Finite Group Databasebeta

← D61×#1407 #29600294

Subgroups — D61×#1407 #29600294

Order 15616.

416 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#497×D61C211yesmaximal, characteristic
2#355×D61C211yesmaximal, characteristic
3#354×D61C211yesmaximal, characteristic
4#21443980C211yesmaximal, characteristic, complemented
5#21443979C211yesmaximal, characteristic, complemented
6#21443978C211yesmaximal, characteristic, complemented
7C61×#1407C211yesmaximal, characteristic, complemented
8C2×Q16×D61—21no—
9C2×SD16×D61—21no—
10C4⋊Q8×D61C411yescharacteristic, complemented
11#124×D61C2211yescharacteristic
12#16840157C2211yescharacteristic
13#16840156C411yescharacteristic, complemented
14#16840155—21no—
15#16840154C411yescharacteristic, complemented
16#16840153—21no—
17#101×D61—21no—
18#99×D61—21no—
19#97×D61C411yescharacteristic, complemented
20#16839559C2211yescharacteristic
21#16839558—21no—
22#16839557C2211yescharacteristic
23#16839556—21no—
24C61×#497C2211yescharacteristic
25C61×#355C2211yescharacteristic
26C61×#354C2211yescharacteristic
27C2×Q8×D61—21no—
28C2×Q8×D61D411yescharacteristic
29C2×D4×D61D411yescharacteristic
30C2×Dic244—21no—
31C2×#11758202—21no—
32C2×#11758202—21no—
33Q16×D61—42no—
34Q16×D61—42no—
35C2×#11758190—21no—
36C2×#11758200—21no—
37C2×#11758201—21no—
38SD16×D61—42no—
39SD16×D61—42no—
40M16×D61—41no—
41C2×C8×D61—21no—
42#14519777C2×C411yescharacteristic, complemented
43#14519776—41no—
44#14519775—21no—
45#14519766D411yescharacteristic
46#14519765C2×C411yescharacteristic
47#14519764D411yescharacteristic
48#14519763—41no—
49C4⋊C4×D61—41no—
50C22⋊C4×D61—41no—
51C22⋊C4×D61—41no—
52C42×D61C2×C411yescharacteristic
53#14519696—21no—
54#14519695—41no—
55#14519692—21no—
56#14519691—41no—
57#14519688C2×C411yescharacteristic, complemented
58#14519687—21no—
59C2×Q16×C61—21no—
60C2×SD16×C61—21no—
61C4⋊Q8×C61C2×C411yescharacteristic, complemented
62#124×C61C2311yescharacteristic
63#101×C61—21no—
64#99×C61—21no—
65#97×C61C2×C411yescharacteristic, complemented
66C23×D61—21no—
67C2×Q8×C61—21no—
68C2×Q8×C61C2×D411yescharacteristic
69C2×D4×C61C2×D411yescharacteristic
70C2×C22⋊D61—21no—
71Q8×D61—41no—
72Q8×D61—41no—
73Q8×D61—41no—
74Q8×D61—41no—
75Q8×D61—41no—
76Q8×D61—41no—
77D4×D61—41no—
78D4×D61—41no—
79C2×D244C22⋊C411yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—41no—
83C2×C4×D61—81no—
84C2×C4×D61C22⋊C411yescharacteristic
85C2×Dic122—21no—
86C2×Dic122—21no—
87C2×Dic122—41no—
88C2×Dic122C22⋊C411yescharacteristic
89Q16×C61—42no—
90SD16×C61—42no—
91M16×C61—41no—
92C2×C8×C61—21no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C22⋊C4×C61—41no—
96C42×C61C22×C411yescharacteristic
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99#11758202—42no—
100#11758202—42no—
101#11758201—42no—
102#11758200—42no—
103#11758198—41no—
104#11758198—41no—
105#11758198—81no—
106C4⋊Dic61—41no—
107#11758196—42no—
108C4×Dic61—21no—
109C4×Dic61C22⋊C411yescharacteristic
110#11758194—41no—
111C2×#92418—21no—
112Dic244—42no—
113#11758190—42no—
114#11758189—81no—
115C8×D61—22no—
116C8×D61—22no—
117C8×D61—81no—
118C23×C61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—82no—
123C22×D61#9911yescharacteristic
124Q8×C61—41no—
125Q8×C61—41no—
126Q8×C61—41no—
127D4×C61—41no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—81no—
132C2×C4×C61C2×C22⋊C411yescharacteristic
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—41no—
137C2×Dic61—81no—
138C2×Dic61#9911yescharacteristic
139D244—41no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—42no—
143C4×D61—41no—
144C4×D61—41no—
145C4×D61—81no—
146C4×D61—81no—
147C4×D61—162no—
148Dic122—41no—
149Dic122—41no—
150Dic122—41no—
151Dic122—81no—
152Dic122—81no—
153Dic122—81no—
154C8×C61—22no—
155C8×C61—81no—
156#92418—22no—
157#92418—81no—
158C2×#1407—611nomaximal, Sylow
159C22×C61—41no—
160C22×C61—81no—
161C22×C61C2×#9911yescharacteristic
162C2×D61—22no—
163C2×D61—41no—
164C2×D61—82no—
165C2×D61—81no—
166C2×D61—161no—
167C2×D61#35311yescharacteristic
168C2×D61#35311yescharacteristic
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—81no—
173C4×C61—161no—
174Dic61—21no—
175Dic61—41no—
176Dic61—41no—
177Dic61—81no—
178Dic61—161no—
179C2×#497—611no—
180C2×#355—611no—
181C2×#354—611no—
