Finite Group Databasebeta

← #33104041

Subgroups — #33104041

Order 18688.

980 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988665C211yesmaximal, characteristic
2C2×#17988659C211yesmaximal, characteristic
3C2×#17988614C211yesmaximal, characteristic, complemented
4C2×#17988611C211yesmaximal, characteristic, complemented
5#22610655C211yesmaximal, characteristic, complemented
6#22610650C211yesmaximal, characteristic, complemented
7#22610116C211yesmaximal, characteristic, complemented
8#22610116C211yesmaximal, characteristic, complemented
9#22610116C211yesmaximal, characteristic, complemented
10#22610111C211yesmaximal, characteristic, complemented
11#22610085C211yesmaximal, characteristic, complemented
12#22609915C211yesmaximal, characteristic, complemented
13#22609911C211yesmaximal, characteristic, complemented
14#22609788C211yesmaximal, characteristic, complemented
15C73×#2290C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18C22×#11924012C2211yescharacteristic
19C23×#10596831C2211yescharacteristic
20#17988665—24no—
21#17988659—24no—
22#17988614—24no—
23#17988611—24no—
24C2×C4⋊#10596831C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×C4⋊#10596831C2211yescharacteristic
27C2×C4⋊#10596831C2211yescharacteristic
28C2×C4⋊#10596831C2211yescharacteristic
29C2×C4⋊#10596831C2211yescharacteristic
30C2×C4⋊#10596831C2211yescharacteristic
31C2×C4⋊#10596831C2211yescharacteristic
32C2×C4⋊#10596831C2211yescharacteristic
33C2×C4⋊#10596831C2211yescharacteristic
34C2×C4⋊#10596831C2211yescharacteristic
35C2×C4⋊#10596831C2211yescharacteristic
36C2×C22⋊#10596831C2211yescharacteristic
37C2×C22⋊#10596831C2211yescharacteristic
38C2×C22⋊#10596831C2211yescharacteristic
39C2×C22⋊#10596831C2211yescharacteristic
40C2×#14556502C2211yescharacteristic
41C2×C4×#10596831C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48C2×C4×D4×C73C2211yescharacteristic
49C2×#117×C73C2211yescharacteristic
50C22×C42×C73C2211yescharacteristic
51#388×C73C411yescharacteristic
52#388×C73C411yescharacteristic
53#387×C73C411yescharacteristic
54#387×C73C411yescharacteristic
55#386×C73C411yescharacteristic
56#386×C73C411yescharacteristic
57#385×C73C411yescharacteristic
58#385×C73C411yescharacteristic
59C4×C4⋊C4×C73C2211yescharacteristic
60C4×C22⋊C4×C73C2211yescharacteristic
61C4×C22⋊C4×C73C2211yescharacteristic
62#376×C73C2211yescharacteristic
63C2×#11924012—22no—
64C2×#11924012—22no—
65C2×#11924012—22no—
66C2×#11924012—22no—
67C2×#11924012—22no—
68C2×#11924012—22no—
69C2×#11924012—41no—
70C2×#11924012—41no—
71C2×#11924012—41no—
72C22×#10596831—22no—
73C22×#10596831—22no—
74C22×#10596831—41no—
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C22×#10596831C2311yescharacteristic
81C22×#10596831C2311yescharacteristic
82C22×#10596831C2311yescharacteristic
83C4⋊#10596831—22no—
84C4⋊#10596831—22no—
85C4⋊#10596831—22no—
86C4⋊#10596831—22no—
87C4⋊#10596831—22no—
88C4⋊#10596831—22no—
89C4⋊#10596831—22no—
90C4⋊#10596831—22no—
91C4⋊#10596831—22no—
92C4⋊#10596831—41no—
93C4⋊#10596831—41no—
