Finite Group Databasebeta

← C2×#22624322 #33993678

Subgroups — C2×#22624322 #33993678

Order 18688.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624322C2132yesmaximal, direct product factor
2C2×#17989334C214yesmaximal, complemented
3C2×#17989302C212yesmaximal, complemented
4C2×#17989302C211yesmaximal, characteristic, complemented
5C2×#17989297C211yesmaximal, characteristic, complemented
6C2×#17989283C212yesmaximal, complemented
7C2×#17989275C212yesmaximal, complemented
8C2×Q8×D292C211yesmaximal, characteristic, complemented
9C2×#17989245C212yesmaximal, complemented
10C2×#17989241C211yesmaximal, characteristic, complemented
11C2×#17989215C212yesmaximal, complemented
12C2×#17989203C214yesmaximal, complemented
13C2×#17989192C212yesmaximal, complemented
14C2×#17989166C212yesmaximal, complemented
15C2×#17989160C212yesmaximal, complemented
16C2×#17989144C211yesmaximal, characteristic, complemented
17C2×#17989137C211yesmaximal, characteristic, complemented
18C2×#529×C73C211yesmaximal, characteristic, complemented
19C22×#11924028C2212yes—
20C22×#11924027C2212yes—
21C22×Q8×D73C2212yes—
22#17989334C22164yescomplemented
23#17989302C22116yescomplemented
24#17989302C22132yescomplemented
25#17989297C22116yescomplemented
26#17989283C22132yescomplemented
27#17989275C22132yescomplemented
28Q8×D292C22116yescomplemented
29#17989245C22132yescomplemented
30#17989241C22116yescomplemented
31#17989215C22132yescomplemented
32#17989203C22164yescomplemented
33#17989192C22132yescomplemented
34#17989166C22132yescomplemented
35#17989160C22132yescomplemented
36#17989144C22116yescomplemented
37#17989137C22116yescomplemented
38C2×#14556591C2211yescharacteristic
39C2×#14556591C2212yes—
40C2×#14556591C2211yescharacteristic
41C2×#14556591C2211yescharacteristic
42C2×#14556590C2214yes—
43C2×#14556588C2211yescharacteristic
44C2×#14556586C2214yes—
45C2×#14556583C2212yes—
46C2×#14556583C2212yes—
47C2×#14556582C2214yes—
48C2×#14556579C2212yes—
49C2×#14556577C2214yes—
50C2×#14556577C2214yes—
51C2×#14556577C2214yes—
52C2×#14556576C2214yes—
53C2×#14556576C2214yes—
54C2×#14556575C2214yes—
55C2×#14556573C2214yes—
56C2×#14556571C2212yes—
57C2×#14556571C2212yes—
58C2×#14556571C2214yes—
59C2×#14556570C2212yes—
60C2×#14556570C2212yes—
61C2×#14556569C2214yes—
62C2×#14556568C2214yes—
63C2×#14556568C2214yes—
64C2×#14556567C2212yes—
65C2×#14556565C2212yes—
66C2×#14556565C2212yes—
67C2×#14556565C2212yes—
68C2×#14556565C2211yescharacteristic
69C2×#14556565C2211yescharacteristic
70C2×#14556564C2214yes—
71C2×#14556564C2214yes—
72C2×#14556563C2214yes—
73C2×#14556562C2214yes—
74C2×#14556562C2212yes—
75C2×C4×Dic146C2212yes—
76C2×C4×Dic146C2212yes—
77C2×C4×D292C2212yes—
