Finite Group Databasebeta

← C2×#22624008 #33994187

Subgroups — C2×#22624008 #33994187

Order 18688.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624008C2132yesmaximal, direct product factor
2C2×#17989323C211yesmaximal, characteristic, complemented
3C2×#17989320C212yesmaximal, complemented
4C2×#17989317C211yesmaximal, characteristic, complemented
5C2×#17989298C211yesmaximal, characteristic, complemented
6C2×#17989296C212yesmaximal, complemented
7C2×#17989257C211yesmaximal, characteristic, complemented
8C2×#17989243C212yesmaximal, complemented
9C2×#17989237C212yesmaximal, complemented
10C2×#17989236C214yesmaximal, complemented
11C2×#17989202C212yesmaximal, complemented
12C2×#17989201C214yesmaximal, complemented
13C2×#17989132C212yesmaximal, complemented
14C2×#17989121C211yesmaximal, characteristic, complemented
15C2×#17989118C212yesmaximal, complemented
16C2×#17989066C212yesmaximal, complemented
17C22×C4×Dic146C211yesmaximal, characteristic, complemented
18C2×#532×C73C211yesmaximal, characteristic, complemented
19C22×#11924027C2212yes—
20C22×#11924027C2214yes—
21C23×Dic146C2211yescharacteristic
22#17989323C22116yescomplemented
23#17989320C22132yescomplemented
24#17989317C22116yescomplemented
25#17989298C22116yescomplemented
26#17989296C22132yescomplemented
27#17989257C22116yescomplemented
28#17989243C22132yescomplemented
29#17989237C22132yescomplemented
30#17989236C22164yescomplemented
31#17989202C22132yescomplemented
32#17989201C22164yescomplemented
33#17989132C22132yescomplemented
34C2×#14556590C2212yes—
35C2×#14556590C2212yes—
36C2×#14556589C2214yes—
37C2×#14556587C2212yes—
38#17989121C22116yescomplemented
39#17989118C22132yescomplemented
40C2×#14556585C2212yes—
41C2×#14556584C2214yes—
42C2×#14556583C2211yescharacteristic
43C2×#14556582C2212yes—
44C2×#14556579C2211yescharacteristic
45C2×#14556578C2212yes—
46C2×#14556578C2212yes—
47C2×#14556577C2214yes—
48C2×#14556577C2214yes—
49C2×#14556574C2214yes—
50C2×#14556574C2212yes—
51C2×#14556573C2214yes—
52C2×#14556572C2214yes—
53C2×#14556572C2214yes—
54C2×#14556571C2212yes—
55C2×#14556570C2214yes—
56C2×#14556570C2211yescharacteristic
57C2×#14556568C2214yes—
58C2×#14556568C2214yes—
59C2×#14556567C2214yes—
60C2×#14556565C2211yescharacteristic
61C2×#14556563C2214yes—
62C2×#14556563C2214yes—
63C2×#14556562C2212yes—
64#17989066C22132yescomplemented
65C2×C4×Dic146C2211yescharacteristic
66C2×C4×Dic146C2211yescharacteristic
67C2×C4×Dic146C2212yes—
68C2×C4×Dic146C2211yescharacteristic
69C2×C4×Dic146C2212yes—
70C2×C4×Dic146C2211yescharacteristic
71C2×C4×Dic146C2211yescharacteristic
72C2×C4×Dic146C22116yescomplemented
73C2×#14556556C2212yes—
74C2×#14556556C2212yes—