94C4⋊#10596831D414yescomplemented
95C22⋊#10596831—22no—
96C22⋊#10596831—22no—
97C22⋊#10596831—22no—
98C22⋊#10596831—22no—
99#14556502—22no—
100C4×#10596831—22no—
101C22×D4×C73C2×C411yescharacteristic
102C23×C4×C73C2×C411yescharacteristic
103C23×C4×C73C2×C411yescharacteristic
104C23×C4×C73C2311yescharacteristic
105C23×C4×C73C2311yescharacteristic
106C4×D4×C73D414yes—
107C4×D4×C73Q814yes—
108#117×C73—22no—
109#117×C73—22no—
110C2×C4⋊C4×C73C2×C411yescharacteristic
111C2×C4⋊C4×C73C2×C411yescharacteristic
112C2×C4⋊C4×C73C2×C411yescharacteristic
113C2×C4⋊C4×C73C2×C411yescharacteristic
114C2×C4⋊C4×C73C2×C411yescharacteristic
115C2×C22⋊C4×C73C2×C411yescharacteristic
116C2×C22⋊C4×C73C2×C411yescharacteristic
117C2×C22⋊C4×C73C2×C411yescharacteristic
118C2×C22⋊C4×C73C2×C411yescharacteristic
119C2×C22⋊C4×C73C2×C411yescharacteristic
120C2×C22⋊C4×C73C2×C411yescharacteristic
121C2×C22⋊C4×C73C2×C411yescharacteristic
122C2×C22⋊C4×C73C2×C411yescharacteristic
123C2×C42×C73—22no—
124C2×C42×C73—22no—
125C2×C42×C73C2×C411yescharacteristic
126C2×C42×C73C2×C411yescharacteristic
127C2×C42×C73C2311yescharacteristic
128C2×C42×C73C2311yescharacteristic
129C2×C42×C73C2311yescharacteristic
130C2×C42×C73C2311yescharacteristic
131C2×C42×C73C2311yescharacteristic
132#95×C73C2×C411yescharacteristic
133#95×C73C2×C411yescharacteristic
134#95×C73C2×C411yescharacteristic
135#95×C73C2×C411yescharacteristic
136#95×C73C2×C411yescharacteristic
137#95×C73C2×C411yescharacteristic
138#95×C73C2×C411yescharacteristic
139#95×C73C2×C411yescharacteristic
140#95×C73C2×C411yescharacteristic
141#95×C73C2×C411yescharacteristic
142#11924012—44no—
143#11924012—44no—
144#11924012—44no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—44no—
168C2×#10596831C2×D412yes—
169C2×#10596831C2×D412yes—
170C24×C73C22×C411yescharacteristic
171C24×C73C22×C411yescharacteristic
172C2×D4×C73—41no—
173C2×D4×C73—41no—
174C2×D4×C73C4⋊C414yes—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—22no—
184C22×C4×C73—22no—
185C22×C4×C73—22no—
186C22×C4×C73—41no—
187C22×C4×C73—41no—
188C22×C4×C73—41no—
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C22×C411yescharacteristic
195C22×C4×C73C22×C411yescharacteristic
196C22×C4×C73C22×C411yescharacteristic
197C22×C4×C73C22×C411yescharacteristic
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200C22×C4×C73C22×C411yescharacteristic
201C22×C4×C73C2×D412yes—
202C22×C4×C73C2×D412yes—
203C22×C4×C73C2×Q812yes—
204C22×C4×C73C2×Q812yes—
205C22×C4×C73C2411yescharacteristic
206C4⋊C4×C73—22no—
207C4⋊C4×C73—22no—
208C4⋊C4×C73—22no—
209C4⋊C4×C73—41no—
210C4⋊C4×C73C4⋊C414yes—
211C22⋊C4×C73—22no—
212C22⋊C4×C73—22no—
213C22⋊C4×C73—22no—
214C22⋊C4×C73—41no—
215C22⋊C4×C73—41no—
216C22⋊C4×C73—41no—
217C22⋊C4×C73C4⋊C414yes—
218C22⋊C4×C73C4⋊C414yes—
219C42×C73—22no—
220C42×C73—22no—
221C42×C73—21no—
222C42×C73—21no—
223C42×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73C2×D412yes—
228C42×C73C2×D412yes—
229C42×C73C2×Q812yes—
230C42×C73#4112yes—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73C2×C4⋊C412yes—
