Finite Group Databasebeta

← C2×#22622639 #33965636

Subgroups — C2×#22622639 #33965636

Order 18688.

2198 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989296C211yesmaximal, characteristic, complemented
2C2×#17989258C211yesmaximal, characteristic, complemented
3#22622639C2116yesmaximal, direct product factor
4C2×#17988952C211yesmaximal, characteristic, complemented
5C2×#17988950C211yesmaximal, characteristic, complemented
6C2×#17988932C211yesmaximal, characteristic, complemented
7C2×#17988887C211yesmaximal, characteristic, complemented
8C2×#17988886C211yesmaximal, characteristic, complemented
9C2×#17988876C211yesmaximal, characteristic, complemented
10C2×#17988782C211yesmaximal, characteristic, complemented
11C2×#17988780C211yesmaximal, characteristic, complemented
12C2×#17988780C211yesmaximal, characteristic, complemented
13C2×#17988715C211yesmaximal, characteristic, complemented
14C2×#17988696C211yesmaximal, characteristic, complemented
15C2×#17988667C211yesmaximal, characteristic, complemented
16C2×#442×C73C211yesmaximal, characteristic, complemented
17C22×#11924028—21no—
18C22×#11924013C2211yescharacteristic
19C22×#11924013C2211yescharacteristic
20#17989296—24no—
21#17989296C2218yescomplemented
22#17989258—24no—
23#17989258C2218yescomplemented
24C2×#14556590C2211yescharacteristic
25C2×#14556588C2211yescharacteristic
26C2×#14556587C2211yescharacteristic
27C2×#14556587C2211yescharacteristic
28C2×#14556583C2211yescharacteristic
29C2×#14556582C2211yescharacteristic
30C2×#14556570—21no—
31C2×#14556568—21no—
32C2×#14556568—21no—
33C2×#14556565—21no—
34C2×#14556564—21no—
35C2×#14556564—21no—
36C2×C4×Dic146C2211yescharacteristic
37C2×D4×Dic73C2211yescharacteristic
38C2×D4×Dic73C2211yescharacteristic
39C2×#14556553C2211yescharacteristic
40C2×#14556553C2211yescharacteristic
41C22×#11924007—21no—
42#17988952C2218yescomplemented
43#17988950C2218yescomplemented
44#17988932C2218yescomplemented
45#17988887C2218yescomplemented
46#17988886C2218yescomplemented
47#17988876C2218yescomplemented
48#17988782C2218yescomplemented
49#17988780C2218yescomplemented
50#17988780C2218yescomplemented
51#17988715C2218yescomplemented
52#17988696C2218yescomplemented
53#17988667C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556522C2211yescharacteristic
56C2×C4⋊#10596831C2211yescharacteristic
57C2×#14556520C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556513C2211yescharacteristic
60C2×#14556513C2211yescharacteristic
61C2×#14556513C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556512C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556511C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×D8×C73C2211yescharacteristic
70C2×C4×D4×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#442×C73C2218yescomplemented
73C2×#106×C73C2211yescharacteristic
74C2×#102×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C2×#11924028—28no—
78C2×#11924028—48no—
79C22×Dic146—21no—
80C22×Dic146D411yescharacteristic
81C22×D292—21no—
82C22×D292—21no—
