Finite Group Databasebeta

← #29571484

Subgroups — #29571484

Order 15616.

846 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840291C211yesmaximal, characteristic
2#21445582C211yesmaximal, characteristic, complemented
3#21445582C211yesmaximal, characteristic, complemented
4C2×#16839503C211yesmaximal, characteristic, complemented
5C2×#16839503C211yesmaximal, characteristic, complemented
6C2×#16839502C211yesmaximal, characteristic, complemented
7C2×C61×#329C211yesmaximal, characteristic, complemented
8#16840291—22no—
9#16840291—22no—
10#16840291—22no—
11#16840291—22no—
12C2×#14519770—21no—
13C2×#14519769C2211yescharacteristic
14C2×#14519759—21no—
15C2×#14519753C411yescharacteristic
16C2×#14519748C411yescharacteristic
17C2×Q8×Dic61C411yescharacteristic
18C2×D4×Dic61C411yescharacteristic
19C2×#14519737—21no—
20C2×#14519733—21no—
21C2×C42×D61C2211yescharacteristic
22C2×#14519689—21no—
23C2×#14519689—21no—
24C2×#14519688C2211yescharacteristic
25C2×#14519688C2211yescharacteristic
26#16839516—21no—
27#16839516—21no—
28#16839503—22no—
29#16839503—22no—
30#16839502—22no—
31C2×#124×C61C2211yescharacteristic
32C2×#97×C61C2211yescharacteristic
33C2×#97×C61C2211yescharacteristic
34C61×#329—22no—
35C22×C22⋊D61—21no—
36C23×Dic61—21no—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40C22×#92418—21no—
41C22×#92418—21no—
42#14519770—24no—
43#14519770—24no—
44#14519769—21no—
45#14519769—21no—
46#14519769D412yes—
47#14519769D412yes—
48#14519759—24no—
49#14519759—24no—
50#14519753—22no—
51#14519753—22no—
52#14519748—22no—
53#14519748—22no—
54Q8×Dic61—22no—
55Q8×Dic61—22no—
56D4×Dic61—22no—
57D4×Dic61—22no—
58#14519737—24no—
59#14519737—24no—
60#14519733—24no—
61#14519733—24no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61C2×C411yescharacteristic
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×#11758196—21no—
66C2×#11758196—21no—
67C2×#11758196—21no—
68C2×C22⋊Dic61—21no—
69C2×C22⋊Dic61—21no—
70C2×#11758198—21no—
71C2×C4×Dic61—21no—
72C2×C4×Dic61C2×C411yescharacteristic
73C2×C4×Dic61D411yescharacteristic
74C2×C4×Dic61D411yescharacteristic
75C42×D61—21no—
76C42×D61—21no—
77C42×D61—21no—
78C42×D61—21no—
79#14519689—24no—
80#14519689—24no—
81#14519688—21no—
82#14519688—21no—
83#14519688—21no—
84#14519688—21no—
85C22×Q8×C61C2×C411yescharacteristic
86C22×D4×C61C2×C411yescharacteristic
87C22×C8×C61—21no—
88C22×C8×C61—21no—
89#124×C61—21no—
90#124×C61—21no—
91#124×C61D412yes—
92#124×C61D412yes—
93C2×C22⋊C4×C61—21no—
94C2×C22⋊C4×C61—21no—
95C2×C42×C61C2311yescharacteristic
96#97×C61—21no—
97#97×C61—21no—
98#97×C61—21no—
99#97×C61—21no—
100C24×C61—21no—
101C23×D61C22⋊C411yescharacteristic
102C2×Q8×C61—21no—
103C2×Q8×C61—41no—
104C2×Q8×C61—41no—
105C2×Q8×C61C22⋊C412yes—
106C2×D4×C61—21no—
107C2×D4×C61—41no—
108C2×D4×C61—41no—
109C2×D4×C61C22⋊C412yes—
110C22×C4×C61—21no—
111C22×C4×C61C22×C411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C2×C22⋊D61—24no—
115C2×C22⋊D61—42no—
116C2×C22⋊D61—42no—
117C22×Dic61—24no—
118C22×Dic61—21no—
119C22×Dic61—21no—
120C22×Dic61—42no—
121C22×Dic61—42no—
122C22×Dic61C22⋊C411yescharacteristic
123C22×Dic61C22⋊C411yescharacteristic
124C22×Dic61C22⋊C411yescharacteristic
125C2×C4×D61—22no—
126C2×C4×D61—21no—
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×C4×D61—22no—
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C8×C61—22no—
138C2×C8×C61—22no—
139C2×C8×C61—41no—
140C2×C8×C61—41no—
141C2×C8×C61—41no—
142C2×C8×C61—41no—
143C22⋊C4×C61—22no—
144C22⋊C4×C61—22no—
145C22⋊C4×C61—22no—
146C22⋊C4×C61—22no—
147C42×C61C2×D411yescharacteristic
148C42×C61C2×D411yescharacteristic
149C42×C61C2×D411yescharacteristic
150C42×C61C2×D411yescharacteristic
151C22⋊Dic61—24no—
152C22⋊Dic61—24no—
153#11758198—24no—
154C4⋊Dic61—24no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61C22⋊C412yes—
158C4⋊Dic61C22⋊C412yes—
159#11758196—24no—
160#11758196—22no—
161#11758196—22no—
