Finite Group Databasebeta

← #33102044

Subgroups — #33102044

Order 18688.

1202 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989121C211yesmaximal, characteristic
2C2×#17988658C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D73C211yesmaximal, characteristic, complemented
4#22610869C211yesmaximal, characteristic, complemented
5#22610865C211yesmaximal, characteristic, complemented
6#22610227C211yesmaximal, characteristic, complemented
7#22610223C211yesmaximal, characteristic, complemented
8#22610223C211yesmaximal, characteristic, complemented
9#22610222C211yesmaximal, characteristic, complemented
10#22610001C211yesmaximal, characteristic, complemented
11#22609999C211yesmaximal, characteristic, complemented
12#22609914C211yesmaximal, characteristic, complemented
13#22609696C211yesmaximal, characteristic, complemented
14#22609626C211yesmaximal, characteristic, complemented
15C2×#336×C73C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18#17989121—24no—
19#17989121—24no—
20C2×#14556585C411yescharacteristic
21C2×#14556585C411yescharacteristic
22C2×#14556583C411yescharacteristic
23C2×#14556579C411yescharacteristic
24C2×#14556574C411yescharacteristic
25C2×#14556574C411yescharacteristic
26C2×#14556570C411yescharacteristic
27C2×#14556565C411yescharacteristic
28C2×C4×Dic146C2211yescharacteristic
29C2×C4×D292C2211yescharacteristic
30C2×C4×C22⋊D73C2211yescharacteristic
31C2×C4×C22⋊D73C2211yescharacteristic
32C2×#14556548C2211yescharacteristic
33C2×#14556548C2211yescharacteristic
34#17988658—24no—
35C8×C22⋊D73—24no—
36C2×#14556520C2211yescharacteristic
37C2×#14556520C2211yescharacteristic
38C2×C22⋊#10596831C2211yescharacteristic
39C2×C22⋊#10596831C2211yescharacteristic
40C2×#14556503C2211yescharacteristic
41C2×#14556503C2211yescharacteristic
42C2×#14556503C2211yescharacteristic
43C2×#14556503C2211yescharacteristic
44C2×#14556503C2211yescharacteristic
45C2×#14556503C2211yescharacteristic
46C2×#14556501C2211yescharacteristic
47C2×C8×Dic73C2211yescharacteristic
48#17988342C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51#17988342C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55#17988341C2211yescharacteristic
56C23×C8×C73C2211yescharacteristic
57C23×C8×C73C2211yescharacteristic
58C22×C42×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C22×Dic146C2×C411yescharacteristic
64C22×D292C2×C411yescharacteristic
65C22×C22⋊D73C2×C411yescharacteristic
66C22×C22⋊D73C2×C411yescharacteristic
67C22×C4×D73C2311yescharacteristic
68C22×C4×D73C2311yescharacteristic
69C2×#11924011—22no—
70C2×#11924011—22no—
71C2×#11924011—41no—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C2×C8×D73—22no—
77C2×C8×D73—22no—
78C2×C8×D73—41no—
79#14556585—24no—
80#14556585—24no—
81#14556583—24no—
82#14556579—24no—
83#14556574—24no—
84#14556574—24no—
85#14556570—24no—
86#14556565—24no—
87C4×Dic146—22no—
88C4×Dic146—22no—
89C4×D292—22no—
90C4×D292—22no—
91C4×C22⋊D73—22no—
92C4×C22⋊D73—22no—
93C4×C22⋊D73D414yes—
94C4×C22⋊D73D414yes—
95#14556548—22no—
96#14556548—22no—
97#14556548—22no—
98#14556548—22no—
99C2×C4⋊Dic73C2×C411yescharacteristic
100C2×C4⋊Dic73C2×C411yescharacteristic
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×#11924007C2×C411yescharacteristic
104C2×#11924007C2×C411yescharacteristic
105C2×#11924007C2×C411yescharacteristic
106C2×#11924007C2×C411yescharacteristic
107C2×#11924007C2×C411yescharacteristic
108C2×#11924007C2×C411yescharacteristic
