Finite Group Databasebeta

← C2×#22611104 #33113409

Subgroups — C2×#22611104 #33113409

Order 18688.

1234 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989144C211yesmaximal, characteristic, complemented
2C2×#17988603C211yesmaximal, characteristic
3C22×#14556519C211yesmaximal, characteristic
4C2×#17988560C211yesmaximal, characteristic
5#22611104C218yesmaximal, direct product factor
6C2×#17988358C211yesmaximal, characteristic, complemented
7C2×#17988343C211yesmaximal, characteristic, complemented
8C2×#339×C73C211yesmaximal, characteristic, complemented
9C22×#11924028C2211yescharacteristic
10C22×#11924012C2211yescharacteristic
11#17989144—22no—
12#17989144—22no—
13#17989144—22no—
14#17989144C2214yescomplemented
15C2×#14556591—21no—
16C2×#14556583—21no—
17C2×#14556570—22no—
18C2×C4×Dic146—22no—
19C2×#14556550C2211yescharacteristic
20C2×#14556550C2211yescharacteristic
21#17988603—22no—
22#17988603C2214yes—
23C2×#14556519—21no—
24C2×#14556519—22no—
25C2×#14556519—21no—
26C2×#14556519C2214yes—
27C2×#14556517—22no—
28#17988560—22no—
29#17988560C2214yes—
30C2×#14556505—22no—
31#17988358C2214yescomplemented
32#17988343C2214yescomplemented
33C22×M16×C73C2211yescharacteristic
34C2×#117×C73C2211yescharacteristic
35C22×C42×C73C2211yescharacteristic
36#339×C73C2214yescomplemented
37C2×#11924028—21no—
38C2×#11924028—21no—
39C2×#11924028—21no—
40C2×#11924028—21no—
41C2×#11924028—21no—
42C2×#11924028—21no—
43C2×#11924028—21no—
44C2×#11924028—21no—
45C2×#11924028—21no—
46C2×#11924028—21no—
47C2×#11924028Q812yescomplemented
48C2×#11924028C2312yes—
49C22×Dic146—22no—
50C22×Dic146Q811yescharacteristic, complemented
51C22×D292Q811yescharacteristic, complemented
52C22×C22⋊D73—21no—
53C22×C4×D73—21no—
54C2×#11924012—21no—
55C2×#11924012—21no—
56C2×#11924012—21no—
57C2×#11924012—21no—
58C2×#11924012—21no—
59C2×#11924012C2312yes—
60C22×#10596831—21no—
61#14556591—24no—
62#14556591—24no—
63#14556583—24no—
64#14556583—24no—
65#14556570—28no—
66#14556570—28no—
67C4×Dic146—28no—
68C4×Dic146—28no—
69#14556550—21no—
70#14556550—21no—
71#14556550—21no—
72#14556550—21no—
73#14556550D412yes—
74#14556550D412yes—
75#14556550C2312yes—
76#14556550C2312yes—
77C2×C4⋊Dic73—22no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—21no—
80C2×#11924007—24no—
81C2×C22⋊Dic73—21no—
82C2×C22⋊Dic73D412yes—
83C2×C4×Dic73—21no—
84C2×C4×Dic73D412yes—
85#14556519—24no—
86#14556519—24no—
87#14556517—28no—
88#14556505—28no—
89C23×C4×C73—21no—
90C23×C4×C73C2311yescharacteristic
91C2×M16×C73—21no—
92C2×M16×C73—21no—
93C2×M16×C73—21no—
94C2×M16×C73—21no—
95C2×M16×C73—21no—
96C2×M16×C73C2312yes—
97C22×C8×C73—21no—
98#117×C73—21no—
99#117×C73—21no—
100#117×C73—21no—
101#117×C73C2312yes—
102C2×C4⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C42×C73—21no—
105C2×C42×C73—21no—
106C2×C42×C73—21no—
107C2×C42×C73—21no—
108C2×C42×C73D411yescharacteristic
109C2×C42×C73D412yes—
110C2×C42×C73D411yescharacteristic
111C2×C42×C73C2312yes—
112C23×D73—21no—
113#11924028—22no—
114#11924028—22no—
115#11924028—22no—
116#11924028—22no—
117#11924028—22no—
118#11924028—22no—
119#11924028—22no—
120#11924028—22no—
121#11924028—41no—
122#11924028—41no—
123#11924028—41no—
