Finite Group Databasebeta

← D61×#2961 #30544380

Subgroups — D61×#2961 #30544380

Order 15616.

1894 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2#21454760C211yesmaximal, characteristic, complemented
3#21454759C211yesmaximal, characteristic, complemented
4#21454758C212yesmaximal, complemented
5#21454757C212yesmaximal, complemented
6#21454756C211yesmaximal, characteristic, complemented
7#21454755C218yesmaximal, complemented
8#446×D61C218yesmaximal, complemented
9#424×D61C212yesmaximal
10#423×D61C211yesmaximal, characteristic
11#405×D61C212yesmaximal
12C2×#97×D61C211yesmaximal, characteristic
13C61×#2961C211yesmaximal, characteristic, complemented
14C2×M16×D61C2212yes—
15C22×C8×D61C2211yescharacteristic
16C22×C8×D61C2211yescharacteristic
17#16840319C2211yescharacteristic
18#16840318C412yes—
19#16840317C412yes—
20#16840316C2214yes—
21#16840315C2212yes—
22#16840314C414yes—
23C4⋊Q8×D61C412yes—
24#125×D61C412yes—
25C22⋊Q8×D61C414yes—
26C4×Q8×D61C2214yes—
27#117×D61C2212yes—
28C2×C42×D61C2211yescharacteristic
29#16839893C2218yescomplemented
30#16839892C2218yescomplemented
31#16839891C2218yescomplemented
32#16839891C2218yescomplemented
33#16839890C2218yescomplemented
34#16839890C2218yescomplemented
35#16839889C2218yescomplemented
36#16839790C2212yes—
37#16839789C2212yes—
38#16839788C2212yes—
39#16839787C2218yes—
40#16839786C2211yescharacteristic
41#16839785C2212yes—
42#16839784C2214yes—
43C4⋊C8×D61C2214yes—
44C4⋊C8×D61C2218yes—
45#16839720C2212yes—
46#16839719C2214yes—
47#16839718C2212yes—
48#16839717C2212yes—
49#16839716C2214yes—
50C2×#14519688C2211yescharacteristic
51C2×#14519687C2211yescharacteristic
52C2×#14519687C2211yescharacteristic
53#97×D61C2214yes—
54#97×D61C2214yes—
55#97×D61C2214yes—
56C4×C8×D61C2214yes—
57C61×#533C2211yescharacteristic
58C61×#446C2218yescomplemented
59C61×#424C2212yes—
60C61×#423C2211yescharacteristic
61C61×#405C2212yes—
62C2×#97×C61C2211yescharacteristic
63C2×Q8×D61C2×C414yes—
64C22×C4×D61C2×C412yes—
65C22×C4×D61C2311yescharacteristic
66C2×#11758194C2312yes—
67C2×#11758189C2314yes—
68M16×D61—28no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C2×C8×D61—24no—
72C2×C8×D61Q818yescomplemented
73C2×C8×D61C2314yes—
74C2×C8×D61C2312yes—
75C2×C8×D61C2312yes—
76C2×C8×D61C2312yes—
77C2×C8×D61C2312yes—
78#14519777C2×C412yes—
79#14519776C2×C414yes—
80#14519776C2×C414yes—
81#14519775C2×C414yes—
82#14519769C2×C412yes—
83#14519768C2×C414yes—
84#14519767C2×C418yes—
85#14519757C2×C414yes—
86#14519756C2×C414yes—
87#14519755C2×C418yes—
88#14519754C2×C418yes—
89#14519753C2×C414yes—
90Q8×Dic61C2×C414yes—