78C2×C4×D292C2212yes—
79C2×C4×D292C2211yescharacteristic
80C2×C4×D292C2212yes—
81C2×C4×D292C2211yescharacteristic
82C2×#14556551C2214yes—
83C2×#14556550C2212yes—
84C2×#14556550C2212yes—
85C2×#14556549C2212yes—
86C2×#14556549C2214yes—
87C22×C4⋊Dic73C2212yes—
88C2×C4⋊C4×D73C2212yes—
89#529×C73C22116yescomplemented
90C2×#126×C73C2212yes—
91C2×#125×C73C2211yescharacteristic
92C2×#124×C73C2211yescharacteristic
93C2×#123×C73C2212yes—
94C2×C22⋊Q8×C73C2211yescharacteristic
95C2×#121×C73C2211yescharacteristic
96C2×C4×Q8×C73C2211yescharacteristic
97C2×C4×D4×C73C2211yescharacteristic
98C2×C4×D4×C73C2212yes—
99C2×#117×C73C2212yes—
100C22×C42×C73C2211yescharacteristic
101C2×#11924028—48no—
102C2×#11924028C23116yes—
103C2×#11924027—48no—
104C2×#11924027C23116yes—
105C22×Dic146C2312yes—
106C22×Dic146C2312yes—
107C22×Dic146C2314yes—
108C22×Dic146C2312yes—
109C2×Q8×D73—48no—
110C2×Q8×D73C23116yes—
111C22×D292C2311yescharacteristic
112C22×D292C2311yescharacteristic
113C22×D292C2312yes—
114C22×D292C2312yes—
115C22×C22⋊D73C2314yes—
116C22×C22⋊D73C2312yes—
117C22×C22⋊D73C2312yes—
118C22×C22⋊D73C2314yes—
119C23×Dic73C2314yes—
120C22×C4×D73C2312yes—
121C22×C4×D73C2312yes—
122C22×C4×D73C2314yes—
123C22×C4×D73C2314yes—
124#14556591C2318yes—
125#14556591C2318yes—
126#14556591C2318yes—
127#14556591C23116yes—
128#14556590C23132yes—
129#14556588C2318yes—
130#14556586C23132yes—
131#14556583C23116yes—
132#14556583C23116yes—
133#14556582C23132yes—
134#14556579C23116yes—
135#14556577C23132yes—
136#14556577C23132yes—
137#14556577C23132yes—
138#14556576C23132yes—
139#14556576C23132yes—
140#14556575C23132yes—
141#14556573C23132yes—
142#14556571C23116yes—
143#14556571C23116yes—
144#14556571C23132yes—
145#14556570C23116yes—
146#14556570C23116yes—
147#14556569C23132yes—
148#14556568C23132yes—
149#14556568C23132yes—
150#14556567C23116yes—
151#14556565C2318yes—
152#14556565C2318yes—
153#14556565C23116yes—
154#14556565C23116yes—
155#14556565C23116yes—
156#14556564C23132yes—
157#14556564C23132yes—
158#14556563C23132yes—
159#14556562C23116yes—
160#14556562C23132yes—
161C4×Dic146C23116yes—
162C4×Dic146C23116yes—
163C4×D292C2318yes—
164C4×D292C23116yes—
165C4×D292C2318yes—
166C4×D292C23116yes—
167C4×D292C23116yes—
168#14556551C23132yes—
169#14556550C23116yes—
170#14556550C23116yes—
171#14556549C23116yes—
172#14556549C23132yes—
173C2×C4⋊Dic73C2314yes—
174C2×C4⋊Dic73C2311yescharacteristic
175C2×C4⋊Dic73C2312yes—
176C2×C4⋊Dic73C2312yes—
177C2×C4⋊Dic73C2311yescharacteristic
178C2×C4⋊Dic73C2314yes—
179C2×C4⋊Dic73C2312yes—
180C2×C4⋊Dic73C2312yes—
181C2×C4⋊Dic73C2312yes—
182C2×C4⋊Dic73C23116yes—
183C2×#11924007C2314yes—
184C2×#11924007C2314yes—