124#11924028—41no—
125#11924028—41no—
126#11924028—41no—
127#11924028—41no—
128#11924028—41no—
129C2×Dic146—21no—
130C2×Dic146—21no—
131C2×Dic146—21no—
132C2×Dic146—21no—
133C2×Dic146—28no—
134C2×Dic146—21no—
135C2×Dic146—48no—
136C2×Dic146C2×Q812yescomplemented
137C2×D292—21no—
138C2×D292—21no—
139C2×D292—21no—
140C2×D292—21no—
141C2×D292—21no—
142C2×D292C2×Q812yescomplemented
143C2×C22⋊D73—22no—
144C2×C22⋊D73—22no—
145C2×C22⋊D73—41no—
146C2×C22⋊D73—41no—
147C2×C22⋊D73—41no—
148C2×C22⋊D73—41no—
149C22×Dic73—22no—
150C22×Dic73—22no—
151C22×Dic73—21no—
152C2×C4×D73—22no—
153C2×C4×D73—22no—
154C2×C4×D73—41no—
155C2×C4×D73—41no—
156C2×C4×D73—41no—
157C2×C4×D73—41no—
158#11924012—22no—
159#11924012—22no—
160#11924012—41no—
161#11924012—41no—
162C2×#10596831—22no—
163C2×#10596831—41no—
164C2×#10596831—41no—
165C4⋊Dic73—28no—
166C4⋊Dic73—22no—
167C4⋊Dic73—22no—
168C4⋊Dic73—22no—
169C4⋊Dic73—22no—
170#11924007—216no—
171C22⋊Dic73—22no—
172C22⋊Dic73—22no—
173C22⋊Dic73—22no—
174C22⋊Dic73C2×D414yes—
175C4×Dic73—22no—
176C4×Dic73—22no—
177C4×Dic73—22no—
178C4×Dic73C2×D414yes—
179C24×C73C2×D411yescharacteristic
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—22no—
183C22×C4×C73—22no—
184C22×C4×C73—44no—
185C22×C4×C73—41no—
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73C2×Q811yescharacteristic
192C22×C4×C73C2×Q811yescharacteristic
193C22×C4×C73#4111yescharacteristic
194C22×C4×C73#4111yescharacteristic
195C22×C4×C73#4111yescharacteristic
196C22×C4×C73#4111yescharacteristic
197C22×C4×C73#4111yescharacteristic
198C22×C4×C73#4111yescharacteristic
199C22×C4×C73C2411yescharacteristic
200M16×C73—22no—
201M16×C73—22no—
202M16×C73—41no—
203M16×C73—41no—
204C2×C8×C73—22no—
205C2×C8×C73—41no—
206C2×C8×C73—41no—
207C4⋊C4×C73—22no—
208C4⋊C4×C73—41no—
209C22⋊C4×C73—22no—
210C22⋊C4×C73—41no—
211C42×C73—22no—
212C42×C73—21no—
213C42×C73—21no—
214C42×C73—22no—
215C42×C73—22no—
216C42×C73—41no—
217C42×C73C2×D412yes—
218C42×C73C2×D412yes—
219C23×C73—42no—
220C23×C73#12011yescharacteristic
221C23×C73#12011yescharacteristic
222C23×C73C22⋊Q811yescharacteristic
223C23×C73C22⋊Q811yescharacteristic
224C23×C73#12411yescharacteristic
225C23×C73#12411yescharacteristic
226C23×C73C22×D411yescharacteristic
227C22×D73—22no—
228C22×D73—41no—
229C22×D73—41no—
230C22×D73—82no—
231C2×C4×C73—24no—
232C2×C4×C73—22no—
233C2×C4×C73—22no—
234C2×C4×C73—44no—
235C2×C4×C73—44no—
236C2×C4×C73—42no—
237C2×C4×C73—42no—
238C2×C4×C73—82no—
239C2×C4×C73#12011yescharacteristic
240C2×C4×C73#12011yescharacteristic
241C2×C4×C73C22⋊Q811yescharacteristic
242C2×C4×C73C22⋊Q811yescharacteristic
243C2×C4×C73C22⋊Q811yescharacteristic
244C2×C4×C73C22⋊Q811yescharacteristic
245C2×C4×C73C22⋊Q811yescharacteristic
246C2×C4×C73C22⋊Q811yescharacteristic
247C2×C4×C73C22⋊Q811yescharacteristic
248C2×C4×C73C22⋊Q811yescharacteristic
249C2×C4×C73C22⋊Q811yescharacteristic
250C2×C4×C73C22⋊Q811yescharacteristic
251C2×C4×C73#12411yescharacteristic
252C2×C4×C73#12411yescharacteristic
253C2×C4×C73#12411yescharacteristic
254C2×C4×C73#12411yescharacteristic
255C2×C4×C73#12411yescharacteristic
256C2×C4×C73#12411yescharacteristic
257C2×C4×C73#12411yescharacteristic
258C2×C4×C73#12411yescharacteristic