109C2×C22⋊Dic73C2×C411yescharacteristic
110C2×C22⋊Dic73C2×C411yescharacteristic
111C2×#11924005C2×C411yescharacteristic
112C2×#11924005C2×C411yescharacteristic
113C2×#11924005C2×C411yescharacteristic
114C2×#11924005C2×C411yescharacteristic
115C2×#11924005C2×C411yescharacteristic
116C2×#11924005C2×C411yescharacteristic
117C2×#11924005C2×C411yescharacteristic
118C2×#11924005C2×C411yescharacteristic
119C2×C4×Dic73C2311yescharacteristic
120C2×C4×Dic73C2311yescharacteristic
121#14556520—22no—
122#14556520—22no—
123C22⋊#10596831—22no—
124C22⋊#10596831—22no—
125#14556503—22no—
126#14556503—22no—
127#14556503—22no—
128#14556503—22no—
129#14556503—41no—
130#14556503—41no—
131#14556501—22no—
132C8×Dic73—22no—
133C23×C4×C73C2×C411yescharacteristic
134C23×C4×C73C2×C411yescharacteristic
135C23×C4×C73C2311yescharacteristic
136C22×C8×C73—22no—
137C22×C8×C73—22no—
138C22×C8×C73—22no—
139C22×C8×C73—22no—
140C22×C8×C73—41no—
141C22×C8×C73—41no—
142C22×C8×C73C2311yescharacteristic
143C22×C8×C73C2311yescharacteristic
144C22×C8×C73C2311yescharacteristic
145C22×C8×C73C2311yescharacteristic
146C2×C42×C73—22no—
147C2×C42×C73—22no—
148C2×C42×C73C2×C411yescharacteristic
149C2×C42×C73C2×C411yescharacteristic
150C2×C42×C73C2311yescharacteristic
151C2×C42×C73C2311yescharacteristic
152C23×D73C22×C411yescharacteristic
153C23×D73C22×C411yescharacteristic
154C2×Dic146—22no—
155C2×Dic146—22no—
156C2×Dic146—41no—
157C2×D292—22no—
158C2×D292—22no—
159C2×D292—41no—
160C2×C22⋊D73—22no—
161C2×C22⋊D73—22no—
162C2×C22⋊D73—22no—
163C2×C22⋊D73—22no—
164C2×C22⋊D73—22no—
165C2×C22⋊D73C22⋊C414yes—
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C22×C411yescharacteristic
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C22×C411yescharacteristic
171C22×Dic73C22×C411yescharacteristic
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—21no—
176C2×C4×D73—21no—
177C2×C4×D73—21no—
178C2×C4×D73—21no—
179C2×C4×D73—21no—
180C2×C4×D73—21no—
181C2×C4×D73—21no—
182C2×C4×D73C2×D412yes—
183C2×C4×D73C2×D412yes—
184#11924011—44no—
185C2×#10596831—21no—
186C2×#10596831—21no—
187C2×#10596831—21no—
188C2×#10596831—21no—
189C2×#10596831—21no—
190C2×#10596831—21no—
191C2×#10596831—21no—
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C8×D73—44no—
198C4⋊Dic73—22no—
199C4⋊Dic73—22no—
200#11924007—22no—
201#11924007—22no—
202#11924007—22no—
203#11924007—22no—
204#11924007—22no—
205#11924007—22no—
206#11924007—22no—
207#11924007C22⋊C414yes—
208C22⋊Dic73—22no—
209C22⋊Dic73C22⋊C414yes—
210#11924005—22no—
211#11924005—22no—
212#11924005—22no—
213#11924005—22no—
214#11924005—22no—
215#11924005—22no—
216#11924005—22no—
217#11924005C22⋊C414yes—
218C4×Dic73—21no—
219C4×Dic73—21no—
220C4×Dic73C2×D412yes—
221C4×Dic73C2×D412yes—
222C24×C73C22×C411yescharacteristic
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73—22no—
232C22×C4×C73—41no—
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C22×C411yescharacteristic
236C22×C4×C73C22×C411yescharacteristic
237C22×C4×C73C22×C411yescharacteristic
238C22×C4×C73C2×D412yes—
239C22×C4×C73C2×D412yes—
240C22×C4×C73C2411yescharacteristic
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C2×C8×C73—44no—
252C2×C8×C73—44no—
253C2×C8×C73#4112yes—
254C2×C8×C73#4112yes—
255C42×C73—22no—
256C42×C73—22no—
257C42×C73—21no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73C2×C22⋊C412yes—
266C23×C73#13112yes—
267C23×C73#13112yes—
268C23×C73C23×C411yescharacteristic
269C22×D73—21no—