75C2×C4×D292C2211yescharacteristic
76C2×D4×Dic73C2212yes—
77C2×D4×Dic73C2212yes—
78C2×D4×Dic73C2214yes—
79C2×D4×Dic73C2212yes—
80C2×#14556553C2212yes—
81C2×C4×C22⋊D73C2214yes—
82C2×C4×C22⋊D73C2212yes—
83C2×#14556551C2214yes—
84C2×#14556548C2212yes—
85C2×#14556547C2214yes—
86C22×C4⋊Dic73C2211yescharacteristic
87C22×#11924007C2212yes—
88C22×#11924007C2214yes—
89C2×C4⋊C4×D73C2212yes—
90C22×C4×Dic73C2212yes—
91C22×#41×C73C2212yes—
92#532×C73C22116yescomplemented
93C2×C4⋊Q8×C73C2211yescharacteristic
94C2×#127×C73C2211yescharacteristic
95C2×#124×C73C2212yes—
96C2×#121×C73C2212yes—
97C2×#121×C73C2212yes—
98C2×C4×D4×C73C2212yes—
99C2×C4×D4×C73C2212yes—
100C22×C42×C73C2211yescharacteristic
101C2×#11924027—216no—
102C2×#11924027—416no—
103C2×#11924027C23116yes—
104C2×#11924027C23132yes—
105C22×Dic146—28no—
106C22×Dic146C2318yes—
107C22×Dic146C2312yes—
108C22×Dic146C2311yescharacteristic
109C22×Dic146C2311yescharacteristic
110C22×Dic146C2314yes—
111C22×Dic146C2311yescharacteristic
112C22×D292C2311yescharacteristic
113C22×C22⋊D73C2314yes—
114C22×C22⋊D73C2312yes—
115C22×C22⋊D73C2314yes—
116C23×Dic73C2312yes—
117C23×Dic73C2312yes—
118C23×Dic73C2314yes—
119C23×Dic73C2314yes—
120C22×C4×D73C2312yes—
121C22×C4×D73C2314yes—
122#14556590C23116yes—
123#14556590C23116yes—
124#14556589C23132yes—
125#14556587C23116yes—
126#14556585C23116yes—
127#14556584C23132yes—
128#14556583C2318yes—
129#14556582C23116yes—
130#14556579C2318yes—
131#14556578C23116yes—
132#14556578C23116yes—
133#14556577C23132yes—
134#14556577C23132yes—
135#14556574C23116yes—
136#14556574C23132yes—
137#14556573C23132yes—
138#14556572C23132yes—
139#14556572C23132yes—
140#14556571C23116yes—
141#14556570C2318yes—
142#14556570C23132yes—
143#14556568C23132yes—
144#14556568C23132yes—
145#14556567C23132yes—
146#14556565C2318yes—
147#14556563C23132yes—
148#14556563C23132yes—
149#14556562C23116yes—
150C4×Dic146C2318yes—
151C4×Dic146C23116yes—
152C4×Dic146C2318yes—
153C4×Dic146C2318yes—
154C4×Dic146C23116yes—
155C4×Dic146C2318yes—
156C4×Dic146C2318yes—
157#14556556C23116yes—
158#14556556C23116yes—
159C4×D292C2318yes—
160D4×Dic73C23116yes—
161D4×Dic73C23132yes—
162D4×Dic73C23116yes—
163D4×Dic73C23116yes—
164#14556553C23116yes—
165C4×C22⋊D73C23116yes—
166C4×C22⋊D73C23132yes—
167#14556551C23132yes—
168#14556548C23116yes—
169#14556547C23132yes—
170C2×C4⋊Dic73C2311yescharacteristic
171C2×C4⋊Dic73C2311yescharacteristic
172C2×C4⋊Dic73C2318yes—
173C2×C4⋊Dic73C2311yescharacteristic
174C2×C4⋊Dic73C2312yes—
175C2×C4⋊Dic73C2311yescharacteristic
176C2×C4⋊Dic73C2314yes—
177C2×#11924007C2312yes—
178C2×#11924007C2312yes—
179C2×#11924007C2314yes—
180C2×#11924007C2314yes—
181C2×#11924007C23116yes—