185C2×#11924007C2314yes—
186C2×#11924007C2314yes—
187C4⋊C4×D73C23116yes—
188C2×C22⋊Dic73C2314yes—
189C2×C22⋊Dic73C2314yes—
190C2×#11924005C2312yes—
191C2×#11924005C2314yes—
192C2×#11924005C2314yes—
193C2×#11924005C2312yes—
194C2×#11924005C2314yes—
195C2×#11924005C2314yes—
196C2×#11924005C2312yes—
197C2×#11924005C2312yes—
198C2×C4×Dic73C2314yes—
199C2×C4×Dic73C2314yes—
200C22×Q8×C73C2311yescharacteristic
201C22×D4×C73C2311yescharacteristic
202C22×D4×C73C2312yes—
203C23×C4×C73C2311yescharacteristic
204C23×C4×C73C2311yescharacteristic
205C23×C4×C73C2312yes—
206C23×C4×C73C2311yescharacteristic
207#126×C73C23116yes—
208#125×C73C2318yes—
209#124×C73C2318yes—
210#123×C73C23116yes—
211C22⋊Q8×C73C2318yes—
212#121×C73C2318yes—
213C4×Q8×C73C2318yes—
214C4×D4×C73C2318yes—
215C4×D4×C73C23116yes—
216#117×C73C23116yes—
217C2×C4⋊C4×C73C2312yes—
218C2×C4⋊C4×C73C2312yes—
219C2×C4⋊C4×C73C2311yescharacteristic
220C2×C4⋊C4×C73C2312yes—
221C2×C4⋊C4×C73C2311yescharacteristic
222C2×C4⋊C4×C73C2312yes—
223C2×C22⋊C4×C73C2312yes—
224C2×C22⋊C4×C73C2312yes—
225C2×C22⋊C4×C73C2312yes—
226C2×C22⋊C4×C73C2312yes—
227C2×C22⋊C4×C73C2312yes—
228C2×C42×C73C2311yescharacteristic
229C2×C42×C73C2311yescharacteristic
230C2×C42×C73C2312yes—
231C2×C42×C73C2318yes—
232C2×C42×C73C2311yescharacteristic
233C2×C42×C73C2311yescharacteristic
234C23×D73C2412yes—
235C23×D73C2412yes—
236#11924028—432no—
237#11924027—432no—
238C2×Dic146—28no—
239C2×Dic146—48no—
240C2×Dic146—44no—
241C2×Dic146—44no—
242C2×Dic146C2418yes—
243C2×Dic146C2418yes—
244C2×Dic146C2418yes—
245C2×Dic146C24116yes—
246Q8×D73—432no—
247C2×D292—24no—
248C2×D292—24no—
249C2×D292—44no—
250C2×D292—44no—
251C2×D292C2414yes—
252C2×D292C2414yes—
253C2×D292C2418yes—
254C2×D292C2418yes—
255C2×C22⋊D73—48no—
256C2×C22⋊D73—48no—
257C2×C22⋊D73—44no—
258C2×C22⋊D73—44no—
259C2×C22⋊D73C24116yes—
260C2×C22⋊D73C2418yes—
261C2×C22⋊D73C24116yes—
262C2×C22⋊D73C2418yes—
263C22×Dic73—48no—
264C22×Dic73C2414yes—
265C22×Dic73C2412yes—
266C22×Dic73C2414yes—
267C22×Dic73C2412yes—
268C22×Dic73C24116yes—
269C2×C4×D73—28no—
270C2×C4×D73—28no—
271C2×C4×D73—48no—
272C2×C4×D73—48no—
273C2×C4×D73C2418yes—
274C2×C4×D73C2418yes—
275C2×C4×D73C24116yes—
276C2×C4×D73C24116yes—
277C4⋊Dic73C2418yes—
278C4⋊Dic73C2414yes—
279C4⋊Dic73C2418yes—
280C4⋊Dic73C24116yes—
281C4⋊Dic73C24116yes—
282C4⋊Dic73C2418yes—
283C4⋊Dic73C2414yes—
284C4⋊Dic73C2418yes—
285C4⋊Dic73C2418yes—
286#11924007C24116yes—
287#11924007C24116yes—
288#11924007C24116yes—
289#11924007C24116yes—
290C22⋊Dic73C24116yes—
291C22⋊Dic73C24116yes—
292#11924005C2418yes—
293#11924005C24116yes—
294#11924005C24116yes—
295#11924005C2418yes—
296#11924005C24116yes—
297#11924005C24116yes—
