Finite Group Databasebeta

← C2×#22615760 #33253046

Subgroups — C2×#22615760 #33253046

Order 18688.

2614 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556581C211yesmaximal, characteristic, complemented
2C22×#14556547C211yesmaximal, characteristic
3#22615760C2116yesmaximal, direct product factor
4C2×#17988521C211yesmaximal, characteristic, complemented
5C2×#17988520C211yesmaximal, characteristic, complemented
6C2×#17988518C211yesmaximal, characteristic, complemented
7C2×#17988517C211yesmaximal, characteristic, complemented
8C2×#17988510C211yesmaximal, characteristic
9C2×#17988510C211yesmaximal, characteristic
10C2×#17988510C211yesmaximal, characteristic
11C2×#17988484C211yesmaximal, characteristic, complemented
12C2×#17988482C211yesmaximal, characteristic, complemented
13C2×#17988456C211yesmaximal, characteristic, complemented
14C2×#17988445C211yesmaximal, characteristic
15C2×#17988445C211yesmaximal, characteristic
16C2×#396×C73C211yesmaximal, characteristic
17C24×Dic73C2211yescharacteristic
18C2×#14556581—28no—
19C2×#14556581C2218yescomplemented
20C2×#14556547—28no—
21C2×#14556547C2218yes—
22C22×C4⋊Dic73C2211yescharacteristic
23C22×C4⋊Dic73C2211yescharacteristic
24C22×C4⋊Dic73C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×#11924007C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×#11924007C2211yescharacteristic
30C22×#11924007C2211yescharacteristic
31C22×#11924007C2211yescharacteristic
32C22×#11924007C2211yescharacteristic
33C22×#11924007C2211yescharacteristic
34C22×#11924007C2211yescharacteristic
35C22×#11924007C2211yescharacteristic
36C22×#11924007C2211yescharacteristic
37C22×C22⋊Dic73C2211yescharacteristic
38C22×C22⋊Dic73C2211yescharacteristic
39C22×C22⋊Dic73C2211yescharacteristic
40C22×C4×Dic73C2211yescharacteristic
41C22×C4×Dic73C2211yescharacteristic
42#17988521C2218yescomplemented
43#17988520C2218yescomplemented
44#17988518C2218yescomplemented
45#17988517C2218yescomplemented
46#17988510C2218yes—
47#17988510C2218yes—
48#17988510C2218yes—
49#17988484C2218yescomplemented
50#17988482C2218yescomplemented
51#17988456C2218yescomplemented
52#17988445C2218yes—
53#17988445C2218yes—
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#14556498C2211yescharacteristic
61C22×C4⋊C4×C73C2211yescharacteristic
62C22×C4⋊C4×C73C2211yescharacteristic
63C22×C4⋊C4×C73C2211yescharacteristic
64C22×C22⋊C4×C73C2211yescharacteristic
65C22×C22⋊C4×C73C2211yescharacteristic
66C22×C22⋊C4×C73C2211yescharacteristic
67#396×C73C2218yes—
68C2×#95×C73C2211yescharacteristic
69C23×Dic73—24no—
70C23×Dic73—24no—
71C23×Dic73Q818yes—
72C23×Dic73C2311yescharacteristic
73C23×Dic73C2311yescharacteristic
74C23×Dic73C2311yescharacteristic
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2314yes—
80C23×Dic73C2311yescharacteristic
81#14556581—232no—
82#14556547—232no—
83C2×C4⋊Dic73—24no—
84C2×C4⋊Dic73—42no—
85C2×C4⋊Dic73—42no—
86C2×C4⋊Dic73C2314yes—
87C2×C4⋊Dic73C2314yes—
88C2×C4⋊Dic73C2314yes—
89C2×#11924007—24no—
90C2×#11924007—24no—
91C2×#11924007—24no—
92C2×#11924007—24no—
93C2×#11924007—24no—
94C2×#11924007—24no—
95C2×#11924007—24no—
96C2×#11924007—24no—
97C2×#11924007—42no—