182C2×#11924007C23132yes—
183C2×#11924007C2314yes—
184C2×#11924007C2312yes—
185C2×#11924007C2312yes—
186C2×#11924007C2312yes—
187C2×#11924007C2312yes—
188C2×#11924007C2312yes—
189C2×#11924007C2312yes—
190C4⋊C4×D73C23116yes—
191C2×C22⋊Dic73C2314yes—
192C2×C22⋊Dic73C2312yes—
193C2×C22⋊Dic73C2314yes—
194C2×C22⋊Dic73C2314yes—
195C2×C22⋊Dic73C2314yes—
196C2×#11924005C2312yes—
197C2×#11924005C2312yes—
198C2×#11924005C2312yes—
199C2×#11924005C2314yes—
200C2×#11924005C2312yes—
201C2×C4×Dic73C2312yes—
202C2×C4×Dic73C2314yes—
203C2×C4×Dic73C2312yes—
204C2×C4×Dic73C23116yes—
205C2×C4×Dic73C2312yes—
206C2×C4×Dic73C2312yes—
207C2×C4×Dic73C2312yes—
208C2×#41×C73—48no—
209C2×#41×C73C23116yes—
210C22×Q8×C73C2312yes—
211C22×D4×C73C2312yes—
212C22×D4×C73C2312yes—
213C22×D4×C73C2314yes—
214C22×D4×C73C2312yes—
215C23×C4×C73C2311yescharacteristic
216C23×C4×C73C2311yescharacteristic
217C23×C4×C73C2311yescharacteristic
218C23×C4×C73C2314yes—
219C4⋊Q8×C73C2318yes—
220#127×C73C2318yes—
221#124×C73C23116yes—
222#121×C73C23116yes—
223#121×C73C23116yes—
224C4×D4×C73C23116yes—
225C4×D4×C73C23116yes—
226C2×C4⋊C4×C73C2312yes—
227C2×C4⋊C4×C73C2312yes—
228C2×C22⋊C4×C73C2314yes—
229C2×C22⋊C4×C73C2314yes—
230C2×C42×C73C2318yes—
231C2×C42×C73C2311yescharacteristic
232C2×C42×C73C2311yescharacteristic
233C2×C42×C73C2311yescharacteristic
234C2×C42×C73C2311yescharacteristic
235C23×D73C2412yes—
236#11924027—264no—
237#11924027—464no—
238C2×Dic146—24no—
239C2×Dic146—24no—
240C2×Dic146—28no—
241C2×Dic146—232no—
242C2×Dic146—48no—
243C2×Dic146#4118yescomplemented
244C2×Dic146C2414yes—
245C2×Dic146C2418yes—
246C2×Dic146C2414yes—
247C2×Dic146C24116yes—
248C2×Dic146C2414yes—
249C2×D292—24no—
250C2×D292C2414yes—
251C2×C22⋊D73—28no—
252C2×C22⋊D73—216no—
253C2×C22⋊D73—48no—
254C2×C22⋊D73C24116yes—
255C2×C22⋊D73C2418yes—
256C2×C22⋊D73C24116yes—
257C22×Dic73—28no—
258C22×Dic73—28no—
259C22×Dic73—216no—
260C22×Dic73—48no—
261C22×Dic73C2412yes—
262C22×Dic73C2412yes—
263C22×Dic73C2412yes—
264C22×Dic73C2412yes—
265C22×Dic73C2418yes—
266C22×Dic73C2418yes—
267C22×Dic73C2412yes—
268C22×Dic73C2412yes—
269C22×Dic73C24116yes—
270C22×Dic73C24116yes—
271C22×Dic73C2412yes—
272C2×C4×D73—28no—
273C2×C4×D73—48no—
274C2×C4×D73C2418yes—
275C2×C4×D73C24116yes—
276C4⋊Dic73C2414yes—
277C4⋊Dic73C2414yes—
278C4⋊Dic73C2418yes—
279C4⋊Dic73C2414yes—
280C4⋊Dic73C2414yes—
281C4⋊Dic73C24116yes—
282#11924007C24116yes—
283#11924007C2418yes—
284#11924007C2418yes—
285#11924007C24116yes—
286#11924007C2418yes—
287#11924007C2418yes—
288#11924007C2418yes—
289#11924007C2418yes—
290#11924007C2418yes—
291#11924007C24116yes—
292#11924007C2418yes—
293C22⋊Dic73C24116yes—
294C22⋊Dic73C2418yes—
