Finite Group Databasebeta

← #30603467

Subgroups — #30603467

Order 15616.

622 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#108C211yesmaximal, characteristic
2#21461524C212yesmaximal
3#21461511C211yesmaximal, characteristic
4C2×#16840631C212yesmaximal
5C2×#16839787C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×D61⋊M16C2212yes—
8C2×#14519848—21no—
9D61⋊#108—24no—
10C2×#14519847—21no—
11#16840642—22no—
12#16840642—22no—
13#16840638—21no—
14#16840638—21no—
15#16840631—24no—
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519734C2211yescharacteristic
19#16839787—21no—
20#16839787—21no—
21#16839787—21no—
22#16839787—21no—
23C2×C4⋊#92418C411yescharacteristic
24C2×#14519706C411yescharacteristic
25C2×#14519706C411yescharacteristic
26C2×C4⋊C8×C61C411yescharacteristic
27C2×#11758213—22no—
28C2×#11758213—22no—
29D61⋊M16—22no—
30D61⋊M16—22no—
31D61⋊M16—22no—
32D61⋊M16—22no—
33D61⋊M16—22no—
34D61⋊M16—22no—
35D61⋊M16D414yes—
36D61⋊M16Q814yes—
37C2×#11758217—22no—
38C2×#11758217—22no—
39C2×D61⋊C8—22no—
40C2×D61⋊C8—22no—
41#14519848—24no—
42#14519847—24no—
43C22×C4×D61C2311yescharacteristic
44C2×#11758189—21no—
45C2×#11758189—21no—
46C2×#11758189—22no—
47C2×#11758189—22no—
48C22×#92418C2×C411yescharacteristic
49C22×#92418C2×C411yescharacteristic
50C2×C8×D61—22no—
51C2×C8×D61—22no—
52C2×C8×D61D411yescharacteristic
53C2×C8×D61D411yescharacteristic
54C2×C8×D61D411yescharacteristic
55C2×C8×D61D411yescharacteristic
56#14519734—21no—
57#14519734—21no—
58#14519734—21no—
59#14519734—21no—
60C2×#11758196D411yescharacteristic
61C2×#11758196D411yescharacteristic
62C2×#11758198Q811yescharacteristic
63C2×#11758198Q811yescharacteristic
64C2×C4×Dic61C2×C411yescharacteristic
65C4⋊#92418—21no—
66C4⋊#92418—21no—
67#14519706—21no—
68#14519706—21no—
69#14519706—21no—
70#14519706—21no—
71C22×C8×C61C2×C411yescharacteristic
72C22×C8×C61C2×C411yescharacteristic
73C2×C42×C61C2×C411yescharacteristic
74C4⋊C8×C61—21no—
75C4⋊C8×C61—21no—
76C23×D61C2×Q811yescharacteristic
77C22×C4×C61C4⋊C411yescharacteristic
78C22×C4×C61C4⋊C411yescharacteristic
79C22×C4×C61C22×C411yescharacteristic
80C22×Dic61C4⋊C411yescharacteristic
81C22×Dic61C4⋊C411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C2×C4×D61C2×D412yes—
84C2×C4×D61C2×D411yescharacteristic
85C2×C4×D61C2×D411yescharacteristic
86C2×C4×D61C2×Q812yes—
87C2×C4×D61#4112yes—
88C2×C4×D61#4111yescharacteristic
89C2×C4×D61#4112yes—
90C2×C4×D61#4111yescharacteristic
91#11758217—24no—
92#11758217—24no—
93#11758217—42no—
94#11758217—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97#11758213—24no—
98#11758213—24no—
99#11758213—42no—
100#11758213—42no—
101D61⋊C8—24no—
102D61⋊C8—24no—
103D61⋊C8—42no—
104D61⋊C8—42no—
105C2×C8×C61—22no—
106C2×C8×C61—21no—
107C2×C8×C61—22no—
108C2×C8×C61C22⋊C411yescharacteristic
109C2×C8×C61C22⋊C411yescharacteristic
110C42×C61—21no—
111C42×C61—21no—
112#11758198—21no—
113#11758198—21no—
114#11758198—21no—
115#11758198—21no—
116#11758196—21no—
117#11758196—21no—
118#11758196—21no—
119#11758196—21no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C2×#92418—22no—
123C2×#92418—21no—
124C2×#92418—22no—
125C2×#92418C22⋊C411yescharacteristic
126C2×#92418C22⋊C411yescharacteristic
127#11758189—41no—
128#11758189—42no—
129#11758189—41no—
130C8×D61—21no—
131C8×D61—21no—
132C8×D61—22no—
133C8×D61—22no—
134C8×D61—21no—
135C8×D61—21no—
136C23×C61C2×C4⋊C411yescharacteristic
137C22×D61—41no—
138C22×D61—41no—
139C22×D61C22⋊Q811yescharacteristic
140C22×D61C22⋊Q811yescharacteristic
141C22×D61#12512yes—
142C22×D61C4⋊Q812yes—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61#11711yescharacteristic
149C2×C4×C61C4×D412yes—
