Finite Group Databasebeta

← C2×#22623843 #33994348

Subgroups — C2×#22623843 #33994348

Order 18688.

7758 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623843C2132yesmaximal, direct product factor
2C2×#17989309C212yesmaximal, complemented
3C2×#17989300C212yesmaximal, complemented
4C2×#17989293C212yesmaximal, complemented
5C2×#17989290C212yesmaximal, complemented
6C2×#17989281C212yesmaximal, complemented
7C2×#17989249C212yesmaximal, complemented
8C2×#17989247C212yesmaximal, complemented
9C2×#17989239C212yesmaximal, complemented
10C2×#17989210C212yesmaximal, complemented
11C2×#17989209C212yesmaximal, complemented
12C2×#17989167C212yesmaximal, complemented
13C2×#17989142C211yesmaximal, characteristic, complemented
14C2×#17989138C211yesmaximal, characteristic, complemented
15C2×#17989138C211yesmaximal, characteristic, complemented
16C2×#17989137C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D73C211yesmaximal, characteristic, complemented
18C2×#17989069C212yesmaximal, complemented
19C2×C4×#11924028C211yesmaximal, characteristic, complemented
20C2×#533×C73C211yesmaximal, characteristic, complemented
21C22×#11924029C2212yes—
22C22×#11924029C2212yes—
23C22×#11924028C2211yescharacteristic
24C22×#11924028C2212yes—
25C22×Q8×D73C2212yes—
26#17989309C22132yescomplemented
27#17989300C22132yescomplemented
28#17989293C22132yescomplemented
29#17989290C22132yescomplemented
30#17989281C22132yescomplemented
31#17989249C22132yescomplemented
32#17989247C22132yescomplemented
33#17989239C22132yescomplemented
34#17989210C22132yescomplemented
35#17989209C22132yescomplemented
36#17989167C22132yescomplemented
37#17989142C22116yescomplemented
38#17989138C22116yescomplemented
39#17989138C22116yescomplemented
40#17989137C22116yescomplemented
41C2×#14556591C2211yescharacteristic
42C2×#14556590C2212yes—
43C2×#14556590C2212yes—
44C2×#14556589C2212yes—
45C4⋊Q8×D73C22116yescomplemented
46C2×#14556588C2211yescharacteristic
47C2×#14556586C2214yes—
48C2×#14556585C2214yes—
49C2×#14556582C2212yes—
50C2×#14556580C2212yes—
51C2×#14556580C2212yes—
52C2×#14556579C2214yes—
53C2×#14556579C2212yes—
54C2×#14556577C2214yes—
55C2×#14556576C2214yes—
56C2×#14556573C2214yes—
57C2×#14556571C2214yes—
58C2×#14556571C2212yes—
59C2×#14556569C2214yes—
60C2×#14556569C2214yes—
61C2×#14556567C2212yes—
62C2×#14556566C2212yes—
63C2×#14556566C2214yes—
64C2×#14556566C2212yes—
65C2×#14556566C2212yes—
66C2×#14556566C2212yes—
67C2×#14556565C2212yes—
68C2×#14556565C2212yes—
69C2×#14556564C2214yes—
70C2×#14556564C2214yes—
71#17989069C22132yescomplemented
72C4×#11924028C22116yescomplemented
73C2×Q8×Dic73C2212yes—
74C2×C4×Dic146C2211yescharacteristic
75C2×C4×Dic146C2211yescharacteristic
76C2×#14556556C2212yes—
77C2×C4×D292C2212yes—
78C2×C4×D292C2211yescharacteristic
79C2×C4×D292C2211yescharacteristic
80C2×C4×D292C2214yes—
81C2×C4×D292C2212yes—
82C2×#14556553C2212yes—
83C2×#14556553C2214yes—
84C2×#14556553C2212yes—
85C2×#14556553C2212yes—
86C2×#14556553C2212yes—
