Finite Group Databasebeta

← C2×#22611103 #33113408

Subgroups — C2×#22611103 #33113408

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×#17988604C211yesmaximal, characteristic
3C2×#17988561C211yesmaximal, characteristic
4#22611103C218yesmaximal, direct product factor
5C2×#17988359C211yesmaximal, characteristic, complemented
6C2×#17988347C211yesmaximal, characteristic, complemented
7C2×#17988344C211yesmaximal, characteristic, complemented
8C22×#104×C73C211yesmaximal, characteristic
9C22×#11924012C2211yescharacteristic
10#17989144—22no—
11#17989144—22no—
12#17989144—22no—
13#17989144C2214yescomplemented
14C2×#14556591—21no—
15C2×#14556583—21no—
16C2×#14556570—22no—
17C2×C4×Dic146—22no—
18C2×#14556550C2211yescharacteristic
19C2×#14556550C2211yescharacteristic
20C2×#14556550C2211yescharacteristic
21#17988604—22no—
22#17988604C2214yes—
23C2×#14556518—22no—
24#17988561—22no—
25#17988561C2214yes—
26C2×#14556506—22no—
27#17988359C2214yescomplemented
28#17988347C2214yescomplemented
29#17988344C2214yescomplemented
30C22×#41×C73C2211yescharacteristic
31C22×M16×C73C2211yescharacteristic
32C22×C42×C73C2211yescharacteristic
33C2×#104×C73—21no—
34C2×#104×C73—22no—
35C2×#104×C73—21no—
36C2×#104×C73C2214yes—
37C22×Dic146—22no—
38C2×#11924012—21no—
39C2×#11924012—21no—
40C2×#11924012—21no—
41C2×#11924012—21no—
42C2×#11924012—21no—
43C2×#11924012C2312yes—
44C22×#10596831—21no—
45#14556591—24no—
46#14556591—24no—
47#14556583—24no—
48#14556583—24no—
49#14556570—28no—
50#14556570—28no—
51C4×Dic146—28no—
52C4×Dic146—28no—
53#14556550—21no—
54#14556550—21no—
55#14556550—21no—
56#14556550—21no—
57#14556550—21no—
58#14556550—21no—
59#14556550—21no—
60#14556550D412yes—
61#14556550D412yes—
62#14556550C2312yes—
63#14556550C2312yes—
64#14556550C2312yes—
65C2×C4⋊Dic73—22no—
66C2×C4⋊Dic73—21no—
67C2×C4⋊Dic73—21no—
68C2×C4⋊Dic73—21no—
69C2×#11924007—24no—
70C2×C22⋊Dic73—21no—
71C2×C22⋊Dic73—21no—
72C2×C22⋊Dic73D412yes—
73C2×C4×Dic73—21no—
74C2×C4×Dic73—21no—
75C2×C4×Dic73D412yes—
76#14556518—28no—
77#14556506—28no—
78C2×#41×C73—21no—
79C2×#41×C73—21no—
80C2×#41×C73—21no—
81C2×#41×C73—21no—
82C2×#41×C73—21no—
83C2×#41×C73—21no—
84C2×#41×C73—21no—
85C2×#41×C73—21no—
86C2×#41×C73—21no—
87C2×#41×C73—21no—
88C2×#41×C73Q812yescomplemented
89C2×#41×C73C2312yes—
90C22×Q8×C73Q811yescharacteristic, complemented
91C22×D4×C73—21no—
92C22×D4×C73Q811yescharacteristic, complemented
93C23×C4×C73—21no—
94C23×C4×C73—21no—
95C23×C4×C73C2311yescharacteristic
96C2×M16×C73—21no—
97C2×M16×C73—21no—
98C2×M16×C73—21no—
99C2×M16×C73—21no—
100C2×M16×C73—21no—
101C2×M16×C73C2312yes—
102C22×C8×C73—21no—
103C2×C42×C73—21no—
104C2×C42×C73—21no—
105C2×C42×C73—21no—
106C2×C42×C73D411yescharacteristic
107C2×C42×C73D412yes—
108C2×C42×C73D411yescharacteristic
109C2×C42×C73C2312yes—
110#104×C73—24no—
111#104×C73—24no—
112C2×Dic146—28no—
113C2×Dic146—48no—
114C22×Dic73—22no—
115C22×Dic73—22no—
116C22×Dic73—41no—
117#11924012—22no—
118#11924012—22no—
119#11924012—41no—
120#11924012—41no—
121C2×#10596831—22no—
122C2×#10596831—41no—
123C2×#10596831—41no—
124C4⋊Dic73—28no—
125C4⋊Dic73—22no—
126C4⋊Dic73—22no—
127C4⋊Dic73—22no—
128C4⋊Dic73—22no—
129C4⋊Dic73—22no—
130C4⋊Dic73—41no—
131#11924007—216no—
132C22⋊Dic73—22no—
133C22⋊Dic73—22no—
134C22⋊Dic73—22no—
135C22⋊Dic73—22no—
136C22⋊Dic73—41no—
137C22⋊Dic73C2×D414yes—
138C4×Dic73—22no—
139C4×Dic73—22no—
140C4×Dic73—22no—
141C4×Dic73—22no—
142C4×Dic73—41no—
143C4×Dic73C2×D414yes—
144C24×C73—21no—
145C24×C73C2×D411yescharacteristic
146#41×C73—22no—
147#41×C73—22no—