295C22⋊Dic73C24116yes—
296C22⋊Dic73C24116yes—
297C22⋊Dic73C24116yes—
298#11924005C2418yes—
299#11924005C2418yes—
300#11924005C2418yes—
301#11924005C24116yes—
302#11924005C2418yes—
303C4×Dic73C2418yes—
304C4×Dic73C2418yes—
305C4×Dic73C2418yes—
306C4×Dic73C2418yes—
307C4×Dic73C24116yes—
308C4×Dic73C2418yes—
309C24×C73C2414yes—
310C24×C73C2411yescharacteristic
311#41×C73—432no—
312C2×Q8×C73—44no—
313C2×Q8×C73C2418yes—
314C2×D4×C73—216no—
315C2×D4×C73—28no—
316C2×D4×C73—28no—
317C2×D4×C73—44no—
318C2×D4×C73C2418yes—
319C2×D4×C73C2418yes—
320C2×D4×C73C24116yes—
321C2×D4×C73C2418yes—
322C22×C4×C73—24no—
323C22×C4×C73—24no—
324C22×C4×C73—24no—
325C22×C4×C73—48no—
326C22×C4×C73C2411yescharacteristic
327C22×C4×C73C2411yescharacteristic
328C22×C4×C73C2414yes—
329C22×C4×C73C2414yes—
330C22×C4×C73C2411yescharacteristic
331C22×C4×C73C2411yescharacteristic
332C22×C4×C73C2414yes—
333C22×C4×C73C2414yes—
334C22×C4×C73C24116yes—
335C22×C4×C73C2411yescharacteristic
336C22×C4×C73C2411yescharacteristic
337C4⋊C4×C73C2418yes—
338C4⋊C4×C73C2418yes—
339C22⋊C4×C73C24116yes—
340C22⋊C4×C73C24116yes—
341C42×C73C2414yes—
342C42×C73C2414yes—
343C42×C73C2414yes—
344C42×C73C2414yes—
345C23×C73—22no—
346C23×C73—22no—
347C23×C73—28no—
348C23×C73—28no—
349C23×C73—28no—
350C23×C73H(5,𝔽2)14yes—
351C23×C73C2518yes—
352C23×C73C2512yes—
353C23×C73C2511yescharacteristic
354C22×D73—24no—
355C22×D73—24no—
356C22×D73—24no—
357C22×D73C2514yes—
358Q8×C73—48no—
359D4×C73—232no—
360D4×C73—216no—
361D4×C73—216no—
362D4×C73—48no—
363C2×C4×C73—22no—
364C2×C4×C73—22no—
365C2×C4×C73—22no—
366C2×C4×C73—28no—
367C2×C4×C73—28no—
368C2×C4×C73—22no—
369C2×C4×C73—28no—
370C2×C4×C73—28no—
371C2×C4×C73—416no—
372C2×C4×C73C2×#4114yes—
373C2×C4×C732−1+414yes—
374C2×C4×C73C2512yes—
375C2×C4×C73C2512yes—
376C2×C4×C73C2512yes—
377C2×C4×C73C2512yes—
378C2×C4×C73C2518yes—
379C2×C4×C73C2512yes—
380C2×C4×C73C2512yes—
381C22⋊D73—216no—
382C22⋊D73—232no—
383C22⋊D73—416no—
384C2×Dic73—24no—
385C2×Dic73—24no—
386C2×Dic73—24no—
387C2×Dic73—24no—
388C2×Dic73—216no—
389C2×Dic73—24no—
390C2×Dic73—24no—
391C2×Dic73—216no—
392C2×Dic73—232no—
393C2×Dic73—416no—
394C2×Dic73C2×#4118yes—
395C2×Dic73C2514yes—
396C2×Dic73C2514yes—
397C2×Dic73C2514yes—
398C2×Dic73C2514yes—
399C2×Dic73C2514yes—
400C2×Dic73C2514yes—
401C2×Dic73C2514yes—
402D292—28no—
403C4×D73—216no—
404C4×D73—416no—
405Dic146—28no—
406Dic146—28no—
407Dic146—216no—
408Dic146—416no—
409Dic146C2×#41116yescomplemented
410C22×C73—22no—
411C22×C73—22no—
412C22×C73—28no—
413C22×C73—28no—
414C22×C73—28no—
415C22×C73—28no—
416C22×C73—416no—
417C22×C73C22×#4112yes—
418C22×C73C2×H(5,𝔽2)14yes—
419C22×C73C2×H(5,𝔽2)12yes—
420C22×C73C2×2−1+412yes—