83C22×D292C2311yescharacteristic
84C22×D292C2311yescharacteristic
85C22×C22⋊D73—21no—
86C22×C22⋊D73—21no—
87C22×C22⋊D73—21no—
88C22×C22⋊D73—21no—
89C23×Dic73—21no—
90C23×Dic73—21no—
91C22×C4×D73—21no—
92C22×C4×D73—21no—
93C2×#11924013—24no—
94C2×#11924013—24no—
95C2×#11924013C2314yes—
96C2×#11924013C2314yes—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99#14556590—22no—
100#14556590C2314yes—
101#14556588—22no—
102#14556588C2314yes—
103#14556587—22no—
104#14556587—22no—
105#14556587C2314yes—
106#14556587C2314yes—
107#14556583—22no—
108#14556583C2314yes—
109#14556582—22no—
110#14556582C2314yes—
111#14556570—28no—
112#14556568—28no—
113#14556568—28no—
114#14556565—28no—
115#14556564—28no—
116#14556564—28no—
117C4×Dic146D414yes—
118C4×Dic146C2314yes—
119D4×Dic73—22no—
120D4×Dic73—22no—
121D4×Dic73C2314yes—
122D4×Dic73C2314yes—
123#14556553—22no—
124#14556553—22no—
125#14556553C2314yes—
126#14556553C2314yes—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73D411yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×C4⋊Dic73C2311yescharacteristic
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—28no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007D411yescharacteristic
137C2×#11924007D411yescharacteristic
138C2×C22⋊Dic73—21no—
139C2×C22⋊Dic73—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×C4×Dic73C2311yescharacteristic
143C2×C4×Dic73C2311yescharacteristic
144#14556524C2314yes—
145#14556522C2314yes—
146C4⋊#10596831C2314yes—
147#14556520C2314yes—
148#14556520C2314yes—
149#14556513C2314yes—
150#14556513C2314yes—
151#14556513C2314yes—
152#14556513C2314yes—
153#14556512C2314yes—
154#14556512C2314yes—
155#14556511C2314yes—
156#14556511C2314yes—
157#14556501C2314yes—
158C8×Dic73C2314yes—
159C22×D4×C73C2311yescharacteristic
160C22×D4×C73C2311yescharacteristic
161C23×C4×C73—21no—
162C23×C4×C73—21no—
163C2×D8×C73—24no—
164C2×D8×C73C2314yes—
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C4×D4×C73—22no—
168C4×D4×C73—22no—
169C4×D4×C73C2314yes—
170C4×D4×C73C2314yes—
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C22⋊C4×C73—21no—
174C2×C22⋊C4×C73—21no—
175C2×C42×C73C2311yescharacteristic
176#106×C73C2314yes—
177#102×C73C2314yes—
178#102×C73C2314yes—
179#97×C73C2314yes—
180C23×D73—21no—
181C23×D73—21no—
182#11924028—432no—
183C2×Dic146—24no—
184C2×Dic146—24no—
185C2×Dic146—82no—
186C2×Dic146C2×D414yes—
187C2×D292—22no—
188C2×D292—22no—
189C2×D292—22no—
190C2×D292—22no—
191C2×D292—21no—
192C2×D292—21no—
193C2×D292—24no—
194C2×D292—24no—
195C2×D292—44no—
196C2×D292—82no—
197C2×D292C2412yes—
198C2×D292C2412yes—
199C2×C22⋊D73—24no—
200C2×C22⋊D73—24no—
201C2×C22⋊D73—24no—
202C2×C22⋊D73—24no—
203C2×C22⋊D73—44no—
204C2×C22⋊D73—44no—
205C2×C22⋊D73—82no—
206C2×C22⋊D73—82no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73—24no—
210C22×Dic73—24no—
211C22×Dic73—44no—
212C22×Dic73—82no—
213C22×Dic73C2×D411yescharacteristic
214C22×Dic73C2×D411yescharacteristic
215C22×Dic73C2×D411yescharacteristic
216C22×Dic73C2×D411yescharacteristic
