Finite Group Databasebeta

← C2×#22622997 #33966990

Subgroups — C2×#22622997 #33966990

Order 18688.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989322C211yesmaximal, characteristic, complemented
2#22622997C2116yesmaximal, direct product factor
3C2×#17988979C211yesmaximal, characteristic, complemented
4C2×#17988977C211yesmaximal, characteristic
5C2×#17988969C211yesmaximal, characteristic, complemented
6C2×#17988809C211yesmaximal, characteristic, complemented
7C2×#17988806C211yesmaximal, characteristic, complemented
8C2×#17988787C211yesmaximal, characteristic, complemented
9C2×#17988802C211yesmaximal, characteristic, complemented
10C2×#17988799C211yesmaximal, characteristic, complemented
11C2×#17988789C211yesmaximal, characteristic, complemented
12C2×#17988718C211yesmaximal, characteristic, complemented
13C2×#17988697C211yesmaximal, characteristic, complemented
14C2×#17988692C211yesmaximal, characteristic, complemented
15C2×C4×#11924015C211yesmaximal, characteristic, complemented
16C2×#556×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924016C2211yescharacteristic
20C22×#11924015C2211yescharacteristic
21C22×#11924015C2211yescharacteristic
22C22×#11924015C2211yescharacteristic
23C22×#11924015C2211yescharacteristic
24C22×#11924013C2211yescharacteristic
25C22×#11924013C2211yescharacteristic
26#17989322—24no—
27#17989322C2218yescomplemented
28C2×#14556588C2211yescharacteristic
29C2×#14556580—21no—
30C2×#14556579C2211yescharacteristic
31C2×#14556579C2211yescharacteristic
32C2×#14556576—21no—
33C2×#14556576—21no—
34C2×C4×Dic146C2211yescharacteristic
35C2×C4×D292C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C2×#14556553—21no—
38#17988979C2218yescomplemented
39#17988977C2218yes—
40#17988969C2218yescomplemented
41#17988809C2218yescomplemented
42#17988806C2218yescomplemented
43#17988802C2218yescomplemented
44#17988799C2218yescomplemented
45#17988789C2218yescomplemented
46#17988787C2218yescomplemented
47#17988718C2218yescomplemented
48#17988697C2218yescomplemented
49#17988692C2218yescomplemented
50C4×#11924015C2218yescomplemented
51C2×#14556522C2211yescharacteristic
52C2×C4⋊#10596831C2211yescharacteristic
53C2×C4⋊#10596831C2211yescharacteristic
54C2×C4⋊#10596831C2211yescharacteristic
55C2×#14556515C2211yescharacteristic
56C2×#14556515C2211yescharacteristic
57C2×#14556514C2211yescharacteristic
58C2×#14556512C2211yescharacteristic
59C2×#14556511C2211yescharacteristic
60C2×#14556511C2211yescharacteristic
61C2×#14556502C2211yescharacteristic
62C2×#14556502C2211yescharacteristic
63C2×C4×#10596831C2211yescharacteristic
64#556×C73—24no—
65#556×C73C2218yescomplemented
66C2×C4⋊Q8×C73C2211yescharacteristic
67C2×#126×C73—21no—
68C2×#126×C73—21no—
69C2×#124×C73C2211yescharacteristic
70C2×#124×C73C2211yescharacteristic
71C2×C22⋊Q8×C73—21no—
72C2×C4×Q8×C73C2211yescharacteristic
73C2×C4×Q8×C73C2211yescharacteristic
74C2×C4×Q8×C73C2211yescharacteristic
75C2×C4×D4×C73C2211yescharacteristic
