Finite Group Databasebeta

← D61×#1696 #29662643

Subgroups — D61×#1696 #29662643

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#500×D61C211yesmaximal, characteristic
2#477×D61C212yesmaximal
3#446×D61C211yesmaximal, characteristic
4#21445348C211yesmaximal, characteristic, complemented
5#21445347C211yesmaximal, characteristic, complemented
6#21445346C212yesmaximal, complemented
7#21445345C212yesmaximal, complemented
8#21445344C211yesmaximal, characteristic, complemented
9#334×D61C211yesmaximal, characteristic
10#333×D61C212yesmaximal
11C61×#1696C211yesmaximal, characteristic, complemented
12C4⋊Q8×D61C2212yes—
13C4×Q8×D61C2211yescharacteristic
14#16840167C2211yescharacteristic
15#16840166—21no—
16#16840166—21no—
17#16840165C2212yes—
18#16840058C2212yes—
19#16840057C2212yes—
20#16840056—22no—
21#16840055—22no—
22#16840054C2212yes—
23#16839893C2211yescharacteristic
24#16839892C2211yescharacteristic
25#16839891—21no—
26#16839890—21no—
27#16839889C2211yescharacteristic
28#107×D61—21no—
29#107×D61—21no—
30#107×D61—22no—
31C4⋊C8×D61—21no—
32C4⋊C8×D61C2211yescharacteristic
33C4⋊C8×D61C2212yes—
34#103×D61—22no—
35#97×D61—21no—
36C4×C8×D61C2211yescharacteristic
37#16839513C2211yescharacteristic
38#16839512C2212yes—
39#16839511C2212yes—
40#16839510C2212yes—
41#16839510C2212yes—
42C61×#500C2211yescharacteristic
43C61×#477C2212yes—
44C61×#446C2211yescharacteristic
45C61×#334C2211yescharacteristic
46C61×#333C2212yes—
47C2×Q8×D61—22no—
48C2×Q8×D61D411yescharacteristic
49C2×C8×D61—21no—
50C2×C8×D61—22no—
51C2×C8×D61D411yescharacteristic
52C2×C8×D61D411yescharacteristic
53#14519777C2312yes—
54#14519776—22no—
55#14519776—22no—
56#14519775—22no—
57Q8×Dic61D411yescharacteristic
58C4×Dic122—21no—
59C4×Dic122C2311yescharacteristic
60#14519742—21no—
61#14519742D411yescharacteristic
62C4⋊C4×D61—21no—
63C4⋊C4×D61—22no—
64C4⋊C4×D61—22no—
65C4⋊C4×D61D411yescharacteristic
66C42×D61—21no—
67C42×D61C2311yescharacteristic
68#14519711—21no—
69#14519711—21no—
70#14519711—22no—
71#14519710—22no—
72#14519710—22no—
73#14519710—22no—
74#14519710—22no—
75C4⋊#92418—21no—
76C4⋊#92418C2311yescharacteristic
77C4⋊#92418C2312yes—
78#14519706—21no—
79#14519706—22no—
80#14519706—21no—
81#14519706—21no—
82#14519702—22no—
83#14519701—22no—
84#14519700—22no—
85#14519688—21no—
86#14519687—21no—
87#14519687—21no—
88C4×#92418C2311yescharacteristic
89C8×Dic61D411yescharacteristic
90C8×Dic61D411yescharacteristic
91C4⋊Q8×C61C2312yes—
92C4×Q8×C61C2311yescharacteristic
93#107×C61—21no—
94#107×C61—21no—
95#107×C61—22no—
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2311yescharacteristic
98C4⋊C8×C61C2312yes—
99#103×C61—22no—
100#97×C61—21no—
101C4×C8×C61C2311yescharacteristic
102C2×Q8×C61—22no—
103C2×Q8×C61C2×D411yescharacteristic
104Q8×D61—24no—
105Q8×D61—84no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—42no—
109C2×C4×D61C2×D411yescharacteristic
110C2×C4×D61C2×D411yescharacteristic
111C2×C4×D61#4111yescharacteristic
112C2×Dic122—21no—
113C2×Dic122—22no—
114C2×Dic122—42no—
115C2×Dic122C2×D411yescharacteristic
116C2×C8×C61—21no—
117C2×C8×C61—22no—
118C2×C8×C61C2×D411yescharacteristic
119C2×C8×C61C2×D411yescharacteristic