217C2×C4×D73—24no—
218C2×C4×D73—24no—
219C2×C4×D73—44no—
220C2×C4×D73—44no—
221#11924013—28no—
222#11924013—28no—
223C2×#10596831—22no—
224C2×#10596831—22no—
225C2×#10596831C2412yes—
226C2×#10596831C2412yes—
227C4⋊Dic73—21no—
228C4⋊Dic73—21no—
229C4⋊Dic73—24no—
230C4⋊Dic73C2×D414yes—
231C4⋊Dic73C2412yes—
232C4⋊Dic73C2412yes—
233#11924007—24no—
234#11924007—24no—
235#11924007—24no—
236#11924007—24no—
237#11924007C2×D414yes—
238#11924007C2×D414yes—
239C22⋊Dic73—24no—
240C22⋊Dic73—24no—
241#11924005—24no—
242#11924005—24no—
243C4×Dic73C2×D412yes—
244C4×Dic73C2×D412yes—
245C4×Dic73C2412yes—
246C4×Dic73C2412yes—
247C24×C73—21no—
248C24×C73—21no—
249C2×D4×C73—21no—
250C2×D4×C73—21no—
251C2×D4×C73—22no—
252C2×D4×C73—22no—
253C2×D4×C73—22no—
254C2×D4×C73#4114yescomplemented
255C2×D4×C73C2412yes—
256C2×D4×C73C2412yes—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—24no—
260C22×C4×C73—24no—
261C22×C4×C73—44no—
262C22×C4×C73—82no—
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2411yescharacteristic
266D8×C73—28no—
267C2×C8×C73—22no—
268C2×C8×C73—22no—
269C2×C8×C73C2412yes—
270C2×C8×C73C2412yes—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73C2412yes—
274C4⋊C4×C73C2412yes—
275C22⋊C4×C73—24no—
276C22⋊C4×C73—24no—
277C42×C73C2×D412yes—
278C42×C73C2412yes—
279C23×C73—24no—
280C23×C73—22no—
281C23×C73—22no—
282C23×C73—42no—
283C23×C73—42no—
284C23×C73—42no—
285C23×C73—42no—
286C23×C73—42no—
287C23×C73C22×D411yescharacteristic
288C22×D73—22no—
289C22×D73—22no—
290C22×D73—42no—
291C22×D73—42no—
292C22×D73—42no—
293C22×D73—42no—
294C22×D73—42no—
295C22×D73—42no—
296D4×C73—24no—
297D4×C73—22no—
298D4×C73—22no—
299D4×C73—22no—
300D4×C73—42no—
301D4×C73C2×#4114yescomplemented
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—48no—
307C2×C4×C73—42no—
308C2×C4×C73—42no—
309C2×C4×C73—84no—
310C2×C4×C73C22×D412yes—
311C2×C4×C73C22×D412yes—
312C2×C4×C73C22×D411yescharacteristic
313C2×C4×C73C2×#4112yes—
314C2×C4×C732−1+412yes—
315C2×C4×C73C2511yescharacteristic
316C22⋊D73—48no—
317C22⋊D73—48no—
318C22⋊D73—84no—
319C22⋊D73—84no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—42no—
326C2×Dic73—42no—
327C2×Dic73—48no—
328C2×Dic73—84no—
329C2×Dic73AGL(1,ℤ/8)14yes—
330C2×Dic73C22×D412yes—
331C2×Dic73C22×D412yes—
332C2×Dic73C22×D412yes—
333C2×Dic73C22×D412yes—
334D292—22no—
335D292—22no—
336D292—22no—
337D292—22no—
338D292—48no—
339D292—42no—
340D292—42no—
341D292—84no—
342C4×D73—48no—
343C4×D73—48no—
344Dic146—28no—
345Dic146—84no—
346C8×C73—22no—
347C8×C73—22no—
348#10596831—22no—
349#10596831—22no—
350C22×C73—24no—
351C22×C73—48no—
352C22×C73—42no—
353C22×C73—42no—
354C22×C73—42no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—84no—
358C22×C73#54812yes—
359C22×C73C2×AGL(1,ℤ/8)12yes—
360C22×C73#57612yes—
361C22×C73C23×D411yescharacteristic
362C2×D73—42no—
363C2×D73—42no—
364C2×D73—42no—
365C2×D73—42no—
366C2×D73—42no—
367C2×D73—42no—
368C2×D73—84no—
369C2×D73—84no—
370C4×C73—22no—
371C4×C73—22no—
372C4×C73—42no—