148#41×C73—22no—
149#41×C73—22no—
150#41×C73—22no—
151#41×C73—22no—
152#41×C73—22no—
153#41×C73—22no—
154#41×C73—41no—
155#41×C73—41no—
156#41×C73—41no—
157#41×C73—41no—
158#41×C73—41no—
159#41×C73—41no—
160#41×C73—41no—
161#41×C73—41no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73C2×Q812yescomplemented
168C2×D4×C73—22no—
169C2×D4×C73—22no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—41no—
176C2×D4×C73—41no—
177C2×D4×C73—41no—
178C2×D4×C73—41no—
179C2×D4×C73C2×Q812yescomplemented
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—22no—
183C22×C4×C73—21no—
184C22×C4×C73—22no—
185C22×C4×C73—22no—
186C22×C4×C73—22no—
187C22×C4×C73—44no—
188C22×C4×C73—41no—
189C22×C4×C73—41no—
190C22×C4×C73—41no—
191C22×C4×C73—41no—
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73C2×Q811yescharacteristic
198C22×C4×C73C2×Q811yescharacteristic
199C22×C4×C73#4111yescharacteristic
200C22×C4×C73#4111yescharacteristic
201C22×C4×C73#4111yescharacteristic
202C22×C4×C73#4111yescharacteristic
203C22×C4×C73#4111yescharacteristic
204C22×C4×C73#4111yescharacteristic
205C22×C4×C73C2411yescharacteristic
206M16×C73—22no—
207M16×C73—22no—
208M16×C73—41no—
209M16×C73—41no—
210C2×C8×C73—22no—
211C2×C8×C73—41no—
212C2×C8×C73—41no—
213C42×C73—22no—
214C42×C73—21no—
215C42×C73—21no—
216C42×C73—22no—
217C42×C73C2×D412yes—
218C42×C73C2×D412yes—
219C23×C73—22no—
220C23×C73—42no—
221C23×C73—41no—
222C23×C73—41no—
223C23×C73—82no—
224C23×C73#12011yescharacteristic
225C23×C73#12011yescharacteristic
226C23×C73C22⋊Q811yescharacteristic
227C23×C73C22⋊Q811yescharacteristic
228C23×C73#12411yescharacteristic
229C23×C73#12411yescharacteristic
230C23×C73C22×D411yescharacteristic
231Q8×C73—22no—
232Q8×C73—22no—
233Q8×C73—41no—
234Q8×C73—41no—
235D4×C73—22no—
236D4×C73—22no—
237D4×C73—42no—
238D4×C73—42no—
239D4×C73—42no—
240D4×C73—42no—
241D4×C73—41no—
242D4×C73—41no—
243C2×C4×C73—24no—
244C2×C4×C73—22no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—44no—
248C2×C4×C73—44no—
249C2×C4×C73—42no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—42no—
253C2×C4×C73—42no—
254C2×C4×C73—42no—
255C2×C4×C73—42no—
256C2×C4×C73#12011yescharacteristic
257C2×C4×C73#12011yescharacteristic
258C2×C4×C73C22⋊Q811yescharacteristic
259C2×C4×C73C22⋊Q811yescharacteristic
260C2×C4×C73C22⋊Q811yescharacteristic
261C2×C4×C73C22⋊Q811yescharacteristic
262C2×C4×C73C22⋊Q811yescharacteristic
263C2×C4×C73C22⋊Q811yescharacteristic
264C2×C4×C73C22⋊Q811yescharacteristic
265C2×C4×C73C22⋊Q811yescharacteristic
266C2×C4×C73C22⋊Q811yescharacteristic
267C2×C4×C73C22⋊Q811yescharacteristic
268C2×C4×C73#12411yescharacteristic
269C2×C4×C73#12411yescharacteristic
270C2×C4×C73#12411yescharacteristic
271C2×C4×C73#12411yescharacteristic
272C2×C4×C73#12411yescharacteristic
273C2×C4×C73#12411yescharacteristic
274C2×C4×C73#12411yescharacteristic
275C2×C4×C73#12411yescharacteristic
276C2×C4×C73#12411yescharacteristic
277C2×C4×C73#12411yescharacteristic
278C2×C4×C73C22×D411yescharacteristic
279C2×C4×C73C22×D411yescharacteristic
280C2×C4×C73C22×Q811yescharacteristic
281C2×C4×C73C2×#4111yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×Dic73—24no—
285C2×Dic73—24no—
286C2×Dic73—44no—
287C2×Dic73—44no—
288C2×Dic73—42no—
289C2×Dic73—82no—
290Dic146—416no—
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—42no—
301C22×C73—82no—
302C22×C73—82no—
303C22×C73—82no—
304C22×C73#39311yescharacteristic
305C22×C73#39311yescharacteristic
306C22×C73#39311yescharacteristic
307C22×C73#39311yescharacteristic