87C2×C4×C22⋊D73C2211yescharacteristic
88C2×C4×C22⋊D73C2211yescharacteristic
89C2×C4×C22⋊D73C2211yescharacteristic
90C2×C4×C22⋊D73C2211yescharacteristic
91C2×#14556550C2211yescharacteristic
92C2×#14556549C2212yes—
93C2×#14556548C2211yescharacteristic
94C2×#14556548C2211yescharacteristic
95C2×#14556548C2214yes—
96C2×C4⋊C4×D73C2212yes—
97C2×C4⋊C4×D73C2214yes—
98C2×C4⋊C4×D73C2212yes—
99C2×C42×D73C2211yescharacteristic
100C2×C42×D73C2211yescharacteristic
101#533×C73C22116yescomplemented
102C2×C4⋊Q8×C73C2211yescharacteristic
103C2×C4⋊Q8×C73C2211yescharacteristic
104C2×#125×C73C2212yes—
105C2×C22⋊Q8×C73C2212yes—
106C2×C22⋊Q8×C73C2212yes—
107C2×C4×Q8×C73C2212yes—
108C2×C4×Q8×C73C2212yes—
109C2×#117×C73C2212yes—
110C22×C42×C73C2211yescharacteristic
111C2×#11924029—216no—
112C2×#11924029—48no—
113C2×#11924029C23116yes—
114C2×#11924029C23116yes—
115C2×#11924028—28no—
116C2×#11924028—48no—
117C2×#11924028C2318yes—
118C2×#11924028C23116yes—
119C22×Dic146C2312yes—
120C22×Dic146C2311yescharacteristic
121C22×Dic146C2314yes—
122C2×Q8×D73—48no—
123C2×Q8×D73C23116yes—
124C22×D292C2312yes—
125C22×D292C2312yes—
126C22×D292C2312yes—
127C22×D292C2311yescharacteristic
128C22×D292C2314yes—
129C22×D292C2314yes—
130C22×C22⋊D73C2311yescharacteristic
131C22×C22⋊D73C2311yescharacteristic
132C22×C22⋊D73C2314yes—
133C22×C4×D73C2311yescharacteristic
134C22×C4×D73C2311yescharacteristic
135C22×C4×D73C2311yescharacteristic
136C22×C4×D73C2314yes—
137C22×C4×D73C2311yescharacteristic
138C22×C4×D73C2311yescharacteristic
139C22×C4×D73C2314yes—
140C22×C4×D73C2314yes—
141C22×C4×D73C2314yes—
142C22×C4×D73C2311yescharacteristic
143#14556591C2318yes—
144#14556590C23116yes—
145#14556590C23116yes—
146#14556589C23116yes—
147#14556588C2318yes—
148#14556586C23132yes—
149#14556585C23132yes—
150#14556582C23116yes—
151#14556580C23116yes—
152#14556580C23116yes—
153#14556579C23116yes—
154#14556579C23132yes—
155#14556577C23132yes—
156#14556576C23132yes—
157#14556573C23132yes—
158#14556571C23116yes—
159#14556571C23132yes—
160#14556569C23132yes—
161#14556569C23132yes—
162#14556567C23116yes—
163#14556566C23116yes—
164#14556566C23116yes—
165#14556566C23116yes—
166#14556566C23116yes—
167#14556566C23132yes—
168#14556565C23116yes—
169#14556565C23116yes—
170#14556564C23132yes—
171#14556564C23132yes—
172Q8×Dic73C23116yes—
173C4×Dic146C2318yes—
174C4×Dic146C2318yes—
175#14556556C23116yes—
176C4×D292C23116yes—
177C4×D292C23116yes—
178C4×D292C2318yes—
179C4×D292C23132yes—
180C4×D292C2318yes—
181#14556553C23116yes—
182#14556553C23116yes—
183#14556553C23116yes—
184#14556553C23116yes—
185#14556553C23132yes—
186C4×C22⋊D73C2318yes—
187C4×C22⋊D73C2318yes—
188C4×C22⋊D73C2318yes—
189C4×C22⋊D73C2318yes—
190#14556550C2318yes—
191#14556549C23116yes—
192#14556548C2318yes—
193#14556548C23132yes—
194#14556548C2318yes—
195C2×C4⋊Dic73C2312yes—
196C2×C4⋊Dic73C2312yes—
197C2×C4⋊Dic73C2314yes—
198C2×C4⋊Dic73C2311yescharacteristic
199C2×C4⋊Dic73C2311yescharacteristic
200C2×#11924007C2314yes—
201C2×#11924007C2314yes—
