
489C22×C4—1461no—
490C22×C4—1461no—
491C22×C4—1461no—
492C22×C4—1461no—
493C22×C4—1461no—
494C2×C8—2924no—
495C2×C8—732no—
496C2×C8—732no—
497C2×C8—732no—
498C2×C8—732no—
499C2×C8—1461no—
500C2×C8—1461no—
501C2×C8—1461no—
502C2×C8—1461no—
503C2×C8—1461no—
504C2×C8—1461no—
505C2×C8—1461no—
506C2×C8—1461no—
507C2×C8—1461no—
508C2×C8—1461no—
509C2×C8—1461no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C4⋊C4—2921no—
520C4⋊C4—731no—
521C4⋊C4—731no—
522C4⋊C4—731no—
523C4⋊C4—731no—
524C4⋊C4—731no—
525C4⋊C4—731no—
526C4⋊C4—731no—
527C4⋊C4—731no—
528C4⋊C4—731no—
529C4⋊C4—1462no—
530C4⋊C4—1462no—
531C4⋊C4C2×#1059684211yescharacteristic, complemented
532C4⋊C4C2×#1059684211yescharacteristic, complemented
533C4⋊C4C2×#1059684211yescharacteristic, complemented
534C22⋊C4—2921no—
535C22⋊C4—731no—
536C22⋊C4—731no—
537C22⋊C4—731no—
538C22⋊C4—731no—
539C22⋊C4—731no—
540C22⋊C4—731no—
541C22⋊C4—731no—
542C22⋊C4—731no—
543C22⋊C4—731no—
544C22⋊C4—1462no—
545C22⋊C4—1462no—
546C22⋊C4C2×#1059684211yescharacteristic
547C22⋊C4C2×#1059684211yescharacteristic
548C22⋊C4C2×#1059684211yescharacteristic
549C42—2921no—
550C42—731no—
551C42—731no—
552C42—731no—
553C42—1461no—
554C42—1461no—
555C42—1461no—
556C42—1461no—
557C42—1461no—
558C42—1461no—
559C42—1461no—
560C42—1461no—
561C42—1461no—
562C42—1461no—
563C42—1461no—
564C42—1461no—
565C42—1462no—
566C42—1462no—
567C42C2×#1059684211yescharacteristic, complemented
568C23—731no—
569C23—731no—
570C23—1461no—
571C23—1461no—
572C23—1461no—
573C23—1461no—
574C23—1461no—
575C23—1461no—
576C23C22×#1059684211yescharacteristic
577C2×C4—2921no—
578C2×C4—2921no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—731no—
582C2×C4—731no—
583C2×C4—731no—
584C2×C4—731no—
585C2×C4—731no—
586C2×C4—731no—
587C2×C4—732no—
588C2×C4—732no—
589C2×C4—731no—
590C2×C4—731no—
591C2×C4—731no—
592C2×C4—731no—
593C2×C4—731no—
594C2×C4—731no—
595C2×C4—1461no—
596C2×C4—1461no—
597C2×C4—1461no—
598C2×C4—1461no—
599C2×C4—1461no—
600C2×C4—1461no—
601C2×C4—1461no—
602C2×C4—1461no—
603C2×C4—1461no—
604C2×C4—1461no—
605C2×C4—1461no—
606C2×C4—1461no—
607C2×C4—1461no—
608C2×C4—1461no—
609C2×C4—1461no—
610C2×C4—1461no—
611C2×C4—1461no—
612C2×C4—1461no—
613C2×C4—1461no—
614C2×C4—1461no—
615C2×C4—1461no—
616C2×C4—1461no—
617C2×C4—1461no—
618C2×C4—1461no—
619C2×C4—1461no—
620C2×C4—1461no—
621C2×C4—1461no—
622C2×C4—1461no—
623C2×C4—1461no—
624C2×C4—1461no—
625C2×C4—1461no—
626C2×C4C22×#1059684211yescharacteristic
627C2×C4C22×#1059684211yescharacteristic
628C2×C4C22×#1059684211yescharacteristic
629C2×C4C22×#1059684211yescharacteristic
630C2×C4C22×#1059684211yescharacteristic
631C2×C4C22×#1059684211yescharacteristic
632C8—2921no—
633C8—2921no—
634C8—2921no—
635C8—2921no—
636C8—1462no—
637C8—1462no—
638C8—1462no—
639C8—1462no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—2921no—
644C22—2921no—
645C22—2921no—
646C22—2921no—
647C22—731no—
648C22—731no—
649C22—731no—
650C22—731no—
651C22—731no—
652C22—731no—
653C22—1461no—
654C22—1461no—
655C22—1461no—
656C22C23×#1059684211yescharacteristic
657C4—21no—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—21no—
662C4—21no—
663C4—2921no—
664C4—2921no—
665C4—2921no—
666C4—2921no—
667C4—2921no—
668C4—731no—
669C4—731no—
670C4—731no—
671C4—731no—
672C4—1462no—
673C4—1462no—
674C4—1461no—
675C4—1461no—
676C4—1461no—
677C4—1461no—
678C4—1461no—
679C4—1461no—
680C2—41no—
681C2—2921no—
682C2—731no—
683C2—731no—
684C2—731no—
685C2—731no—
686C2#41×#1059684211yescharacteristic
687C2#41×#1059684211yescharacteristic
688C2#2262717511yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10596842
commutator, socleC22×C73C23×C8
Fitting#126×C73C8
prime radicalC23×D73C22×C4
cosocleC22×#64408C24
hypercenter#126#10596842
hypocenterC73#23278
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #22627080C2semidirect
5. #22627078C2semidirect
6. #22627078C2semidirect
7. #22627078C2semidirect
9. C4⋊C4×#10596842C2semidirect
10. C4⋊C4×#10596842C2semidirect
11. C4×C4⋊#10596842C2semidirect
14. #22627065C2semidirect
113. #14556586C8semidirect
114. #14556586C8semidirect
115. #14556586C8semidirect
116. #14556585C8semidirect
117. #14556584C8semidirect
118. #14556584C8semidirect
119. #14556584C8semidirect
127. #126×C73C8semidirect
195. C4⋊Dic73C2×C8semidirect
196. C4⋊Dic73C2×C8semidirect
197. C4⋊Dic73C2×C8semidirect
198. #11924007C2×C8semidirect
199. #11924007C2×C8semidirect
200. #11924007C2×C8semidirect
201. #11924007C2×C8semidirect
202. #11924007C2×C8semidirect
203. #11924007C2×C8semidirect
213. C4×Dic73C2×C8semidirect
214. C4×Dic73C2×C8semidirect
215. C4×Dic73C2×C8semidirect
216. C4⋊C4×C73C2×C8semidirect
217. C4⋊C4×C73C2×C8semidirect
218. C4⋊C4×C73C2×C8semidirect
222. C42×C73C2×C8semidirect
360. C73#23278semidirect
423. #126#10596842semidirect
531. C4⋊C4C2×#10596842semidirect
532. C4⋊C4C2×#10596842semidirect
533. C4⋊C4C2×#10596842semidirect
567. C42C2×#10596842semidirect

Maximal subgroups

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

subgroupindex
#226270802
#226270792
#226270782
#226270762
C4⋊C4×#105968422
C4×C4⋊#105968422
C22⋊C4×#105968422
#226270652
#126×#644082
#2327873