Finite Group Databasebeta

← C2×#22623789 #33994057

Subgroups — C2×#22623789 #33994057

Order 18688.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623789C2132yesmaximal, direct product factor
2C2×#17989320C212yesmaximal, complemented
3C2×#17989315C212yesmaximal, complemented
4C2×#17989309C212yesmaximal, complemented
5C2×#17989307C212yesmaximal, complemented
6C2×#17989305C212yesmaximal, complemented
7C2×#17989292C212yesmaximal, complemented
8C2×#17989276C212yesmaximal, complemented
9C2×#17989272C212yesmaximal, complemented
10C2×#17989179C214yesmaximal, complemented
11C2×#17989163C211yesmaximal, characteristic, complemented
12C2×#17989158C211yesmaximal, characteristic, complemented
13C2×#17989140C211yesmaximal, characteristic, complemented
14C2×#17989133C211yesmaximal, characteristic
15C2×#17989117C214yesmaximal, complemented
16C2×#17989068C211yesmaximal, characteristic, complemented
17C22×#14556556C211yesmaximal, characteristic, complemented
18C2×#520×C73C211yesmaximal, characteristic, complemented
19C22×#11924028C2211yescharacteristic
20C23×Dic146C2211yescharacteristic
21#17989320C22132yescomplemented
22#17989315C22132yescomplemented
23#17989309C22132yescomplemented
24#17989307C22132yescomplemented
25#17989305C22132yescomplemented
26#17989292C22132yescomplemented
27#17989276C22132yescomplemented
28#17989272C22132yescomplemented
29#17989179C22164yescomplemented
30#17989163C22116yescomplemented
31#17989158C22116yescomplemented
32#17989140C22116yescomplemented
33#17989133C22116yes—
34C2×#14556591C2212yes—
35C2×#14556590C2211yescharacteristic
36C2×#14556590C2211yescharacteristic
37C2×#14556589C2212yes—
38C2×#14556589C2211yescharacteristic
39C2×#14556587C2211yescharacteristic
40#17989117C22164yescomplemented
41C2×#14556586C2214yes—
42C2×#14556585C2214yes—
43C2×#14556584C2214yes—
44C2×#14556584C2214yes—
45C2×#14556583C2214yes—
46C2×#14556582C2211yescharacteristic
47C2×#14556582C2211yescharacteristic
48C2×#14556581C2214yes—
49C2×#14556581C2214yes—
50C2×#14556580C2211yescharacteristic
51C2×#14556579C2212yes—
52C2×#14556578C2212yes—
53C2×#14556578C2211yescharacteristic
54C2×#14556577C2214yes—
55C2×#14556575C2214yes—
56C2×#14556574C2214yes—
57C2×#14556573C2214yes—
58C2×#14556572C2214yes—
59C2×#14556571C2212yes—
60C2×#14556571C2212yes—
61C2×#14556570C2212yes—
62C2×#14556570C2212yes—
63C2×#14556570C2214yes—
64C2×#14556569C2214yes—
65C2×#14556568C2212yes—
66C2×#14556568C2212yes—
67C2×#14556563C2212yes—
68C2×#14556563C2212yes—
69#17989068C22116yescomplemented
70C2×C4×Dic146C2212yes—
71C2×C4×Dic146C2214yes—
72C2×C4×Dic146C2212yes—
73C2×#14556556C2212yes—