298#11924005C2418yes—
299#11924005C2418yes—
300C4×Dic73C24116yes—
301C4×Dic73C24116yes—
302C24×C73C2412yes—
303C24×C73C2411yescharacteristic
304C2×Q8×C73—24no—
305C2×Q8×C73C2414yes—
306C2×D4×C73—24no—
307C2×D4×C73—44no—
308C2×D4×C73C2414yes—
309C2×D4×C73C2418yes—
310C22×C4×C73—24no—
311C22×C4×C73—24no—
312C22×C4×C73—28no—
313C22×C4×C73—42no—
314C22×C4×C73C2411yescharacteristic
315C22×C4×C73C2411yescharacteristic
316C22×C4×C73C2411yescharacteristic
317C22×C4×C73C2411yescharacteristic
318C22×C4×C73C2414yes—
319C22×C4×C73C2414yes—
320C22×C4×C73C2412yes—
321C22×C4×C73C2412yes—
322C22×C4×C73C2412yes—
323C22×C4×C73C2418yes—
324C22×C4×C73C2414yes—
325C22×C4×C73C2411yescharacteristic
326C22×C4×C73C2411yescharacteristic
327C4⋊C4×C73C2418yes—
328C4⋊C4×C73C2418yes—
329C4⋊C4×C73C2414yes—
330C4⋊C4×C73C2418yes—
331C4⋊C4×C73C2414yes—
332C4⋊C4×C73C2418yes—
333C22⋊C4×C73C2418yes—
334C22⋊C4×C73C2418yes—
335C22⋊C4×C73C2418yes—
336C22⋊C4×C73C2418yes—
337C22⋊C4×C73C2418yes—
338C42×C73C2414yes—
339C42×C73C2414yes—
340C42×C73C2414yes—
341C42×C73C2414yes—
342C42×C73C2418yes—
343C23×C73—22no—
344C23×C73—24no—
345C23×C73—24no—
346C23×C73—22no—
347C23×C73—22no—
348C23×C73—24no—
349C23×C73C2514yes—
350C23×C73C2512yes—
351C23×C73C2511yescharacteristic
352C22×D73—24no—
353C22×D73—24no—
354C22×D73—24no—
355C22×D73—24no—
356C22×D73—24no—
357C22×D73—24no—
358C22×D73C2514yes—
359C22×D73C2514yes—
360Q8×C73—28no—
361D4×C73—28no—
362D4×C73—48no—
363C2×C4×C73—22no—
364C2×C4×C73—24no—
365C2×C4×C73—22no—
366C2×C4×C73—24no—
367C2×C4×C73—22no—
368C2×C4×C73—22no—
369C2×C4×C73—24no—
370C2×C4×C73—28no—
371C2×C4×C73—28no—
372C2×C4×C73—216no—
373C2×C4×C73—44no—
374C2×C4×C73H(5,𝔽2)14yes—
375C2×C4×C732−1+414yes—
376C2×C4×C73C2512yes—
377C2×C4×C73C2512yes—
378C2×C4×C73C2512yes—
379C2×C4×C73C2512yes—
380C2×C4×C73C2514yes—
381C2×C4×C73C2514yes—
382C2×C4×C73C2514yes—
383C2×C4×C73C2512yes—
384C2×C4×C73C2512yes—
385C22⋊D73—416no—
386C22⋊D73—416no—
387C22⋊D73—48no—
388C22⋊D73—48no—
389C2×Dic73—24no—
390C2×Dic73—24no—
391C2×Dic73—28no—
392C2×Dic73—28no—
393C2×Dic73—416no—
394C2×Dic73C2518yes—
395C2×Dic73C2514yes—
396C2×Dic73C2518yes—
397C2×Dic73C2514yes—
398D292—28no—
399D292—28no—
400D292—48no—
401D292—48no—
402C4×D73—216no—
403C4×D73—216no—
404C4×D73—416no—
405C4×D73—416no—
406Dic146—216no—
407Dic146—416no—
408Dic146—48no—
409Dic146—48no—
410C22×C73—24no—
411C22×C73—22no—
412C22×C73—24no—
413C22×C73—22no—
414C22×C73—24no—
415C22×C73—22no—
416C22×C73—44no—
417C22×C73—48no—
418C22×C73C2×H(5,𝔽2)12yes—
419C22×C73C2×2−1+412yes—
420C22×C73#58512yes—
421C22×C73C2611yescharacteristic
422C2×D73—24no—
423C2×D73—24no—
424C2×D73—24no—
425C2×D73—24no—
426C2×D73—24no—
427C2×D73—24no—