373C4×C73—42no—
374C4×C73#54812yes—
375C4×C73C22×#4111yescharacteristic
376C4×C73C2×2−1+411yescharacteristic
377Dic73—22no—
378Dic73—22no—
379Dic73—22no—
380Dic73—42no—
381Dic73—42no—
382Dic73C2×AGL(1,ℤ/8)14yes—
383C2×#3366—731nomaximal, Sylow
384C2×C73—44no—
385C2×C73—82no—
386C2×C73#336614yescomplemented
387C2×C73C2×#54811yescharacteristic
388C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
389C2×C73C2×#57611yescharacteristic
390D73—82no—
391D73—82no—
392C2×#554—731no—
393C2×#550—731no—
394#3366—7316no—
395C2×#490—731no—
396C2×#490—731no—
397C2×#486—731no—
398C2×#478—731no—
399C2×#478—731no—
400C2×#476—731no—
401C2×#459—731no—
402C2×#459—731no—
403C2×#459—731no—
404C2×#446—731no—
405C2×#442—731no—
406C2×#442D7311yescharacteristic, complemented
407C2×C4×D8—731no—
408C73C2×#336611yescharacteristic, complemented, Sylow
409C22×#41—1461no—
410C22×D8—731no—
411C22×D8—731no—
412C22×D8C2×D7311yescharacteristic
413#554—738no—
414#554—1464no—
415#550—738no—
416#550—1464no—
417C2×C4⋊Q8—731no—
418C2×#127—731no—
419C2×#127—731no—
420C2×#127—731no—
421C2×#125—731no—
422C2×#125—731no—
423C2×C22⋊Q8—1461no—
424C2×C22⋊Q8—1461no—
425C2×C22⋊Q8—1461no—
426C2×#121—1461no—
427C2×#121—1461no—
428C2×#121—1461no—
429C2×C4×Q8—731no—
430C2×C4×D4—731no—
431C2×C4×D4—731no—
432C2×C4×D4—731no—
433C2×C4×D4—731no—
434C2×C4×D4C2×D7311yescharacteristic
435C2×C4×D4C2×D7311yescharacteristic
436C22×C4⋊C4—1461no—
437#490—738no—
438#490—738no—
439#486—738no—
440#478—738no—
441#478—738no—
442#476—738no—
443#459—738no—
444#459—738no—
445#459—738no—
446#446—738no—
447#442—738no—
448#442C2×D7318yescomplemented
449C4×D8—738no—
450C2×#107—731no—
451C2×#106—731no—
452C2×#106C2×D7311yescharacteristic
453C2×C4⋊C8—731no—
454C2×C4⋊C8—731no—
455C2×C4⋊C8—731no—
456C2×#102—731no—
457C2×#102—731no—
458C2×#102—731no—
459C2×#102—731no—
460C2×#102—731no—
461C2×#102—731no—
462C2×#102—731no—
463C2×#102—731no—
464C2×#102C2×D7311yescharacteristic
465C2×#102C2×D7311yescharacteristic
466C2×#97—731no—
467C2×#97C2×D7311yescharacteristic
468C2×C4×C8—731no—
469C2×#41—2928no—
470C2×#41—1468no—
471C22×Q8—731no—
472C22×Q8—1461no—
473C22×D4—731no—
474C22×D4—731no—
475C22×D4—1461no—
476C22×D4—1461no—
477C22×D4—1461no—
478C22×D4—1461no—
479C22×D4—1461no—
480C22×D4—1461no—
481C22×D4C22×D7311yescharacteristic
482C22×D4C22×D7311yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—1461no—
486C23×C4—1461no—
487C23×C4—1461no—
488C23×C4—1461no—
489C2×D8—24no—
490C2×D8—734no—
491C2×D8—734no—
492C2×D8—1464no—
493C2×D8—1464no—
494C2×D8C22×D7314yes—
495C22×C8—731no—
496C22×C8—731no—
497C22×C8C22×D7311yescharacteristic
498C22×C8C22×D7311yescharacteristic
499C4⋊Q8—734no—
500C4⋊Q8—1462no—
501#127—734no—
502#127—734no—
503#127—734no—
504#127—1462no—
505#127—1462no—
506#127—1462no—
507#125—734no—
508#125—734no—
509#125—1462no—
510#125—1462no—
511C22⋊Q8—1468no—
512C22⋊Q8—1468no—
513C22⋊Q8—1468no—
514#121—1468no—
515#121—1468no—
516#121—1468no—
517C4×Q8—734no—
518C4×Q8—734no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—734no—