98C2×#11924007—42no—
99C2×#11924007—42no—
100C2×#11924007—42no—
101C2×#11924007C2314yes—
102C2×#11924007C2314yes—
103C2×#11924007C2314yes—
104C2×#11924007C2314yes—
105C2×#11924007C2314yes—
106C2×#11924007C2314yes—
107C2×#11924007C2314yes—
108C2×#11924007C2314yes—
109C2×#11924007C2314yes—
110C2×#11924007C2314yes—
111C2×#11924007C2314yes—
112C2×#11924007C2314yes—
113C2×C22⋊Dic73—24no—
114C2×C22⋊Dic73—42no—
115C2×C22⋊Dic73—42no—
116C2×C22⋊Dic73C2314yes—
117C2×C22⋊Dic73C2314yes—
118C2×C22⋊Dic73C2314yes—
119C2×C4×Dic73—24no—
120C2×C4×Dic73D418yes—
121C2×C4×Dic73C2314yes—
122C2×C4×Dic73C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125#14556498C2314yes—
126#14556498C2314yes—
127#14556498C2314yes—
128#14556498C2314yes—
129#14556498C2314yes—
130C25×C73C2311yescharacteristic
131C23×C4×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2311yescharacteristic
136C23×C4×C73C2311yescharacteristic
137C2×C4⋊C4×C73—24no—
138C2×C4⋊C4×C73—42no—
139C2×C4⋊C4×C73—42no—
140C2×C4⋊C4×C73C2314yes—
141C2×C4⋊C4×C73C2314yes—
142C2×C4⋊C4×C73C2314yes—
143C2×C22⋊C4×C73—24no—
144C2×C22⋊C4×C73—42no—
145C2×C22⋊C4×C73—42no—
146C2×C22⋊C4×C73C2314yes—
147C2×C22⋊C4×C73C2314yes—
148C2×C22⋊C4×C73C2314yes—
149#95×C73C2314yes—
150C22×Dic73—22no—
151C22×Dic73—22no—
152C22×Dic73—22no—
153C22×Dic73—22no—
154C22×Dic73—232no—
155C22×Dic73—28no—
156C22×Dic73—28no—
157C22×Dic73—22no—
158C22×Dic73—22no—
159C22×Dic73—22no—
160C22×Dic73—22no—
161C22×Dic73—22no—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73—22no—
166C22×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—22no—
169C22×Dic73—22no—
170C22×Dic73—22no—
171C22×Dic73—22no—
172C22×Dic73C2×D414yes—
173C22×Dic73C2×D414yes—
174C22×Dic73C2×Q814yes—
175C22×Dic73C2×Q8116yes—
176C22×Dic73C2×Q814yes—
177C22×Dic73#4114yes—
178C22×Dic73C2412yes—
179C22×Dic73C2412yes—
180C22×Dic73C2412yes—
181C22×Dic73C2412yes—
182C22×Dic73C2412yes—
183C22×Dic73C2412yes—
184C22×Dic73C2412yes—
185C22×Dic73C2412yes—
186C4⋊Dic73—28no—
187C4⋊Dic73—44no—
188C4⋊Dic73—44no—
189#11924007—28no—
190#11924007—28no—
191#11924007—28no—
192#11924007—28no—
193#11924007—28no—
194#11924007—28no—
195#11924007—28no—
196#11924007—28no—
197#11924007—44no—
198#11924007—44no—
199#11924007—44no—
200#11924007—44no—
201C22⋊Dic73—28no—
202C22⋊Dic73—44no—
203C22⋊Dic73—44no—
204C4×Dic73—28no—
205C4×Dic73C2×D4116yes—
206C24×C73—22no—
207C24×C73—22no—
208C24×C73—22no—
209C24×C73—22no—
210C24×C73—22no—
211C24×C73—22no—
212C24×C73C2×Q814yes—
213C24×C73C2412yes—
214C24×C73C2411yescharacteristic
215C22×C4×C73—22no—
216C22×C4×C73—22no—
217C22×C4×C73—22no—
218C22×C4×C73—22no—
219C22×C4×C73—22no—
220C22×C4×C73—22no—
221C22×C4×C73—22no—
222C22×C4×C73—22no—
223C22×C4×C73—22no—
224C22×C4×C73—22no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73—22no—
232C22×C4×C73C2×D414yes—
233C22×C4×C73C2412yes—
234C22×C4×C73C2412yes—
235C22×C4×C73C2412yes—
236C22×C4×C73C2412yes—
237C22×C4×C73C2412yes—
238C22×C4×C73C2412yes—
239C4⋊C4×C73—28no—
240C4⋊C4×C73—44no—
241C4⋊C4×C73—44no—
242C22⋊C4×C73—28no—
243C22⋊C4×C73—44no—
244C22⋊C4×C73—44no—
245C23×C73—28no—
246C23×C73—28no—
247C23×C73—28no—
248C23×C73—22no—
249C23×C73—22no—