202C2×#11924007C2311yescharacteristic
203C2×#11924007C2311yescharacteristic
204C2×#11924007C2311yescharacteristic
205C2×#11924007C2311yescharacteristic
206C2×#11924007C2314yes—
207C4⋊C4×D73C23116yes—
208C4⋊C4×D73C23116yes—
209C4⋊C4×D73C23132yes—
210C2×C22⋊Dic73C2311yescharacteristic
211C2×C22⋊Dic73C2311yescharacteristic
212C2×#11924005C2311yescharacteristic
213C2×#11924005C2311yescharacteristic
214C2×#11924005C2311yescharacteristic
215C2×#11924005C2311yescharacteristic
216C2×#11924005C2314yes—
217C2×#11924005C2314yes—
218C2×#11924005C2314yes—
219C2×#11924005C2314yes—
220C2×#11924005C2314yes—
221C2×#11924005C2314yes—
222C2×#11924005C2314yes—
223C2×C4×Dic73C2311yescharacteristic
224C2×C4×Dic73C2311yescharacteristic
225C2×C4×Dic73C2311yescharacteristic
226C2×C4×Dic73C2311yescharacteristic
227C2×C4×Dic73C2311yescharacteristic
228C2×C4×Dic73C2311yescharacteristic
229C2×C4×Dic73C2314yes—
230C42×D73C2318yes—
231C42×D73C2318yes—
232C22×Q8×C73C2312yes—
233C22×Q8×C73C2312yes—
234C23×C4×C73C2311yescharacteristic
235C23×C4×C73C2311yescharacteristic
236C23×C4×C73C2311yescharacteristic
237C4⋊Q8×C73C2318yes—
238C4⋊Q8×C73C2318yes—
239#125×C73C23116yes—
240C22⋊Q8×C73C23116yes—
241C22⋊Q8×C73C23116yes—
242C4×Q8×C73C23116yes—
243C4×Q8×C73C23116yes—
244#117×C73C23116yes—
245C2×C4⋊C4×C73C2312yes—
246C2×C4⋊C4×C73C2312yes—
247C2×C4⋊C4×C73C2312yes—
248C2×C4⋊C4×C73C2314yes—
249C2×C4⋊C4×C73C2314yes—
250C2×C4⋊C4×C73C2312yes—
251C2×C22⋊C4×C73C2314yes—
252C2×C42×C73C2311yescharacteristic
253C2×C42×C73C2318yes—
254C2×C42×C73C2311yescharacteristic
255C2×C42×C73C2311yescharacteristic
256C2×C42×C73C2311yescharacteristic
257C2×C42×C73C2314yes—
258C23×D73C2411yescharacteristic
259C23×D73C2414yes—
260C23×D73C2411yescharacteristic
261#11924029—264no—
262#11924029—432no—
263#11924028—232no—
264#11924028—432no—
265C2×Dic146—28no—
266C2×Dic146—24no—
267C2×Dic146—48no—
268C2×Dic146C2418yes—
269C2×Dic146C2414yes—
270C2×Dic146C24116yes—
271Q8×D73—432no—
272C2×D292—24no—
273C2×D292—216no—
274C2×D292—28no—
275C2×D292—28no—
276C2×D292—28no—
277C2×D292—48no—
278C2×D292C2418yes—
279C2×D292C24116yes—
280C2×D292C2418yes—
281C2×D292C2418yes—
282C2×D292C2414yes—
283C2×D292C24116yes—
284C2×C22⋊D73—24no—
285C2×C22⋊D73—24no—
286C2×C22⋊D73—48no—
287C2×C22⋊D73C2414yes—
288C2×C22⋊D73C2414yes—
289C2×C22⋊D73C24116yes—
290C22×Dic73C2411yescharacteristic
291C22×Dic73C2411yescharacteristic
292C22×Dic73C2411yescharacteristic
293C22×Dic73C2411yescharacteristic
294C22×Dic73C2411yescharacteristic
295C22×Dic73C2414yes—
296C22×Dic73C2411yescharacteristic
297C2×C4×D73—24no—
298C2×C4×D73—24no—
299C2×C4×D73—24no—
300C2×C4×D73—24no—
301C2×C4×D73—24no—
302C2×C4×D73—216no—
303C2×C4×D73—48no—
304C2×C4×D73—48no—
305C2×C4×D73—48no—
306C2×C4×D73#4118yescomplemented
307C2×C4×D73C2414yes—
308C2×C4×D73C2414yes—
309C2×C4×D73C2414yes—
310C2×C4×D73C2414yes—
311C2×C4×D73C2414yes—
312C2×C4×D73C24116yes—
313C2×C4×D73C24116yes—
314C2×C4×D73C24116yes—
315C2×C4×D73C24116yes—
316C2×C4×D73C2414yes—