421C22×C73C2611yescharacteristic
422C2×D73—24no—
423C2×D73—24no—
424C2×D73—24no—
425C2×D73—48no—
426C4×C73—22no—
427C4×C73—28no—
428C4×C73—22no—
429C4×C73—22no—
430C4×C73—22no—
431C4×C73C22×#4114yes—
432C4×C73C2×2−1+414yes—
433Dic73—24no—
434Dic73—24no—
435Dic73—24no—
436Dic73—24no—
437Dic73—24no—
438Dic73—24no—
439Dic73C22×#4118yes—
440C2×#3522—731nomaximal, Sylow
441C2×C73—24no—
442C2×C73—48no—
443C2×C73#352214yescomplemented
444C2×C73C23×#4111yescharacteristic
445C2×C73C22×H(5,𝔽2)11yescharacteristic
446C2×C73C22×2−1+411yescharacteristic
447D73—44no—
448#3522—7332no—
449C2×#559—731no—
450C2×#559—732no—
451C2×Q82—731no—
452C2×#554—731no—
453C2×#554—732no—
454C2×#550—731no—
455C2×#548—732no—
456C2×#547—734no—
457C2×#547—732no—
458C2×#542—734no—
459C2×#542—732no—
460C2×#532—732no—
461C2×#532D7311yescharacteristic, complemented
462C2×#529—731no—
463C2×#529—732no—
464C2×#520—732no—
465C22×C4×Q8—731no—
466C73C2×#352211yescharacteristic, complemented, Sylow
467C22×#41—734no—
468C22×#41—732no—
469C22×#41C2×D7312yes—
470C23×Q8—731no—
471#559—7316no—
472#559—7332no—
473Q82—7316no—
474#554—7316no—
475#554—7332no—
476#550—7316no—
477#548—7332no—
478#547—7364no—
479#547—7332no—
480#542—7364no—
481#542—7332no—
482#532—7332no—
483#532C2×D73116yescomplemented
484C2×C4⋊Q8—734no—
485C2×C4⋊Q8—732no—
486C2×C4⋊Q8—732no—
487C2×C4⋊Q8C2×D7311yescharacteristic
488C2×#127—732no—
489C2×#127C2×D7311yescharacteristic
490#529—7332no—
491#529—7316no—
492C2×#126—734no—
493C2×#126—732no—
494C2×#125—732no—
495C2×#125—731no—
496C2×#124—732no—
497C2×#124—732no—
498C2×#124—734no—
499C2×#124—734no—
500C2×#124—731no—
501C2×#124C2×D7312yes—
502C2×#123—734no—
503C2×#123—734no—
504C2×#123—732no—
505C2×#123—734no—
506C2×#123—734no—
507C2×C22⋊Q8—734no—
508C2×C22⋊Q8—731no—
509C2×C22⋊Q8—734no—
510C2×C22⋊Q8—732no—
511C2×C22⋊Q8—734no—
512C2×C22⋊Q8—734no—
513C2×#121—734no—
514C2×#121—732no—
515C2×#121—734no—
516C2×#121—731no—
517C2×#121C2×D7312yes—
518C2×#121C2×D7312yes—
519#520—7332no—
520C2×C4×Q8—732no—
521C2×C4×Q8—732no—
522C2×C4×Q8—731no—
523C2×C4×Q8—732no—
524C2×C4×Q8—731no—
525C2×C4×Q8—731no—
526C2×C4×Q8—731no—
527C2×C4×Q8—732no—
528C2×C4×Q8—7316no—
529C2×C4×Q8—731no—
530C2×C4×D4—732no—
531C2×C4×D4—734no—
532C2×C4×D4—732no—
533C2×C4×D4—732no—
534C2×C4×D4—734no—
535C2×C4×D4—732no—
536C2×C4×D4—732no—
537C2×C4×D4—734no—
538C2×C4×D4—731no—
539C2×C4×D4C2×D7312yes—
540C2×C4×D4C2×D7312yes—
541C2×#117—734no—
542C2×#117—732no—
543C22×C4⋊C4—732no—
544C22×C4⋊C4—731no—
545C22×C4⋊C4—734no—
546C22×C4⋊C4—732no—
547C22×C42—732no—
548C22×C42C2×D7311yescharacteristic
549C2×#41—48no—
550C2×#41—29216no—
551C2×#41—7332no—
552C2×#41—7316no—
553C2×#41—14616no—
554C2×#41C22×D73116yes—