74C2×#14556556C2212yes—
75C2×#14556556C2212yes—
76C2×#14556556C2212yes—
77C2×#14556556C2212yes—
78C2×#14556556C22116yescomplemented
79C2×#14556553C2212yes—
80C2×C4×C22⋊D73C2214yes—
81C2×C4×C22⋊D73C2214yes—
82C2×C4×C22⋊D73C2212yes—
83C2×C4×C22⋊D73C2212yes—
84C2×#14556550C2211yescharacteristic
85C2×#14556550C2214yes—
86C2×#14556549C2212yes—
87C2×#14556548C2214yes—
88C22×#11924007C2212yes—
89C2×C4⋊C4×D73C2212yes—
90C22×C4×Dic73C2212yes—
91C22×C4×Dic73C2211yescharacteristic
92C22×#41×C73C2211yescharacteristic
93#520×C73C22116yescomplemented
94C2×C4×Q8×C73C2212yes—
95C2×C4×D4×C73C2212yes—
96C2×C4×D4×C73C2214yes—
97C2×#117×C73C2211yescharacteristic
98C2×#117×C73C2212yes—
99C22×C4⋊C4×C73C2211yescharacteristic
100C22×C4⋊C4×C73C2212yes—
101C2×#11924028—28no—
102C2×#11924028C2318yes—
103C22×Dic146—28no—
104C22×Dic146C2311yescharacteristic
105C22×Dic146C2312yes—
106C22×Dic146C2312yes—
107C22×Dic146C2318yes—
108C22×Dic146C2312yes—
109C22×Dic146C2312yes—
110C22×D292C2311yescharacteristic
111C22×C22⋊D73C2312yes—
112C22×C22⋊D73C2312yes—
113C22×C22⋊D73C2312yes—
114C23×Dic73C2312yes—
115C23×Dic73C2311yescharacteristic
116C23×Dic73C2311yescharacteristic
117C22×C4×D73C2312yes—
118C22×C4×D73C2314yes—
119#14556591C23116yes—
120#14556590C2318yes—
121#14556590C2318yes—
122#14556589C2318yes—
123#14556589C23116yes—
124#14556587C2318yes—
125#14556586C23132yes—
126#14556585C23132yes—
127#14556584C23132yes—
128#14556584C23132yes—
129#14556583C23132yes—
130#14556582C2318yes—
131#14556582C2318yes—
132#14556581C23132yes—
133#14556581C23132yes—
134#14556580C2318yes—
135#14556579C23116yes—
136#14556578C2318yes—
137#14556578C23116yes—
138#14556577C23132yes—
139#14556575C23132yes—
140#14556574C23132yes—
141#14556573C23132yes—
142#14556572C23132yes—
143#14556571C23116yes—
144#14556571C23116yes—
145#14556570C23116yes—
146#14556570C23116yes—
147#14556570C23132yes—
148#14556569C23132yes—
149#14556568C23116yes—
150#14556568C23116yes—
151#14556563C23116yes—
152#14556563C23116yes—
153C4×Dic146C23116yes—
154C4×Dic146C23116yes—
155C4×Dic146C23132yes—
156#14556556C23116yes—
157#14556556C23116yes—
158#14556556C23116yes—
159#14556556C23116yes—
160#14556556C23116yes—
161#14556553C23116yes—
162C4×C22⋊D73C23116yes—
163C4×C22⋊D73C23116yes—
164C4×C22⋊D73C23132yes—
165C4×C22⋊D73C23132yes—
166#14556550C2318yes—
167#14556550C23132yes—
168#14556549C23116yes—
169#14556548C23132yes—
170C2×C4⋊Dic73C2311yescharacteristic
171C2×C4⋊Dic73C2311yescharacteristic
172C2×C4⋊Dic73C2314yes—
173C2×C4⋊Dic73C2314yes—
174C2×C4⋊Dic73C2312yes—
175C2×C4⋊Dic73C2312yes—
176C2×#11924007C2314yes—
177C2×#11924007C2312yes—