76C2×#117×C73—21no—
77C22×Dic146C2311yescharacteristic
78C22×D292—21no—
79C22×D292—21no—
80C22×D292C2311yescharacteristic
81C22×D292C2311yescharacteristic
82C22×C4×D73—21no—
83C22×C4×D73—21no—
84C2×#11924018—24no—
85C2×#11924018—42no—
86C2×#11924018C2314yes—
87C2×#11924018C2314yes—
88C2×#11924016—42no—
89C2×#11924016C2314yes—
90C2×#11924015—24no—
91C2×#11924015—42no—
92C2×#11924015—42no—
93C2×#11924015—42no—
94C2×#11924015C2314yes—
95C2×#11924015C2314yes—
96C2×#11924015C2314yes—
97C2×#11924015C2314yes—
98C2×#11924013—24no—
99C2×#11924013—42no—
100C2×#11924013C2314yes—
101C2×#11924013C2314yes—
102C22×#10596831C2311yescharacteristic
103C22×#10596831C2311yescharacteristic
104C22×#10596831C2311yescharacteristic
105C22×#10596831C2311yescharacteristic
106#14556588—22no—
107#14556588C2314yes—
108#14556580—28no—
109#14556579—22no—
110#14556579—22no—
111#14556579C2314yes—
112#14556579C2314yes—
113#14556576—28no—
114#14556576—28no—
115C4×Dic146—22no—
116C4×Dic146C2314yes—
117C4×D292—22no—
118C4×D292—22no—
119C4×D292C2314yes—
120C4×D292C2314yes—
121#14556553—28no—
122C2×C4⋊Dic73C2311yescharacteristic
123C2×#11924007—21no—
124C2×#11924005—21no—
125C2×#11924005—21no—
126C2×#11924005—21no—
127C2×#11924005—21no—
128C2×#11924005—21no—
129C2×#11924005—21no—
130C2×C4×Dic73—21no—
131#14556522C2314yes—
132C4⋊#10596831C2314yes—
133C4⋊#10596831C2314yes—
134C4⋊#10596831C2314yes—
135#14556515C2314yes—
136#14556515C2314yes—
137#14556514C2314yes—
138#14556512C2314yes—
139#14556511C2314yes—
140#14556511C2314yes—
141#14556502C2314yes—
142#14556502C2314yes—
143C4×#10596831C2314yes—
144C22×Q8×C73D411yescharacteristic
145C22×Q8×C73C2311yescharacteristic
146C22×Q8×C73C2311yescharacteristic
147C22×D4×C73C2311yescharacteristic
148C23×C4×C73—21no—
149C4⋊Q8×C73—22no—
150C4⋊Q8×C73C2314yes—
151#126×C73—28no—
152#126×C73—28no—
153#124×C73—22no—
154#124×C73—22no—
155#124×C73C2314yes—
156#124×C73C2314yes—
157C22⋊Q8×C73—28no—
158C4×Q8×C73—22no—
159C4×Q8×C73—22no—
160C4×Q8×C73D414yes—
161C4×Q8×C73C2314yes—
162C4×Q8×C73C2314yes—
163C4×Q8×C73C2314yes—
164C4×D4×C73—22no—
165C4×D4×C73C2314yes—
166#117×C73—28no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73—21no—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73D411yescharacteristic
172C2×C4⋊C4×C73D411yescharacteristic
173C2×C4⋊C4×C73D411yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73—21no—
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180C2×C42×C73—21no—
181C2×C42×C73—21no—
182C2×C42×C73C2311yescharacteristic
183C2×C42×C73C2311yescharacteristic
184C2×C42×C73C2311yescharacteristic
185C23×D73—21no—
186C23×D73—21no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—21no—
190C2×Dic146C2412yes—
191C2×D292—22no—
192C2×D292—22no—
193C2×D292—22no—
194C2×D292—22no—
195C2×D292—24no—
196C2×D292—21no—
197C2×D292—21no—
198C2×D292—24no—
199C2×D292—44no—
200C2×D292—82no—
201C2×D292C2412yes—
202C2×D292C2412yes—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C2×C4×D73—24no—