182#1407—611no—
183#1407—611no—
184#1407—611no—
185#1407D6111yescharacteristic, direct product factor
186C2×C61—21no—
187C2×C61—81no—
188C2×C61C2×#35311yescharacteristic
189D61—21no—
190D61—81no—
191D61#140712yesdirect product factor
192C22×Q16—1221no—
193C22×SD16—1221no—
194C2×C4⋊Q8—611no—
195C2×#124—611no—
196#497—611no—
197#497—611no—
198#497—611no—
199#497—1221no—
200#497—1221no—
201#497C2×D6111yescharacteristic
202C2×#101—1221no—
203C2×#99—1221no—
204C2×#97—611no—
205#355—611no—
206#355—1221no—
207#355C2×D6111yescharacteristic
208#354—611no—
209#354—1221no—
210#354C2×D6111yescharacteristic
211C61C2×#140711yescharacteristic, complemented, Sylow
212C22×Q8—611no—
213C22×Q8—1221no—
214C22×D4—611no—
215C2×Q16—21no—
216C2×Q16—1221no—
217C2×Q16—1221no—
218C2×Q16—1221no—
219C2×Q16—2442no—
220C2×Q16—2442no—
221C2×SD16—21no—
222C2×SD16—1221no—
223C2×SD16—1221no—
224C2×SD16—1221no—
225C2×SD16—2442no—
226C2×SD16—2442no—
227C2×M16—2441no—
228C22×C8—1221no—
229C4⋊Q8—611no—
230C4⋊Q8—1221no—
231C4⋊Q8—2441no—
232C4⋊Q8C4×D6111yescharacteristic, complemented
233#124—611no—
234#124—611no—
235#124—611no—
236#124—2441no—
237#124C22×D6111yescharacteristic
238C2×C4⋊C4—2441no—
239C2×C22⋊C4—2441no—
240C2×C22⋊C4—2441no—
241C2×C42—611no—
242#101—21no—
243#101—1221no—
244#101—2441no—
245#99—21no—
246#99—1221no—
247#99—2441no—
248#97—611no—
249#97—1221no—
250#97C4×D6111yescharacteristic, complemented
251C24—1221no—
252C2×Q8—21no—
253C2×Q8—611no—
254C2×Q8—1221no—
255C2×Q8—1221no—
256C2×Q8—2441no—
257C2×Q8—2441no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C2×Q8—2441no—
261C2×Q8—2441no—
262C2×Q8—2441no—
263C2×Q8D4×D6111yescharacteristic
264C2×D4—611no—
265C2×D4—1221no—
266C2×D4—2441no—
267C2×D4—2441no—
268C2×D4D4×D6111yescharacteristic
269C22×C4—611no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—4881no—
273C22×C4—2441no—
274Q16—42no—
275Q16—2442no—
276Q16—2442no—
277Q16—2442no—
278SD16—42no—
279SD16—2442no—
280SD16—2442no—
281SD16—2442no—
282M16—41no—
283M16—4881no—
284M16—2441no—
285C2×C8—21no—
286C2×C8—1222no—
287C2×C8—1222no—
288C2×C8—1221no—
289C2×C8—4881no—
290C4⋊C4—41no—
291C4⋊C4—2441no—
292C4⋊C4—2442no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—4881no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C42—611no—
301C42—1221no—
302C42C2×C4×D6111yescharacteristic
303C23—21no—
304C23—611no—
305C23—1221no—
306C23—4882no—
307C23—2441no—
308C23—2441no—
309Q8—41no—
310Q8—41no—
311Q8—41no—
312Q8—4881no—
313Q8—4881no—
314Q8—4881no—
315Q8—2441no—
316Q8—2441no—
317Q8—2441no—
318D4—41no—
319D4—4881no—
320D4—2441no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—611no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—9762no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2442no—
337C2×C4—2441no—
338C2×C4C22⋊C4×D6111yescharacteristic
339C8—22no—
340C8—81no—
341C8—1222no—
342C8—4881no—
343C22—41no—
344C22—81no—
345C22—611no—
346C22—611no—
347C22—1222no—
348C22—9761no—
349C22—4881no—
350C22—4882no—
351C22—2441no—
352C22#99×D6111yescharacteristic
353C4—21no—
354C4—41no—
355C4—41no—
356C4—81no—
357C4—161no—
358C4—1221no—
359C4—9761no—
360C4—4881no—
361C4—2441no—
362C4—2441no—
363C2—21no—
364C2—81no—
365C2—612no—
366C2—1221no—
367C2—4881no—
368C2#353×D6111yescharacteristic
subgroupG/H
centerC2#353×D61
commutatorC42×C61C22×C4
Frattini#124C22×D61
FittingC61×#1407C2
socleC2×C61C2×#353
prime radicalC2×D4×D61D4
cosocle#124×C61C23
hypercenter#1407D61
hypocenterC61C2×#1407
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #1407

Complements

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

NH ≅ G/Ntype
4. #21443980C2semidirect
5. #21443979C2semidirect
6. #21443978C2semidirect
7. C61×#1407C2semidirect
10. C4⋊Q8×D61C4semidirect
13. #16840156C4semidirect
15. #16840154C4semidirect
19. #97×D61C4semidirect
42. #14519777C2×C4semidirect
57. #14519688C2×C4semidirect
61. C4⋊Q8×C61C2×C4semidirect
65. #97×C61C2×C4semidirect
185. #1407D61direct (N × H)
191. D61#1407direct (N × H)
211. C61C2×#1407semidirect
232. C4⋊Q8C4×D61semidirect
250. #97C4×D61semidirect

Maximal subgroups

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

subgroupindex
#497×D612
#355×D612
#354×D612
#214439802
#214439792
#214439782
C61×#14072
C2×#140761