317C4⋊Dic73C2418yes—
318C4⋊Dic73C2418yes—
319C4⋊Dic73C24116yes—
320C4⋊Dic73C2414yes—
321C4⋊Dic73C2414yes—
322#11924007C2414yes—
323#11924007C24116yes—
324#11924007C24116yes—
325#11924007C2414yes—
326#11924007C2414yes—
327#11924007C2414yes—
328#11924007C24116yes—
329C22⋊Dic73C2414yes—
330C22⋊Dic73C2414yes—
331#11924005C2414yes—
332#11924005C2414yes—
333#11924005C2414yes—
334#11924005C2414yes—
335#11924005C24116yes—
336#11924005C24116yes—
337#11924005C24116yes—
338#11924005C24116yes—
339#11924005C24116yes—
340#11924005C24116yes—
341#11924005C24116yes—
342C4×Dic73C2414yes—
343C4×Dic73C2414yes—
344C4×Dic73C2414yes—
345C4×Dic73C2414yes—
346C4×Dic73C2414yes—
347C4×Dic73C2414yes—
348C4×Dic73C24116yes—
349C24×C73C2411yescharacteristic
350C2×Q8×C73—28no—
351C2×Q8×C73—28no—
352C2×Q8×C73C2418yes—
353C2×Q8×C73C2418yes—
354C22×C4×C73—24no—
355C22×C4×C73—24no—
356C22×C4×C73—24no—
357C22×C4×C73C2411yescharacteristic
358C22×C4×C73C2411yescharacteristic
359C22×C4×C73C2411yescharacteristic
360C22×C4×C73C2414yes—
361C22×C4×C73C2414yes—
362C22×C4×C73C2414yes—
363C22×C4×C73C2414yes—
364C22×C4×C73C2414yes—
365C22×C4×C73C2411yescharacteristic
366C22×C4×C73C2411yescharacteristic
367C22×C4×C73C2411yescharacteristic
368C4⋊C4×C73C2418yes—
369C4⋊C4×C73C2418yes—
370C4⋊C4×C73C24116yes—
371C4⋊C4×C73C24116yes—
372C4⋊C4×C73C2418yes—
373C4⋊C4×C73C2418yes—
374C22⋊C4×C73C24116yes—
375C42×C73C2414yes—
376C42×C73C2414yes—
377C42×C73C2414yes—
378C42×C73C2414yes—
379C42×C73C24116yes—
380C23×C73—22no—
381C23×C73—22no—
382C23×C73—22no—
383C23×C73C2512yes—
384C23×C73C2511yescharacteristic
385C22×D73—22no—
386C22×D73—22no—
387C22×D73—22no—
388C22×D73—28no—
389C22×D73—22no—
390C22×D73—28no—
391C22×D73—22no—
392C22×D73—28no—
393C22×D73C2×#4114yes—
394C22×D73C2518yes—
395C22×D73C2512yes—
396C22×D73C2512yes—
397Q8×C73—216no—
398Q8×C73—216no—
399C2×C4×C73—22no—
400C2×C4×C73—28no—
401C2×C4×C73—22no—
402C2×C4×C73—28no—
403C2×C4×C73—22no—
404C2×C4×C73—28no—
405C2×C4×C73—28no—
406C2×C4×C73—28no—
407C2×C4×C73C2×#4114yes—
408C2×C4×C73H(5,𝔽2)14yes—
409C2×C4×C732−1+414yes—
410C2×C4×C73C2512yes—
411C2×C4×C73C2512yes—
412C2×C4×C73C2512yes—
413C2×C4×C73C2518yes—
414C2×C4×C73C2518yes—
415C2×C4×C73C2512yes—
416C2×C4×C73C2512yes—
417C2×C4×C73C2512yes—
418C22⋊D73—28no—
419C22⋊D73—28no—
420C22⋊D73—416no—
421C2×Dic73—22no—
422C2×Dic73—22no—
423C2×Dic73—22no—
424C2×Dic73—28no—
425C2×Dic73—22no—
426C2×Dic73—22no—
427C2×Dic73C2×#4114yes—
428C2×Dic73C2512yes—
429C2×Dic73C2512yes—
430C2×Dic73C2512yes—
431C2×Dic73C2512yes—
432C2×Dic73C2512yes—
433C2×Dic73C2518yes—
434C2×Dic73C2512yes—
435D292—28no—
436D292—232no—
437D292—216no—
438D292—216no—
439D292—216no—
440D292—416no—
441C4×D73—28no—
442C4×D73—28no—
443C4×D73—28no—
444C4×D73—28no—
445C4×D73—28no—
446C4×D73—232no—
447C4×D73—416no—
448C4×D73—416no—
449C4×D73—416no—
450C4×D73C2×#41116yescomplemented
451Dic146—216no—
452Dic146—28no—
453Dic146—416no—
454C22×C73—22no—
455C22×C73—22no—
456C22×C73—22no—
457C22×C73—44no—
458C22×C73C22×#4112yes—