178C2×#11924007C2312yes—
179C2×#11924007C2314yes—
180C2×#11924007C2312yes—
181C2×#11924007C2312yes—
182C2×#11924007C23116yes—
183C2×#11924007C2314yes—
184C2×#11924007C2314yes—
185C2×#11924007C2314yes—
186C2×#11924007C2312yes—
187C2×#11924007C2312yes—
188C4⋊C4×D73C23116yes—
189C2×C22⋊Dic73C2312yes—
190C2×C22⋊Dic73C2312yes—
191C2×C22⋊Dic73C2314yes—
192C2×C22⋊Dic73C2312yes—
193C2×C22⋊Dic73C2314yes—
194C2×#11924005C2312yes—
195C2×#11924005C2314yes—
196C2×#11924005C2314yes—
197C2×#11924005C2312yes—
198C2×#11924005C2314yes—
199C2×C4×Dic73C2311yescharacteristic
200C2×C4×Dic73C2312yes—
201C2×C4×Dic73C2311yescharacteristic
202C2×C4×Dic73C2318yes—
203C2×C4×Dic73C2314yes—
204C2×C4×Dic73C2311yescharacteristic
205C2×C4×Dic73C2314yes—
206C2×C4×Dic73C2311yescharacteristic
207C2×C4×Dic73C23116yes—
208C2×C4×Dic73C2314yes—
209C2×#41×C73—28no—
210C2×#41×C73C2318yes—
211C22×Q8×C73C2311yescharacteristic
212C22×D4×C73C2311yescharacteristic
213C22×D4×C73C2312yes—
214C23×C4×C73C2312yes—
215C23×C4×C73C2312yes—
216C23×C4×C73C2314yes—
217C23×C4×C73C2311yescharacteristic
218C4×Q8×C73C23116yes—
219C4×D4×C73C23132yes—
220C4×D4×C73C23116yes—
221#117×C73C2318yes—
222#117×C73C23116yes—
223C2×C4⋊C4×C73C2311yescharacteristic
224C2×C4⋊C4×C73C2311yescharacteristic
225C2×C4⋊C4×C73C2312yes—
226C2×C4⋊C4×C73C2312yes—
227C2×C4⋊C4×C73C2314yes—
228C2×C4⋊C4×C73C23116yes—
229C2×C4⋊C4×C73C2318yes—
230C2×C22⋊C4×C73C2312yes—
231C2×C22⋊C4×C73C2314yes—
232C2×C42×C73C2312yes—
233C2×C42×C73C2314yes—
234C23×D73C2412yes—
235#11924028—232no—
236C2×Dic146—28no—
237C2×Dic146—28no—
238C2×Dic146—232no—
239C2×Dic146—24no—
240C2×Dic146—28no—
241C2×Dic146—44no—
242C2×Dic146C2418yes—
243C2×Dic146C2418yes—
244C2×Dic146C2414yes—
245C2×Dic146C2418yes—
246C2×Dic146C2418yes—
247C2×D292—24no—
248C2×D292C2414yes—
249C2×C22⋊D73—28no—
250C2×C22⋊D73—28no—
251C2×C22⋊D73—44no—
252C2×C22⋊D73C2418yes—
253C2×C22⋊D73C2418yes—
254C2×C22⋊D73C2418yes—
255C22×Dic73—28no—
256C22×Dic73—24no—
257C22×Dic73—42no—
258C22×Dic73C2411yescharacteristic
259C22×Dic73C2414yes—
260C22×Dic73C2412yes—
261C22×Dic73C2411yescharacteristic
262C22×Dic73C2414yes—
263C22×Dic73C2412yes—
264C22×Dic73C2411yescharacteristic
265C22×Dic73C2418yes—
266C22×Dic73C2412yes—
267C22×Dic73C2414yes—
268C22×Dic73C2411yescharacteristic
269C2×C4×D73—28no—
270C2×C4×D73—48no—
271C2×C4×D73C2418yes—
272C2×C4×D73C24116yes—
273C4⋊Dic73C2414yes—
274C4⋊Dic73C2414yes—
275C4⋊Dic73C2418yes—
276C4⋊Dic73C24116yes—
277C4⋊Dic73C2418yes—
278C4⋊Dic73C24116yes—
279#11924007C24116yes—
280#11924007C24116yes—
281#11924007C24116yes—
282#11924007C2418yes—
283#11924007C24116yes—
284#11924007C2418yes—