250C23×C73—22no—
251C23×C73—22no—
252C23×C73—22no—
253C23×C73—22no—
254C23×C73—44no—
255C23×C73—44no—
256C23×C73—44no—
257C23×C73—44no—
258C23×C73C22×D412yes—
259C23×C73C22×Q814yes—
260C23×C73C22×Q812yes—
261C23×C73C2×#4112yes—
262C23×C73H(5,𝔽2)12yes—
263C23×C73H(5,𝔽2)12yes—
264C23×C732−1+412yes—
265C23×C732−1+412yes—
266C23×C73C2511yescharacteristic
267C2×C4×C73—28no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—44no—
286C2×C4×C73—44no—
287C2×C4×C73—44no—
288C2×C4×C73—44no—
289C2×C4×C73—44no—
290C2×C4×C73C22×D414yes—
291C2×Dic73—28no—
292C2×Dic73—28no—
293C2×Dic73—22no—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—232no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—22no—
302C2×Dic73—22no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—44no—
314C2×Dic73—44no—
315C2×Dic73—44no—
316C2×Dic73—44no—
317C2×Dic73—44no—
318C2×Dic73C22⋊Q8116yes—
319C2×Dic73C22×D414yes—
320C2×Dic73C22×D414yes—
321C2×Dic73C22×Q814yes—
322C2×Dic73C22×Q814yes—
323C2×Dic73C2×#4114yes—
324C22×C73—24no—
325C22×C73—24no—
326C22×C73—24no—
327C22×C73—416no—
328C22×C73—42no—
329C22×C73—42no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73C2×C22⋊Q814yes—
333C22×C73#53714yes—
334C22×C73#53714yes—
335C22×C73#54014yes—
336C22×C73#54114yes—
337C22×C73#54414yes—
338C22×C73#54414yes—
339C22×C73C23×D411yescharacteristic
340C22×C73C23×Q811yescharacteristic
341C22×C73C22×#4111yescharacteristic
342C22×C73C2×H(5,𝔽2)11yescharacteristic
343C22×C73C2×H(5,𝔽2)11yescharacteristic
344C22×C73C2×2−1+411yescharacteristic
345C22×C73C2×2−1+411yescharacteristic
346C4×C73—24no—
347C4×C73—42no—
348C4×C73—42no—
349C4×C73—42no—
350C4×C73—42no—
351C4×C73—42no—
352Dic73—24no—
353Dic73—24no—
354Dic73—42no—
355Dic73—42no—
356Dic73—42no—
357Dic73—42no—
358Dic73—42no—
359Dic73C2×C22⋊Q818yes—
360C2×#2629—731nomaximal, Sylow
361C2×C73—44no—
362C2×C73#262918yescomplemented
363C2×C73C22×C22⋊Q811yescharacteristic
364C2×C73C2×#53711yescharacteristic
365C2×C73C2×#53711yescharacteristic
366C2×C73C2×#54011yescharacteristic
367C2×C73C2×#54111yescharacteristic
368C2×C73C2×#54411yescharacteristic
369C2×C73C2×#54411yescharacteristic
370C22×#125—731no—
371C22×#117—731no—
372#2629—7316no—
373C2×#398—731no—
374C2×#398—731no—
375C2×#398—731no—
376C2×#398—731no—
377C2×#396—731no—
378C2×#396—731no—
379C2×#396—731no—
380C2×#396D7311yescharacteristic
381C2×#389—731no—
382C2×#389—731no—
383C2×#384—731no—
384C2×#380—731no—
385C2×#380—731no—
386C73C2×#262911yescharacteristic, complemented, Sylow
387C24×C4—731no—
388C2×#125—738no—
389C2×#125—1468no—
390C2×#117—738no—
391C2×#117—1468no—
392C22×C4⋊C4—731no—
393C22×C4⋊C4—731no—
394C22×C4⋊C4—731no—
395C22×C4⋊C4—731no—
396C22×C4⋊C4—731no—
397C22×C4⋊C4—731no—
398C22×C4⋊C4—731no—
399C22×C4⋊C4—731no—
400C22×C4⋊C4—731no—
401C22×C4⋊C4—731no—
402C22×C4⋊C4—731no—
403C22×C4⋊C4—731no—
404C22×C4⋊C4—731no—
405C22×C4⋊C4—731no—
406C22×C4⋊C4—731no—
407C22×C4⋊C4C2×D7311yescharacteristic
408C22×C4⋊C4C2×D7311yescharacteristic
409C22×C4⋊C4C2×D7311yescharacteristic
410C22×C22⋊C4—731no—
411C22×C22⋊C4—731no—
412C22×C22⋊C4—731no—
413C22×C22⋊C4C2×D7311yescharacteristic
414C22×C22⋊C4C2×D7311yescharacteristic