459C22×C73C2×H(5,𝔽2)12yes—
460C22×C73C2×2−1+412yes—
461C22×C73C2611yescharacteristic
462C2×D73—22no—
463C2×D73—22no—
464C2×D73—28no—
465C2×D73—28no—
466C2×D73—22no—
467C2×D73—22no—
468C2×D73—28no—
469C2×D73—22no—
470C2×D73—28no—
471C2×D73—44no—
472C2×D73—416no—
473C2×D73C22×#4114yes—
474C4×C73—22no—
475C4×C73—28no—
476C4×C73—28no—
477C4×C73—22no—
478C4×C73—22no—
479C4×C73C22×#4114yes—
480C4×C73C2×H(5,𝔽2)14yes—
481C4×C73C2×2−1+414yes—
482Dic73—22no—
483Dic73—28no—
484Dic73—22no—
485Dic73—22no—
486Dic73—22no—
487Dic73—22no—
488Dic73C22×#4114yes—
489C2×#3511—731nomaximal, Sylow
490C2×C73—42no—
491C2×C73#351114yescomplemented
492C2×C73C23×#4111yescharacteristic
493C2×C73C22×H(5,𝔽2)11yescharacteristic
494C2×C73C22×2−1+411yescharacteristic
495D73—24no—
496D73—48no—
497D73—42no—
498#3511—7332no—
499C2×#556—732no—
500C2×#555—732no—
501C2×#554—732no—
502C2×#553—732no—
503C2×#553—732no—
504C2×#548—732no—
505C2×#548—732no—
506C2×#547—732no—
507C2×#542—732no—
508C2×#542—732no—
509C2×#537—732no—
510C2×#533—731no—
511C2×#533D7311yescharacteristic, complemented
512C2×#532—731no—
513C2×#532—731no—
514C2×#532—731no—
515C22×C4⋊Q8—731no—
516C2×#520—732no—
517C2×C4×#41—731no—
518C73C2×#351111yescharacteristic, complemented, Sylow
519C22×#41—732no—
520C22×#41—732no—
521C22×#41—732no—
522C22×#41—731no—
523C23×Q8—732no—
524#556—7332no—
525#555—7332no—
526#554—7332no—
527#553—7332no—
528#553—7332no—
529#548—7332no—
530#548—7332no—
531#547—7332no—
532#542—7332no—
533#542—7332no—
534#537—7332no—
535#533—7316no—
536#533C2×D73116yescomplemented
537#532—7316no—
538#532—7316no—
539#532—7316no—
540C2×C4⋊Q8—732no—
541C2×C4⋊Q8—7316no—
542C2×C4⋊Q8—732no—
543C2×C4⋊Q8—732no—
544C2×C4⋊Q8—731no—
545C2×C4⋊Q8C2×D7311yescharacteristic
546C2×C4⋊Q8C2×D7311yescharacteristic
547C2×#127—731no—
548C2×#126—734no—
549C2×#126—734no—
550C2×#125—732no—
551C2×#125C2×D7312yes—
552C2×#124—732no—
553C2×#124—732no—
554C2×#124—734no—
555C2×#124—732no—
556C2×#124—734no—
557C2×#123—734no—
558C2×#123—734no—
559C2×C22⋊Q8—732no—
560C2×C22⋊Q8—732no—
561C2×C22⋊Q8—734no—
562C2×C22⋊Q8—734no—
563C2×C22⋊Q8—734no—
564C2×C22⋊Q8C2×D7312yes—
565C2×C22⋊Q8C2×D7312yes—
566C2×#121—732no—
567C2×#121—732no—
568C2×#121—732no—
569C2×#121—732no—
570C2×#121—732no—
571C2×#121—732no—
572C2×#121—734no—
573C2×#121—734no—
574C2×#121—734no—
575#520—7332no—
576C4×#41—7316no—
577C2×C4×Q8—732no—
578C2×C4×Q8—732no—
579C2×C4×Q8—731no—
580C2×C4×Q8—731no—
581C2×C4×Q8C2×D7312yes—
582C2×C4×Q8C2×D7312yes—
583C2×C4×D4—731no—
584C2×C4×D4—731no—
585C2×C4×D4—731no—
586C2×C4×D4—731no—
587C2×C4×D4—732no—
588C2×C4×D4—734no—
589C2×C4×D4—732no—
590C2×C4×D4—732no—
591C2×C4×D4—732no—
592C2×C4×D4—731no—
593C2×C4×D4—731no—
594C2×C4×D4—732no—
595C2×C4×D4—734no—
596C2×C4×D4—732no—
597C2×#117—731no—
598C2×#117—732no—
599C2×#117—731no—
600C2×#117—731no—
601C2×#117—734no—
602C2×#117C2×D7312yes—
603C22×C4⋊C4—732no—
604C22×C4⋊C4—734no—
605C22×C4⋊C4—732no—
606C22×C42—731no—
607C22×C42—731no—
608C22×C42C2×D7311yescharacteristic