285#11924007C2418yes—
286#11924007C2418yes—
287#11924007C2418yes—
288#11924007C2418yes—
289#11924007C24116yes—
290C22⋊Dic73C2418yes—
291C22⋊Dic73C2418yes—
292C22⋊Dic73C24116yes—
293C22⋊Dic73C2418yes—
294C22⋊Dic73C24116yes—
295#11924005C2418yes—
296#11924005C24116yes—
297#11924005C24116yes—
298#11924005C2418yes—
299#11924005C24116yes—
300C4×Dic73C24116yes—
301C4×Dic73C2414yes—
302C4×Dic73C2414yes—
303C4×Dic73C24116yes—
304C4×Dic73C2414yes—
305C4×Dic73C2414yes—
306C4×Dic73C24116yes—
307C4×Dic73C2418yes—
308C24×C73C2412yes—
309C24×C73C2411yescharacteristic
310#41×C73—232no—
311C2×Q8×C73—24no—
312C2×Q8×C73C2414yes—
313C2×D4×C73—28no—
314C2×D4×C73—24no—
315C2×D4×C73C2418yes—
316C2×D4×C73C2414yes—
317C22×C4×C73—28no—
318C22×C4×C73—44no—
319C22×C4×C73—48no—
320C22×C4×C73#4118yes—
321C22×C4×C73C2412yes—
322C22×C4×C73C2412yes—
323C22×C4×C73C2414yes—
324C22×C4×C73C2412yes—
325C22×C4×C73C2418yes—
326C22×C4×C73C2418yes—
327C22×C4×C73C24116yes—
328C22×C4×C73C2411yescharacteristic
329C22×C4×C73C2411yescharacteristic
330C22×C4×C73C2414yes—
331C4⋊C4×C73C2418yes—
332C4⋊C4×C73C2414yes—
333C4⋊C4×C73C2418yes—
334C4⋊C4×C73C24116yes—
335C4⋊C4×C73C2414yes—
336C22⋊C4×C73C2418yes—
337C22⋊C4×C73C24116yes—
338C42×C73C24116yes—
339C42×C73C2418yes—
340C23×C73—22no—
341C23×C73—22no—
342C23×C73—24no—
343C23×C73—24no—
344C23×C73—24no—
345C23×C73C2×#4114yes—
346C23×C73C2514yes—
347C23×C73C2512yes—
348C23×C73C2511yescharacteristic
349C22×D73—24no—
350C22×D73—24no—
351C22×D73—24no—
352C22×D73C2514yes—
353Q8×C73—28no—
354D4×C73—216no—
355D4×C73—28no—
356C2×C4×C73—24no—
357C2×C4×C73—24no—
358C2×C4×C73—28no—
359C2×C4×C73—24no—
360C2×C4×C73—216no—
361C2×C4×C73—416no—
362C2×C4×C73—48no—
363C2×C4×C73C2×#4114yes—
364C2×C4×C73C2×#4114yes—
365C2×C4×C73C2×#41116yes—
366C2×C4×C73C2514yes—
367C2×C4×C73C2514yes—
368C2×C4×C73C2518yes—
369C2×C4×C73C2514yes—
370C2×C4×C73C2512yes—
371C2×C4×C73C2512yes—
372C22⋊D73—216no—
373C22⋊D73—216no—
374C22⋊D73—48no—
375C2×Dic73—24no—
376C2×Dic73—216no—
377C2×Dic73—28no—
378C2×Dic73—22no—
379C2×Dic73—24no—
380C2×Dic73—24no—
381C2×Dic73—22no—
382C2×Dic73—22no—
383C2×Dic73—28no—
384C2×Dic73—44no—
385C2×Dic732−1+414yes—
386C2×Dic73C2512yes—
387C2×Dic73C2514yes—
388C2×Dic73C2512yes—
389C2×Dic73C2518yes—
390C2×Dic73C2514yes—
391C2×Dic73C2512yes—
392C2×Dic73C2514yes—
393C2×Dic73C2512yes—
394D292—28no—
395C4×D73—216no—
396C4×D73—416no—
397Dic146—216no—
398Dic146—216no—
399Dic146—28no—
400Dic146—216no—
401Dic146—48no—
402C22×C73—22no—
403C22×C73—22no—
404C22×C73—28no—
405C22×C73—24no—
406C22×C73—24no—
407C22×C73—24no—
408C22×C73—48no—
409C22×C73C22×#4114yes—
410C22×C73C22×#4112yes—
