Finite Group Databasebeta

← C2×#22610598 #33088563

Subgroups — C2×#22610598 #33088563

Order 18688.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988635C211yesmaximal, characteristic, complemented
2C2×#17988605C211yesmaximal, characteristic
3C22×#14556517C211yesmaximal, characteristic
4C2×#17988569C211yesmaximal, characteristic
5C2×M16×Dic73C211yesmaximal, characteristic, complemented
6#22610598C218yesmaximal, direct product factor
7C2×#17988346C211yesmaximal, characteristic, complemented
8C2×#344×C73C211yesmaximal, characteristic, complemented
9C22×#11924028C2211yescharacteristic
10C22×#11924012C2211yescharacteristic
11C22×#11924012C2211yescharacteristic
12C22×C4×Dic73C2211yescharacteristic
13#17988635—22no—
14#17988635C2214yescomplemented
15C2×#14556526—22no—
16#17988605—22no—
17#17988605C2214yes—
18C2×#14556519—22no—
19C2×#14556517—21no—
20C2×#14556517—21no—
21C2×#14556517—22no—
22C2×#14556517C2214yes—
23#17988569C414yescomplemented
24#17988569C2214yes—
25C2×#14556509C412yescomplemented
26C2×#14556507C412yescomplemented
27M16×Dic73—22no—
28M16×Dic73C2214yescomplemented
29C2×#14556501—21no—
30C2×C8×Dic73—21no—
31#17988346C2214yescomplemented
32C22×M16×C73C2211yescharacteristic
33C22×M16×C73C2211yescharacteristic
34C2×#117×C73C2211yescharacteristic
35#344×C73C2214yescomplemented
36C2×#11924028—21no—
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×#11924028C2×C412yes—
47C2×#11924028C2312yes—
48C22×Dic146C2×C411yescharacteristic
49C22×D292C2×C411yescharacteristic
50C22×C22⋊D73—21no—
51C23×Dic73—21no—
52C22×C4×D73—21no—
53C2×#11924012—21no—
54C2×#11924012—21no—
55C2×#11924012—21no—
56C2×#11924012—21no—
57C2×#11924012—21no—
58C2×#11924012—21no—
59C2×#11924012C2×C412yes—
60C2×#11924012C2×C412yes—
61C2×#11924012D412yes—
62C2×#11924012D412yes—
63C2×#11924012C2312yes—
64C2×#11924012C2312yes—
65C22×#10596831—21no—
66C22×#10596831—21no—
67C2×C4×Dic73—21no—
68C2×C4×Dic73—21no—
69C2×C4×Dic73—21no—
70C2×C4×Dic73D411yescharacteristic
71C2×C4×Dic73D411yescharacteristic
72C2×C4×Dic73D412yes—
73C2×C4×Dic73C2312yes—
74#14556526—28no—
75#14556519—28no—
76#14556517—24no—
77#14556517—24no—
78#14556509C2×C418yescomplemented
79#14556507C2×C418yescomplemented
80#14556501—24no—
81C8×Dic73—24no—
82C23×C4×C73C2311yescharacteristic
83C2×M16×C73—21no—
84C2×M16×C73—21no—
85C2×M16×C73—21no—
86C2×M16×C73—21no—
87C2×M16×C73—21no—
88C2×M16×C73—21no—
89C2×M16×C73—21no—
90C2×M16×C73—21no—
91C2×M16×C73C2×C412yes—
92C2×M16×C73C2×C412yes—
93C2×M16×C73C2312yes—
94C2×M16×C73C2312yes—
95C22×C8×C73—21no—
96C22×C8×C73—21no—
97#117×C73—21no—
98#117×C73—21no—
99#117×C73—21no—
100#117×C73C2312yes—
101C2×C4⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C42×C73—21no—
104C23×D73—21no—
105#11924028—22no—
106#11924028—22no—
107#11924028—22no—
108#11924028—22no—
109#11924028—22no—
110#11924028—22no—
111#11924028—22no—
112#11924028—22no—
113#11924028—41no—
114#11924028—41no—
115#11924028—41no—
116#11924028—41no—
117#11924028—41no—
118#11924028—41no—
119#11924028—41no—
120#11924028—41no—