91C4×Dic122C2318yes—
92C4×Dic122C2314yes—
93#14519742C2×C414yes—
94#14519742C2×C418yes—
95#14519736C2312yes—
96#14519735C2×C414yes—
97#14519734C2314yes—
98#14519733C2×C414yes—
99C4⋊C4×D61C2×C414yes—
100C4⋊C4×D61C2×C418yes—
101C4⋊C4×D61C2×C414yes—
102C22⋊C4×D61C2×C414yes—
103C2×C4×Dic61C2×C412yes—
104C2×C4×Dic61C2311yescharacteristic
105C42×D61C2×C411yescharacteristic
106C42×D61C2×C411yescharacteristic
107C42×D61C2×C411yescharacteristic
108C42×D61C2×C411yescharacteristic
109C42×D61C2312yes—
110C42×D61C2312yes—
111C42×D61C2314yes—
112C4⋊#92418C2314yes—
113C4⋊#92418C2318yes—
114#14519706C2318yes—
115#14519706C2318yes—
116#14519706C2318yes—
117#14519688C2314yes—
118#14519688C2314yes—
119#14519687C2314yes—
120#14519687C2314yes—
121#14519687C2314yes—
122#14519687C2314yes—
123C4×#92418C2314yes—
124C8×Dic61C2314yes—
125C8×Dic61C2314yes—
126C2×M16×C61C2312yes—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C4⋊Q8×C61C2×C412yes—
130#125×C61C2×C412yes—
131C22⋊Q8×C61C2×C414yes—
132C4×Q8×C61C2314yes—
133#117×C61C2312yes—
134C2×C42×C61C2311yescharacteristic
135C4⋊C8×C61C2314yes—
136C4⋊C8×C61C2318yes—
137#97×C61C2314yes—
138#97×C61C2314yes—
139C4×C8×C61C2314yes—
140C23×D61C22×C411yescharacteristic
141C2×Q8×C61C22×C414yes—
142C22×C4×C61C22×C412yes—
143C22×C4×C61C2411yescharacteristic
144C22×Dic61C22×C412yes—
145C22×Dic61C22×C411yescharacteristic
146Q8×D61—48no—
147C2×C4×D61—44no—
148C2×C4×D61C22×C412yes—
149C2×C4×D61C22×C412yes—
150C2×C4×D61C22×C418yes—
151C2×C4×D61C22×C412yes—
152C2×C4×D61C22×C412yes—
153C2×C4×D61C22×C411yescharacteristic
154C2×C4×D61C22×C411yescharacteristic
155C2×C4×D61C2×Q814yes—
156C2×C4×D61#4114yes—
157C2×C4×D61C2411yescharacteristic
158C2×C4×D61C2411yescharacteristic
159C2×Dic122C22×C418yes—
160C2×Dic122C22×C414yes—
161M16×C61—24no—
162C2×C8×C61—22no—
163C2×C8×C61C2×Q814yescomplemented
164C2×C8×C61C2414yes—
165C2×C8×C61C2412yes—
166C2×C8×C61C2412yes—
167C4⋊C4×C61C22×C414yes—
168C4⋊C4×C61C22×C418yes—
169C4⋊C4×C61C22×C414yes—
170C22⋊C4×C61C22×C414yes—
171C42×C61C22×C411yescharacteristic
172C42×C61C22×C411yescharacteristic
173C42×C61C2414yes—
174C42×C61C2412yes—
175C22⋊Dic61C22×C414yes—
176#11758198C22×C418yes—
177C4⋊Dic61C22×C414yes—
178C4⋊Dic61C22×C414yes—
179C4⋊Dic61C22×C418yes—
180#11758196C22×C418yes—
181#11758196C22×C418yes—
182#11758196C22×C418yes—
183#11758196C22×C418yes—
184C4×Dic61C22×C411yescharacteristic
185C4×Dic61C22×C411yescharacteristic
186C4×Dic61C22×C412yes—
187C4×Dic61C22×C412yes—
188C4×Dic61C22×C412yes—
189C4×Dic61C22×C412yes—
190C4×Dic61C22×C418yes—
191C4×Dic61C2414yes—
192C4×Dic61C2412yes—
193#11758194—24no—