259C2×C4×C73#12411yescharacteristic
260C2×C4×C73#12411yescharacteristic
261C2×C4×C73C22×D411yescharacteristic
262C2×C4×C73C22×D411yescharacteristic
263C2×C4×C73C22×Q811yescharacteristic
264C2×C4×C73C2×#4111yescharacteristic
265C2×C4×C73C2×#4111yescharacteristic
266C2×C4×C73C2×#4111yescharacteristic
267C22⋊D73—42no—
268C22⋊D73—42no—
269C22⋊D73—42no—
270C22⋊D73—42no—
271C2×Dic73—24no—
272C2×Dic73—24no—
273C2×Dic73—22no—
274C2×Dic73—44no—
275C2×Dic73—44no—
276C2×Dic73—41no—
277C2×Dic73—41no—
278D292—22no—
279D292—22no—
280D292—41no—
281D292—41no—
282C4×D73—42no—
283C4×D73—42no—
284C4×D73—42no—
285C4×D73—42no—
286Dic146—22no—
287Dic146—22no—
288Dic146—416no—
289Dic146—41no—
290Dic146—41no—
291C8×C73—42no—
292#10596831—42no—
293C22×C73—22no—
294C22×C73—22no—
295C22×C73—22no—
296C22×C73—41no—
297C22×C73—41no—
298C22×C73—41no—
299C22×C73—41no—
300C22×C73#39311yescharacteristic
301C22×C73#39311yescharacteristic
302C22×C73#39311yescharacteristic
303C22×C73#39311yescharacteristic
304C22×C73C2×#12011yescharacteristic
305C22×C73C2×C22⋊Q811yescharacteristic
306C22×C73C2×#12411yescharacteristic
307C2×D73—42no—
308C2×D73—82no—
309C2×D73—82no—
310C2×D73—82no—
311C4×C73—24no—
312C4×C73—42no—
313C4×C73—82no—
314C4×C73#39311yescharacteristic
315C4×C73#39311yescharacteristic
316C4×C73#39311yescharacteristic
317C4×C73#39311yescharacteristic
318C4×C73C2×C22⋊Q811yescharacteristic
319C4×C73C2×C22⋊Q811yescharacteristic
320C4×C73C2×#12411yescharacteristic
321C4×C73C2×#12411yescharacteristic
322Dic73—44no—
323Dic73—44no—
324Dic73—42no—
325C2×#2031—731nomaximal, Sylow
326C2×C73—21no—
327C2×C73—21no—
328C2×C73—21no—
329C2×C73—21no—
330C2×C73—21no—
331C2×C73—21no—
332C2×C73#203112yescomplemented
333C2×C73C2×#39311yescharacteristic
334D73—82no—
335C2×#533—731no—
336C2×#421—731no—
337C22×#104—731no—
338C2×#410—731no—
339#2031—738no—
340C2×#344—731no—
341C2×#339D7311yescharacteristic, complemented
342C2×H(3,ℤ/4)—731no—
343C73C2×#203111yescharacteristic, complemented, Sylow
344C22×#41—731no—
345C22×M16—731no—
346C22×M16C2×D7311yescharacteristic
347#533—734no—
348#533—1462no—
349#533—1462no—
350#533—1462no—
351C2×C4⋊Q8—1461no—
352C2×#125—1461no—
353C2×C22⋊Q8—1462no—
354C2×C4×Q8—1462no—
355C2×#117—731no—
356C2×#117—731no—
357C2×#117C2×D7311yescharacteristic
358C22×C42C2×D7311yescharacteristic
359#421—734no—
360#421—1462no—
361C2×#104—734no—
362C2×#104—1462no—
363C2×#104—1461no—
364C2×#104—1461no—
365C2×#104—1462no—
366#410—734no—
367#410—1462no—
368C2×#99—1462no—
369#344—734no—
370#339C2×D7314yescomplemented
371H(3,ℤ/4)—734no—
372C2×#41—732no—
373C2×#41—732no—
374C2×#41—1461no—
375C2×#41—1461no—
376C2×#41—1461no—
377C2×#41—1461no—
378C2×#41—1461no—
379C2×#41—1461no—
380C2×#41—1461no—
381C2×#41—1461no—
382C2×#41—1461no—
383C2×#41—1461no—
384C22×Q8—731no—
385C22×Q8—1462no—
386C22×D4—731no—
387C22×D4—1461no—
388C23×C4—21no—
389C23×C4—1461no—
390C23×C4C22×D7311yescharacteristic
391C2×M16—21no—
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—732no—
397C2×M16—1461no—
398C2×M16—1461no—
399C2×M16—1461no—
400C2×M16—1461no—
401C2×M16—1461no—
402C2×M16C22×D7312yes—
403C22×C8—21no—
404C22×C8—1461no—
405C4⋊Q8—1464no—
406C4⋊Q8—1464no—
407#125—1464no—