244C23×C73C2×C4⋊C412yes—
245C23×C73C23×C411yescharacteristic
246D4×C73—44no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—44no—
285C2×C4×C73—44no—
286C2×C4×C73C2×C4⋊C412yes—
287C2×C4×C73C2×C4⋊C412yes—
288C2×C4×C73C2×C4⋊C412yes—
289C2×C4×C73C2×C4⋊C412yes—
290C2×C4×C73C4×D412yes—
291C2×C4×C73C4×D412yes—
292C2×C4×C73#13112yes—
293C2×C4×C73C22×D411yescharacteristic
294C2×C4×C73C22×D411yescharacteristic
295C2×C4×C73C22×Q811yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×C4×C73H(5,𝔽2)11yescharacteristic
298C2×C4×C732−1+411yescharacteristic
299#10596831—22no—
300#10596831—22no—
301#10596831—41no—
302#10596831—41no—
303#10596831—41no—
304#10596831—41no—
305#10596831—41no—
306#10596831—41no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—22no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—41no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73C22×C4⋊C411yescharacteristic
322C22×C73C2×C4×D411yescharacteristic
323C22×C73#52011yescharacteristic
324C22×C73C2×#13111yescharacteristic
325C22×C73#56811yescharacteristic
326C22×C73#56811yescharacteristic
327C22×C73#56811yescharacteristic
328C4×C73—22no—
329C4×C73—22no—
330C4×C73—22no—
331C4×C73—22no—
332C4×C73—22no—
333C4×C73—22no—
334C4×C73—22no—
335C4×C73—41no—
336C4×C73—41no—
337C4×C73—41no—
338C4×C73—41no—
339C4×C73—41no—
340C4×C73D4211yescharacteristic
341C4×C73#54711yescharacteristic
342C4×C73D4×Q811yescharacteristic
343C4×C73#55411yescharacteristic
344#22649—731nomaximal, Sylow
345C2×C73—42no—
346C2×C73—42no—
347C2×C73D4×C4⋊C411yescharacteristic
348C2×C73#290511yescharacteristic
349C2×C73#290611yescharacteristic
350C2×C73#293011yescharacteristic
351C2×C73#293311yescharacteristic
352C2×C73#299311yescharacteristic
353C2×C73#299511yescharacteristic
354C2×#436—731no—
355C2×#435—731no—
356C2×#424—731no—
357C2×#423—731no—
358#2290D7311yescharacteristic
359#1940—731no—
360#1939—731no—
361#1851—731no—
362#1851—731no—
363#1851—731no—
364#1850—731no—
365#1843—731no—
366#1798—731no—
367#1797—731no—
368#1768—731no—
369C73#2264911yescharacteristic, complemented, Sylow
370C22×M16—731no—
371C22×M16—731no—
372C22×M16—731no—
373C23×C8—731no—
374C2×C4×D4C2×D7311yescharacteristic
375C2×#117C2×D7311yescharacteristic
376C22×C42C2×D7311yescharacteristic
377#436—1464no—
378#435—1464no—
379#424—1464no—
380#423—1464no—
381C2×C4⋊C8—731no—
382C2×C4⋊C8—731no—
383C2×C4⋊C8—731no—
384C2×C4⋊C8—731no—
385C2×C4⋊C8—731no—
386C2×C4⋊C8—731no—
387C2×C4⋊C8—731no—
388C2×C4⋊C8—731no—
389C2×C4⋊C8—731no—
390C2×C4⋊C8—731no—
391C2×C4⋊C8—731no—
392C2×C4⋊C8—731no—
393C2×C22⋊C8—731no—
394C2×C22⋊C8—731no—
395C2×C22⋊C8—731no—
396C2×C22⋊C8—731no—
397C2×#97—731no—
398C2×C4×C8—731no—
399#388Dic7311yescharacteristic
400#388Dic7311yescharacteristic
401#387Dic7311yescharacteristic
402#387Dic7311yescharacteristic
403#386Dic7311yescharacteristic
404#386Dic7311yescharacteristic
405#385Dic7311yescharacteristic
406#385Dic7311yescharacteristic
407C4×C4⋊C4C2×D7311yescharacteristic
408C4×C22⋊C4C2×D7311yescharacteristic