411C22×C73C2×2−1+412yes—
412C22×C73#58512yes—
413C22×C73C2611yescharacteristic
414C2×D73—24no—
415C2×D73—24no—
416C2×D73—24no—
417C2×D73—48no—
418C4×C73—24no—
419C4×C73—24no—
420C4×C73—24no—
421C4×C73—28no—
422C4×C73C22×#4114yes—
423C4×C73C22×#4114yes—
424Dic73—28no—
425Dic73—24no—
426Dic73—24no—
427Dic73—22no—
428Dic73—22no—
429Dic73—24no—
430Dic73—22no—
431Dic73C2×2−1+414yes—
432C2×#3507—731nomaximal, Sylow
433C2×C73—24no—
434C2×C73—44no—
435C2×C73#350714yescomplemented
436C2×C73C23×#4111yescharacteristic
437C2×C73C22×2−1+411yescharacteristic
438C2×C73C2×#58511yescharacteristic
439D73—44no—
440#3507—7332no—
441C2×#559—732no—
442C2×#557—732no—
443C2×#556—732no—
444C2×#556—732no—
445C2×#556—732no—
446C2×#554—732no—
447C2×#552—732no—
448C2×#552—732no—
449C2×#539—734no—
450C2×#536—731no—
451C2×#536—731no—
452C2×#533—731no—
453C2×#532—731no—
454C2×#529—734no—
455C2×#520—731no—
456C2×#520D7311yescharacteristic, complemented
457C22×C4×Q8—731no—
458C73C2×#350711yescharacteristic, complemented, Sylow
459C22×#41—731no—
460C22×#41C2×D7311yescharacteristic
461C23×Q8—731no—
462#559—7332no—
463#557—7332no—
464#556—7332no—
465#556—7332no—
466#556—7332no—
467#554—7332no—
468#552—7332no—
469#552—7332no—
470#539—7364no—
471#536—7316no—
472#536—7316no—
473#533—7316no—
474#532—7316no—
475C2×C4⋊Q8—731no—
476C2×C4⋊Q8—732no—
477C2×C4⋊Q8—731no—
478C2×C4⋊Q8—731no—
479C2×C4⋊Q8—732no—
480C2×#127—731no—
481#529—7364no—
482C2×#126—734no—
483C2×#126—734no—
484C2×#126—734no—
485C2×#126—734no—
486C2×#125—734no—
487C2×#125—731no—
488C2×#125—731no—
489C2×#125—734no—
490C2×#125—734no—
491C2×#124—731no—
492C2×#124—731no—
493C2×#124—732no—
494C2×#124—734no—
495C2×#124—732no—
496C2×#123—734no—
497C2×#123—734no—
498C2×#123—734no—
499C2×#123—734no—
500C2×C22⋊Q8—732no—
501C2×C22⋊Q8—732no—
502C2×C22⋊Q8—734no—
503C2×C22⋊Q8—732no—
504C2×C22⋊Q8—732no—
505C2×C22⋊Q8—734no—
506C2×C22⋊Q8—732no—
507C2×C22⋊Q8—732no—
508C2×#121—732no—
509C2×#121—732no—
510#520—7316no—
511#520C2×D73116yescomplemented
512C2×C4×Q8—732no—
513C2×C4×Q8—732no—
514C2×C4×Q8—732no—
515C2×C4×Q8—732no—
516C2×C4×Q8—7316no—
517C2×C4×Q8—732no—
518C2×C4×Q8—734no—
519C2×C4×Q8—732no—
520C2×C4×Q8—732no—
521C2×C4×Q8C2×D7312yes—
522C2×C4×D4—734no—
523C2×C4×D4—734no—
524C2×C4×D4—732no—
525C2×C4×D4—732no—
526C2×C4×D4—732no—
527C2×C4×D4C2×D7314yes—
528C2×C4×D4C2×D7312yes—
529C2×#117—731no—
530C2×#117—734no—
531C2×#117—732no—
532C2×#117—734no—
533C2×#117C2×D7311yescharacteristic
534C2×#117C2×D7312yes—
535C22×C4⋊C4—732no—
536C22×C4⋊C4—732no—
537C22×C4⋊C4C2×D7311yescharacteristic
538C22×C4⋊C4C2×D7312yes—
539C22×C42—732no—
540C22×C42—731no—