428C2×D73—48no—
429C2×D73—48no—
430C4×C73—24no—
431C4×C73—22no—
432C4×C73—22no—
433C4×C73—24no—
434C4×C73—22no—
435C4×C73—24no—
436C4×C73—22no—
437C4×C73C2×H(5,𝔽2)14yes—
438C4×C73C2×2−1+414yes—
439Dic73—28no—
440Dic73—24no—
441Dic73—24no—
442Dic73—28no—
443C2×#3547—731nomaximal, Sylow
444C2×C73—44no—
445C2×C73—42no—
446C2×C73#354714yescomplemented
447C2×C73C22×H(5,𝔽2)11yescharacteristic
448C2×C73C22×2−1+411yescharacteristic
449C2×C73C2×#58511yescharacteristic
450D73—44no—
451D73—44no—
452#3547—7332no—
453C2×#562—734no—
454C2×#555—732no—
455C2×#555—731no—
456C2×#554—731no—
457C2×#553—732no—
458C2×#552—732no—
459C2×D4×Q8—731no—
460C2×#548—732no—
461C2×#547—731no—
462C2×#544—732no—
463C2×#542—734no—
464C2×#540—732no—
465C2×#537—732no—
466C2×#536—732no—
467C2×#533—731no—
468C2×#532—731no—
469C2×#529D7311yescharacteristic, complemented
470C73C2×#354711yescharacteristic, complemented, Sylow
471C22×#41—732no—
472C22×#41—732no—
473C23×Q8—732no—
474#562—7364no—
475#555—7332no—
476#555—7316no—
477#554—7316no—
478#553—7332no—
479#552—7332no—
480D4×Q8—7316no—
481#548—7332no—
482#547—7316no—
483#544—7332no—
484#542—7364no—
485#540—7332no—
486#537—7332no—
487#536—7332no—
488#533—7316no—
489#532—7316no—
490C2×C4⋊Q8—734no—
491C2×C4⋊Q8—731no—
492C2×C4⋊Q8—731no—
493C2×C4⋊Q8—731no—
494C2×C4⋊Q8—732no—
495C2×#127—731no—
496#529C2×D73116yescomplemented
497C2×#126—734no—
498C2×#126C2×D7312yes—
499C2×#125—734no—
500C2×#125—732no—
501C2×#125—732no—
502C2×#125C2×D7311yescharacteristic
503C2×#124—734no—
504C2×#124—734no—
505C2×#124—734no—
506C2×#124—732no—
507C2×#124C2×D7311yescharacteristic
508C2×#123—734no—
509C2×#123—734no—
510C2×#123—734no—
511C2×#123—734no—
512C2×#123C2×D7312yes—
513C2×C22⋊Q8—732no—
514C2×C22⋊Q8—732no—
515C2×C22⋊Q8—732no—
516C2×C22⋊Q8—732no—
517C2×C22⋊Q8—732no—
518C2×C22⋊Q8—734no—
519C2×C22⋊Q8—734no—
520C2×C22⋊Q8—734no—
521C2×C22⋊Q8—734no—
522C2×C22⋊Q8C2×D7311yescharacteristic
523C2×#121—732no—
524C2×#121—734no—
525C2×#121—734no—
526C2×#121—731no—
527C2×#121—731no—
528C2×#121—732no—
529C2×#121—732no—
530C2×#121—732no—
531C2×#121—734no—
532C2×#121—734no—
533C2×#121C2×D7311yescharacteristic
534C2×C4×Q8—732no—
535C2×C4×Q8—732no—
536C2×C4×Q8C2×D7311yescharacteristic
537C2×C4×D4—734no—
538C2×C4×D4—731no—
539C2×C4×D4—732no—
540C2×C4×D4—731no—
541C2×C4×D4—732no—
542C2×C4×D4—732no—
543C2×C4×D4C2×D7311yescharacteristic
544C2×C4×D4C2×D7312yes—
545C2×#117—732no—
546C2×#117—732no—
547C2×#117—732no—
548C2×#117—734no—
549C2×#117C2×D7312yes—
550C22×C4⋊C4—732no—
551C22×C4⋊C4—732no—
552C22×C42C2×D7311yescharacteristic
553C2×#41—2928no—
554C2×#41—2928no—
555C2×#41—7316no—
556C2×#41—7316no—
557C22×Q8—2928no—
558C22×Q8—7316no—
559C22×Q8—732no—