162#11758196—22no—
163#11758196—22no—
164C4×Dic61—24no—
165C4×Dic61—21no—
166C4×Dic61—21no—
167C4×Dic61—21no—
168C4×Dic61—21no—
169C4×Dic61—21no—
170C4×Dic61—21no—
171C2×#92418—22no—
172C2×#92418—22no—
173C2×#92418—41no—
174C2×#92418—41no—
175C2×#92418—41no—
176C2×#92418—41no—
177C23×C61—22no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61—41no—
183C23×C61—41no—
184C23×C61C2×C22⋊C411yescharacteristic
185C22×D61—21no—
186C22×D61—21no—
187C22×D61—21no—
188C22×D61—21no—
189C22×D61—21no—
190C22×D61—21no—
191C22×D61#10412yes—
192Q8×C61—42no—
193Q8×C61—42no—
194D4×C61—42no—
195D4×C61—42no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—22no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61C2×C22⋊C411yescharacteristic
206C2×C4×C61C2×C22⋊C411yescharacteristic
207C2×C4×C61#12011yescharacteristic
208C2×C4×C61#12011yescharacteristic
209C2×C4×C61#12011yescharacteristic
210C2×C4×C61#12011yescharacteristic
211C22⋊D61—48no—
212C2×Dic61—21no—
213C2×Dic61—21no—
214C2×Dic61—21no—
215C2×Dic61—21no—
216C2×Dic61—22no—
217C2×Dic61—22no—
218C2×Dic61—21no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—48no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61#10412yes—
228C4×D61—42no—
229C4×D61—42no—
230C4×D61—42no—
231C4×D61—42no—
232C4×D61—42no—
233C4×D61—42no—
234C8×C61—42no—
235C8×C61—42no—
236#92418—42no—
237#92418—42no—
238#8336—611nomaximal, Sylow
239C22×C61—42no—
240C22×C61—42no—
241C22×C61—42no—
242C22×C61—81no—
243C22×C61—81no—
244C22×C61—81no—
245C22×C61—81no—
246C22×C61#37911yescharacteristic
247C22×C61#41311yescharacteristic
248C22×C61#41311yescharacteristic
249C22×C61C2×#10411yescharacteristic
250C22×C61C2×#10411yescharacteristic
251C22×C61#42111yescharacteristic
252C22×C61#42111yescharacteristic
253C2×D61—22no—
254C2×D61—22no—
255C2×D61—22no—
256C2×D61—41no—
257C2×D61—41no—
258C2×D61—41no—
259C2×D61—41no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—42no—
267Dic61—22no—
268Dic61—41no—
269Dic61—41no—
270Dic61—42no—
271Dic61—42no—
272C2×#529—611no—
273#1749—611no—
274#1749—611no—
275C2×#330—611no—
276C2×#330—611no—
277C2×#329—611no—
278C2×#329D6111yescharacteristic, complemented
279C2×C61—82no—
280C2×C61#152411yescharacteristic
281C2×C61#152911yescharacteristic
282C2×C61#153211yescharacteristic
283C2×C61#153511yescharacteristic
284C2×C61#178511yescharacteristic
285C2×C61#178911yescharacteristic
286C2×C61#178911yescharacteristic
287D61—42no—
288#529—1222no—
289#529—1222no—
290#529—1222no—
291#529—1222no—
292C2×#126—1221no—
293C2×#125—611no—
294C2×#124C2×D6111yescharacteristic
295C2×#123—1221no—
296C2×C22⋊Q8—611no—
297C2×#121—611no—
298C2×C4×Q8—611no—
299C2×C4×D4—611no—
300C2×C4×D4—1221no—
301C2×#117—1221no—
302C22×C42—611no—
303C2×C22⋊C8—1221no—
304C2×C22⋊C8—1221no—
305C2×#97—611no—
306C2×#97—611no—
307C2×#97C2×D6111yescharacteristic
308C2×#97C2×D6111yescharacteristic
309#336—1221no—
310#336—1221no—
311#330—1222no—
312#330—1222no—
313#329—22no—
314#329—1222no—
315C61#833611yescharacteristic, complemented, Sylow
316C22×Q8C4×D6111yescharacteristic
317C22×D4—1221no—
318C22×D4C4×D6111yescharacteristic
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4—1221no—
323C22×C8—21no—
324C22×C8—21no—
325C22×C8—1221no—
326C22×C8—1221no—
327#126—1224no—
328#126—1224no—
329#125—612no—
330#125—612no—
331#125—1221no—
332#125—1221no—
333#124—21no—
334#124—21no—
335#124D24412yes—
336#124C22⋊D6112yes—
337#123—1224no—
338#123—1224no—
339C22⋊Q8—1222no—
340C22⋊Q8—1222no—
341#121—1222no—
342#121—1222no—
343C4×Q8—1222no—
344C4×Q8—1222no—
345C4×D4—1224no—
346C4×D4—1224no—
347C4×D4—1222no—
348C4×D4—1222no—
349#117—1224no—
350#117—1224no—
351C2×C4⋊C4—611no—
352C2×C4⋊C4—611no—
353C2×C4⋊C4—1221no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1221no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—1221no—
360C2×C22⋊C4—1221no—
361C2×C22⋊C4—1221no—
362C2×C42—611no—
363C2×C42—611no—