194C2×#92418—22no—
195C2×#92418C2×Q814yescomplemented
196C2×#92418C2414yes—
197C2×#92418C2412yes—
198C2×#92418C2412yes—
199#11758189—28no—
200C8×D61—24no—
201C8×D61—24no—
202C8×D61—28no—
203C8×D61C2×Q818yes—
204C8×D61C2×Q818yescomplemented
205C23×C61C23×C411yescharacteristic
206C22×D61—24no—
207C22×D61C4×Q814yes—
208C22×D61C23×C411yescharacteristic
209C22×D61C23×C411yescharacteristic
210Q8×C61—44no—
211C2×C4×C61—42no—
212C2×C4×C61C23×C412yes—
213C2×C4×C61C23×C412yes—
214C2×C4×C61C23×C418yes—
215C2×C4×C61C23×C411yescharacteristic
216C2×C4×C61C22×Q812yes—
217C2×C4×C61C2×#4112yes—
218C2×C4×C61C2511yescharacteristic
219C2×Dic61—42no—
220C2×Dic61C4×Q814yes—
221C2×Dic61C23×C412yes—
222C2×Dic61C23×C412yes—
223C2×Dic61C23×C418yes—
224C2×Dic61C23×C411yescharacteristic
225C2×Dic61C23×C411yescharacteristic
226C4×D61—24no—
227C4×D61—24no—
228C4×D61—216no—
229C4×D61—42no—
230C4×D61—42no—
231C4×D61C4×Q814yes—
232C4×D61C4×Q814yes—
233C4×D61C22×Q812yes—
234C4×D61C22×Q812yes—
235C4×D61C2×#4112yes—
236C4×D61C2×#4112yes—
237Dic122—48no—
238Dic122—44no—
239C8×C61—22no—
240C8×C61—24no—
241C8×C61C22×Q814yes—
242#92418—22no—
243#92418—24no—
244#92418C22×Q814yes—
245C2×#2961—611nomaximal, Sylow
246C22×C61—22no—
247C22×C61C2×C4×Q812yes—
248C22×C61C24×C411yescharacteristic
249C2×D61—22no—
250C2×D61—28no—
251C2×D61C2×C4×Q812yes—
252C2×D61C2×C4×Q812yes—
253C2×D61#56814yes—
254C4×C61—22no—
255C4×C61—28no—
256C4×C61—22no—
257C4×C61C2×C4×Q812yes—
258C4×C61C23×Q811yescharacteristic
259C4×C61C22×#4111yescharacteristic
260Dic61—22no—
261Dic61—28no—
262Dic61—22no—
263Dic61C2×C4×Q812yes—
264Dic61C2×C4×Q812yes—
265C2×#533—611no—
266#2961—618no—
267#2961—612no—
268#2961—611no—
269#2961—612no—
270#2961—611no—
271#2961—611no—
272#2961D6111yescharacteristic, direct product factor
273C2×#446—618no—
274C2×#424—612no—
275C2×#423—611no—
276C2×#405—612no—
277C22×#97—611no—
278C2×C61—22no—
279C2×C61C22×C4×Q811yescharacteristic
280C2×C61C2×#56812yes—
281D61—22no—
282D61#296114yesdirect product factor
283C22×M16—612no—
284C23×C8—611no—
285C23×C8—611no—
286#533—612no—
287#533—612no—
288#533—614no—
289#533—614no—
290#533—612no—
291#533—611no—
292#533C2×D6111yescharacteristic
293C2×C4⋊Q8—612no—
294C2×#125—612no—
295C2×C22⋊Q8—614no—
296C2×C4×Q8—614no—
297C2×#117—612no—
298C22×C42—611no—
299#446—618no—
300#446—618no—
301#446—618no—
302#446—618no—
303#446—618no—
304#446—618no—
305#446—618no—
306#446C2×D6118yescomplemented
307#424—612no—
308#424—612no—
309#424—612no—
310#424—618no—
311#424C2×D6112yes—
312#423—612no—
313#423—611no—
314#423—614no—
315#423C2×D6111yescharacteristic