121C2×Dic146—21no—
122C2×Dic146—21no—
123C2×Dic146—21no—
124C2×Dic146—21no—
125C2×Dic146—21no—
126C2×Dic146C22×C412yes—
127C2×D292—21no—
128C2×D292—21no—
129C2×D292—21no—
130C2×D292—21no—
131C2×D292—21no—
132C2×D292C22×C412yes—
133C2×C22⋊D73—22no—
134C2×C22⋊D73—22no—
135C2×C22⋊D73—41no—
136C2×C22⋊D73—41no—
137C2×C22⋊D73—41no—
138C2×C22⋊D73—41no—
139C22×Dic73—21no—
140C22×Dic73—21no—
141C22×Dic73—22no—
142C22×Dic73—21no—
143C22×Dic73—22no—
144C22×Dic73—44no—
145C2×C4×D73—22no—
146C2×C4×D73—22no—
147C2×C4×D73—41no—
148C2×C4×D73—41no—
149C2×C4×D73—41no—
150C2×C4×D73—41no—
151#11924012—22no—
152#11924012—22no—
153#11924012—22no—
154#11924012—22no—
155#11924012—22no—
156#11924012—22no—
157#11924012C22×C414yes—
158#11924012C2×D414yes—
159C2×#10596831—22no—
160C2×#10596831—22no—
161C2×#10596831—22no—
162C2×#10596831—22no—
163C2×#10596831—22no—
164C2×#10596831—22no—
165C4×Dic73—21no—
166C4×Dic73—22no—
167C4×Dic73—21no—
168C4×Dic73—22no—
169C4×Dic73C2×D412yes—
170C4×Dic73C2×D412yes—
171C24×C73#4111yescharacteristic
172C22×C4×C73—41no—
173C22×C4×C73C22×C411yescharacteristic
174C22×C4×C73C22×C411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73#4111yescharacteristic
180C22×C4×C73#4111yescharacteristic
181C22×C4×C73#4111yescharacteristic
182C22×C4×C73#4111yescharacteristic
183C22×C4×C73#4111yescharacteristic
184C22×C4×C73#4111yescharacteristic
185C22×C4×C73#4111yescharacteristic
186C22×C4×C73C2411yescharacteristic
187M16×C73—22no—
188M16×C73—22no—
189M16×C73—22no—
190M16×C73—22no—
191M16×C73—22no—
192M16×C73—41no—
193M16×C73—41no—
194M16×C73C22×C414yes—
195C2×C8×C73—22no—
196C2×C8×C73—22no—
197C2×C8×C73—22no—
198C2×C8×C73—22no—
199C2×C8×C73—41no—
200C2×C8×C73—41no—
201C4⋊C4×C73—22no—
202C4⋊C4×C73—41no—
203C22⋊C4×C73—22no—
204C22⋊C4×C73—41no—
205C42×C73—22no—
206C42×C73—41no—
207C23×C73—42no—
208C23×C73#11711yescharacteristic
209C23×C73#11711yescharacteristic
210C23×C73#12311yescharacteristic
211C23×C73#12311yescharacteristic
212C23×C73#12411yescharacteristic
213C23×C73#12411yescharacteristic
214C23×C73C2×#4111yescharacteristic
215C22×D73—22no—
216C22×D73—41no—
217C22×D73—41no—
218C22×D73—82no—
219C2×C4×C73—42no—
220C2×C4×C73—82no—
221C2×C4×C73#11711yescharacteristic
222C2×C4×C73#11711yescharacteristic
223C2×C4×C73C4×D411yescharacteristic
224C2×C4×C73C4×D411yescharacteristic
225C2×C4×C73C4×D411yescharacteristic
226C2×C4×C73C4×D411yescharacteristic
227C2×C4×C73C4×D411yescharacteristic
228C2×C4×C73C4×D411yescharacteristic
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73#12111yescharacteristic
232C2×C4×C73#12111yescharacteristic
233C2×C4×C73#12111yescharacteristic
234C2×C4×C73#12111yescharacteristic
235C2×C4×C73#12311yescharacteristic
236C2×C4×C73#12311yescharacteristic
237C2×C4×C73#12411yescharacteristic
238C2×C4×C73#12411yescharacteristic
239C2×C4×C73#12611yescharacteristic
240C2×C4×C73#12611yescharacteristic
241C2×C4×C73#12611yescharacteristic
242C2×C4×C73#12611yescharacteristic
243C2×C4×C73C23×C411yescharacteristic
244C2×C4×C73C22×D411yescharacteristic