120C4⋊C4×C61—21no—
121C4⋊C4×C61—22no—
122C4⋊C4×C61—22no—
123C4⋊C4×C61C2×D411yescharacteristic
124C42×C61—21no—
125C42×C61C2411yescharacteristic
126C4⋊Dic61—21no—
127C4⋊Dic61—22no—
128C4⋊Dic61—22no—
129C4⋊Dic61C2×D411yescharacteristic
130#11758196—21no—
131#11758196—21no—
132#11758196—21no—
133#11758196—42no—
134#11758196—42no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138C4×Dic61C2×D411yescharacteristic
139C4×Dic61C2×D411yescharacteristic
140C4×Dic61#4111yescharacteristic
141C2×#92418—21no—
142C2×#92418—22no—
143C2×#92418C2×D411yescharacteristic
144C2×#92418C2×D411yescharacteristic
145C8×D61—22no—
146C8×D61—42no—
147C8×D61—44no—
148C8×D61Q1614yes—
149C22×D61#12111yescharacteristic
150Q8×C61—22no—
151Q8×C61—82no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—42no—
155C2×C4×C61C22×D411yescharacteristic
156C2×C4×C61C22×D411yescharacteristic
157C2×C4×C61C2×#4111yescharacteristic
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—42no—
161C2×Dic61#12111yescharacteristic
162C2×Dic61#12111yescharacteristic
163C2×Dic61#12111yescharacteristic
164C4×D61—22no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—84no—
168C4×D61C2×Q1612yes—
169C4×D61#13712yes—
170C4×D61#13714yes—
171Dic122—22no—
172Dic122—42no—
173Dic122—84no—
174Dic122—82no—
175C8×C61—21no—
176C8×C61—41no—
177C8×C61—42no—
178C8×C61C2×Q1612yes—
179#92418—21no—
180#92418—41no—
181#92418—42no—
182#92418C2×Q1612yes—
183C2×#1696—611nomaximal, Sylow
184C22×C61C2×#12111yescharacteristic
185C2×D61#46212yes—
186C2×D61#47012yes—
187C2×D61#47212yes—
188C4×C61—21no—
189C4×C61—41no—
190C4×C61—41no—
191C4×C61—82no—
192C4×C61C22×Q1611yescharacteristic
193C4×C61C2×#13711yescharacteristic
194C4×C61C2×#13712yes—
195Dic61—21no—
196Dic61—41no—
197Dic61—41no—
198Dic61—82no—
199Dic61#46212yes—
200Dic61#47012yes—
201C2×#500—611no—
202C2×#477—612no—
203C2×#446—611no—
204#1696—611no—
205#1696—612no—
206#1696—611no—
207#1696—611no—
208#1696—612no—
209#1696D6111yescharacteristic, direct product factor
210C2×#334—611no—
211C2×#333—612no—
212C2×C61C2×#46211yescharacteristic
213C2×C61C2×#47011yescharacteristic
214C2×C61C2×#47211yescharacteristic
215D61#169614yesdirect product factor
216C2×C4⋊Q8—612no—
217C2×C4×Q8—611no—
218#500—612no—
219#500—611no—
220#500—1221no—
221#500—1221no—
222#500C2×D6111yescharacteristic
223#477—612no—
224#477—612no—
225#477—612no—
226#477—1222no—
227#477—1222no—
228#477C2×D6112yes—
229#446—611no—
230#446—611no—
231#446—611no—
232#446—1221no—
233#446—1221no—
234#446C2×D6111yescharacteristic
235C2×#107—1222no—
236C2×#107—1221no—
237C2×#107—1221no—
238C2×C4⋊C8—612no—
239C2×C4⋊C8—611no—
240C2×C4⋊C8—1221no—
241C2×#103—1222no—
242C2×#97—1221no—
243C2×C4×C8—611no—
244#334—612no—
245#334—611no—
246#334C2×D6111yescharacteristic
247#333—612no—
248#333—612no—
249#333—612no—
250#333C2×D6112yes—
251C61C2×#169611yescharacteristic, complemented, Sylow
252C22×Q8—611no—
253C22×Q8—1222no—
254C22×C8—611no—
255C22×C8—611no—
256C22×C8—1221no—
257C22×C8—1222no—
258C4⋊Q8—612no—
259C4⋊Q8—1222no—
260C4⋊Q8—1222no—
261C4⋊Q8—1222no—
262C4⋊Q8C22×D6112yes—
263C4×Q8—611no—
264C4×Q8—611no—
265C4×Q8—611no—
266C4×Q8—1221no—
267C4×Q8—1221no—
268C4×Q8C22×D6111yescharacteristic