560C22×Q8—734no—
561C22×Q8—732no—
562C22×Q8—732no—
563C22×Q8C22×D7311yescharacteristic
564C22×D4—734no—
565C22×D4—732no—
566C22×D4—734no—
567C22×D4—732no—
568C22×D4—732no—
569C22×D4—732no—
570C22×D4—731no—
571C22×D4—731no—
572C22×D4C22×D7311yescharacteristic
573C22×D4C22×D7312yes—
574C23×C4—734no—
575C23×C4—734no—
576C23×C4—734no—
577C23×C4—732no—
578C23×C4—732no—
579C23×C4C22×D7312yes—
580C23×C4C22×D7311yescharacteristic
581C23×C4C22×D7311yescharacteristic
582C23×C4C22×D7311yescharacteristic
583C4⋊Q8—7332no—
584C4⋊Q8—738no—
585C4⋊Q8—738no—
586C4⋊Q8—738no—
587C4⋊Q8—7316no—
588#127—738no—
589#126—7332no—
590#126C22×D73116yes—
591#125—7332no—
592#125—7316no—
593#125—7316no—
594#125C22×D7318yes—
595#124—7332no—
596#124—7332no—
597#124—7332no—
598#124—7316no—
599#124C22×D7318yes—
600#123—7332no—
601#123—7332no—
602#123—7332no—
603#123—7332no—
604#123C22×D73116yes—
605C22⋊Q8—7316no—
606C22⋊Q8—7316no—
607C22⋊Q8—7316no—
608C22⋊Q8—7316no—
609C22⋊Q8—7316no—
610C22⋊Q8—7332no—
611C22⋊Q8—7332no—
612C22⋊Q8—7332no—
613C22⋊Q8—7332no—
614C22⋊Q8C22×D7318yes—
615#121—7316no—
616#121—7332no—
617#121—7332no—
618#121—738no—
619#121—738no—
620#121—7316no—
621#121—7316no—
622#121—7316no—
623#121—7332no—
624#121—7332no—
625#121C22×D7318yes—
626C4×Q8—7316no—
627C4×Q8—7316no—
628C4×Q8C22×D7318yes—
629C4×D4—7332no—
630C4×D4—738no—
631C4×D4—7316no—
632C4×D4—738no—
633C4×D4—7316no—
634C4×D4—7316no—
635C4×D4C22×D7318yes—
636C4×D4C22×D73116yes—
637#117—7316no—
638#117—7316no—
639#117—7316no—
640#117—7332no—
641#117C22×D73116yes—
642C2×C4⋊C4—731no—
643C2×C4⋊C4—732no—
644C2×C4⋊C4—732no—
645C2×C4⋊C4—734no—
646C2×C4⋊C4—734no—
647C2×C4⋊C4—7316no—
648C2×C4⋊C4—732no—
649C2×C4⋊C4—731no—
650C2×C4⋊C4—734no—
651C2×C4⋊C4—732no—
652C2×C4⋊C4—734no—
653C2×C4⋊C4—734no—
654C2×C4⋊C4—734no—
655C2×C4⋊C4—732no—
656C2×C4⋊C4—7316no—
657C2×C4⋊C4C22×D7311yescharacteristic
658C2×C4⋊C4C22×D7311yescharacteristic
659C2×C4⋊C4C22×D7312yes—
660C2×C4⋊C4C22×D7312yes—
661C2×C4⋊C4C22×D7312yes—
662C2×C4⋊C4C22×D7312yes—
663C2×C22⋊C4—734no—
664C2×C22⋊C4—734no—
665C2×C22⋊C4—732no—
666C2×C22⋊C4—734no—
667C2×C22⋊C4—734no—
668C2×C22⋊C4—732no—
669C2×C22⋊C4—734no—
670C2×C22⋊C4—732no—
671C2×C22⋊C4—734no—
672C2×C22⋊C4—732no—
673C2×C22⋊C4C22×D7312yes—
674C2×C22⋊C4C22×D7312yes—
675C2×C22⋊C4C22×D7312yes—
676C2×C22⋊C4C22×D7312yes—
677C2×C22⋊C4C22×D7312yes—
678C2×C42—734no—
679C2×C42—734no—
680C2×C42C22×D7311yescharacteristic
681C2×C42C22×D7312yes—
682C2×C42C22×D7311yescharacteristic
683C2×C42C22×D7311yescharacteristic
684C2×C42C22×D7311yescharacteristic
685C2×C42C22×D7318yes—
686C24—732no—
687C24—732no—
688C24C23×D7311yescharacteristic
689C24C23×D7312yes—
690#41—29232no—
691#41—29232no—