409C4×C22⋊C4C2×D7311yescharacteristic
410#376C2×D7311yescharacteristic
411#336—731no—
412#336—731no—
413#336—731no—
414#336—731no—
415#336—731no—
416#336—731no—
417C22×D4C2×Dic7311yescharacteristic
418C23×C4C2×Dic7311yescharacteristic
419C23×C4C2×Dic7311yescharacteristic
420C23×C4C22×D7311yescharacteristic
421C23×C4C22×D7311yescharacteristic
422C2×M16—2921no—
423C2×M16—2921no—
424C2×M16—2921no—
425C2×M16—1462no—
426C2×M16—1462no—
427C2×M16—1462no—
428C2×M16—1462no—
429C2×M16—1462no—
430C2×M16—1462no—
431C22×C8—2921no—
432C22×C8—731no—
433C22×C8—731no—
434C22×C8—731no—
435C22×C8—731no—
436C22×C8—731no—
437C22×C8—731no—
438C22×C8—731no—
439C22×C8—731no—
440C22×C8—1462no—
441C22×C8—1462no—
442C4×D4Dic14614yes—
443C4×D4D29214yes—
444#117—22no—
445#117—22no—
446C2×C4⋊C4C2×Dic7311yescharacteristic
447C2×C4⋊C4C2×Dic7311yescharacteristic
448C2×C4⋊C4C2×Dic7311yescharacteristic
449C2×C4⋊C4C2×Dic7311yescharacteristic
450C2×C4⋊C4C2×Dic7311yescharacteristic
451C2×C22⋊C4C2×Dic7311yescharacteristic
452C2×C22⋊C4C2×Dic7311yescharacteristic
453C2×C22⋊C4C2×Dic7311yescharacteristic
454C2×C22⋊C4C2×Dic7311yescharacteristic
455C2×C22⋊C4C2×Dic7311yescharacteristic
456C2×C22⋊C4C2×Dic7311yescharacteristic
457C2×C22⋊C4C2×Dic7311yescharacteristic
458C2×C22⋊C4C2×Dic7311yescharacteristic
459C2×C42—22no—
460C2×C42—22no—
461C2×C42C2×Dic7311yescharacteristic
462C2×C42C2×Dic7311yescharacteristic
463C2×C42C22×D7311yescharacteristic
464C2×C42C22×D7311yescharacteristic
465C2×C42C22×D7311yescharacteristic
466C2×C42C22×D7311yescharacteristic
467C2×C42C22×D7311yescharacteristic
468C4⋊C8—2921no—
469C4⋊C8—2921no—
470C4⋊C8—734no—
471C4⋊C8—1462no—
472C4⋊C8—1462no—
473C4⋊C8—1462no—
474C4⋊C8—1462no—
475C4⋊C8—1462no—
476C4⋊C8—1462no—
477C4⋊C8—1462no—
478C4⋊C8—1462no—
479C4⋊C8—1462no—
480C22⋊C8—1462no—
481C22⋊C8—1462no—
482C22⋊C8—1462no—
483C22⋊C8—1462no—
484#97—1462no—
485C4×C8—1462no—
486#95C2×Dic7311yescharacteristic
487#95C2×Dic7311yescharacteristic
488#95C2×Dic7311yescharacteristic
489#95C2×Dic7311yescharacteristic
490#95C2×Dic7311yescharacteristic
491#95C2×Dic7311yescharacteristic
492#95C2×Dic7311yescharacteristic
493#95C2×Dic7311yescharacteristic
494#95C2×Dic7311yescharacteristic
495#95C2×Dic7311yescharacteristic
496C24C22×Dic7311yescharacteristic
497C24C22×Dic7311yescharacteristic
498C2×D4—41no—
499C2×D4—41no—
500C2×D4C4⋊Dic7314yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4C22×Dic7311yescharacteristic
516C22×C4C22×Dic7311yescharacteristic
517C22×C4C22×Dic7311yescharacteristic
518C22×C4C22×Dic7311yescharacteristic
519C22×C4C22×Dic7311yescharacteristic
520C22×C4C22×Dic7311yescharacteristic
521C22×C4C22×Dic7311yescharacteristic
522C22×C4C22×Dic7311yescharacteristic
523C22×C4C22×Dic7311yescharacteristic
524C22×C4C22×Dic7311yescharacteristic
525C22×C4C22×Dic7311yescharacteristic
526C22×C4C22×Dic7311yescharacteristic
527C22×C4C2×D29212yes—
528C22×C4C2×D29212yes—
529C22×C4C2×Dic14612yes—
530C22×C4C2×Dic14612yes—
531C22×C4C23×D7311yescharacteristic
532M16—2924no—
533M16—2924no—
534M16—2924no—