555C22×Q8—734no—
556C22×Q8—731no—
557C22×Q8—731no—
558C22×Q8—732no—
559C22×Q8—731no—
560C22×Q8—738no—
561C22×Q8—1468no—
562C22×Q8C22×D7312yes—
563C22×D4—734no—
564C22×D4—734no—
565C22×D4—732no—
566C22×D4—731no—
567C22×D4C22×D7312yes—
568C22×D4C22×D7312yes—
569C22×D4C22×D7314yes—
570C22×D4C22×D7312yes—
571C23×C4—734no—
572C23×C4—734no—
573C23×C4—732no—
574C23×C4—734no—
575C23×C4—732no—
576C23×C4—732no—
577C23×C4C22×D7311yescharacteristic
578C23×C4C22×D7311yescharacteristic
579C23×C4C22×D7311yescharacteristic
580C23×C4C22×D7314yes—
581C4⋊Q8—7332no—
582C4⋊Q8—7316no—
583C4⋊Q8—7316no—
584C4⋊Q8C22×D7318yes—
585#127—7316no—
586#127C22×D7318yes—
587#126—7332no—
588#126—7316no—
589#125—7316no—
590#125—738no—
591#124—7316no—
592#124—7316no—
593#124—7332no—
594#124—7332no—
595#124—738no—
596#124C22×D73116yes—
597#123—7332no—
598#123—7332no—
599#123—7316no—
600#123—7332no—
601#123—7332no—
602C22⋊Q8—7332no—
603C22⋊Q8—738no—
604C22⋊Q8—7332no—
605C22⋊Q8—7316no—
606C22⋊Q8—7332no—
607C22⋊Q8—7332no—
608#121—7332no—
609#121—7316no—
610#121—7332no—
611#121—738no—
612#121C22×D73116yes—
613#121C22×D73116yes—
614C4×Q8—7316no—
615C4×Q8—7316no—
616C4×Q8—738no—
617C4×Q8—7316no—
618C4×Q8—738no—
619C4×Q8—738no—
620C4×Q8—738no—
621C4×Q8—7316no—
622C4×Q8—738no—
623C4×D4—7316no—
624C4×D4—7332no—
625C4×D4—7316no—
626C4×D4—7316no—
627C4×D4—7332no—
628C4×D4—7316no—
629C4×D4—7316no—
630C4×D4—7332no—
631C4×D4—738no—
632C4×D4C22×D73116yes—
633C4×D4C22×D73116yes—
634#117—7332no—
635#117—7316no—
636C2×C4⋊C4—732no—
637C2×C4⋊C4—731no—
638C2×C4⋊C4—734no—
639C2×C4⋊C4—732no—
640C2×C4⋊C4—734no—
641C2×C4⋊C4—732no—
642C2×C4⋊C4—731no—
643C2×C4⋊C4—732no—
644C2×C4⋊C4—732no—
645C2×C4⋊C4—732no—
646C2×C4⋊C4—7316no—
647C2×C4⋊C4—738no—
648C2×C4⋊C4—7332no—
649C2×C4⋊C4—732no—
650C2×C4⋊C4—731no—
651C2×C4⋊C4—731no—
652C2×C4⋊C4—732no—
653C2×C4⋊C4—734no—
654C2×C4⋊C4—734no—
655C2×C4⋊C4—732no—
656C2×C4⋊C4—7316no—
657C2×C4⋊C4C22×D7312yes—
658C2×C4⋊C4C22×D7312yes—
659C2×C22⋊C4—734no—
660C2×C22⋊C4—732no—
661C2×C22⋊C4—734no—
662C2×C22⋊C4—734no—
663C2×C22⋊C4—734no—
664C2×C22⋊C4—732no—
665C2×C22⋊C4—732no—
666C2×C22⋊C4—732no—
667C2×C22⋊C4—734no—
668C2×C22⋊C4—732no—
669C2×C22⋊C4C22×D7314yes—
670C2×C22⋊C4C22×D7314yes—
671C2×C42—732no—
672C2×C42—734no—
673C2×C42—732no—
674C2×C42—732no—
675C2×C42—732no—
676C2×C42—732no—
677C2×C42—7316no—
678C2×C42C22×D7311yescharacteristic
679C2×C42C22×D7311yescharacteristic
680C2×C42C22×D7311yescharacteristic
681C2×C42C22×D7311yescharacteristic
682C2×C42C22×D7318yes—
683C24—732no—
684C24C23×D7314yes—
685C24C23×D7311yescharacteristic
686#41—432no—
687#41—29264no—
688#41—14664no—
689C2×Q8—44no—
690C2×Q8—2928no—
691C2×Q8—738no—
692C2×Q8—7316no—