415C22×C22⋊C4C2×D7311yescharacteristic
416C22×C42—731no—
417C22×C42—731no—
418#398—738no—
419#398—738no—
420#398—738no—
421#398—738no—
422#396—738no—
423#396—738no—
424#396—738no—
425#396C2×D7318yes—
426#389—738no—
427#389—738no—
428#384—738no—
429#380—738no—
430#380—738no—
431C2×#95—731no—
432C2×#95—731no—
433C2×#95—731no—
434C2×#95—731no—
435C2×#95—731no—
436C2×#95—731no—
437C2×#95—731no—
438C2×#95C2×D7311yescharacteristic
439C25C22×D7311yescharacteristic
440C23×C4—731no—
441C23×C4—738no—
442C23×C4—734no—
443C23×C4—731no—
444C23×C4—731no—
445C23×C4—731no—
446C23×C4—731no—
447C23×C4—731no—
448C23×C4—731no—
449C23×C4—731no—
450C23×C4—1464no—
451C23×C4—1464no—
452C23×C4C22×D7311yescharacteristic
453C23×C4C22×D7311yescharacteristic
454C23×C4C22×D7311yescharacteristic
455C23×C4C22×D7311yescharacteristic
456C23×C4C22×D7311yescharacteristic
457C23×C4C22×D7311yescharacteristic
458#125—14632no—
459#117—14632no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—2922no—
464C2×C4⋊C4—2922no—
465C2×C4⋊C4—2922no—
466C2×C4⋊C4—2922no—
467C2×C4⋊C4—2922no—
468C2×C4⋊C4—2922no—
469C2×C4⋊C4—734no—
470C2×C4⋊C4—734no—
471C2×C4⋊C4—734no—
472C2×C4⋊C4—734no—
473C2×C4⋊C4—734no—
474C2×C4⋊C4—734no—
475C2×C4⋊C4—734no—
476C2×C4⋊C4—734no—
477C2×C4⋊C4—734no—
478C2×C4⋊C4—734no—
479C2×C4⋊C4—734no—
480C2×C4⋊C4—734no—
481C2×C4⋊C4—734no—
482C2×C4⋊C4—734no—
483C2×C4⋊C4—734no—
484C2×C4⋊C4—1464no—
485C2×C4⋊C4—1464no—
486C2×C4⋊C4—1464no—
487C2×C4⋊C4—1464no—
488C2×C4⋊C4—1464no—
489C2×C4⋊C4—1464no—
490C2×C4⋊C4—1464no—
491C2×C4⋊C4—1464no—
492C2×C4⋊C4—1464no—
493C2×C4⋊C4C22×D7314yes—
494C2×C4⋊C4C22×D7314yes—
495C2×C4⋊C4C22×D7314yes—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—2922no—
500C2×C22⋊C4—2922no—
501C2×C22⋊C4—734no—
502C2×C22⋊C4—734no—
503C2×C22⋊C4—734no—
504C2×C22⋊C4—1464no—
505C2×C22⋊C4C22×D7314yes—
506C2×C22⋊C4C22×D7314yes—
507C2×C22⋊C4C22×D7314yes—
508C2×C42—738no—
509C2×C42—734no—
510C2×C42—734no—
511C2×C42—1464no—
512#95—734no—
513#95—734no—
514#95—734no—
515#95—734no—
516#95—734no—
517#95—734no—
518#95—734no—
519#95C22×D7314yes—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24Q8×D7314yes—
527C24C23×D7312yes—
528C24C23×D7311yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—734no—
547C22×C4—734no—
548C22×C4—734no—
549C22×C4—732no—
550C22×C4—734no—
551C22×C4—7316no—
552C22×C4—734no—
553C22×C4—732no—
554C22×C4—732no—
555C22×C4—732no—
556C22×C4—732no—
557C22×C4—732no—
558C22×C4—732no—
559C22×C4—732no—
560C22×C4—1462no—
561C22×C4—1462no—
562C22×C4—1462no—
563C22×C4—1462no—
564C22×C4—1462no—
565C22×C4—1462no—
566C22×C4—1462no—
567C22×C4—1462no—
568C22×C4—1462no—
569C22×C4—1462no—
570C22×C4—1462no—
571C22×C4—1462no—
572C22×C4—1462no—
573C22×C4—1462no—
574C22×C4—1462no—
575C22×C4—1468no—
576C22×C4—1468no—
577C22×C4—14632no—
578C22×C4—1462no—
579C22×C4—1462no—
580C22×C4—1462no—
581C22×C4—1462no—
582C22×C4D4×D7314yes—
583C22×C4C23×D7312yes—
584C22×C4C23×D7312yes—
585C22×C4C23×D7312yes—
586C22×C4C23×D7312yes—
587C22×C4C23×D7312yes—
588C22×C4C23×D7312yes—
589C4⋊C4—28no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—2924no—
593C4⋊C4—2924no—
594C4⋊C4—2924no—
595C4⋊C4—2924no—