364C2×C42—611no—
365C2×C42—1221no—
366C2×C42—1221no—
367C2×C42—1221no—
368C2×C42—1221no—
369C2×C42—1221no—
370C2×C42C22×D6111yescharacteristic
371C22⋊C8—1224no—
372C22⋊C8—1224no—
373#97—21no—
374#97—21no—
375#97—21no—
376#97—21no—
377#97—1221no—
378#97—1221no—
379#97—1221no—
380#97—1221no—
381C24—21no—
382C24—611no—
383C2×Q8—21no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8#1175819812yes—
387C2×D4—21no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—1224no—
391C2×D4—2442no—
392C2×D4—2442no—
393C2×D4#1175819812yes—
394C22×C4—21no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—1222no—
399C22×C4—1222no—
400C22×C4—1224no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—1221no—
405C22×C4—1221no—
406C22×C4—1221no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4—2441no—
410C22×C4—2441no—
411C22×C4—2441no—
412C22×C4—2441no—
413C22×C4—2442no—
414C22×C4—2442no—
415C22×C4C2×C4×D6111yescharacteristic
416C22×C4D4×D6111yescharacteristic
417C22×C4D4×D6111yescharacteristic
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—1222no—
425C2×C8—1222no—
426C2×C8—2441no—
427C2×C8—2441no—
428C2×C8—2441no—
429C2×C8—2441no—
430C4⋊C4—612no—
431C4⋊C4—612no—
432C4⋊C4—1224no—
433C4⋊C4—1224no—
434C4⋊C4—1221no—
435C4⋊C4—1221no—
436C4⋊C4—1222no—
437C4⋊C4—1222no—
438C4⋊C4—1222no—
439C4⋊C4—1222no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—1224no—
445C22⋊C4—1224no—
446C22⋊C4—1224no—
447C42—1224no—
448C42—1221no—
449C42—1221no—
450C42—1221no—
451C42—1221no—
452C42—1221no—
453C42—1221no—
454C42C2×D24411yescharacteristic
455C42D4×D6111yescharacteristic
456C42D4×D6111yescharacteristic
457C42C2×C22⋊D6111yescharacteristic
458C23—22no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—612no—
466C23—1221no—
467C23—1221no—
468C23—1221no—
469C23—1221no—
470C23—1221no—
471C23—1221no—
472C23C22⋊C4×D6111yescharacteristic
473Q8—42no—
474Q8—42no—
475D4—42no—
476D4—42no—
477D4—2448no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—612no—
488C2×C4—1221no—
489C2×C4—1221no—
490C2×C4—1221no—
491C2×C4—1221no—
492C2×C4—1221no—
493C2×C4—1221no—
494C2×C4—1221no—
495C2×C4—1221no—
496C2×C4—1222no—
497C2×C4—1222no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4—2448no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4C22⋊C4×D6111yescharacteristic
510C2×C4C2×#1175819811yescharacteristic
511C2×C4#1451974511yescharacteristic
512C2×C4#1451974511yescharacteristic
513C2×C4#1451974711yescharacteristic
514C2×C4#1451974711yescharacteristic
515C8—42no—
516C8—42no—
517C8—2442no—
518C8—2442no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—1222no—
527C22—1222no—
528C22—1222no—
529C22—2441no—
530C22—2441no—
531C22—2441no—
532C22—2441no—
533C22#1683961711yescharacteristic
534C22#1683974311yescharacteristic
535C22#1683974311yescharacteristic
536C22#104×D6111yescharacteristic
537C22#104×D6111yescharacteristic
538C22#1683977711yescharacteristic
539C22#1683977711yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—42no—
547C4—1222no—
548C4—2441no—
549C4—2441no—
550C4—2442no—
551C4—2442no—
552C2—82no—
553C2—2442no—
554C2#2144440411yescharacteristic
555C2#2144442311yescharacteristic
556C2#2144443611yescharacteristic
557C2#2144444711yescharacteristic
558C2#2144574411yescharacteristic
559C2#2144576111yescharacteristic
560C2#2144576111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#329C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C42×C61C23
hypercenterC2×#329D61
hypocenterC61#8336
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. #21445582C2semidirect
3. #21445582C2semidirect
4. C2×#16839503C2semidirect
5. C2×#16839503C2semidirect
6. C2×#16839502C2semidirect
7. C2×C61×#329C2semidirect
278. C2×#329D61semidirect
315. C61#8336semidirect

Maximal subgroups

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

subgroupindex
C2×#168402912
#214455822
C2×#168395032
C2×#168395022
C2×C61×#3292
#833661