Finite Group Databasebeta

← #30617321

Subgroups — #30617321

Order 15616.

792 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462313C211yesmaximal, characteristic
2#21462259C211yesmaximal, characteristic
3#21461999C211yesmaximal, characteristic
4#21461930C211yesmaximal, characteristic
5#21461881C211yesmaximal, characteristic
6#21461880C211yesmaximal, characteristic
7#21461783C211yesmaximal, characteristic
8#21461783C211yesmaximal, characteristic
9#21461688C211yesmaximal, characteristic
10#21461635C211yesmaximal, characteristic
11#107×#6923C211yesmaximal, characteristic
12#21461608C211yesmaximal, characteristic
13#21461592C211yesmaximal, characteristic
14#103×#6923C211yesmaximal, characteristic
15#479×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20D61⋊(C4⋊C8)C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519831C2211yescharacteristic
24C2×C8×#6923C2211yescharacteristic
25#16840713—21no—
26#16840713—21no—
27#16840713C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840711—21no—
30#16840711—21no—
31#16840708C2211yescharacteristic
32C4⋊C4×#6923—21no—
33C4⋊C4×#6923—21no—
34C4⋊C4×#6923C2211yescharacteristic
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4⋊C4×#6923C2211yescharacteristic
38C4×C4⋊#6923—21no—
39C4×C4⋊#6923C2211yescharacteristic
40#16840698—21no—
41#16840698C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#125×D61C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54#16840072C411yescharacteristic, complemented
55#16840071C411yescharacteristic, complemented
56#16840070C411yescharacteristic, complemented
57#16840069C411yescharacteristic, complemented
58#16840068C411yescharacteristic, complemented
59#16840067C411yescharacteristic, complemented
60#16840066C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#103×D61C2211yescharacteristic
66C61×#479C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69Q8×#6923—22no—
70Q8×#6923—22no—
71Q8×#6923—22no—
72Q8×#6923Q814yes—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4×#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923C2311yescharacteristic
91C2×C4×#6923C2311yescharacteristic
92#14519846—22no—
93#14519846—22no—
94#14519844—21no—
95C4⋊#92420—21no—
96#14519840—22no—
97#14519840—22no—
98#14519831—22no—
99C8×#6923—22no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4D411yescharacteristic
108(C2×#6923)⋊C4D411yescharacteristic
109(C2×#6923)⋊C4D411yescharacteristic
110(C2×#6923)⋊C4D411yescharacteristic
111C2×Q8×D61C2311yescharacteristic
112C2×C8×D61C2311yescharacteristic
113C2×C8×D61C2311yescharacteristic
114#14519769C2×C411yescharacteristic
115#14519768C2×C411yescharacteristic
116#14519768C2×C411yescharacteristic
117#14519767—21no—
118#14519767—21no—
119Q8×Dic61C2×C411yescharacteristic
120C4×Dic122—21no—
121C4×Dic122C2×C411yescharacteristic
122#14519742—21no—
123#14519742C2×C411yescharacteristic
124C4⋊C4×D61—21no—
125C4⋊C4×D61—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61C2311yescharacteristic
128C4⋊C4×D61C2311yescharacteristic
129C4⋊C4×D61C2311yescharacteristic
130C42×D61—21no—
131C42×D61C2311yescharacteristic
132#14519711C2×C411yescharacteristic
133#14519710C2×C411yescharacteristic
134#14519710C2×C411yescharacteristic
135#14519709C2×C411yescharacteristic
136#14519708C2×C411yescharacteristic
137#14519708C2×C411yescharacteristic
138C4⋊#92418C2×C411yescharacteristic
139#14519706C2×C411yescharacteristic
140#14519706C2×C411yescharacteristic
141#14519702C2×C411yescharacteristic
142#14519702C2×C411yescharacteristic