596C4⋊C4—2924no—
597C4⋊C4—2924no—
598C4⋊C4—1468no—
599C4⋊C4—1468no—
600C4⋊C4—1468no—
601C4⋊C4—1468no—
602C4⋊C4—1468no—
603C4⋊C4—1468no—
604C4⋊C4—1468no—
605C4⋊C4—1468no—
606C4⋊C4—1468no—
607C22⋊C4—28no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—2924no—
611C22⋊C4—2924no—
612C22⋊C4—1468no—
613C42—7316no—
614C42—1468no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23C2×D4×D7312yes—
629C23C2×Q8×D7314yes—
630C23C2×Q8×D7312yes—
631C23#41×D7312yes—
632C23#1455663612yes—
633C23#1455663612yes—
634C23#1455663812yes—
635C23#1455663812yes—
636C23C24×D7311yescharacteristic
637C2×C4—22no—
638C2×C4—28no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—2924no—
661C2×C4—2924no—
662C2×C4—2924no—
663C2×C4—2924no—
664C2×C4—2924no—
665C2×C4—734no—
666C2×C4—734no—
667C2×C4—734no—
668C2×C4—7316no—
669C2×C4—734no—
670C2×C4—734no—
671C2×C4—1462no—
672C2×C4—1462no—
673C2×C4—1462no—
674C2×C4—1462no—
675C2×C4—1462no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4—1462no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—14632no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1468no—
692C2×C4—1468no—
693C2×C4C2×D4×D7314yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—416no—
702C22C22⋊Q8×D7314yes—
703C22#1798916414yes—
704C22#1798916614yes—
705C22#1798918714yes—
706C22#1798919414yes—
707C22#1798921614yes—
708C22#1798921614yes—
709C22C22×D4×D7311yescharacteristic
710C22C22×Q8×D7311yescharacteristic
711C22C2×#41×D7311yescharacteristic
712C22C2×#1455663611yescharacteristic
713C22C2×#1455663611yescharacteristic
714C22C2×#1455663811yescharacteristic
715C22C2×#1455663811yescharacteristic
716C4—24no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—2922no—
723C4—2922no—
724C4—2922no—
725C4—2922no—
726C4—2922no—
727C4—738no—
728C4—1464no—
729C4—1464no—
730C2—44no—
731C2#2261576018yesdirect product factor
732C2C2×C22⋊Q8×D7311yescharacteristic
733C2C2×#1798916411yescharacteristic
734C2C2×#1798916611yescharacteristic
735C2C2×#1798918711yescharacteristic
736C2C2×#1798919411yescharacteristic
737C2C2×#1798921611yescharacteristic
738C2C2×#1798921611yescharacteristic
subgroupG/H
centerC24C23×D73
commutator, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC2×#396×C73C2
socleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×#396D73
hypocenterC73C2×#2629
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14556581C2semidirect
3. #22615760C2direct (N × H)
4. C2×#17988521C2semidirect
5. C2×#17988520C2semidirect
6. C2×#17988518C2semidirect
7. C2×#17988517C2semidirect
11. C2×#17988484C2semidirect
12. C2×#17988482C2semidirect
13. C2×#17988456C2semidirect
19. C2×#14556581C22semidirect
42. #17988521C22semidirect
43. #17988520C22semidirect
44. #17988518C22semidirect
45. #17988517C22semidirect
49. #17988484C22semidirect
50. #17988482C22semidirect
51. #17988456C22semidirect
362. C2×C73#2629semidirect
386. C73C2×#2629semidirect
731. C2#22615760direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565812
C22×#145565472
#226157602
C2×#179885212
C2×#179885202
C2×#179885182
C2×#179885172
C2×#179885102
C2×#179884842
C2×#179884822
C2×#179884562
C2×#179884452
C2×#396×C732
C2×#262973