535C2×C8—2924no—
536C2×C8—732no—
537C2×C8—732no—
538C2×C8—1461no—
539C2×C8—1461no—
540C2×C8—1461no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8—1461no—
548C2×C8—1461no—
549C2×C8—1461no—
550C2×C8—1461no—
551C2×C8—1461no—
552C2×C8—1461no—
553C2×C8—1461no—
554C2×C8—1461no—
555C2×C8—1461no—
556C2×C8—1461no—
557C2×C8—1461no—
558C2×C8—1461no—
559C2×C8—1461no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—41no—
564C4⋊C4C4⋊Dic7314yes—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4C4⋊Dic7314yes—
572C22⋊C4C4⋊Dic7314yes—
573C42—22no—
574C42—22no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42D4×D7312yes—
582C42C2×D29212yes—
583C42C2×Dic14612yes—
584C42#1192402712yes—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23C2×C4⋊Dic7312yes—
598C23C2×C4⋊Dic7312yes—
599C23C23×Dic7311yescharacteristic
600D4—44no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4C2×C4⋊Dic7312yes—
641C2×C4C2×C4⋊Dic7312yes—
642C2×C4C2×C4⋊Dic7312yes—
643C2×C4C2×C4⋊Dic7312yes—
644C2×C4D4×Dic7312yes—
645C2×C4D4×Dic7312yes—
646C2×C4#1455659812yes—
647C2×C4C2×D4×D7311yescharacteristic
648C2×C4C22×D29211yescharacteristic
649C2×C4C22×Dic14611yescharacteristic
650C2×C4C2×#1192402711yescharacteristic
651C2×C4#1455663711yescharacteristic
652C2×C4#1455663811yescharacteristic
653C8—2921no—
654C8—2921no—
655C8—2921no—
656C8—2921no—
657C8—2921no—
658C8—2921no—
659C8—1462no—
660C8—1462no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22C22×C4⋊Dic7311yescharacteristic
676C22C2×D4×Dic7311yescharacteristic
677C22#1798907011yescharacteristic
678C22C2×#1455659811yescharacteristic
679C22#1798935411yescharacteristic
680C22#1798935411yescharacteristic
681C22#1798935411yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—41no—
690C4—41no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4D4×D29211yescharacteristic
695C4#1798924111yescharacteristic
696C4D4×Dic14611yescharacteristic
697C4#1798929411yescharacteristic
698C2—42no—
699C2—42no—
700C2D4×C4⋊Dic7311yescharacteristic
701C2#2261849511yescharacteristic
702C2#2261849911yescharacteristic
703C2#2261863511yescharacteristic
704C2#2261865811yescharacteristic
705C2#2261908011yescharacteristic
706C2#2261910111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#2290C2
prime radicalC22×D4×C73C2×C4
cosocleC22×C4×C73C24
hypercenter#2290D73
hypocenterC73#22649
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
3. C2×#17988614C2semidirect
4. C2×#17988611C2semidirect
5. #22610655C2semidirect
6. #22610650C2semidirect
7. #22610116C2semidirect
8. #22610116C2semidirect
9. #22610116C2semidirect
10. #22610111C2semidirect
11. #22610085C2semidirect
12. #22609915C2semidirect
13. #22609911C2semidirect
14. #22609788C2semidirect
94. C4⋊#10596831D4semidirect
369. C73#22649semidirect

Maximal subgroups

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

subgroupindex
C2×#179886652
C2×#179886592
C2×#179886142
C2×#179886112
#226106552
#226106502
#226101162
#226101112
#226100852
#226099152
#226099112
#226097882
C73×#22902
#2264973