269C2×C4⋊C4—611no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1222no—
272C2×C4⋊C4—1222no—
273C2×C42—611no—
274C2×C42—1221no—
275#107—21no—
276#107—21no—
277#107—22no—
278#107—1222no—
279#107—1222no—
280#107—1222no—
281#107—1222no—
282#107—1221no—
283#107—1221no—
284#107—1222no—
285C4⋊C8—21no—
286C4⋊C8—611no—
287C4⋊C8—612no—
288C4⋊C8—1221no—
289C4⋊C8—1221no—
290C4⋊C8—1222no—
291C4⋊C8—1221no—
292C4⋊C8—1221no—
293C4⋊C8C22×D6111yescharacteristic
294C4⋊C8C22×D6112yes—
295#103—22no—
296#103—1222no—
297#103—1222no—
298#103—1222no—
299#97—21no—
300#97—1221no—
301#97—1221no—
302#97—1221no—
303C4×C8—611no—
304C4×C8—611no—
305C4×C8—611no—
306C4×C8C22×D6111yescharacteristic
307C2×Q8—22no—
308C2×Q8—611no—
309C2×Q8—1221no—
310C2×Q8—1224no—
311C2×Q8—1222no—
312C2×Q8—4884no—
313C2×Q8—2442no—
314C2×Q8D4×D6111yescharacteristic
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—2442no—
321C2×C8—21no—
322C2×C8—22no—
323C2×C8—611no—
324C2×C8—614no—
325C2×C8—611no—
326C2×C8—1222no—
327C2×C8—1221no—
328C2×C8—1222no—
329C2×C8—2442no—
330C2×C8—2444no—
331C2×C8D4×D6111yescharacteristic
332C2×C8D4×D6111yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—611no—
337C4⋊C4—1221no—
338C4⋊C4—1221no—
339C4⋊C4—1221no—
340C4⋊C4—1221no—
341C4⋊C4—1222no—
342C4⋊C4—1222no—
343C4⋊C4—2442no—
344C4⋊C4—2442no—
345C4⋊C4D4×D6111yescharacteristic
346C42—21no—
347C42—611no—
348C42—611no—
349C42—611no—
350C42—1221no—
351C42—1221no—
352C42—1221no—
353C42C23×D6111yescharacteristic
354C23—611no—
355Q8—22no—
356Q8—82no—
357Q8—1222no—
358Q8—4882no—
359Q8—4884no—
360Q8—2442no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—612no—
367C2×C4—612no—
368C2×C4—614no—
369C2×C4—611no—
370C2×C4—1222no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—4884no—
374C2×C4—2442no—
375C2×C4—2442no—
376C2×C4—2442no—
377C2×C4C2×D4×D6111yescharacteristic
378C2×C4C2×D4×D6111yescharacteristic
379C2×C4#41×D6111yescharacteristic
380C8—21no—
381C8—42no—
382C8—41no—
383C8—612no—
384C8—1221no—
385C8—2442no—
386C8—2441no—
387C8Q16×D6112yes—
388C22—612no—
389C22—612no—
390C22—612no—
391C22#121×D6111yescharacteristic
392C4—21no—
393C4—41no—
394C4—41no—
395C4—82no—
396C4—612no—
397C4—612no—
398C4—1221no—
399C4—4882no—
400C4—2441no—
401C4—2441no—
402C4C2×Q16×D6111yescharacteristic
403C4#137×D6112yes—
404C4#137×D6111yescharacteristic
405C2—614no—
406C2#462×D6111yescharacteristic
407C2#470×D6111yescharacteristic
408C2#472×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1696C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1696D61
hypocenterC61C2×#1696
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1696

Complements

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

NH ≅ G/Ntype
4. #21445348C2semidirect
5. #21445347C2semidirect
6. #21445346C2semidirect
7. #21445345C2semidirect
8. #21445344C2semidirect
11. C61×#1696C2semidirect
209. #1696D61direct (N × H)
215. D61#1696direct (N × H)
251. C61C2×#1696semidirect

Maximal subgroups

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

subgroupindex
#500×D612
#477×D612
#446×D612
#214453482
#214453472
#214453462
#214453452
#214453442
#334×D612
#333×D612
C61×#16962
C2×#169661