541C2×#41—28no—
542C2×#41—738no—
543C2×#41—1468no—
544C2×#41C22×D7318yes—
545C22×Q8—732no—
546C22×Q8—732no—
547C22×Q8—732no—
548C22×Q8—732no—
549C22×Q8—731no—
550C22×Q8—738no—
551C22×Q8—1468no—
552C22×Q8C22×D7311yescharacteristic
553C22×D4—732no—
554C22×D4—732no—
555C22×D4—732no—
556C22×D4—731no—
557C22×D4C22×D7312yes—
558C22×D4C22×D7311yescharacteristic
559C23×C4—731no—
560C23×C4—734no—
561C23×C4—732no—
562C23×C4—731no—
563C23×C4—732no—
564C23×C4C22×D7312yes—
565C23×C4C22×D7312yes—
566C23×C4C22×D7314yes—
567C23×C4C22×D7311yescharacteristic
568C4⋊Q8—738no—
569C4⋊Q8—7316no—
570C4⋊Q8—738no—
571C4⋊Q8—738no—
572C4⋊Q8—7316no—
573#127—738no—
574#126—7332no—
575#126—7332no—
576#126—7332no—
577#126—7332no—
578#125—7332no—
579#125—738no—
580#125—738no—
581#125—7332no—
582#125—7332no—
583#124—738no—
584#124—738no—
585#124—7316no—
586#124—7332no—
587#124—7316no—
588#123—7332no—
589#123—7332no—
590#123—7332no—
591#123—7332no—
592C22⋊Q8—7316no—
593C22⋊Q8—7316no—
594C22⋊Q8—7332no—
595C22⋊Q8—7316no—
596C22⋊Q8—7316no—
597C22⋊Q8—7332no—
598C22⋊Q8—7316no—
599C22⋊Q8—7316no—
600#121—7316no—
601#121—7316no—
602C4×Q8—7316no—
603C4×Q8—7316no—
604C4×Q8—7316no—
605C4×Q8—7316no—
606C4×Q8—7316no—
607C4×Q8—7332no—
608C4×Q8—7316no—
609C4×Q8—7316no—
610C4×Q8C22×D73116yes—
611C4×D4—7332no—
612C4×D4—7332no—
613C4×D4—7316no—
614C4×D4—7316no—
615C4×D4—7316no—
616C4×D4C22×D73132yes—
617C4×D4C22×D73116yes—
618#117—738no—
619#117—7332no—
620#117—7316no—
621#117—7332no—
622#117C22×D7318yes—
623#117C22×D73116yes—
624C2×C4⋊C4—731no—
625C2×C4⋊C4—734no—
626C2×C4⋊C4—734no—
627C2×C4⋊C4—734no—
628C2×C4⋊C4—7316no—
629C2×C4⋊C4—731no—
630C2×C4⋊C4—732no—
631C2×C4⋊C4—732no—
632C2×C4⋊C4—734no—
633C2×C4⋊C4—734no—
634C2×C4⋊C4—732no—
635C2×C4⋊C4—732no—
636C2×C4⋊C4—732no—
637C2×C4⋊C4—732no—
638C2×C4⋊C4—732no—
639C2×C4⋊C4—734no—
640C2×C4⋊C4—734no—
641C2×C4⋊C4—732no—
642C2×C4⋊C4—7316no—
643C2×C4⋊C4C22×D7312yes—
644C2×C4⋊C4C22×D7311yescharacteristic
645C2×C4⋊C4C22×D7312yes—
646C2×C4⋊C4C22×D7314yes—
647C2×C4⋊C4C22×D7318yes—
648C2×C4⋊C4C22×D73116yes—
649C2×C4⋊C4C22×D7311yescharacteristic
650C2×C22⋊C4—732no—
651C2×C22⋊C4—732no—
652C2×C22⋊C4—734no—
653C2×C22⋊C4—732no—
654C2×C22⋊C4—734no—
655C2×C22⋊C4—732no—
656C2×C22⋊C4—734no—
657C2×C22⋊C4—734no—
658C2×C22⋊C4—732no—
659C2×C22⋊C4—734no—
660C2×C22⋊C4C22×D7312yes—
661C2×C22⋊C4C22×D7314yes—
662C2×C42—734no—
663C2×C42—734no—
664C2×C42—732no—
665C2×C42—731no—
666C2×C42—731no—
667C2×C42—734no—
668C2×C42—731no—
669C2×C42—731no—
670C2×C42—7316no—
671C2×C42—738no—
672C2×C42C22×D7314yes—
673C2×C42C22×D7312yes—
674C24—732no—
675C24C23×D7312yes—
676C24C23×D7311yescharacteristic