245C2×C4×C73C22×D411yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×C4×C73C2×#4111yescharacteristic
248C2×C4×C73C2×#4111yescharacteristic
249C22⋊D73—42no—
250C22⋊D73—42no—
251C22⋊D73—42no—
252C22⋊D73—42no—
253C2×Dic73—24no—
254C2×Dic73—22no—
255C2×Dic73—22no—
256C2×Dic73—22no—
257C2×Dic73—44no—
258C2×Dic73—44no—
259C2×Dic73—42no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262D292—22no—
263D292—22no—
264D292—41no—
265D292—41no—
266C4×D73—42no—
267C4×D73—42no—
268C4×D73—42no—
269C4×D73—42no—
270Dic146—22no—
271Dic146—22no—
272Dic146—41no—
273Dic146—41no—
274C8×C73—24no—
275C8×C73—42no—
276#10596831—24no—
277#10596831—24no—
278C22×C73—22no—
279C22×C73—22no—
280C22×C73—22no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73—41no—
285C22×C73#38811yescharacteristic
286C22×C73#38811yescharacteristic
287C22×C73#38811yescharacteristic
288C22×C73#38811yescharacteristic
289C22×C73C2×#11711yescharacteristic
290C22×C73C2×#12311yescharacteristic
291C22×C73C2×#12411yescharacteristic
292C2×D73—42no—
293C2×D73—82no—
294C2×D73—82no—
295C2×D73—82no—
296C4×C73—82no—
297C4×C73#38811yescharacteristic
298C4×C73#38811yescharacteristic
299C4×C73#38811yescharacteristic
300C4×C73#38811yescharacteristic
301C4×C73C2×C4×D411yescharacteristic
302C4×C73C2×C4×D411yescharacteristic
303C4×C73C2×#12111yescharacteristic
304C4×C73C2×#12611yescharacteristic
305Dic73—24no—
306Dic73—42no—
307Dic73—42no—
308C2×#1932—731nomaximal, Sylow
309C2×C73—21no—
310C2×C73—21no—
311C2×C73—21no—
312C2×C73—21no—
313C2×C73—21no—
314C2×C73—21no—
315C2×C73#193212yescomplemented
316C2×C73C2×#38811yescharacteristic
317D73—82no—
318C2×#430—731no—
319C2×#421—731no—
320C22×#104—731no—
321C2×#413—731no—
322C2×C4×M16—731no—
323#1932—738no—
324C2×#344D7311yescharacteristic, complemented
325C2×#339—731no—
326C73C2×#193211yescharacteristic, complemented, Sylow
327C22×#41—731no—
328C22×M16—731no—
329C22×M16—731no—
330C22×M16C2×D7311yescharacteristic
331C22×M16C2×D7311yescharacteristic
332C2×#117C2×D7311yescharacteristic
333C22×C42—731no—
334#430—734no—
335#430—1462no—
336C2×#108—1462no—
337#421—734no—
338#421—1462no—
339C2×#104—734no—
340C2×#104—1462no—
341C2×#104—1461no—
342C2×#104—1461no—
343C2×#104—1462no—
344#413—734no—
345#413—734no—
346C2×#101—732no—
347C2×#100—732no—
348C4×M16—734no—
349C4×M16—1462no—
350C2×#97—1461no—
351C2×C4×C8—1461no—
352#344C2×D7314yescomplemented
353#339—734no—
354C2×#41—732no—
355C2×#41—732no—
356C2×#41—1461no—
357C2×#41—1461no—
358C2×#41—1461no—
359C2×#41—1461no—
360C2×#41—1461no—
361C2×#41—1461no—
362C2×#41—1461no—
363C2×#41—1461no—
364C2×#41—1461no—
365C2×#41—1461no—
366C22×Q8—731no—
367C22×D4—731no—
368C22×D4—1461no—
369C23×C4—1461no—
370C23×C4—1461no—
371C23×C4C22×D7311yescharacteristic
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—732no—
381C2×M16—732no—
382C2×M16—732no—
383C2×M16—732no—
384C2×M16—732no—
385C2×M16—732no—
386C2×M16—1461no—
387C2×M16—1461no—
388C2×M16—1461no—
389C2×M16—1461no—
390C2×M16—1461no—
391C2×M16—1461no—
392C2×M16C4×D7312yes—