206C2×C4×D73—24no—
207C2×C4×D73—82no—
208C2×C4×D73—82no—
209#11924018—28no—
210#11924018—44no—
211#11924016—44no—
212#11924015—28no—
213#11924015—44no—
214#11924015—44no—
215#11924015—44no—
216#11924013—28no—
217#11924013—44no—
218C2×#10596831—22no—
219C2×#10596831—22no—
220C2×#10596831—22no—
221C2×#10596831#4114yes—
222C2×#10596831C2412yes—
223C2×#10596831C2412yes—
224C2×#10596831C2412yes—
225C2×#10596831C2412yes—
226C4⋊Dic73—21no—
227C4⋊Dic73C2412yes—
228#11924007—24no—
229#11924005—24no—
230#11924005—24no—
231#11924005—24no—
232#11924005—24no—
233#11924005—24no—
234#11924005—24no—
235C4×Dic73—24no—
236C24×C73—21no—
237C2×Q8×C73—21no—
238C2×Q8×C73—21no—
239C2×Q8×C73—22no—
240C2×Q8×C73—22no—
241C2×Q8×C73—22no—
242C2×Q8×C73—22no—
243C2×Q8×C73—42no—
244C2×Q8×C73C2×D414yes—
245C2×Q8×C73C2412yes—
246C2×Q8×C73C2412yes—
247C2×D4×C73—21no—
248C2×D4×C73—22no—
249C2×D4×C73—22no—
250C2×D4×C73C2412yes—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—24no—
255C22×C4×C73—44no—
256C22×C4×C73C2×D411yescharacteristic
257C22×C4×C73C2×D411yescharacteristic
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2411yescharacteristic
263C4⋊C4×C73—24no—
264C4⋊C4×C73—24no—
265C4⋊C4×C73—24no—
266C4⋊C4×C73—24no—
267C4⋊C4×C73—21no—
268C4⋊C4×C73C2×D414yes—
269C4⋊C4×C73C2×D414yes—
270C4⋊C4×C73C2×D414yes—
271C4⋊C4×C73C2412yes—
272C22⋊C4×C73—24no—
273C22⋊C4×C73—24no—
274C22⋊C4×C73—24no—
275C22⋊C4×C73—24no—
276C22⋊C4×C73—24no—
277C42×C73—24no—
278C42×C73—24no—
279C42×C73C2×D412yes—
280C42×C73C2×D412yes—
281C42×C73C2×D412yes—
282C42×C73C2412yes—
283C42×C73C2412yes—
284C42×C73C2412yes—
285C23×C73—22no—
286C23×C73—42no—
287C23×C73—42no—
288C23×C73—42no—
289C23×C73C22×D411yescharacteristic
290C22×D73—22no—
291C22×D73—22no—
292C22×D73—42no—
293C22×D73—42no—
294C22×D73—42no—
295C22×D73—42no—
296C22×D73—42no—
297C22×D73—42no—
298Q8×C73—22no—
299Q8×C73—22no—
300Q8×C73—22no—
301Q8×C73—22no—
302Q8×C73—44no—
303Q8×C73—42no—
304Q8×C73—42no—
305D4×C73—22no—
306D4×C73—22no—
307D4×C73—42no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—48no—
318C2×C4×C73—42no—
319C2×C4×C73—42no—
320C2×C4×C73—42no—
321C2×C4×C73C22×D412yes—
322C2×C4×C73C22×D412yes—
323C2×C4×C73C22×D412yes—
324C2×C4×C73C22×D412yes—
325C2×C4×C73C22×D412yes—
326C2×C4×C73C22×D412yes—
327C2×C4×C73C22×D411yescharacteristic
328C2×C4×C73C2×#4112yes—
329C2×C4×C73H(5,𝔽2)12yes—
330C2×C4×C73C2511yescharacteristic
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—42no—
334C2×Dic73—42no—
335D292—22no—
336D292—22no—
337D292—22no—
338D292—22no—
339D292—48no—
340D292—42no—
341D292—42no—
342D292—84no—
343C4×D73—84no—
344C4×D73—84no—
345Dic146—22no—
346Dic146—22no—
347Dic146—42no—
348#10596831—22no—
349#10596831—22no—
350#10596831—22no—
351#10596831C2×#4114yes—
352C22×C73—42no—
353C22×C73—42no—
354C22×C73—42no—
355C22×C73—84no—
356C22×C73#55012yes—
357C22×C73#57512yes—
358C22×C73#57712yes—
359C22×C73C23×D411yescharacteristic
360C2×D73—42no—