677#41—232no—
678#41—14632no—
679C2×Q8—24no—
680C2×Q8—2924no—
681C2×Q8—738no—
682C2×Q8—738no—
683C2×Q8—738no—
684C2×Q8—738no—
685C2×Q8—734no—
686C2×Q8—1468no—
687C2×Q8—1468no—
688C2×Q8—1468no—
689C2×Q8—14632no—
690C2×Q8—1464no—
691C2×Q8C23×D7314yes—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—2924no—
695C2×D4—738no—
696C2×D4—738no—
697C2×D4—738no—
698C2×D4—734no—
699C2×D4—1468no—
700C2×D4—1468no—
701C2×D4—1464no—
702C2×D4C23×D7318yes—
703C2×D4C23×D7314yes—
704C22×C4—28no—
705C22×C4—44no—
706C22×C4—48no—
707C22×C4—2928no—
708C22×C4—2922no—
709C22×C4—734no—
710C22×C4—7316no—
711C22×C4—731no—
712C22×C4—734no—
713C22×C4—738no—
714C22×C4—731no—
715C22×C4—732no—
716C22×C4—734no—
717C22×C4—731no—
718C22×C4—732no—
719C22×C4—731no—
720C22×C4—732no—
721C22×C4—738no—
722C22×C4—1464no—
723C22×C4—1468no—
724C22×C4—1468no—
725C22×C4#1192402818yes—
726C22×C4C23×D7318yes—
727C22×C4C23×D7314yes—
728C22×C4C23×D7312yes—
729C22×C4C23×D7312yes—
730C22×C4C23×D7312yes—
731C22×C4C23×D7318yes—
732C22×C4C23×D73116yes—
733C22×C4C23×D7314yes—
734C22×C4C23×D7311yescharacteristic
735C22×C4C23×D7311yescharacteristic
736C4⋊C4—7316no—
737C4⋊C4—7316no—
738C4⋊C4—7316no—
739C4⋊C4—738no—
740C4⋊C4—7316no—
741C4⋊C4—738no—
742C4⋊C4—738no—
743C4⋊C4—738no—
744C4⋊C4—738no—
745C4⋊C4—7316no—
746C4⋊C4—738no—
747C4⋊C4—734no—
748C4⋊C4—734no—
749C4⋊C4—738no—
750C4⋊C4—7316no—
751C4⋊C4—738no—
752C4⋊C4—7316no—
753C4⋊C4C23×D7318yes—
754C4⋊C4C23×D7314yes—
755C4⋊C4C23×D7318yes—
756C4⋊C4C23×D73116yes—
757C4⋊C4C23×D7314yes—
758C22⋊C4—738no—
759C22⋊C4—738no—
760C22⋊C4—7316no—
761C22⋊C4—738no—
762C22⋊C4—7316no—
763C22⋊C4—738no—
764C22⋊C4—7316no—
765C22⋊C4—7316no—
766C22⋊C4—738no—
767C22⋊C4—7316no—
768C22⋊C4C23×D7318yes—
769C22⋊C4C23×D73116yes—
770C42—7316no—
771C42—734no—
772C42—734no—
773C42—7316no—
774C42—734no—
775C42—734no—
776C42—7316no—
777C42—738no—
778C42C23×D73116yes—
779C42C23×D7318yes—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—734no—
786C23—1464no—
787C23—1464no—
788C23—1464no—
789C23C2×#1192402814yes—
790C23C24×D7314yes—
791C23C24×D7312yes—
792C23C24×D7311yescharacteristic
793Q8—28no—
794Q8—2928no—
795Q8—14616no—
796Q8—14616no—
797Q8—14616no—
798Q8—1468no—
799D4—216no—
800D4—28no—
801D4—2928no—
802D4—14616no—
803D4—14616no—
804D4—1468no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—216no—
810C2×C4—48no—
811C2×C4—416no—
812C2×C4—29216no—
813C2×C4—2924no—
814C2×C4—734no—
815C2×C4—732no—
816C2×C4—732no—
817C2×C4—734no—
818C2×C4—738no—
819C2×C4—732no—
820C2×C4—734no—
821C2×C4—732no—
822C2×C4—734no—
823C2×C4—1468no—
824C2×C4—1464no—
825C2×C4—14616no—
826C2×C4—1468no—