522C4×D4—734no—
523C4×D4—734no—
524C4×D4—734no—
525C4×D4—1462no—
526C4×D4—1462no—
527C4×D4—1462no—
528C4×D4—1462no—
529C4×D4C22×D7314yes—
530C4×D4C22×D7314yes—
531C2×C4⋊C4—731no—
532C2×C4⋊C4—731no—
533C2×C4⋊C4—731no—
534C2×C4⋊C4—731no—
535C2×C4⋊C4—731no—
536C2×C4⋊C4—1468no—
537C2×C4⋊C4—1461no—
538C2×C4⋊C4—1461no—
539C2×C4⋊C4—1461no—
540C2×C4⋊C4—1461no—
541C2×C4⋊C4—1461no—
542C2×C4⋊C4C22×D7311yescharacteristic
543C2×C4⋊C4C22×D7311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—1461no—
547C2×C22⋊C4—1461no—
548C2×C22⋊C4—1461no—
549C2×C22⋊C4—1461no—
550C2×C42—731no—
551C2×C42—731no—
552C2×C42C22×D7311yescharacteristic
553#107—734no—
554#106—734no—
555#106C22×D7314yes—
556C4⋊C8—734no—
557C4⋊C8—734no—
558C4⋊C8—734no—
559#102—734no—
560#102—734no—
561#102—734no—
562#102—734no—
563#102—734no—
564#102—734no—
565#102—734no—
566#102—734no—
567#102C22×D7314yes—
568#102C22×D7314yes—
569#97—734no—
570#97C22×D7314yes—
571C4×C8—734no—
572C24—21no—
573C24—21no—
574C24—1461no—
575C24—1461no—
576#41—29232no—
577C2×Q8—5842no—
578C2×Q8—734no—
579C2×Q8—1464no—
580C2×Q8—1464no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—2924no—
587C2×D4—2924no—
588C2×D4—2924no—
589C2×D4—5842no—
590C2×D4—5842no—
591C2×D4—5842no—
592C2×D4—732no—
593C2×D4—732no—
594C2×D4—1464no—
595C2×D4—1464no—
596C2×D4—1464no—
597C2×D4—1464no—
598C2×D4—1461no—
599C2×D4—1461no—
600C2×D4—1464no—
601C2×D4—1464no—
602C2×D4—1462no—
603C2×D4—1462no—
604C2×D4—1462no—
605C2×D4—1462no—
606C2×D4#1192402814yescomplemented
607C2×D4C23×D7312yes—
608C2×D4C23×D7312yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—44no—
614C22×C4—82no—
615C22×C4—2924no—
616C22×C4—2924no—
617C22×C4—2924no—
618C22×C4—5842no—
619C22×C4—731no—
620C22×C4—731no—
621C22×C4—731no—
622C22×C4—731no—
623C22×C4—1464no—
624C22×C4—1464no—
625C22×C4—1464no—
626C22×C4—1461no—
627C22×C4—1461no—
628C22×C4—1464no—
629C22×C4D4×D7311yescharacteristic
630C22×C4D4×D7311yescharacteristic
631C22×C4C23×D7311yescharacteristic
632D8—28no—
633D8—1468no—
634D8—1468no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—732no—
638C2×C8—732no—
639C2×C8—1462no—
640C2×C8—1462no—
641C2×C8C23×D7312yes—
642C2×C8C23×D7312yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—734no—
646C4⋊C4—734no—
647C4⋊C4—734no—
648C4⋊C4—732no—
649C4⋊C4—732no—
650C4⋊C4—1464no—
651C4⋊C4—1464no—
652C4⋊C4—1464no—
653C4⋊C4—1464no—
654C4⋊C4—1464no—
655C4⋊C4—1461no—
656C4⋊C4—1461no—
657C4⋊C4C23×D7312yes—
658C4⋊C4C23×D7312yes—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—1464no—
662C22⋊C4—1464no—
663C22⋊C4—1464no—
664C22⋊C4—1464no—
665C42—732no—
666C42—732no—
667C42—732no—
668C42—732no—
669C42D4×D7312yes—
670C42C23×D7312yes—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—2922no—
680C23—2922no—
681C23—2922no—
682C23—2922no—
683C23—2922no—
684C23—2922no—
685C23—1462no—
686C23—1462no—
687C23C2×D4×D7311yescharacteristic
688Q8—5844no—
689Q8—1468no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—24no—
694D4—42no—
695D4—2928no—