393C2×M16C4×D7312yes—
394C2×M16C22×D7312yes—
395C2×M16C22×D7312yes—
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—1461no—
399C22×C8—1461no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117C22×D7312yes—
404C2×C4⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C42—21no—
407C2×C42—731no—
408C2×C42—731no—
409C2×C42—732no—
410C2×C42—732no—
411C2×C42—1461no—
412C2×C42—1461no—
413C2×C42—1461no—
414#108—1468no—
415#104—1468no—
416#104—1464no—
417#104—1464no—
418#101—738no—
419#100—738no—
420#97—1464no—
421C4×C8—1464no—
422C24—1461no—
423C24#1192402811yescharacteristic
424#41—2921no—
425#41—2921no—
426#41—2921no—
427#41—2921no—
428#41—2921no—
429#41—2921no—
430#41—2921no—
431#41—2921no—
432#41—1462no—
433#41—1462no—
434#41—1462no—
435#41—1462no—
436#41—1462no—
437#41—1462no—
438#41—1462no—
439#41—1462no—
440C2×Q8—732no—
441C2×Q8—1461no—
442C2×Q8—1461no—
443C2×Q8—1461no—
444C2×Q8—1461no—
445C2×Q8—1461no—
446C2×D4—2921no—
447C2×D4—2921no—
448C2×D4—2921no—
449C2×D4—2921no—
450C2×D4—732no—
451C2×D4—1462no—
452C2×D4—1462no—
453C2×D4—1461no—
454C2×D4—1461no—
455C2×D4—1461no—
456C2×D4—1461no—
457C2×D4—1461no—
458C22×C4—41no—
459C22×C4—2924no—
460C22×C4—2921no—
461C22×C4—2921no—
462C22×C4—2921no—
463C22×C4—2921no—
464C22×C4—1461no—
465C22×C4—1461no—
466C22×C4—1462no—
467C22×C4—1462no—
468C22×C4—1462no—
469C22×C4—1462no—
470C22×C4—1461no—
471C22×C4C2×C4×D7311yescharacteristic
472C22×C4C2×C4×D7311yescharacteristic
473C22×C4D4×D7311yescharacteristic
474C22×C4D4×D7311yescharacteristic
475C22×C4D4×D7311yescharacteristic
476C22×C4D4×D7311yescharacteristic
477C22×C4#1192402711yescharacteristic
478C22×C4#1192402711yescharacteristic
479C22×C4#1192402811yescharacteristic
480C22×C4#1192402811yescharacteristic
481C22×C4#1192402811yescharacteristic
482C22×C4#1192402911yescharacteristic
483C22×C4#1192402911yescharacteristic
484C22×C4C23×D7311yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—41no—
491M16—41no—
492M16—734no—
493M16—734no—
494M16—1462no—
495M16—1462no—
496M16—1462no—
497M16—1462no—
498M16—1462no—
499M16—1462no—
500M16C2×C4×D7314yes—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—1462no—
508C2×C8—1462no—
509C2×C8—1462no—
510C2×C8—1462no—
511C2×C8—1462no—
512C2×C8—1462no—
513C4⋊C4—22no—
514C4⋊C4—41no—
515C22⋊C4—22no—
516C22⋊C4—41no—
517C42—22no—
518C42—41no—
519C42—732no—
520C42—732no—
521C42—1461no—
522C42—1462no—
523C42—1461no—
524C42—1462no—
525C23—42no—
526C23—2921no—
527C23—2921no—
528C23—5842no—
529C23—1462no—
530C23#1455654811yescharacteristic
531C23#1455654811yescharacteristic
532C23#1455657611yescharacteristic
533C23#1455657611yescharacteristic
534C23#1455657711yescharacteristic
535C23#1455657711yescharacteristic
536C23C2×#1192402811yescharacteristic
537Q8—2921no—
538Q8—2921no—
539Q8—1462no—
540Q8—1462no—
541D4—2922no—
542D4—2922no—
543D4—2922no—
544D4—2922no—
545D4—2921no—
546D4—2921no—
547D4—1462no—
548D4—1462no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—2922no—
552C2×C4—2921no—
553C2×C4—2921no—
554C2×C4—2924no—