827C2×C4—1462no—
828C2×C4—1464no—
829C2×C4—1464no—
830C2×C4—1462no—
831C2×C4—1462no—
832C2×C4—14616no—
833C2×C4C2×#1192402814yes—
834C2×C4C2×#1192402814yes—
835C2×C4C2×#11924028116yes—
836C2×C4C24×D7318yes—
837C2×C4C24×D7314yes—
838C2×C4C24×D7314yes—
839C2×C4C24×D7314yes—
840C2×C4C24×D7312yes—
841C2×C4C24×D7312yes—
842C22—28no—
843C22—22no—
844C22—22no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—48no—
849C22—2928no—
850C22—1464no—
851C22—1464no—
852C22—1464no—
853C22C22×#1192402814yes—
854C22C22×#1192402812yes—
855C222−1+4×D7312yes—
856C22#1798942212yes—
857C22C25×D7311yescharacteristic
858C4—24no—
859C4—24no—
860C4—28no—
861C4—24no—
862C4—734no—
863C4—1464no—
864C4—1468no—
865C4—1462no—
866C4—1464no—
867C4—1464no—
868C4—1462no—
869C4—1462no—
870C4C22×#1192402814yes—
871C4C22×#1192402814yes—
872C2—24no—
873C2—44no—
874C2—2924no—
875C2#2262378914yesdirect product factor
876C2C23×#1192402811yescharacteristic
877C2C2×2−1+4×D7311yescharacteristic
878C2C2×#1798942211yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#520×C73C2
socleC23×C73C25
prime radicalC2×#17989133C2
hypercenterC2×#520D73
hypocenterC73C2×#3507
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22623789C2direct (N × H)
2. C2×#17989320C2semidirect
3. C2×#17989315C2semidirect
4. C2×#17989309C2semidirect
5. C2×#17989307C2semidirect
6. C2×#17989305C2semidirect
7. C2×#17989292C2semidirect
8. C2×#17989276C2semidirect
9. C2×#17989272C2semidirect
10. C2×#17989179C2semidirect
11. C2×#17989163C2semidirect
12. C2×#17989158C2semidirect
13. C2×#17989140C2semidirect
15. C2×#17989117C2semidirect
16. C2×#17989068C2semidirect
17. C22×#14556556C2semidirect
18. C2×#520×C73C2semidirect
21. #17989320C22semidirect
22. #17989315C22semidirect
23. #17989309C22semidirect
24. #17989307C22semidirect
25. #17989305C22semidirect
26. #17989292C22semidirect
27. #17989276C22semidirect
28. #17989272C22semidirect
29. #17989179C22semidirect
30. #17989163C22semidirect
31. #17989158C22semidirect
32. #17989140C22semidirect
40. #17989117C22semidirect
69. #17989068C22semidirect
78. C2×#14556556C22semidirect
93. #520×C73C22semidirect
435. C2×C73#3507semidirect
456. C2×#520D73semidirect
458. C73C2×#3507semidirect
511. #520C2×D73semidirect
875. C2#22623789direct (N × H)

Maximal subgroups

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

subgroupindex
#226237892
C2×#179893202
C2×#179893152
C2×#179893092
C2×#179893072
C2×#179893052
C2×#179892922
C2×#179892762
C2×#179892722
C2×#179891792
C2×#179891632
C2×#179891582
C2×#179891402
C2×#179891332
C2×#179891172
C2×#179890682
C22×#145565562
C2×#520×C732
C2×#350773