270C22×D73—21no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—21no—
277C22×D73—21no—
278C22×D73—21no—
279C22×D73—21no—
280C22×D73—21no—
281C22×D73—21no—
282C22×D73C2×C22⋊C412yes—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—22no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—44no—
301C2×C4×C73—44no—
302C2×C4×C73C2×C22⋊C412yes—
303C2×C4×C73#13112yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C2×#4111yescharacteristic
307C2×C4×C73C2×#4111yescharacteristic
308C2×C4×C73H(5,𝔽2)11yescharacteristic
309C2×C4×C732−1+411yescharacteristic
310C22⋊D73—28no—
311C22⋊D73—44no—
312C2×Dic73—21no—
313C2×Dic73—21no—
314C2×Dic73—21no—
315C2×Dic73—21no—
316C2×Dic73—21no—
317C2×Dic73—21no—
318C2×Dic73—21no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—21no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325C2×Dic73—21no—
326C2×Dic73—21no—
327C2×Dic73C2×C22⋊C412yes—
328C2×Dic73C2×C22⋊C412yes—
329C2×Dic73C2×C22⋊C412yes—
330D292—44no—
331C4×D73—22no—
332C4×D73—22no—
333C4×D73—22no—
334C4×D73—22no—
335C4×D73—41no—
336C4×D73—41no—
337C4×D73—41no—
338C4×D73—41no—
339Dic146—44no—
340C8×C73—22no—
341C8×C73—22no—
342C8×C73—41no—
343C8×C73—41no—
344#10596831—41no—
345#10596831—41no—
346#10596831—41no—
347#10596831—41no—
348C22×C73—22no—
349C22×C73—22no—
350C22×C73—22no—
351C22×C73—22no—
352C22×C73—22no—
353C22×C73—22no—
354C22×C73#40814yes—
355C22×C73C22×C22⋊C411yescharacteristic
356C22×C73C4×#4111yescharacteristic
357C22×C73#52011yescharacteristic
358C22×C73C2×#13111yescharacteristic
359C22×C73C2×#13111yescharacteristic
360C22×C73C2×#13111yescharacteristic
361C22×C73#56811yescharacteristic
362C2×D73—22no—
363C2×D73—22no—
364C2×D73—22no—
365C2×D73—41no—
366C2×D73—41no—
367C2×D73—41no—
368C2×D73—41no—
369C2×D73—41no—
370C2×D73—41no—
371C2×D73—41no—
372C2×D73—41no—
373C2×D73—41no—
374C2×D73—41no—
375C2×D73—41no—
376C4×C73—22no—
377C4×C73—22no—
378C4×C73—41no—
379C4×C73—41no—
380C4×C73—41no—
381C4×C73#54611yescharacteristic
382C4×C73#54611yescharacteristic
383C4×C73#54711yescharacteristic
384C4×C73#54711yescharacteristic
385Dic73—22no—
386Dic73—22no—
387Dic73—22no—
388Dic73—41no—
389Dic73—41no—
390Dic73—41no—
391#22470—731nomaximal, Sylow
392C2×C73—24no—
393C2×C73#233911yescharacteristic
394C2×C73C2×#40811yescharacteristic
395C2×C73#288011yescharacteristic
396C2×C73#296611yescharacteristic
397C2×C73#296811yescharacteristic
398C2×C73#299211yescharacteristic
399C2×C73#299411yescharacteristic
400D73—42no—
401D73—81no—
402C2×#529—731no—
403C2×#435—731no—
404C2×C8×D4—731no—
405#1985—731no—
406#1984—731no—
407#1870—731no—
408#1869—731no—
409#1869—731no—
410#1869—731no—
411#1818—731no—
412#1817—731no—
413#1798—731no—
414#1750—731no—
415#1729—731no—
416C2×#336D7311yescharacteristic, complemented
417C73#2247011yescharacteristic, complemented, Sylow
418C22×M16—731no—
419C23×C8—731no—
420C23×C8C2×D7311yescharacteristic
421C23×C8C2×D7311yescharacteristic
422#529—1464no—
423#529—1464no—
424C2×#126—731no—
425C2×#126—731no—
426C2×#125—731no—
427C2×#124—731no—
428C2×#123—731no—
429C2×#123—731no—
430C2×C22⋊Q8—731no—
431C2×#121—731no—
432C2×C4×Q8—731no—
433C2×C4×D4—731no—
434C2×C4×D4—731no—
435C2×C4×D4—731no—
436C2×#117—731no—
437C2×#117—731no—
438C22×C42C2×D7311yescharacteristic
439#435—1464no—
440C8×D4—1464no—
441C2×C4⋊C8—731no—
442C2×C4⋊C8—731no—
443C2×C22⋊C8—731no—
444C2×C22⋊C8—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8—731no—
448C2×C22⋊C8—731no—
449C2×C22⋊C8—731no—
450C2×C22⋊C8—731no—