361C2×D73—42no—
362C2×D73—42no—
363C2×D73—42no—
364C2×D73—42no—
365C2×D73—42no—
366C2×D73—84no—
367C2×D73—84no—
368C4×C73—22no—
369C4×C73—22no—
370C4×C73—22no—
371C4×C73—22no—
372C4×C73—22no—
373C4×C73—22no—
374C4×C73—42no—
375C4×C73—42no—
376C4×C73—42no—
377C4×C73#55012yes—
378C4×C73C22×#4111yescharacteristic
379C4×C73C2×H(5,𝔽2)11yescharacteristic
380Dic73—42no—
381Dic73—42no—
382C2×#3401—731nomaximal, Sylow
383C2×C73—82no—
384C2×C73#340114yescomplemented
385C2×C73C2×#55011yescharacteristic
386C2×C73C2×#57511yescharacteristic
387C2×C73C2×#57711yescharacteristic
388D73—82no—
389D73—82no—
390C2×#559—731no—
391C2×#556D7311yescharacteristic, complemented
392#3401—7316no—
393C2×#497—731no—
394C2×#496—731no—
395C2×#495—731no—
396C2×#464—731no—
397C2×#464—731no—
398C2×#460—731no—
399C2×#463—731no—
400C2×#463—731no—
401C2×#461—731no—
402C2×#446—731no—
403C2×#442—731no—
404C2×#441—731no—
405C2×C4×SD16—731no—
406C73C2×#340111yescharacteristic, complemented, Sylow
407C22×Q16—731no—
408C22×Q16—731no—
409C22×SD16—731no—
410C22×SD16—731no—
411C22×SD16—731no—
412C22×SD16—731no—
413C22×SD16—731no—
414C22×D8—731no—
415C22×D8—731no—
416#559—738no—
417#559—1464no—
418#556—24no—
419#556C2×D7318yescomplemented
420C2×C4⋊Q8C2×D7311yescharacteristic
421C2×#127—731no—
422C2×#126—21no—
423C2×#126—21no—
424C2×#124—731no—
425C2×#124—731no—
426C2×#124—1461no—
427C2×#124C2×D7311yescharacteristic
428C2×#124C2×D7311yescharacteristic
429C2×#123—1461no—
430C2×#123—1461no—
431C2×C22⋊Q8—21no—
432C2×C4×Q8—731no—
433C2×C4×Q8C2×D7311yescharacteristic
434C2×C4×Q8C2×D7311yescharacteristic
435C2×C4×Q8C2×D7311yescharacteristic
436C2×C4×D4—731no—
437C2×C4×D4—731no—
438C2×C4×D4—1461no—
439C2×C4×D4C2×D7311yescharacteristic
440C2×#117—21no—
441#497—738no—
442#496—738no—
443#495—738no—
444#464—738no—
445#464—738no—
446#463—738no—
447#463—738no—
448#461—738no—
449#460—738no—
450#446—738no—
451#442—738no—
452#441—738no—
453C4×SD16—738no—
454C2×#106—731no—
455C2×C4⋊C8—731no—
456C2×C4⋊C8—731no—
457C2×C4⋊C8—731no—
458C2×#103—731no—
459C2×#103—731no—
460C2×#103—731no—
461C2×#102—731no—
462C2×#102—731no—
463C2×#102—731no—
464C2×#97—731no—
465C2×#97—731no—
466C2×C4×C8—731no—
467C22×Q8—731no—
468C22×Q8C22⋊D7311yescharacteristic
469C22×Q8C22×D7311yescharacteristic
470C22×Q8C22×D7311yescharacteristic
471C22×D4—731no—
472C22×D4—731no—
473C22×D4—1461no—
474C22×D4—1461no—
475C22×D4C22×D7311yescharacteristic
476C23×C4—21no—
477C23×C4—1461no—
478C23×C4—1461no—
479C2×Q16—2922no—
480C2×Q16—734no—
481C2×Q16—734no—
482C2×Q16—1464no—
483C2×SD16—2922no—
484C2×SD16—2922no—
485C2×SD16—2922no—
486C2×SD16—2922no—
487C2×SD16—734no—
488C2×SD16—734no—
489C2×SD16—734no—
490C2×SD16—734no—
491C2×SD16—734no—
492C2×SD16—1464no—
493C2×D8—2922no—
494C2×D8—734no—
495C2×D8—734no—
496C2×D8—1464no—
497C22×C8—731no—
498C22×C8—731no—
499C22×C8—731no—
500C22×C8—731no—
501C4⋊Q8—22no—
502C4⋊Q8C22×D7314yes—
503#127—734no—
504#127—1462no—
505#126—28no—
506#126—28no—
507#124—22no—