408#125—1464no—
409C22⋊Q8—1468no—
410C22⋊Q8—1468no—
411C4×Q8—1468no—
412C4×Q8—1468no—
413#117—21no—
414#117—21no—
415#117—21no—
416#117—732no—
417#117—732no—
418#117—732no—
419#117—732no—
420#117—1461no—
421#117—1461no—
422#117—1461no—
423#117—1461no—
424#117C22×D7312yes—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—1464no—
427C2×C4⋊C4—1462no—
428C2×C4⋊C4—1461no—
429C2×C4⋊C4—1461no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—732no—
432C2×C22⋊C4—1461no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—732no—
438C2×C42—1461no—
439C2×C42D29211yescharacteristic
440C2×C42D29211yescharacteristic
441C2×C42D29212yes—
442C2×C42C22×D7312yes—
443#104—1468no—
444#104—1464no—
445#104—1464no—
446#99—1468no—
447C24—1461no—
448C24D4×D7311yescharacteristic
449#41—2921no—
450#41—2921no—
451#41—2921no—
452#41—2921no—
453#41—2921no—
454#41—2921no—
455#41—2921no—
456#41—2921no—
457#41—1462no—
458#41—1462no—
459#41—1462no—
460#41—1462no—
461#41—1462no—
462#41—1462no—
463#41—1462no—
464#41—1462no—
465C2×Q8—2928no—
466C2×Q8—732no—
467C2×Q8—1468no—
468C2×Q8—1461no—
469C2×Q8—1461no—
470C2×Q8—1461no—
471C2×Q8—1461no—
472C2×Q8—1461no—
473C2×D4—2921no—
474C2×D4—2921no—
475C2×D4—2921no—
476C2×D4—2921no—
477C2×D4—732no—
478C2×D4—1462no—
479C2×D4—1462no—
480C2×D4—1461no—
481C2×D4—1461no—
482C2×D4—1461no—
483C2×D4—1461no—
484C2×D4—1461no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—41no—
491C22×C4—2921no—
492C22×C4—2921no—
493C22×C4—2921no—
494C22×C4—2921no—
495C22×C4—1462no—
496C22×C4—1462no—
497C22×C4—1461no—
498C22×C4—1462no—
499C22×C4—1462no—
500C22×C4D4×D7311yescharacteristic
501C22×C4D4×D7311yescharacteristic
502C22×C4D4×D7311yescharacteristic
503C22×C4C2×D29211yescharacteristic
504C22×C4C2×D29211yescharacteristic
505C22×C4Q8×D7311yescharacteristic
506C22×C4Q8×D7311yescharacteristic
507C22×C4#1192402711yescharacteristic
508C22×C4#1192402711yescharacteristic
509C22×C4#1192402811yescharacteristic
510C22×C4#1192402811yescharacteristic
511C22×C4#1192402811yescharacteristic
512C22×C4#1192402811yescharacteristic
513C22×C4C23×D7311yescharacteristic
514M16—22no—
515M16—22no—
516M16—41no—
517M16—41no—
518M16—2921no—
519M16—2921no—
520M16—1462no—
521M16—1462no—
522C2×C8—22no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—2921no—
526C2×C8—2921no—
527C2×C8—1462no—
528C4⋊C4—22no—
529C4⋊C4—41no—
530C4⋊C4—14616no—
531C4⋊C4—1468no—
532C4⋊C4—1462no—
533C4⋊C4—1462no—
534C4⋊C4—1462no—
535C4⋊C4—1462no—
536C22⋊C4—22no—
537C22⋊C4—41no—
538C22⋊C4—734no—
539C22⋊C4—1462no—
540C22⋊C4—1462no—
541C22⋊C4—1462no—
542C42—22no—
543C42—21no—
544C42—21no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—734no—
549C42—1462no—
550C42—1462no—
551C42—1462no—
552C42C2×D29212yes—
553C42C2×D29212yes—
554C23—42no—
555C23—2921no—
556C23—2921no—
557C23—5842no—
558C23—1462no—
559C23#1455656111yescharacteristic
560C23#1455656111yescharacteristic
561C23#1455656911yescharacteristic
562C23#1455656911yescharacteristic
563C23#1455657711yescharacteristic
564C23#1455657711yescharacteristic
565C23C2×D4×D7311yescharacteristic
566Q8—29216no—
567Q8—2921no—
568Q8—2921no—
569Q8—1462no—
570Q8—1462no—
571D4—2922no—
572D4—2922no—
573D4—2922no—
574D4—2922no—