451C2×#97—731no—
452C2×C4×C8—731no—
453#336—731no—
454#336—731no—
455#336—731no—
456#336—731no—
457#336—731no—
458#336—731no—
459#336—731no—
460#336—731no—
461#336C2×D7311yescharacteristic
462#336C2×D7311yescharacteristic
463#336C2×D7311yescharacteristic
464#336C2×D7311yescharacteristic
465C22×Q8—731no—
466C22×D4—731no—
467C22×D4—731no—
468C22×D4—731no—
469C23×C4—731no—
470C23×C4—731no—
471C23×C4C4×D7311yescharacteristic
472C23×C4C4×D7311yescharacteristic
473C23×C4C22×D7311yescharacteristic
474C2×M16—2921no—
475C2×M16—1462no—
476C2×M16—1462no—
477C22×C8—22no—
478C22×C8—22no—
479C22×C8—22no—
480C22×C8—22no—
481C22×C8—41no—
482C22×C8—41no—
483C22×C8—2921no—
484C22×C8—731no—
485C22×C8—731no—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8—1462no—
489C22×C8—1462no—
490C22×C8C22×D7311yescharacteristic
491C22×C8C22×D7311yescharacteristic
492C22×C8C22×D7311yescharacteristic
493C22×C8C22×D7311yescharacteristic
494#126—1464no—
495#126—1464no—
496#125—1464no—
497#124—1464no—
498#123—1464no—
499#123—1464no—
500C22⋊Q8—1464no—
501#121—1464no—
502C4×Q8—1462no—
503C4×Q8—1462no—
504C4×D4—734no—
505C4×D4—734no—
506C4×D4—1462no—
507C4×D4—1462no—
508C4×D4—1462no—
509C4×D4—1462no—
510#117—1462no—
511#117—1462no—
512#117—1462no—
513#117—1462no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—731no—
517C2×C4⋊C4—731no—
518C2×C4⋊C4—731no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4—731no—
523C2×C4⋊C4—731no—
524C2×C22⋊C4—731no—
525C2×C22⋊C4—731no—
526C2×C22⋊C4—731no—
527C2×C22⋊C4—731no—
528C2×C22⋊C4—731no—
529C2×C22⋊C4—731no—
530C2×C22⋊C4—731no—
531C2×C22⋊C4—731no—
532C2×C22⋊C4—731no—
533C2×C22⋊C4—731no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—731no—
537C2×C42—731no—
538C2×C42C4×D7311yescharacteristic
539C2×C42C4×D7311yescharacteristic
540C2×C42C22×D7311yescharacteristic
541C2×C42C22×D7311yescharacteristic
542C4⋊C8—1462no—
543C4⋊C8—1462no—
544C22⋊C8—2921no—
545C22⋊C8—2921no—
546C22⋊C8—1462no—
547C22⋊C8—1462no—
548C22⋊C8—1462no—
549C22⋊C8—1462no—
550C22⋊C8—1462no—
551C22⋊C8—1462no—
552#97—1462no—
553C4×C8—1462no—
554C24—731no—
555C24—731no—
556C24C2×C4×D7311yescharacteristic
557C2×Q8—2921no—
558C2×Q8—1462no—
559C2×Q8—1462no—
560C2×D4—2921no—
561C2×D4—734no—
562C2×D4—1462no—
563C2×D4—1462no—
564C2×D4—1462no—
565C2×D4—1462no—
566C2×D4—1462no—
567C2×D4—1462no—
568C2×D4—1462no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—41no—
579C22×C4—731no—
580C22×C4—731no—
581C22×C4—731no—
582C22×C4—732no—
583C22×C4—732no—
584C22×C4—731no—
585C22×C4—731no—
586C22×C4—731no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4C2×C4×D7311yescharacteristic
598C22×C4C2×C4×D7311yescharacteristic
599C22×C4C2×C4×D7311yescharacteristic
600C22×C4C2×C4×D7311yescharacteristic
601C22×C4C2×C4×D7311yescharacteristic
602C22×C4D4×D7312yes—
603C22×C4D4×D7312yes—
604C22×C4C23×D7311yescharacteristic
605M16—2924no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8—44no—
618C2×C8—2924no—
619C2×C8—1461no—
620C2×C8—1461no—
621C2×C8—1461no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8—1461no—
625C2×C8—1461no—
626C2×C8—1461no—
627C2×C8—1461no—
628C2×C8—1461no—
629C2×C8—1461no—
630C2×C8—1461no—
631C2×C8#1192402812yes—
632C2×C8#1192402812yes—
633C4⋊C4—734no—
634C4⋊C4—1462no—
635C4⋊C4—1462no—
636C4⋊C4—1462no—
637C4⋊C4—1462no—
638C4⋊C4—1462no—
639C4⋊C4—1462no—
640C4⋊C4—1462no—
641C4⋊C4—1462no—
642C4⋊C4—1462no—
643C22⋊C4—734no—
644C22⋊C4—734no—
645C22⋊C4—1462no—
646C22⋊C4—1462no—