609C2×#41—2928no—
610C2×#41—2928no—
611C2×#41—7316no—
612C2×#41—7316no—
613C2×#41—7316no—
614C2×#41—738no—
615C2×#41—1468no—
616C2×#41—14616no—
617C22×Q8—2928no—
618C22×Q8—7316no—
619C22×Q8—734no—
620C22×Q8—731no—
621C22×Q8—732no—
622C22×Q8C22×D7312yes—
623C22×Q8C22×D7312yes—
624C22×D4—734no—
625C22×D4—731no—
626C22×D4—731no—
627C22×D4—734no—
628C22×D4—732no—
629C22×D4—734no—
630C22×D4—731no—
631C22×D4—732no—
632C22×D4—732no—
633C23×C4—734no—
634C23×C4—734no—
635C23×C4—734no—
636C23×C4—731no—
637C23×C4—731no—
638C23×C4—734no—
639C23×C4—731no—
640C23×C4—731no—
641C23×C4—731no—
642C23×C4—731no—
643C23×C4C22×D7311yescharacteristic
644C23×C4C22×D7311yescharacteristic
645C23×C4C22×D7311yescharacteristic
646C4⋊Q8—7316no—
647C4⋊Q8—7316no—
648C4⋊Q8—7316no—
649C4⋊Q8—738no—
650C4⋊Q8C22×D7318yes—
651C4⋊Q8C22×D7318yes—
652#127—738no—
653#126—7332no—
654#126—7332no—
655#125—7316no—
656#125C22×D73116yes—
657#124—7316no—
658#124—7316no—
659#124—7332no—
660#124—7316no—
661#124—7332no—
662#123—7332no—
663#123—7332no—
664C22⋊Q8—7316no—
665C22⋊Q8—7316no—
666C22⋊Q8—7332no—
667C22⋊Q8—7332no—
668C22⋊Q8—7332no—
669C22⋊Q8C22×D73116yes—
670C22⋊Q8C22×D73116yes—
671#121—7316no—
672#121—7316no—
673#121—7316no—
674#121—7316no—
675#121—7316no—
676#121—7316no—
677#121—7332no—
678#121—7332no—
679#121—7332no—
680C4×Q8—7316no—
681C4×Q8—7316no—
682C4×Q8—738no—
683C4×Q8—738no—
684C4×Q8C22×D73116yes—
685C4×Q8C22×D73116yes—
686C4×D4—738no—
687C4×D4—738no—
688C4×D4—738no—
689C4×D4—738no—
690C4×D4—7316no—
691C4×D4—7332no—
692C4×D4—7316no—
693C4×D4—7316no—
694C4×D4—7316no—
695C4×D4—738no—
696C4×D4—738no—
697C4×D4—7316no—
698C4×D4—7332no—
699C4×D4—7316no—
700#117—738no—
701#117—7316no—
702#117—738no—
703#117—738no—
704#117—7332no—
705#117C22×D73116yes—
706C2×C4⋊C4—731no—
707C2×C4⋊C4—734no—
708C2×C4⋊C4—732no—
709C2×C4⋊C4—732no—
710C2×C4⋊C4—734no—
711C2×C4⋊C4—734no—
712C2×C4⋊C4—731no—
713C2×C4⋊C4—731no—
714C2×C4⋊C4—731no—
715C2×C4⋊C4—731no—
716C2×C4⋊C4—731no—
717C2×C4⋊C4—734no—
718C2×C4⋊C4—7316no—
719C2×C4⋊C4—7332no—
720C2×C4⋊C4—7316no—
721C2×C4⋊C4C22×D7312yes—
722C2×C4⋊C4C22×D7312yes—
723C2×C4⋊C4C22×D7314yes—
724C2×C4⋊C4C22×D7312yes—
725C2×C4⋊C4C22×D7312yes—
726C2×C4⋊C4C22×D7314yes—
727C2×C22⋊C4—731no—
728C2×C22⋊C4—731no—
729C2×C22⋊C4—731no—
730C2×C22⋊C4—731no—
731C2×C22⋊C4—734no—
732C2×C22⋊C4—734no—
733C2×C22⋊C4—731no—
734C2×C22⋊C4—731no—
735C2×C22⋊C4—734no—
736C2×C22⋊C4—734no—
737C2×C22⋊C4—734no—
738C2×C22⋊C4—734no—
739C2×C22⋊C4—734no—
740C2×C22⋊C4C22×D7314yes—
741C2×C42—731no—
742C2×C42—734no—
743C2×C42—731no—
744C2×C42—731no—
745C2×C42—731no—
746C2×C42—731no—
747C2×C42—731no—
748C2×C42—738no—
749C2×C42—738no—
750C2×C42C22×D7311yescharacteristic
751C2×C42C22×D7314yes—
752C2×C42C22×D7311yescharacteristic
753C2×C42C22×D7311yescharacteristic
754C2×C42C22×D7318yes—
755C2×C42C22×D7311yescharacteristic
756C24—731no—
757C24—734no—
758C24—731no—
759C24C23×D7311yescharacteristic
760#41—29232no—
761#41—29232no—
762#41—14632no—
763#41—14664no—
764C2×Q8—28no—
765C2×Q8—28no—