692C2×Q8—24no—
693C2×Q8—2928no—
694C2×Q8—2924no—
695C2×Q8—2924no—
696C2×Q8—29232no—
697C2×Q8—738no—
698C2×Q8—7316no—
699C2×Q8—738no—
700C2×Q8—738no—
701C2×Q8—1468no—
702C2×Q8C23×D7314yes—
703C2×D4—24no—
704C2×D4—44no—
705C2×D4—2924no—
706C2×D4—2924no—
707C2×D4—2928no—
708C2×D4—2924no—
709C2×D4—2928no—
710C2×D4—2924no—
711C2×D4—7316no—
712C2×D4—738no—
713C2×D4—7316no—
714C2×D4—738no—
715C2×D4—738no—
716C2×D4—738no—
717C2×D4—734no—
718C2×D4—734no—
719C2×D4—1464no—
720C2×D4—1464no—
721C2×D4C23×D7314yes—
722C2×D4C23×D7318yes—
723C22×C4—24no—
724C22×C4—28no—
725C22×C4—24no—
726C22×C4—42no—
727C22×C4—2928no—
728C22×C4—2928no—
729C22×C4—2928no—
730C22×C4—7316no—
731C22×C4—7316no—
732C22×C4—7316no—
733C22×C4—734no—
734C22×C4—732no—
735C22×C4—734no—
736C22×C4—732no—
737C22×C4—738no—
738C22×C4—738no—
739C22×C4—1468no—
740C22×C4—1468no—
741C22×C4C23×D7314yes—
742C22×C4C23×D7314yes—
743C22×C4C23×D7318yes—
744C22×C4C23×D7311yescharacteristic
745C22×C4C23×D7312yes—
746C22×C4C23×D7311yescharacteristic
747C22×C4C23×D7311yescharacteristic
748C22×C4C23×D7311yescharacteristic
749C22×C4C23×D7312yes—
750C22×C4C23×D7312yes—
751C22×C4C23×D7314yes—
752C22×C4C23×D7311yescharacteristic
753C22×C4C23×D7311yescharacteristic
754C4⋊C4—7316no—
755C4⋊C4—7316no—
756C4⋊C4—7316no—
757C4⋊C4—7316no—
758C4⋊C4—734no—
759C4⋊C4—738no—
760C4⋊C4—738no—
761C4⋊C4—7316no—
762C4⋊C4—738no—
763C4⋊C4—734no—
764C4⋊C4—7316no—
765C4⋊C4—738no—
766C4⋊C4—738no—
767C4⋊C4C23×D7314yes—
768C4⋊C4C23×D7314yes—
769C4⋊C4C23×D7318yes—
770C4⋊C4C23×D7318yes—
771C4⋊C4C23×D7318yes—
772C4⋊C4C23×D7318yes—
773C22⋊C4—7316no—
774C22⋊C4—7316no—
775C22⋊C4—738no—
776C22⋊C4—7316no—
777C22⋊C4—7316no—
778C22⋊C4—738no—
779C22⋊C4—7316no—
780C22⋊C4—738no—
781C22⋊C4—7316no—
782C22⋊C4—738no—
783C22⋊C4C23×D7318yes—
784C22⋊C4C23×D7318yes—
785C22⋊C4C23×D7318yes—
786C22⋊C4C23×D7318yes—
787C22⋊C4C23×D7318yes—
788C42—7316no—
789C42—7316no—
790C42C23×D7314yes—
791C42C23×D7314yes—
792C42C23×D7314yes—
793C42C23×D7314yes—
794C42C23×D7318yes—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—734no—
802C23—734no—
803C23—1464no—
804C23—1464no—
805C23—1464no—
806C23—1464no—
807C23—1464no—
808C23—1464no—
809C23C24×D7312yes—
810C23C24×D7314yes—
811C23C24×D7311yescharacteristic
812Q8—28no—
813Q8—29216no—
814Q8—2928no—
815Q8—2928no—
816Q8—14616no—
817D4—28no—
818D4—48no—
819D4—2928no—
820D4—2928no—
821D4—2928no—
822D4—29216no—
823D4—2928no—
824D4—29216no—
825D4—1468no—
826D4—1468no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—28no—
835C2×C4—28no—
836C2×C4—216no—
837C2×C4—44no—
838C2×C4—29216no—
839C2×C4—29216no—
840C2×C4—29216no—
841C2×C4—738no—
842C2×C4—734no—
843C2×C4—738no—
844C2×C4—734no—