647C22⋊C4—1462no—
648C22⋊C4—1462no—
649C22⋊C4—1462no—
650C22⋊C4—1462no—
651C22⋊C4—1462no—
652C22⋊C4—1462no—
653C42—22no—
654C42—22no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—732no—
660C42—732no—
661C42—1461no—
662C42—1461no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—732no—
668C23—1461no—
669C23—1461no—
670C23—1461no—
671C23—1461no—
672C23—1461no—
673C23—1461no—
674C23—1461no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23—1461no—
679C23—1461no—
680C23—1461no—
681C23C22⋊C4×D7312yes—
682C23#1455659712yes—
683C23#1455659912yes—
684C23C22×C4×D7311yescharacteristic
685Q8—2924no—
686D4—2924no—
687D4—2924no—
688D4—1468no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—2921no—
709C2×C4—2921no—
710C2×C4—2921no—
711C2×C4—2921no—
712C2×C4—732no—
713C2×C4—732no—
714C2×C4—732no—
715C2×C4—1461no—
716C2×C4—1461no—
717C2×C4—1461no—
718C2×C4—1461no—
719C2×C4—1461no—
720C2×C4—1461no—
721C2×C4—1461no—
722C2×C4—1461no—
723C2×C4—1461no—
724C2×C4—1461no—
725C2×C4—1461no—
726C2×C4—1461no—
727C2×C4—1461no—
728C2×C4—1461no—
729C2×C4—1461no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4C22⋊C4×D7312yes—
735C2×C4#1455659712yes—
736C2×C4C2×D4×D7311yescharacteristic
737C2×C4C2×D4×D7311yescharacteristic
738C2×C4C2×#1192402811yescharacteristic
739C2×C4C2×#1192402811yescharacteristic
740C2×C4#1455663611yescharacteristic
741C2×C4#1455663911yescharacteristic
742C8—22no—
743C8—22no—
744C8—41no—
745C8—41no—
746C8—2921no—
747C8—2921no—
748C8—2921no—
749C8—2921no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—2921no—
757C22—2921no—
758C22—2921no—
759C22—2921no—
760C22—2921no—
761C22—2921no—
762C22—2921no—
763C22—2921no—
764C22—2921no—
765C22—2921no—
766C22—2921no—
767C22—1462no—
768C22—1462no—
769C22—1462no—
770C22#1798855214yes—
771C22C2×C22⋊C4×D7311yescharacteristic
772C22C4×#1192402811yescharacteristic
773C22#1798906811yescharacteristic
774C22C2×#1455659711yescharacteristic
775C22C2×#1455659711yescharacteristic
776C22C2×#1455659911yescharacteristic
777C22#1798935311yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—2921no—
784C4—2921no—
785C4—2921no—
786C4—1462no—
787C4—1462no—
788C4—1462no—
789C4#1798922711yescharacteristic
790C4#1798922711yescharacteristic
791C4#1798923811yescharacteristic
792C4#1798923811yescharacteristic
793C2—24no—
794C2—2922no—
795C2—5841no—
796C2#2261275811yescharacteristic
797C2C2×#1798855211yescharacteristic
798C2#2261837711yescharacteristic
799C2#2261890611yescharacteristic
800C2#2261892511yescharacteristic
801C2#2261906711yescharacteristic
802C2#2261908711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#336×C73C2
prime radicalC2×#14556565C4
cosocleC22×C4×C73C24
hypercenterC2×#336D73
hypocenterC73#22470
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
2. C2×#17988658C2semidirect
3. C2×C8×C22⋊D73C2semidirect
4. #22610869C2semidirect
5. #22610865C2semidirect
6. #22610227C2semidirect
7. #22610223C2semidirect
8. #22610223C2semidirect
9. #22610222C2semidirect
10. #22610001C2semidirect
11. #22609999C2semidirect
12. #22609914C2semidirect
13. #22609696C2semidirect
14. #22609626C2semidirect
15. C2×#336×C73C2semidirect
416. C2×#336D73semidirect
417. C73#22470semidirect

Maximal subgroups

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

subgroupindex
C2×#179891212
C2×#179886582
C2×C8×C22⋊D732
#226108692
#226108652
#226102272
#226102232
#226102222
#226100012
#226099992
#226099142
#226096962
#226096262
C2×#336×C732
#2247073