555C2×C4—2924no—
556C2×C4—2922no—
557C2×C4—2922no—
558C2×C4—2922no—
559C2×C4—2922no—
560C2×C4—1462no—
561C2×C4—1462no—
562C2×C4—1464no—
563C2×C4—1462no—
564C2×C4#1455654811yescharacteristic
565C2×C4#1455654811yescharacteristic
566C2×C4#1455655111yescharacteristic
567C2×C4#1455655111yescharacteristic
568C2×C4#1455655111yescharacteristic
569C2×C4#1455655111yescharacteristic
570C2×C4#1455655311yescharacteristic
571C2×C4#1455655311yescharacteristic
572C2×C4#1455655311yescharacteristic
573C2×C4#1455655311yescharacteristic
574C2×C4#1455656411yescharacteristic
575C2×C4#1455656411yescharacteristic
576C2×C4#1455656411yescharacteristic
577C2×C4#1455656411yescharacteristic
578C2×C4#1455657611yescharacteristic
579C2×C4#1455657611yescharacteristic
580C2×C4#1455657711yescharacteristic
581C2×C4#1455657711yescharacteristic
582C2×C4#1455658611yescharacteristic
583C2×C4#1455658611yescharacteristic
584C2×C4#1455658611yescharacteristic
585C2×C4#1455658611yescharacteristic
586C2×C4C22×C4×D7311yescharacteristic
587C2×C4C2×D4×D7311yescharacteristic
588C2×C4C2×D4×D7311yescharacteristic
589C2×C4C2×#1192402711yescharacteristic
590C2×C4C2×#1192402811yescharacteristic
591C2×C4C2×#1192402911yescharacteristic
592C8—24no—
593C8—42no—
594C8—1464no—
595C8—1464no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—2922no—
604C22—5842no—
605C22—5842no—
606C22—5842no—
607C22#1798847611yescharacteristic
608C22#1798847611yescharacteristic
609C22#1798847611yescharacteristic
610C22#1798847611yescharacteristic
611C22C2×#1455654811yescharacteristic
612C22C2×#1455657611yescharacteristic
613C22C2×#1455657711yescharacteristic
614C4—82no—
615C4—2922no—
616C4—2922no—
617C4—1464no—
618C4#1798847611yescharacteristic
619C4#1798847611yescharacteristic
620C4#1798847611yescharacteristic
621C4#1798847611yescharacteristic
622C4C2×#1455655111yescharacteristic
623C4C2×#1455655311yescharacteristic
624C4C2×#1455656411yescharacteristic
625C4C2×#1455658611yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—5842no—
633C2#2261059812yesdirect product factor
634C2C2×#1798847611yescharacteristic
subgroupG/H
centerC2×C4#14556564
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#344×C73C2
socleC22×C73#388
prime radicalC22×#11924028C22
cosocleC22×C4×C73C24
hypercenterC2×#344D73
hypocenterC73C2×#1932
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#17988635C2semidirect
5. C2×M16×Dic73C2semidirect
6. #22610598C2direct (N × H)
7. C2×#17988346C2semidirect
8. C2×#344×C73C2semidirect
14. #17988635C22semidirect
23. #17988569C4semidirect
25. C2×#14556509C4semidirect
26. C2×#14556507C4semidirect
28. M16×Dic73C22semidirect
31. #17988346C22semidirect
35. #344×C73C22semidirect
78. #14556509C2×C4semidirect
79. #14556507C2×C4semidirect
315. C2×C73#1932semidirect
324. C2×#344D73semidirect
326. C73C2×#1932semidirect
352. #344C2×D73semidirect
633. C2#22610598direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179886352
C2×#179886052
C22×#145565172
C2×#179885692
C2×M16×Dic732
#226105982
C2×#179883462
C2×#344×C732
C2×#193273