316C2×C4⋊C8—614no—
317C2×C4⋊C8—618no—
318#405—612no—
319#405—612no—
320#405—612no—
321#405—614no—
322#405—614no—
323#405C2×D6112yes—
324C2×#97—611no—
325C2×#97—611no—
326C2×#97—611no—
327C2×#97—614no—
328C2×#97—614no—
329C2×#97—614no—
330C2×#97C2×D6111yescharacteristic
331C2×C4×C8—614no—
332C61C2×#296111yescharacteristic, complemented, Sylow
333C22×Q8—614no—
334C23×C4—611no—
335C23×C4—612no—
336C2×M16—612no—
337C2×M16—614no—
338C2×M16—1228no—
339C2×M16C22×D6112yes—
340C22×C8—611no—
341C22×C8—618no—
342C22×C8—612no—
343C22×C8—612no—
344C22×C8—611no—
345C22×C8—612no—
346C22×C8—612no—
347C22×C8—614no—
348C22×C8—1224no—
349C22×C8C22×D6111yescharacteristic
350C22×C8C22×D6111yescharacteristic
351C4⋊Q8—614no—
352C4⋊Q8—614no—
353C4⋊Q8—614no—
354C4⋊Q8—612no—
355C4⋊Q8C4×D6112yes—
356#125—618no—
357#125—614no—
358#125—612no—
359#125C4×D6112yes—
360C22⋊Q8—614no—
361C22⋊Q8—614no—
362C22⋊Q8—618no—
363C22⋊Q8—614no—
364C22⋊Q8—618no—
365C22⋊Q8C4×D6114yes—
366C4×Q8—614no—
367C4×Q8—614no—
368C4×Q8—618no—
369C4×Q8—614no—
370C4×Q8—618no—
371C4×Q8C22×D6114yes—
372#117—612no—
373#117—614no—
374#117—614no—
375#117—614no—
376#117C22×D6112yes—
377C2×C4⋊C4—614no—
378C2×C4⋊C4—618no—
379C2×C4⋊C4—614no—
380C2×C22⋊C4—614no—
381C2×C42—612no—
382C2×C42—611no—
383C2×C42—611no—
384C2×C42—611no—
385C2×C42—611no—
386C2×C42—611no—
387C2×C42—614no—
388C2×C42—612no—
389C2×C42—612no—
390C2×C42C22×D6111yescharacteristic
391C4⋊C8—618no—
392C4⋊C8—618no—
393C4⋊C8—618no—
394C4⋊C8—614no—
395C4⋊C8—618no—
396C4⋊C8C22×D6114yes—
397C4⋊C8C22×D6118yes—
398#97—614no—
399#97—614no—
400#97—614no—
401#97—614no—
402#97—614no—
403#97—614no—
404#97C22×D6114yes—
405#97C22×D6114yes—
406C4×C8—614no—
407C4×C8—614no—
408C4×C8—614no—
409C4×C8C22×D6114yes—
410C24—611no—
411C2×Q8—618no—
412C2×Q8—614no—
413C2×Q8—2448no—
414C2×Q8C2×C4×D6114yes—
415C22×C4—611no—
416C22×C4—611no—
417C22×C4—611no—
418C22×C4—614no—
419C22×C4—614no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—612no—
423C22×C4—612no—
424C22×C4—612no—
425C22×C4—618no—
426C22×C4—612no—
427C22×C4—612no—
428C22×C4—2444no—
429C22×C4C2×C4×D6112yes—
430C22×C4C23×D6111yescharacteristic
431M16—24no—
432M16—1228no—
433M16—1224no—
434C2×C8—22no—
435C2×C8—614no—
436C2×C8—612no—
437C2×C8—618no—
438C2×C8—618no—
439C2×C8—614no—
440C2×C8—612no—
441C2×C8—1224no—
442C2×C8—1224no—
443C2×C8—1228no—
444C2×C8—1222no—
445C2×C8Q8×D6114yescomplemented
446C2×C8C23×D6114yes—
447C2×C8C23×D6112yes—
448C2×C8C23×D6112yes—
449C4⋊C4—618no—
450C4⋊C4—618no—
451C4⋊C4—618no—
452C4⋊C4—618no—
453C4⋊C4—614no—
454C4⋊C4—618no—
455C4⋊C4—614no—
456C4⋊C4C2×C4×D6114yes—