308C22×C73C2×#12011yescharacteristic
309C22×C73C2×C22⋊Q811yescharacteristic
310C22×C73C2×#12411yescharacteristic
311C4×C73—24no—
312C4×C73—42no—
313C4×C73—42no—
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—82no—
325C2×#2031—731nomaximal, Sylow
326C2×C73—21no—
327C2×C73—21no—
328C2×C73—21no—
329C2×C73—21no—
330C2×C73—21no—
331C2×C73—21no—
332C2×C73—82no—
333C2×C73#203112yescomplemented
334C2×C73C2×#39311yescharacteristic
335C2×#533—731no—
336C2×#421—731no—
337C22×#104D7311yescharacteristic
338C2×#410—731no—
339#2031—738no—
340C2×#344—731no—
341C2×#339—731no—
342C2×H(3,ℤ/4)—731no—
343C73C2×#203111yescharacteristic, complemented, Sylow
344C22×#41C2×D7311yescharacteristic
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×#117—731no—
358C22×C42C2×D7311yescharacteristic
359#421—734no—
360#421—1462no—
361C2×#104—21no—
362C2×#104—21no—
363C2×#104—22no—
364C2×#104—1462no—
365C2×#104C2×D7314yes—
366#410—734no—
367#410—1462no—
368C2×#99—1462no—
369#344—734no—
370#339—734no—
371H(3,ℤ/4)—734no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41Dic14612yescomplemented
383C2×#41C22×D7312yes—
384C22×Q8—1462no—
385C22×Q8Dic14611yescharacteristic, complemented
386C22×D4—21no—
387C22×D4Dic14611yescharacteristic, complemented
388C23×C4—21no—
389C23×C4—21no—
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—732no—
414#117—732no—
415#117—732no—
416#117—732no—
417#117—732no—
418#117—1461no—
419#117—1461no—
420#117—1461no—
421#117—1461no—
422#117—1461no—
423#117—1461no—
424#117—1461no—
425C2×C4⋊C4—1461no—
426C2×C4⋊C4—1464no—
427C2×C4⋊C4—1462no—
428C2×C4⋊C4—1461no—
429C2×C4⋊C4—1461no—
430C2×C22⋊C4—732no—
431C2×C22⋊C4—1461no—
432C2×C22⋊C4—1461no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—732no—
437C2×C42—1461no—
438C2×C42—1461no—
439C2×C42C22⋊D7311yescharacteristic
440C2×C42C22⋊D7311yescharacteristic
441C2×C42C22⋊D7312yes—
442C2×C42C22×D7312yes—
443#104—24no—
444#104—24no—
445#104—1468no—
446#99—1468no—
447C24—21no—
448C24D4×D7311yescharacteristic
449#41—22no—
450#41—22no—
451#41—22no—
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—22no—
457#41—41no—
458#41—41no—
459#41—41no—
460#41—41no—
461#41—41no—
462#41—41no—
463#41—41no—
464#41—41no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—2928no—
471C2×Q8—1468no—
472C2×Q8C2×Dic14612yescomplemented
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4C2×Dic14612yescomplemented
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—44no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—2921no—
498C22×C4—1462no—
499C22×C4—1462no—
500C22×C4D4×D7311yescharacteristic
501C22×C4D4×D7311yescharacteristic
502C22×C4D4×D7311yescharacteristic
503C22×C4C2×C22⋊D7311yescharacteristic
504C22×C4C2×C22⋊D7311yescharacteristic
505C22×C4C2×Dic14611yescharacteristic
506C22×C4C2×Dic14611yescharacteristic
507C22×C4#1192402711yescharacteristic
508C22×C4#1192402711yescharacteristic
509C22×C4#1192402711yescharacteristic
510C22×C4#1192402711yescharacteristic
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—2921no—
529C4⋊C4—14616no—
530C4⋊C4—1468no—
531C4⋊C4—1462no—
532C4⋊C4—1462no—
533C4⋊C4—1462no—
534C4⋊C4—1462no—
535C4⋊C4—1462no—
536C22⋊C4—2921no—
537C22⋊C4—734no—
538C22⋊C4—1462no—
539C22⋊C4—1462no—
540C22⋊C4—1462no—
541C22⋊C4—1462no—
542C42—22no—
543C42—21no—
544C42—21no—
545C42—22no—
546C42—2921no—
547C42—734no—
548C42—1462no—
549C42—1462no—
550C42—1462no—
551C42—1462no—
552C42C2×C22⋊D7312yes—
553C42C2×C22⋊D7312yes—
554C23—22no—
555C23—42no—
556C23—41no—
557C23—41no—
558C23—82no—
559C23#1455655911yescharacteristic