693C2×Q8—734no—
694C2×Q8—734no—
695C2×Q8—738no—
696C2×Q8—734no—
697C2×Q8—1468no—
698C2×Q8—14632no—
699C2×Q8—1464no—
700C2×Q8—1464no—
701C2×Q8C23×D7318yes—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—44no—
706C2×D4—2928no—
707C2×D4—7316no—
708C2×D4—7316no—
709C2×D4—738no—
710C2×D4—734no—
711C2×D4—14616no—
712C2×D4—1468no—
713C2×D4—1464no—
714C2×D4C23×D7318yes—
715C2×D4C23×D7318yes—
716C2×D4C23×D73116yes—
717C2×D4C23×D7318yes—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—48no—
722C22×C4—2928no—
723C22×C4—2928no—
724C22×C4—7316no—
725C22×C4—7316no—
726C22×C4—732no—
727C22×C4—738no—
728C22×C4—738no—
729C22×C4—7316no—
730C22×C4—732no—
731C22×C4—732no—
732C22×C4—732no—
733C22×C4—732no—
734C22×C4—732no—
735C22×C4—732no—
736C22×C4—738no—
737C22×C4—1468no—
738C22×C4—14616no—
739C22×C4—1468no—
740C22×C4—1468no—
741C22×C4C23×D7314yes—
742C22×C4C23×D7314yes—
743C22×C4C23×D7314yes—
744C22×C4C23×D7311yescharacteristic
745C22×C4C23×D7314yes—
746C22×C4C23×D7311yescharacteristic
747C22×C4C23×D7311yescharacteristic
748C22×C4C23×D7311yescharacteristic
749C22×C4C23×D73116yes—
750C22×C4C23×D7311yescharacteristic
751C22×C4C23×D7311yescharacteristic
752C4⋊C4—738no—
753C4⋊C4—7316no—
754C4⋊C4—738no—
755C4⋊C4—7316no—
756C4⋊C4—738no—
757C4⋊C4—738no—
758C4⋊C4—738no—
759C4⋊C4—738no—
760C4⋊C4—738no—
761C4⋊C4—7316no—
762C4⋊C4—738no—
763C4⋊C4—734no—
764C4⋊C4—734no—
765C4⋊C4—738no—
766C4⋊C4—734no—
767C4⋊C4—734no—
768C4⋊C4—7316no—
769C4⋊C4C23×D7318yes—
770C4⋊C4C23×D7318yes—
771C22⋊C4—7316no—
772C22⋊C4—738no—
773C22⋊C4—7316no—
774C22⋊C4—7316no—
775C22⋊C4—7316no—
776C22⋊C4—738no—
777C22⋊C4—738no—
778C22⋊C4—738no—
779C22⋊C4—7316no—
780C22⋊C4—738no—
781C22⋊C4C23×D73116yes—
782C22⋊C4C23×D73116yes—
783C42—738no—
784C42—738no—
785C42—738no—
786C42—738no—
787C42—7316no—
788C42—738no—
789C42C23×D7314yes—
790C42C23×D7314yes—
791C42C23×D7314yes—
792C42C23×D7314yes—
793C23—22no—
794C23—22no—
795C23—28no—
796C23—28no—
797C23—28no—
798C23—734no—
799C23—1464no—
800C23—1464no—
801C23—1464no—
802C23#1455663614yes—
803C23C24×D7318yes—
804C23C24×D7312yes—
805C23C24×D7311yescharacteristic
806Q8—48no—
807Q8—29216no—
808Q8—7316no—
809Q8—14616no—
810Q8—1468no—
811Q8—1468no—
812D4—232no—
813D4—216no—
814D4—216no—
815D4—48no—
816D4—29216no—
817D4—14632no—
818D4—14616no—
819D4—1468no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—28no—
824C2×C4—28no—
825C2×C4—22no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—416no—
829C2×C4—29216no—
830C2×C4—29216no—
831C2×C4—738no—
832C2×C4—734no—
833C2×C4—734no—
834C2×C4—734no—
835C2×C4—734no—
836C2×C4—734no—
837C2×C4—734no—
838C2×C4—734no—
839C2×C4—14616no—
840C2×C4—14632no—
841C2×C4—1464no—
842C2×C4—1464no—