143#14519701C2×C411yescharacteristic
144#14519701C2×C411yescharacteristic
145#14519700C2×C411yescharacteristic
146#14519700C2×C411yescharacteristic
147#125×C61C2×C411yescharacteristic
148C4×Q8×C61C2×C411yescharacteristic
149#107×C61C2×C411yescharacteristic
150#106×C61C2×C411yescharacteristic
151C4⋊C8×C61C2×C411yescharacteristic
152#103×C61C2×C411yescharacteristic
153#103×C61C2×C411yescharacteristic
154C22×#6923—21no—
155C22×#6923—21no—
156C22×#6923—21no—
157C22×#6923—21no—
158C22×#6923C2×D411yescharacteristic
159C22×#6923C2×D411yescharacteristic
160C22×#6923C2×D411yescharacteristic
161C22×#6923C2×D411yescharacteristic
162C2×Q8×C61C22×C411yescharacteristic
163Q8×D61—21no—
164Q8×D61—21no—
165Q8×D61C2×Q812yes—
166Q8×D61#4112yes—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61C2411yescharacteristic
174C2×Dic122—21no—
175C2×Dic122C22×C411yescharacteristic
176C2×#92420—21no—
177C2×#92420—21no—
178C4⋊#6923—24no—
179C4⋊#6923—24no—
180C4⋊#6923—21no—
181C4⋊#6923—21no—
182C4⋊#6923—21no—
183C4⋊#6923—21no—
184C4⋊#6923—21no—
185C4⋊#6923—21no—
186C4⋊#6923—81no—
187C4⋊#6923—81no—
188C4⋊#6923—81no—
189C4⋊#6923—81no—
190C4⋊#6923C2×Q812yes—
191C4⋊#6923#4112yes—
192C4×#6923—24no—
193C4×#6923—24no—
194C4×#6923—21no—
195C4×#6923—21no—
196C4×#6923—81no—
197C4×#6923—81no—
198C4×#6923—81no—
199C4×#6923—81no—
200C4×#6923—81no—
201C4×#6923C2×Q812yes—
202C4×#6923#4112yes—
203D61⋊C8—21no—
204D61⋊C8—21no—
205D61⋊C8—21no—
206D61⋊C8—21no—
207C2×C8×C61C22×C411yescharacteristic
208C2×C8×C61C22×C411yescharacteristic
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61C22×C411yescharacteristic
213C4⋊C4×C61C22×C411yescharacteristic
214C4⋊C4×C61C22×C411yescharacteristic
215C42×C61—21no—
216C42×C61C22×C411yescharacteristic
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61C22×C411yescharacteristic
221C4⋊Dic61C22×C411yescharacteristic
222C4⋊Dic61C22×C411yescharacteristic
223#11758196—21no—
224#11758196—21no—
225#11758196—21no—
226#11758196—21no—
227#11758196—21no—
228#11758196—21no—
229#11758196—21no—
230#11758196—21no—
231#11758196—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61C22×C411yescharacteristic
236C4×Dic61#4111yescharacteristic
237C4×Dic61#4111yescharacteristic
238C2×#92418C22×C411yescharacteristic
239C2×#92418C22×C411yescharacteristic
240C8×D61—21no—
241C8×D61—21no—
242C8×D61—21no—
243C8×D61—21no—
244C22×D61C22×D411yescharacteristic
245C2×#6923—21no—
246C2×#6923—21no—
247C2×#6923—21no—
248C2×#6923—21no—
249C2×#6923—22no—
250C2×#6923—21no—
251C2×#6923—21no—
252C2×#6923—22no—
253C2×#6923—21no—
254C2×#6923—21no—
255C2×#6923—21no—
256C2×#6923—21no—
257C2×#6923—41no—
258C2×#6923—41no—
259C2×#6923—41no—
260C2×#6923—41no—
261C2×#6923—41no—
262C2×#6923—41no—
263C2×#6923—41no—
264C2×#6923—41no—
265C2×#6923—41no—
266C2×#6923—41no—
267C2×#6923C22⋊Q812yes—
268C2×#6923C22⋊Q812yes—
269Q8×C61—21no—
270Q8×C61C4×Q812yes—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61C4×D411yescharacteristic
276C2×C4×C61C4×D411yescharacteristic
277C2×C4×C61C23×C411yescharacteristic
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61C4×D411yescharacteristic
283C2×Dic61C4×D411yescharacteristic
284C2×Dic61C2×#4111yescharacteristic
285C4×D61—22no—
286C4×D61—22no—
287C4×D61—21no—
288C4×D61—21no—
289C4×D61—21no—
290C4×D61—21no—
291C4×D61—41no—
292C4×D61—41no—
293C4×D61—41no—
294C4×D61—41no—
295C4×D61—41no—
296C4×D61—41no—
297C4×D61C22×Q811yescharacteristic
298C4×D61C2×#4111yescharacteristic
299C4×D61C2×#4111yescharacteristic
300C4×D61C2×#4111yescharacteristic