508#124—22no—
509#124—734no—
510#124—734no—
511#124—1468no—
512#124—1462no—
513#124—1462no—
514#124C22×D7314yes—
515#124C22×D7314yes—
516#123—1468no—
517#123—1468no—
518C22⋊Q8—28no—
519C4×Q8—22no—
520C4×Q8—22no—
521C4×Q8—734no—
522C4×Q8—1462no—
523C4×Q8C22⋊D7314yes—
524C4×Q8C22×D7314yes—
525C4×Q8C22×D7314yes—
526C4×Q8C22×D7314yes—
527C4×D4—22no—
528C4×D4—734no—
529C4×D4—734no—
530C4×D4—1468no—
531C4×D4—1462no—
532C4×D4—1462no—
533C4×D4C22×D7314yes—
534#117—28no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—731no—
540C2×C4⋊C4—1461no—
541C2×C4⋊C4C22⋊D7311yescharacteristic
542C2×C4⋊C4C22⋊D7311yescharacteristic
543C2×C4⋊C4C22⋊D7311yescharacteristic
544C2×C4⋊C4C22×D7311yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1461no—
551C2×C22⋊C4—1461no—
552C2×C22⋊C4—1461no—
553C2×C22⋊C4—1461no—
554C2×C22⋊C4—1461no—
555C2×C22⋊C4—1461no—
556C2×C42—21no—
557C2×C42—21no—
558C2×C42—1461no—
559C2×C42C22×D7311yescharacteristic
560C2×C42C22×D7311yescharacteristic
561C2×C42C22×D7311yescharacteristic
562#106—734no—
563C4⋊C8—734no—
564C4⋊C8—734no—
565C4⋊C8—734no—
566#103—734no—
567#103—734no—
568#103—734no—
569#102—734no—
570#102—734no—
571#102—734no—
572#97—734no—
573#97—734no—
574C4×C8—734no—
575C24—21no—
576C24—1461no—
577C24—1461no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—42no—
585C2×Q8—732no—
586C2×Q8—1462no—
587C2×Q8—1462no—
588C2×Q8—1461no—
589C2×Q8C2×C22⋊D7314yes—
590C2×Q8C23×D7312yes—
591C2×Q8C23×D7312yes—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—2924no—
596C2×D4—5842no—
597C2×D4—732no—
598C2×D4—732no—
599C2×D4—1464no—
600C2×D4—1461no—
601C2×D4—1461no—
602C2×D4—1464no—
603C2×D4—1462no—
604C2×D4—1462no—
605C2×D4—1462no—
606C2×D4—1462no—
607C2×D4C23×D7312yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—44no—
613C22×C4—5842no—
614C22×C4—5842no—
615C22×C4—1461no—
616C22×C4—1461no—
617C22×C4—1464no—
618C22×C4—1464no—
619C22×C4C2×C22⋊D7311yescharacteristic
620C22×C4C2×C22⋊D7311yescharacteristic
621C22×C4C2×C22⋊D7311yescharacteristic
622C22×C4C2×C22⋊D7311yescharacteristic
623C22×C4C2×C22⋊D7311yescharacteristic
624C22×C4C2×C22⋊D7311yescharacteristic
625C22×C4C23×D7311yescharacteristic
626Q16—2924no—
627Q16—1468no—
628SD16—2924no—
629SD16—2924no—
630SD16—2924no—
631SD16—2924no—
632SD16—1468no—
633D8—2924no—
634D8—1468no—
635C2×C8—734no—
636C2×C8—732no—
637C2×C8—732no—
638C2×C8—732no—
639C2×C8—732no—
640C2×C8—1462no—
641C2×C8—1462no—
642C2×C8—1462no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—732no—
649C4⋊C4—1464no—
650C4⋊C4—1461no—
651C4⋊C4C2×C22⋊D7314yes—
652C4⋊C4C2×C22⋊D7314yes—
653C4⋊C4C2×C22⋊D7314yes—
654C4⋊C4C23×D7312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1464no—
661C22⋊C4—1464no—
662C22⋊C4—1464no—
663C22⋊C4—1464no—
664C22⋊C4—1464no—
665C22⋊C4—1464no—
666C42—24no—
667C42—24no—
668C42—1464no—
669C42C2×C22⋊D7312yes—
670C42C2×C22⋊D7312yes—
671C42C2×C22⋊D7312yes—
672C42C23×D7312yes—
673C42C23×D7312yes—