766C2×Q8—2928no—
767C2×Q8—29232no—
768C2×Q8—7316no—
769C2×Q8—734no—
770C2×Q8—738no—
771C2×Q8—1464no—
772C2×Q8—1468no—
773C2×Q8C23×D7318yes—
774C2×Q8C23×D7318yes—
775C2×D4—2928no—
776C2×D4—2928no—
777C2×D4—7316no—
778C2×D4—734no—
779C2×D4—734no—
780C2×D4—7316no—
781C2×D4—738no—
782C2×D4—7316no—
783C2×D4—734no—
784C2×D4—738no—
785C2×D4—738no—
786C2×D4—1464no—
787C2×D4—14616no—
788C2×D4—1464no—
789C2×D4—1464no—
790C2×D4—1468no—
791C2×D4—1468no—
792C2×D4—1468no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—2928no—
797C22×C4—2928no—
798C22×C4—2928no—
799C22×C4—7316no—
800C22×C4—7316no—
801C22×C4—7316no—
802C22×C4—731no—
803C22×C4—738no—
804C22×C4—734no—
805C22×C4—731no—
806C22×C4—731no—
807C22×C4—731no—
808C22×C4—731no—
809C22×C4—731no—
810C22×C4—734no—
811C22×C4—734no—
812C22×C4—734no—
813C22×C4—734no—
814C22×C4—734no—
815C22×C4—734no—
816C22×C4—7316no—
817C22×C4—14616no—
818C22×C4—1464no—
819C22×C4—1464no—
820C22×C4—1464no—
821C22×C4—1464no—
822C22×C4—1464no—
823C22×C4C23×D7314yes—
824C22×C4C23×D7314yes—
825C22×C4C23×D7314yes—
826C22×C4C23×D7314yes—
827C22×C4C23×D7311yescharacteristic
828C22×C4C23×D7311yescharacteristic
829C22×C4C23×D7311yescharacteristic
830C22×C4C23×D7314yes—
831C22×C4C23×D7311yescharacteristic
832C22×C4C23×D7311yescharacteristic
833C22×C4C23×D7311yescharacteristic
834C4⋊C4—734no—
835C4⋊C4—7316no—
836C4⋊C4—7316no—
837C4⋊C4—734no—
838C4⋊C4—734no—
839C4⋊C4—734no—
840C4⋊C4—7316no—
841C4⋊C4—738no—
842C4⋊C4—738no—
843C4⋊C4—7316no—
844C4⋊C4—734no—
845C4⋊C4—734no—
846C4⋊C4C23×D7318yes—
847C4⋊C4C23×D7318yes—
848C4⋊C4C23×D73116yes—
849C4⋊C4C23×D7318yes—
850C4⋊C4C23×D7318yes—
851C4⋊C4C23×D73116yes—
852C22⋊C4—734no—
853C22⋊C4—734no—
854C22⋊C4—734no—
855C22⋊C4—734no—
856C22⋊C4—7316no—
857C22⋊C4—7316no—
858C22⋊C4—734no—
859C22⋊C4—734no—
860C22⋊C4—7316no—
861C22⋊C4—7316no—
862C22⋊C4—7316no—
863C22⋊C4—7316no—
864C22⋊C4—7316no—
865C22⋊C4C23×D73116yes—
866C42—734no—
867C42—734no—
868C42—734no—
869C42—734no—
870C42—734no—
871C42—734no—
872C42—7316no—
873C42C23×D7314yes—
874C42C23×D7314yes—
875C42C23×D7314yes—
876C42C23×D7314yes—
877C42C23×D73116yes—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—734no—
882C23—732no—
883C23—738no—
884C23—732no—
885C23—1468no—
886C23—1462no—
887C23—1468no—
888C23—1462no—
889C23—1462no—
890C23—1468no—
891C23—1462no—
892C23—1462no—
893C23C24×D7312yes—
894C23C24×D7311yescharacteristic
895Q8—216no—
896Q8—216no—
897Q8—29216no—
898Q8—1468no—
899Q8—14616no—
900D4—29216no—
901D4—29216no—
902D4—1468no—
903D4—14632no—
904D4—1468no—
905D4—1468no—
906D4—14616no—
907D4—14616no—
908D4—14616no—
909C2×C4—22no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—28no—
913C2×C4—22no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—29216no—
918C2×C4—29216no—
919C2×C4—29216no—
920C2×C4—734no—
921C2×C4—732no—
922C2×C4—7316no—
923C2×C4—732no—
924C2×C4—732no—
925C2×C4—732no—
926C2×C4—732no—
927C2×C4—732no—
928C2×C4—738no—
929C2×C4—14632no—
930C2×C4—1462no—
931C2×C4—1462no—
932C2×C4—1468no—