575D4—2921no—
576D4—2921no—
577D4—1462no—
578D4—1462no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—82no—
587C2×C4—2924no—
588C2×C4—2924no—
589C2×C4—2921no—
590C2×C4—2921no—
591C2×C4—2922no—
592C2×C4—2922no—
593C2×C4—2922no—
594C2×C4—2922no—
595C2×C4—1464no—
596C2×C4—1464no—
597C2×C4—1462no—
598C2×C4#1455656111yescharacteristic
599C2×C4#1455656111yescharacteristic
600C2×C4#1455656911yescharacteristic
601C2×C4#1455656911yescharacteristic
602C2×C4#1455656911yescharacteristic
603C2×C4#1455656911yescharacteristic
604C2×C4#1455656911yescharacteristic
605C2×C4#1455656911yescharacteristic
606C2×C4#1455657111yescharacteristic
607C2×C4#1455657111yescharacteristic
608C2×C4#1455657111yescharacteristic
609C2×C4#1455657111yescharacteristic
610C2×C4#1455657711yescharacteristic
611C2×C4#1455657711yescharacteristic
612C2×C4#1455657711yescharacteristic
613C2×C4#1455657711yescharacteristic
614C2×C4#1455657711yescharacteristic
615C2×C4#1455657711yescharacteristic
616C2×C4#1455657911yescharacteristic
617C2×C4#1455657911yescharacteristic
618C2×C4#1455657911yescharacteristic
619C2×C4#1455657911yescharacteristic
620C2×C4C2×D4×D7311yescharacteristic
621C2×C4C22×D29211yescharacteristic
622C2×C4C2×Q8×D7311yescharacteristic
623C2×C4C2×#1192402711yescharacteristic
624C2×C4C2×#1192402811yescharacteristic
625C2×C4C2×#1192402811yescharacteristic
626C8—42no—
627C8—2922no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—2922no—
636C22—5842no—
637C22—5842no—
638C22—5842no—
639C22#1798850011yescharacteristic
640C22#1798850011yescharacteristic
641C22#1798850011yescharacteristic
642C22#1798850011yescharacteristic
643C22C2×#1455656111yescharacteristic
644C22C2×#1455656911yescharacteristic
645C22C2×#1455657711yescharacteristic
646C4—24no—
647C4—42no—
648C4—82no—
649C4—2924no—
650C4—2924no—
651C4—2922no—
652C4#1798850011yescharacteristic
653C4#1798850011yescharacteristic
654C4#1798850011yescharacteristic
655C4#1798850011yescharacteristic
656C4C2×#1455656911yescharacteristic
657C4C2×#1455657111yescharacteristic
658C4C2×#1455657711yescharacteristic
659C4C2×#1455657911yescharacteristic
660C2—21no—
661C2—21no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—5842no—
667C2#2261110412yesdirect product factor
668C2C2×#1798850011yescharacteristic
subgroupG/H
centerC2×C4#14556577
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC2×#339×C73C2
socleC22×C73#393
prime radicalC22×#11924028C22
hypercenterC2×#339D73
hypocenterC73C2×#2031
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#17989144C2semidirect
5. #22611104C2direct (N × H)
6. C2×#17988358C2semidirect
7. C2×#17988343C2semidirect
8. C2×#339×C73C2semidirect
14. #17989144C22semidirect
31. #17988358C22semidirect
32. #17988343C22semidirect
36. #339×C73C22semidirect
47. C2×#11924028Q8semidirect
50. C22×Dic146Q8semidirect
51. C22×D292Q8semidirect
136. C2×Dic146C2×Q8semidirect
142. C2×D292C2×Q8semidirect
332. C2×C73#2031semidirect
341. C2×#339D73semidirect
343. C73C2×#2031semidirect
370. #339C2×D73semidirect
667. C2#22611104direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891442
C2×#179886032
C22×#145565192
C2×#179885602
#226111042
C2×#179883582
C2×#179883432
C2×#339×C732
C2×#203173