696D4—2928no—
697D4—2928no—
698D4—2922no—
699D4—2922no—
700D4—5844no—
701D4—5844no—
702D4—5844no—
703D4—1462no—
704D4—1462no—
705D4—1462no—
706D4—1462no—
707D4C2×#1192402814yescomplemented
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—84no—
716C2×C4—2928no—
717C2×C4—2928no—
718C2×C4—2922no—
719C2×C4—2922no—
720C2×C4—2928no—
721C2×C4—5844no—
722C2×C4—732no—
723C2×C4—734no—
724C2×C4—732no—
725C2×C4—732no—
726C2×C4—732no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4C2×D4×D7312yes—
733C2×C4C2×D4×D7312yes—
734C2×C4C2×D4×D7311yescharacteristic
735C2×C4C2×#1192402812yes—
736C2×C4#1455663812yes—
737C2×C4C24×D7311yescharacteristic
738C8—22no—
739C8—22no—
740C8—1462no—
741C8—1462no—
742C22—24no—
743C22—42no—
744C22—42no—
745C22—48no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—84no—
750C22—2922no—
751C22—2922no—
752C22—2922no—
753C22—2922no—
754C22—2922no—
755C22—2922no—
756C22—5844no—
757C22—5844no—
758C22#1798924612yes—
759C22AGL(1,ℤ/8)×D7312yes—
760C22#1798939112yes—
761C22C22×D4×D7311yescharacteristic
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—2922no—
767C4—2922no—
768C4—734no—
769C4—1462no—
770C4—1462no—
771C4—1462no—
772C4#1798924612yes—
773C4C22×#1192402811yescharacteristic
774C4C2×#1455663811yescharacteristic
775C2—44no—
776C2—82no—
777C2—5842no—
778C2—5842no—
779C2#2262263914yesdirect product factor
780C2C2×#1798924611yescharacteristic
781C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
782C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#442×C73C2
socleC23×C73C22×D4
hypercenterC2×#442D73
hypocenterC73C2×#3366
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#17989296C2semidirect
2. C2×#17989258C2semidirect
3. #22622639C2direct (N × H)
4. C2×#17988952C2semidirect
5. C2×#17988950C2semidirect
6. C2×#17988932C2semidirect
7. C2×#17988887C2semidirect
8. C2×#17988886C2semidirect
9. C2×#17988876C2semidirect
10. C2×#17988782C2semidirect
11. C2×#17988780C2semidirect
12. C2×#17988780C2semidirect
13. C2×#17988715C2semidirect
14. C2×#17988696C2semidirect
15. C2×#17988667C2semidirect
16. C2×#442×C73C2semidirect
21. #17989296C22semidirect
23. #17989258C22semidirect
42. #17988952C22semidirect
43. #17988950C22semidirect
44. #17988932C22semidirect
45. #17988887C22semidirect
46. #17988886C22semidirect
47. #17988876C22semidirect
48. #17988782C22semidirect
49. #17988780C22semidirect
50. #17988780C22semidirect
51. #17988715C22semidirect
52. #17988696C22semidirect
53. #17988667C22semidirect
72. #442×C73C22semidirect
254. C2×D4×C73#41semidirect
301. D4×C73C2×#41semidirect
386. C2×C73#3366semidirect
406. C2×#442D73semidirect
408. C73C2×#3366semidirect
448. #442C2×D73semidirect
606. C2×D4#11924028semidirect
707. D4C2×#11924028semidirect
779. C2#22622639direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892962
C2×#179892582
#226226392
C2×#179889522
C2×#179889502
C2×#179889322
C2×#179888872
C2×#179888862
C2×#179888762
C2×#179887822
C2×#179887802
C2×#179887152
C2×#179886962
C2×#179886672
C2×#442×C732
C2×#336673