845C2×C4—1464no—
846C2×C4—1468no—
847C2×C4—1464no—
848C2×C4—1468no—
849C2×C4—14616no—
850C2×C4—14616no—
851C2×C4#1455663714yes—
852C2×C4#1455663814yes—
853C2×C4C24×D7312yes—
854C2×C4C24×D7314yes—
855C2×C4C24×D7312yes—
856C2×C4C24×D7312yes—
857C2×C4C24×D7312yes—
858C2×C4C24×D7314yes—
859C2×C4C24×D7314yes—
860C2×C4C24×D7312yes—
861C2×C4C24×D7312yes—
862C22—22no—
863C22—24no—
864C22—22no—
865C22—24no—
866C22—22no—
867C22—24no—
868C22—44no—
869C22—48no—
870C22—2928no—
871C22—2928no—
872C22—1464no—
873C22—1464no—
874C22—1464no—
875C22—1464no—
876C22—1464no—
877C22—1464no—
878C22C2×#1455663712yes—
879C22C2×#1455663812yes—
880C22#1798942312yes—
881C22C25×D7311yescharacteristic
882C4—22no—
883C4—24no—
884C4—22no—
885C4—24no—
886C4—22no—
887C4—22no—
888C4—24no—
889C4—1464no—
890C4—1468no—
891C4—1464no—
892C4—1468no—
893C4C2×#1455663714yes—
894C4C2×#1455663814yes—
895C2—42no—
896C2—44no—
897C2—2924no—
898C2—2924no—
899C2#2262432214yesdirect product factor
900C2C22×#1455663711yescharacteristic
901C2C22×#1455663811yescharacteristic
902C2C2×#1798942311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#529×C73C2
socleC23×C73C25
hypercenterC2×#529D73
hypocenterC73C2×#3547
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22624322C2direct (N × H)
2. C2×#17989334C2semidirect
3. C2×#17989302C2semidirect
4. C2×#17989302C2semidirect
5. C2×#17989297C2semidirect
6. C2×#17989283C2semidirect
7. C2×#17989275C2semidirect
8. C2×Q8×D292C2semidirect
9. C2×#17989245C2semidirect
10. C2×#17989241C2semidirect
11. C2×#17989215C2semidirect
12. C2×#17989203C2semidirect
13. C2×#17989192C2semidirect
14. C2×#17989166C2semidirect
15. C2×#17989160C2semidirect
16. C2×#17989144C2semidirect
17. C2×#17989137C2semidirect
18. C2×#529×C73C2semidirect
22. #17989334C22semidirect
23. #17989302C22semidirect
24. #17989302C22semidirect
25. #17989297C22semidirect
26. #17989283C22semidirect
27. #17989275C22semidirect
28. Q8×D292C22semidirect
29. #17989245C22semidirect
30. #17989241C22semidirect
31. #17989215C22semidirect
32. #17989203C22semidirect
33. #17989192C22semidirect
34. #17989166C22semidirect
35. #17989160C22semidirect
36. #17989144C22semidirect
37. #17989137C22semidirect
89. #529×C73C22semidirect
446. C2×C73#3547semidirect
469. C2×#529D73semidirect
470. C73C2×#3547semidirect
496. #529C2×D73semidirect
899. C2#22624322direct (N × H)

Maximal subgroups

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

subgroupindex
#226243222
C2×#179893342
C2×#179893022
C2×#179892972
C2×#179892832
C2×#179892752
C2×Q8×D2922
C2×#179892452
C2×#179892412
C2×#179892152
C2×#179892032
C2×#179891922
C2×#179891662
C2×#179891602
C2×#179891442
C2×#179891372
C2×#529×C732
C2×#354773