560C23#1455655911yescharacteristic
561C23#1455656811yescharacteristic
562C23#1455656811yescharacteristic
563C23#1455657711yescharacteristic
564C23#1455657711yescharacteristic
565C23C2×D4×D7311yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—41no—
569Q8—41no—
570Q8—29216no—
571D4—22no—
572D4—22no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—42no—
577D4—41no—
578D4—41no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—2924no—
593C2×C4—2924no—
594C2×C4—2922no—
595C2×C4—5842no—
596C2×C4—1464no—
597C2×C4—1464no—
598C2×C4#1455655911yescharacteristic
599C2×C4#1455655911yescharacteristic
600C2×C4#1455656811yescharacteristic
601C2×C4#1455656811yescharacteristic
602C2×C4#1455656811yescharacteristic
603C2×C4#1455656811yescharacteristic
604C2×C4#1455656811yescharacteristic
605C2×C4#1455656811yescharacteristic
606C2×C4#1455657011yescharacteristic
607C2×C4#1455657011yescharacteristic
608C2×C4#1455657011yescharacteristic
609C2×C4#1455657011yescharacteristic
610C2×C4#1455657711yescharacteristic
611C2×C4#1455657711yescharacteristic
612C2×C4#1455657711yescharacteristic
613C2×C4#1455657711yescharacteristic
614C2×C4#1455657711yescharacteristic
615C2×C4#1455657711yescharacteristic
616C2×C4#1455657811yescharacteristic
617C2×C4#1455657811yescharacteristic
618C2×C4#1455657811yescharacteristic
619C2×C4#1455657811yescharacteristic
620C2×C4C2×D4×D7311yescharacteristic
621C2×C4C22×C22⋊D7311yescharacteristic
622C2×C4C22×Dic14611yescharacteristic
623C2×C4C2×#1192402711yescharacteristic
624C2×C4C2×#1192402711yescharacteristic
625C2×C4C2×#1192402811yescharacteristic
626C8—42no—
627C8—2922no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—42no—
636C22—82no—
637C22—82no—
638C22—82no—
639C22#1798849911yescharacteristic
640C22#1798849911yescharacteristic
641C22#1798849911yescharacteristic
642C22#1798849911yescharacteristic
643C22C2×#1455655911yescharacteristic
644C22C2×#1455656811yescharacteristic
645C22C2×#1455657711yescharacteristic
646C4—24no—
647C4—42no—
648C4—42no—
649C4—2924no—
650C4—2924no—
651C4—5842no—
652C4#1798849911yescharacteristic
653C4#1798849911yescharacteristic
654C4#1798849911yescharacteristic
655C4#1798849911yescharacteristic
656C4C2×#1455656811yescharacteristic
657C4C2×#1455657011yescharacteristic
658C4C2×#1455657711yescharacteristic
659C4C2×#1455657811yescharacteristic
660C2—21no—
661C2—21no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—82no—
667C2#2261110312yesdirect product factor
668C2C2×#1798849911yescharacteristic
subgroupG/H
centerC2×C4#14556577
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC22×#104×C73C2
socleC22×C73#393
prime radicalC22×#41×C73C22
hypercenterC22×#104D73
hypocenterC73C2×#2031
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
1. C2×#17989144C2semidirect
4. #22611103C2direct (N × H)
5. C2×#17988359C2semidirect
6. C2×#17988347C2semidirect
7. C2×#17988344C2semidirect
13. #17989144C22semidirect
27. #17988359C22semidirect
28. #17988347C22semidirect
29. #17988344C22semidirect
88. C2×#41×C73Q8semidirect
90. C22×Q8×C73Q8semidirect
92. C22×D4×C73Q8semidirect
167. C2×Q8×C73C2×Q8semidirect
179. C2×D4×C73C2×Q8semidirect
333. C2×C73#2031semidirect
343. C73C2×#2031semidirect
382. C2×#41Dic146semidirect
385. C22×Q8Dic146semidirect
387. C22×D4Dic146semidirect
472. C2×Q8C2×Dic146semidirect
484. C2×D4C2×Dic146semidirect
667. C2#22611103direct (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×#179886042
C2×#179885612
#226111032
C2×#179883592
C2×#179883472
C2×#179883442
C22×#104×C732
C2×#203173