301Dic122—21no—
302Dic122—22no—
303Dic122—22no—
304Dic122C4×Q812yes—
305#92420—41no—
306#92420—41no—
307C8×C61—21no—
308C8×C61—21no—
309#92418—21no—
310#92418—21no—
311#21621—611nomaximal, Sylow
312C22×C61C2×C4×D411yescharacteristic
313C2×D61C2×C22⋊Q811yescharacteristic
314C2×D61#52511yescharacteristic
315C2×D61#57611yescharacteristic
316C2×D61#57711yescharacteristic
317C2×D61#57811yescharacteristic
318C2×D61#57811yescharacteristic
319#6923—22no—
320#6923—22no—
321#6923—42no—
322#6923—41no—
323#6923—42no—
324#6923—41no—
325#6923—81no—
326#6923—81no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—22no—
330C4×C61—41no—
331C4×C61—41no—
332C4×C61—41no—
333C4×C61C2×C4×Q811yescharacteristic
334C4×C61C4×#4111yescharacteristic
335Dic61—21no—
336Dic61—21no—
337Dic61—22no—
338Dic61—41no—
339Dic61—41no—
340Dic61—41no—
341Dic61#52911yescharacteristic
342Dic61#53311yescharacteristic
343C2×#479—611no—
344#2330—611no—
345#2276—611no—
346#1989—611no—
347#1947—611no—
348#1919—611no—
349#1918—611no—
350#1863—611no—
351#1863—611no—
352#1803—611no—
353#1776—611no—
354C4×#107—611no—
355#1768—611no—
356#1763—611no—
357C4×#103—611no—
358C2×C61C4×C22⋊Q811yescharacteristic
359C2×C61#294711yescharacteristic
360C2×C61#295111yescharacteristic
361D61#308211yescharacteristic
362D61#308311yescharacteristic
363D61#311911yescharacteristic
364D61#312711yescharacteristic
365C2×#125—611no—
366C2×C4×Q8—611no—
367C2×C4×Q8—611no—
368C2×C4×Q8—611no—
369#479—611no—
370#479—611no—
371#479—611no—
372#479—611no—
373#479—611no—
374#479—611no—
375#479—611no—
376#479#692311yescharacteristic, complemented
377C2×#107—611no—
378C2×#107—611no—
379C2×#107—611no—
380C2×#106—611no—
381C2×C4⋊C8—611no—
382C2×C4⋊C8—611no—
383C2×#103—611no—
384C2×#103—611no—
385C2×#103—611no—
386C2×#103—611no—
387C2×#97—611no—
388C2×C4×C8—611no—
389#389—611no—
390#389—611no—
391#389—1221no—
392#389—1221no—
393#387—1221no—
394#387—1221no—
395#384—611no—
396C4×C4⋊C4—611no—
397C4×C4⋊C4—611no—
398C4×C4⋊C4—611no—
399C4×C4⋊C4—611no—
400C4×C4⋊C4—611no—
401C4×C4⋊C4—1221no—
402C4×C4⋊C4—1221no—
403C4×C4⋊C4—1221no—
404#376—611no—
405#376—1221no—
406#340—611no—
407#340—611no—
408#340—611no—
409#340—611no—
410#340—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#336—611no—
415#336—611no—
416C61#2162111yescharacteristic, complemented, Sylow
417C22×Q8—611no—
418C22×C8—611no—
419C22×C8—611no—
420C22×C8—611no—
421C22×C8—611no—
422#125—611no—
423#125—611no—
424#125—611no—
425#125—1221no—
426#125—1221no—
427#125C2×#692311yescharacteristic
428C4×Q8—614no—
429C4×Q8—611no—
430C4×Q8—611no—
431C4×Q8—611no—
432C4×Q8—1221no—
433C4×Q8—1221no—
434C4×Q8—1222no—
435C4×Q8—1222no—
436C4×Q8—1222no—
437C4×Q8C2×#692311yescharacteristic
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4—611no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4—1221no—
448C2×C4⋊C4—1221no—
449C2×C4⋊C4—1221no—
450C2×C4⋊C4—1221no—
451C2×C4⋊C4—1221no—
452C2×C4⋊C4—1221no—
453C2×C4⋊C4—1221no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—611no—
457C2×C42—1221no—
458C2×C42—1221no—
459C2×C42—1221no—
460C2×C42—1221no—
461C2×C42—1221no—
462C2×C42—1221no—
463C2×C42—1221no—
464C2×C42—1221no—
465#107—611no—
466#107—611no—
467#107—611no—
468#107—1222no—
469#107—1222no—
470#107C2×#692311yescharacteristic
471#106—611no—
472#106—611no—
473#106—611no—
474#106C2×#692311yescharacteristic
475C4⋊C8—611no—
476C4⋊C8—611no—
477C4⋊C8—611no—
478C4⋊C8—1221no—
479C4⋊C8—1221no—
480C4⋊C8C2×#692311yescharacteristic
481#103—611no—
482#103—611no—
483#103—611no—