933C2×C4—1462no—
934C2×C4—1462no—
935C2×C4—1462no—
936C2×C4—1468no—
937C2×C4—1468no—
938C2×C4—1468no—
939C2×C4—1468no—
940C2×C4—1468no—
941C2×C4#41×D7314yes—
942C2×C4#1455663714yes—
943C2×C4#1455663914yes—
944C2×C4C24×D7318yes—
945C2×C4C24×D7312yes—
946C2×C4C24×D7312yes—
947C2×C4C24×D7312yes—
948C2×C4C24×D7318yes—
949C2×C4C24×D7312yes—
950C2×C4C24×D7312yes—
951C2×C4C24×D7312yes—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—44no—
956C22—29216no—
957C22—2924no—
958C22—734no—
959C22—1468no—
960C22—1462no—
961C22—1468no—
962C22—1462no—
963C22—1462no—
964C22—1468no—
965C22—1468no—
966C22—1462no—
967C22—1462no—
968C22C2×#41×D7312yes—
969C22C2×#1455663712yes—
970C22C2×#1455663912yes—
971C22C25×D7311yescharacteristic
972C4—22no—
973C4—28no—
974C4—22no—
975C4—28no—
976C4—22no—
977C4—734no—
978C4—1462no—
979C4—1462no—
980C4—1468no—
981C4—1462no—
982C4—1462no—
983C4—1462no—
984C4C2×#41×D7314yes—
985C4C2×#1455663714yes—
986C4C2×#1455663914yes—
987C2—42no—
988C2—2928no—
989C2—2922no—
990C2—1464no—
991C2#2262384314yesdirect product factor
992C2C22×#41×D7311yescharacteristic
993C2C22×#1455663711yescharacteristic
994C2C22×#1455663911yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#533×C73C2
socleC23×C73C25
hypercenterC2×#533D73
hypocenterC73C2×#3511
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22623843C2direct (N × H)
2. C2×#17989309C2semidirect
3. C2×#17989300C2semidirect
4. C2×#17989293C2semidirect
5. C2×#17989290C2semidirect
6. C2×#17989281C2semidirect
7. C2×#17989249C2semidirect
8. C2×#17989247C2semidirect
9. C2×#17989239C2semidirect
10. C2×#17989210C2semidirect
11. C2×#17989209C2semidirect
12. C2×#17989167C2semidirect
13. C2×#17989142C2semidirect
14. C2×#17989138C2semidirect
15. C2×#17989138C2semidirect
16. C2×#17989137C2semidirect
17. C2×C4⋊Q8×D73C2semidirect
18. C2×#17989069C2semidirect
19. C2×C4×#11924028C2semidirect
20. C2×#533×C73C2semidirect
26. #17989309C22semidirect
27. #17989300C22semidirect
28. #17989293C22semidirect
29. #17989290C22semidirect
30. #17989281C22semidirect
31. #17989249C22semidirect
32. #17989247C22semidirect
33. #17989239C22semidirect
34. #17989210C22semidirect
35. #17989209C22semidirect
36. #17989167C22semidirect
37. #17989142C22semidirect
38. #17989138C22semidirect
39. #17989138C22semidirect
40. #17989137C22semidirect
45. C4⋊Q8×D73C22semidirect
71. #17989069C22semidirect
72. C4×#11924028C22semidirect
101. #533×C73C22semidirect
306. C2×C4×D73#41semidirect
450. C4×D73C2×#41semidirect
491. C2×C73#3511semidirect
511. C2×#533D73semidirect
518. C73C2×#3511semidirect
536. #533C2×D73semidirect
991. C2#22623843direct (N × H)

Maximal subgroups

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

subgroupindex
#226238432
C2×#179893092
C2×#179893002
C2×#179892932
C2×#179892902
C2×#179892812
C2×#179892492
C2×#179892472
C2×#179892392
C2×#179892102
C2×#179892092
C2×#179891672
C2×#179891422
C2×#179891382
C2×#179891372
C2×C4⋊Q8×D732
C2×#179890692
C2×C4×#119240282
C2×#533×C732
C2×#351173