843C2×C4—1464no—
844C2×C4—1464no—
845C2×C4—1464no—
846C2×C4—14616no—
847C2×C4—1464no—
848C2×C4—14616no—
849C2×C4#41×D7314yes—
850C2×C4#1455663814yes—
851C2×C4C24×D7312yes—
852C2×C4C24×D7318yes—
853C2×C4C24×D7312yes—
854C2×C4C24×D7312yes—
855C2×C4C24×D7312yes—
856C2×C4C24×D7312yes—
857C2×C4C24×D7312yes—
858C22—28no—
859C22—22no—
860C22—22no—
861C22—28no—
862C22—28no—
863C22—28no—
864C22—416no—
865C22—2928no—
866C22—1464no—
867C22—1464no—
868C22—1464no—
869C22C2×#41×D7312yes—
870C22C2×#1455663614yes—
871C22C2×#1455663612yes—
872C22C2×#1455663812yes—
873C22C25×D7311yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—28no—
878C4—22no—
879C4—738no—
880C4—1464no—
881C4—1464no—
882C4—1464no—
883C4—1464no—
884C4—1464no—
885C4—1464no—
886C4C2×#41×D7314yes—
887C4C2×#1455663814yes—
888C2—24no—
889C2—48no—
890C2—2924no—
891C2#2262400814yesdirect product factor
892C2C22×#41×D7311yescharacteristic
893C2C22×#1455663611yescharacteristic
894C2C22×#1455663811yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#532×C73C2
socleC23×C73C25
hypercenterC2×#532D73
hypocenterC73C2×#3522
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #22624008C2direct (N × H)
2. C2×#17989323C2semidirect
3. C2×#17989320C2semidirect
4. C2×#17989317C2semidirect
5. C2×#17989298C2semidirect
6. C2×#17989296C2semidirect
7. C2×#17989257C2semidirect
8. C2×#17989243C2semidirect
9. C2×#17989237C2semidirect
10. C2×#17989236C2semidirect
11. C2×#17989202C2semidirect
12. C2×#17989201C2semidirect
13. C2×#17989132C2semidirect
14. C2×#17989121C2semidirect
15. C2×#17989118C2semidirect
16. C2×#17989066C2semidirect
17. C22×C4×Dic146C2semidirect
18. C2×#532×C73C2semidirect
22. #17989323C22semidirect
23. #17989320C22semidirect
24. #17989317C22semidirect
25. #17989298C22semidirect
26. #17989296C22semidirect
27. #17989257C22semidirect
28. #17989243C22semidirect
29. #17989237C22semidirect
30. #17989236C22semidirect
31. #17989202C22semidirect
32. #17989201C22semidirect
33. #17989132C22semidirect
38. #17989121C22semidirect
39. #17989118C22semidirect
64. #17989066C22semidirect
72. C2×C4×Dic146C22semidirect
92. #532×C73C22semidirect
243. C2×Dic146#41semidirect
409. Dic146C2×#41semidirect
443. C2×C73#3522semidirect
461. C2×#532D73semidirect
466. C73C2×#3522semidirect
483. #532C2×D73semidirect
891. C2#22624008direct (N × H)

Maximal subgroups

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

subgroupindex
#226240082
C2×#179893232
C2×#179893202
C2×#179893172
C2×#179892982
C2×#179892962
C2×#179892572
C2×#179892432
C2×#179892372
C2×#179892362
C2×#179892022
C2×#179892012
C2×#179891322
C2×#179891212
C2×#179891182
C2×#179890662
C22×C4×Dic1462
C2×#532×C732
C2×#352273