484#103—611no—
485#103—611no—
486#103—611no—
487#103—1222no—
488#103—1222no—
489#103C2×#692311yescharacteristic
490#103C2×#692311yescharacteristic
491#97—1222no—
492C4×C8—1222no—
493#95—611no—
494#95—611no—
495#95—611no—
496#95—611no—
497#95—1221no—
498#95—1221no—
499#95—1221no—
500#95—1221no—
501#95—1221no—
502#95—1221no—
503#95—1221no—
504C2×Q8—612no—
505C2×Q8—612no—
506C2×Q8—611no—
507C2×Q8—1221no—
508C2×Q8—1221no—
509C2×Q8—1221no—
510C2×Q8C22×#692311yescharacteristic
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C2×C8—611no—
527C2×C8—611no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8C22×#692311yescharacteristic
539C2×C8C22×#692311yescharacteristic
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—612no—
544C4⋊C4—612no—
545C4⋊C4—611no—
546C4⋊C4—611no—
547C4⋊C4—611no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1221no—
551C4⋊C4—1221no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—1221no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C4⋊C4—1224no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1224no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4—4881no—
569C4⋊C4—4881no—
570C4⋊C4—4881no—
571C4⋊C4—4881no—
572C4⋊C4C22×#692311yescharacteristic
573C4⋊C4C22×#692311yescharacteristic
574C4⋊C4C22×#692311yescharacteristic
575C42—21no—
576C42—612no—
577C42—612no—
578C42—611no—
579C42—611no—
580C42—611no—
581C42—1221no—
582C42—1221no—
583C42—1221no—
584C42—1221no—
585C42—1224no—
586C42—1224no—
587C42—1221no—
588C42—4881no—
589C42—4881no—
590C42—4881no—
591C42—4881no—
592C42—4881no—
593C42C22×#692311yescharacteristic
594C23—611no—
595Q8—21no—
596Q8—612no—
597Q8—1222no—
598Q8—1222no—
599Q8—1221no—
600Q8Q8×#692312yes—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—611no—
606C2×C4—611no—
607C2×C4—611no—
608C2×C4—611no—
609C2×C4—611no—
610C2×C4—612no—
611C2×C4—612no—
612C2×C4—611no—
613C2×C4—611no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4—2441no—
652C2×C4D4×#692311yescharacteristic
653C2×C4D4×#692311yescharacteristic
654C2×C4C23×#692311yescharacteristic
655C8—21no—
656C8—21no—
657C8—1221no—
658C8—1221no—
659C8—2441no—
660C8—2441no—
661C22—611no—
662C22—611no—
663C22—611no—
664C22—611no—
665C22—611no—
666C22—611no—
667C22C2×D4×#692311yescharacteristic
668C4—22no—
669C4—21no—
670C4—21no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—611no—
675C4—611no—
676C4—1222no—
677C4—1222no—
678C4—1222no—
679C4—1221no—
680C4—1221no—
681C4—4881no—
682C4—4881no—
683C4—2441no—
684C4—2441no—
685C4—2442no—
686C4—2442no—
687C4—2441no—
688C4—2441no—
689C4—2441no—
690C4C2×Q8×#692311yescharacteristic
691C4#41×#692311yescharacteristic
692C2—611no—
693C2—611no—
694C2—611no—
695C2—611no—
696C2C22⋊Q8×#692311yescharacteristic
697C2#2146257711yescharacteristic
698C2#2146258111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#479C4
socleC22×C61C2×C4×D4
prime radicalC22×D61C22×D4
cosocleC2×C4×D61C24
hypercenter#479#6923
hypocenterC61#21621
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
54. #16840072C4semidirect
55. #16840071C4semidirect
56. #16840070C4semidirect
57. #16840069C4semidirect
58. #16840068C4semidirect
59. #16840067C4semidirect
60. #16840066C4semidirect
66. C61×#479C4semidirect
376. #479#6923semidirect
416. C61#21621semidirect

Maximal subgroups

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

subgroupindex
#214623132
#214622592
#214619992
#214619302
#214618812
#214618802
#214617832
#214616882
#214616352
#107×#69232
#214616082
#214615922
#103×#69232
#479×D612
#2162161