457C4⋊C4C2×C4×D6118yes—
458C4⋊C4C2×C4×D6114yes—
459C22⋊C4—614no—
460C22⋊C4—618no—
461C22⋊C4C2×C4×D6114yes—
462C42—612no—
463C42—612no—
464C42—612no—
465C42—611no—
466C42—612no—
467C42—611no—
468C42—618no—
469C42—614no—
470C42—612no—
471C42C2×C4×D6111yescharacteristic
472C42C2×C4×D6111yescharacteristic
473C42C23×D6114yes—
474C42C23×D6112yes—
475C23—611no—
476C23—614no—
477C23—611no—
478C23—1224no—
479C23C22×C4×D6111yescharacteristic
480Q8—44no—
481Q8—2444no—
482Q8—2448no—
483C2×C4—42no—
484C2×C4—614no—
485C2×C4—611no—
486C2×C4—611no—
487C2×C4—614no—
488C2×C4—614no—
489C2×C4—612no—
490C2×C4—612no—
491C2×C4—612no—
492C2×C4—612no—
493C2×C4—612no—
494C2×C4—612no—
495C2×C4—618no—
496C2×C4—1224no—
497C2×C4—1224no—
498C2×C4—12216no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4C22×C4×D6112yes—
503C2×C4C22×C4×D6112yes—
504C2×C4C22×C4×D6118yes—
505C2×C4C22×C4×D6111yescharacteristic
506C2×C4C2×Q8×D6112yes—
507C2×C4#41×D6112yes—
508C2×C4C24×D6111yescharacteristic
509C8—22no—
510C8—24no—
511C8—614no—
512C8—1222no—
513C8—1224no—
514C8C2×Q8×D6114yes—
515C22—22no—
516C22—614no—
517C22—612no—
518C22—612no—
519C22—1228no—
520C22—1222no—
521C22C4×Q8×D6112yes—
522C22C23×C4×D6111yescharacteristic
523C4—22no—
524C4—22no—
525C4—28no—
526C4—612no—
527C4—612no—
528C4—1222no—
529C4—1222no—
530C4—1228no—
531C4C4×Q8×D6112yes—
532C4C22×Q8×D6111yescharacteristic
533C4C2×#41×D6111yescharacteristic
534C2—22no—
535C2—614no—
536C2—1222no—
537C2C2×C4×Q8×D6111yescharacteristic
538C2#568×D6112yes—
subgroupG/H
center, FrattiniC2×C4C24×D61
commutator, socleC22×C61C24×C4
FittingC61×#2961C2
prime radicalC23×D61C22×C4
cosocleC2×C4×C61C25
hypercenter#2961D61
hypocenterC61C2×#2961
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #21454760C2semidirect
3. #21454759C2semidirect
4. #21454758C2semidirect
5. #21454757C2semidirect
6. #21454756C2semidirect
7. #21454755C2semidirect
8. #446×D61C2semidirect
13. C61×#2961C2semidirect
29. #16839893C22semidirect
30. #16839892C22semidirect
31. #16839891C22semidirect
32. #16839891C22semidirect
33. #16839890C22semidirect
34. #16839890C22semidirect
35. #16839889C22semidirect
58. C61×#446C22semidirect
72. C2×C8×D61Q8semidirect
163. C2×C8×C61C2×Q8semidirect
195. C2×#92418C2×Q8semidirect
204. C8×D61C2×Q8semidirect
272. #2961D61direct (N × H)
282. D61#2961direct (N × H)
306. #446C2×D61semidirect
332. C61C2×#2961semidirect
445. C2×C8Q8×D61semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#214547602
#214547592
#214547582
#214547572
#214547562
#214547552
#446×D612
#424×D612
#423×D612
#405×D612
C2×#97×D612
C61×#29612
C2×#296161