674C42C23×D7312yes—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—2922no—
680C23—2922no—
681C23—2922no—
682C23—2922no—
683C23—2922no—
684C23—2922no—
685C23—1462no—
686C23—1462no—
687C23C22×C22⋊D7311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—44no—
693Q8—42no—
694Q8—42no—
695Q8—2922no—
696Q8—1462no—
697Q8—1462no—
698D4—22no—
699D4—22no—
700D4—42no—
701D4—2928no—
702D4—2922no—
703D4—2922no—
704D4—5844no—
705D4—1462no—
706D4—1462no—
707D4—1462no—
708D4—1462no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—2922no—
723C2×C4—2922no—
724C2×C4—5844no—
725C2×C4—5844no—
726C2×C4—1462no—
727C2×C4—1462no—
728C2×C4C22×C22⋊D7312yes—
729C2×C4C22×C22⋊D7312yes—
730C2×C4C22×C22⋊D7312yes—
731C2×C4C22×C22⋊D7312yes—
732C2×C4C22×C22⋊D7312yes—
733C2×C4C22×C22⋊D7312yes—
734C2×C4C22×C22⋊D7311yescharacteristic
735C2×C4#41×D7312yes—
736C2×C4#1455663712yes—
737C2×C4C24×D7311yescharacteristic
738C8—734no—
739C8—1462no—
740C8—1462no—
741C8—1462no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—2922no—
747C22—2922no—
748C22—2922no—
749C22—2922no—
750C22—2922no—
751C22—2922no—
752C22—5844no—
753C22—5844no—
754C22#1798925612yes—
755C22#1798938512yes—
756C22#1798939512yes—
757C22C23×C22⋊D7311yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—2922no—
768C4—2922no—
769C4#1798925612yes—
770C4C2×#41×D7311yescharacteristic
771C4C2×#1455663711yescharacteristic
772C2—82no—
773C2—5842no—
774C2—5842no—
775C2#2262299714yesdirect product factor
776C2C2×#1798925611yescharacteristic
777C2C2×#1798938511yescharacteristic
778C2C2×#1798939511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#556×C73C2
socleC23×C73C22×D4
prime radicalC2×#17988977C2
hypercenterC2×#556D73
hypocenterC73C2×#3401
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#17989322C2semidirect
2. #22622997C2direct (N × H)
3. C2×#17988979C2semidirect
5. C2×#17988969C2semidirect
6. C2×#17988809C2semidirect
7. C2×#17988806C2semidirect
8. C2×#17988787C2semidirect
9. C2×#17988802C2semidirect
10. C2×#17988799C2semidirect
11. C2×#17988789C2semidirect
12. C2×#17988718C2semidirect
13. C2×#17988697C2semidirect
14. C2×#17988692C2semidirect
15. C2×C4×#11924015C2semidirect
16. C2×#556×C73C2semidirect
27. #17989322C22semidirect
38. #17988979C22semidirect
40. #17988969C22semidirect
41. #17988809C22semidirect
42. #17988806C22semidirect
43. #17988802C22semidirect
44. #17988799C22semidirect
45. #17988789C22semidirect
46. #17988787C22semidirect
47. #17988718C22semidirect
48. #17988697C22semidirect
49. #17988692C22semidirect
50. C4×#11924015C22semidirect
65. #556×C73C22semidirect
384. C2×C73#3401semidirect
391. C2×#556D73semidirect
406. C73C2×#3401semidirect
419. #556C2×D73semidirect
775. C2#22622997direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893222
#226229972
C2×#179889792
C2×#179889772
C2×#179889692
C2×#179888092
C2×#179888062
C2×#179887872
C2×#179888022
C2×#179887992
C2×#179887892
C2×#179887182
C2×#179886972
C2×#179886922
C2×C4×#119240152
C2×#556×C732
C2×#340173