150C2×C4×C61C4×Q812yes—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61#12112yes—
156C2×Dic61#12111yescharacteristic
157C2×Dic61#12111yescharacteristic
158C2×Dic61C22⋊Q812yes—
159C4×D61#12011yescharacteristic
160C4×D61#12112yes—
161C4×D61C22⋊Q812yes—
162C4×D61C22⋊Q812yes—
163C4×D61#12312yes—
164C4×D61#12311yescharacteristic
165C4×D61#12411yescharacteristic
166C4×D61#12512yes—
167C4×D61#12612yes—
168C4×D61C4⋊Q811yescharacteristic
169#92420—44no—
170#92420—44no—
171C8×C61—21no—
172C8×C61—21no—
173C8×C61—41no—
174#92418—21no—
175#92418—21no—
176#92418—41no—
177#11230—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61#38011yescharacteristic
181C22×C61#38912yes—
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—21no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61#39511yescharacteristic
189C2×D61#39812yes—
190C2×D61#40011yescharacteristic
191C4×C61—41no—
192C4×C61—41no—
193C4×C61#38611yescharacteristic
194C4×C61#38712yes—
195C4×C61#39111yescharacteristic
196Dic61—41no—
197Dic61—41no—
198Dic61#39411yescharacteristic
199Dic61#39612yes—
200Dic61#39811yescharacteristic
201C22×#108—611no—
202C2×#424—611no—
203#1742—612no—
204C2×#341—611no—
205C2×#338—612no—
206C2×C61—22no—
207C2×C61#144111yescharacteristic
208C2×C61#181311yescharacteristic
209C2×C61#181311yescharacteristic
210D61—21no—
211D61—22no—
212D61—21no—
213C22×M16—611no—
214C22×M16—612no—
215C22×M16—612no—
216C23×C8—611no—
217C2×#117—611no—
218C2×#108—1221no—
219C2×#108—1221no—
220C2×#108—1224no—
221#424—1221no—
222#424—1221no—
223#424—1221no—
224#424—1221no—
225C2×C4⋊C8—611no—
226C2×C4⋊C8—611no—
227C2×C4⋊C8—611no—
228C2×C4⋊C8#692311yescharacteristic
229#343—1222no—
230#343—1222no—
231#341—1221no—
232#341—1221no—
233#338—1224no—
234C61#1123011yescharacteristic, complemented, Sylow
235C23×C4—611no—
236C2×M16—614no—
237C2×M16—614no—
238C2×M16—1222no—
239C2×M16—1221no—
240C2×M16—1221no—
241C2×M16—1222no—
242C2×M16—1222no—
243C2×M16—1222no—
244C2×M16—1222no—
245C2×M16—1222no—
246C2×M16—1222no—
247C2×M16—1222no—
248C2×M16—1222no—
249C2×M16—1222no—
250C2×M16—1222no—
251C2×M16—1222no—
252C22×C8—611no—
253C22×C8—611no—
254C22×C8—611no—
255C22×C8—611no—
256C22×C8—611no—
257C22×C8—611no—
258C22×C8—1222no—
259C22×C8—1222no—
260C22×C8—1222no—
261C22×C8—1222no—
262C22×C8C2×#692311yescharacteristic
263C22×C8C2×#692311yescharacteristic
264#117—1221no—
265#117—1221no—
266#117—1221no—
267#117—1221no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—611no—
270C2×C22⋊C4—611no—
271C2×C22⋊C4—611no—
272C2×C42—611no—
273C2×C42C2×#692311yescharacteristic
274#108—1224no—
275#108—1224no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—1221no—
279C4⋊C8—1221no—
280C4⋊C8—1221no—
281C4⋊C8—1221no—
282C4⋊C8—1221no—
283C4⋊C8—1221no—
284C24—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—612no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4C4⋊#692311yescharacteristic
297C22×C4C4⋊#692311yescharacteristic
298C22×C4C22×#692311yescharacteristic
299M16—1224no—
300M16—1224no—
301M16—1224no—
302M16—1224no—
303M16—2441no—
304M16—2442no—
305M16—2441no—
306M16—2442no—
307M16—2442no—
308M16—2442no—
309M16—2442no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—611no—
314C2×C8—611no—
315C2×C8—1221no—
316C2×C8—1221no—
317C2×C8—1222no—
318C2×C8—1222no—
319C2×C8—1221no—
320C2×C8—1221no—
321C2×C8—1222no—
322C2×C8—1224no—
323C2×C8—1224no—
324C2×C8—1221no—
325C2×C8—1222no—
326C2×C8—2442no—
327C2×C8—2442no—
328C2×C8—2442no—
329C2×C8—2442no—
330C2×C8C22⋊#692311yescharacteristic
331C2×C8C22⋊#692311yescharacteristic
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C4⋊C4—1221no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C42—21no—
341C42—21no—
342C42—1221no—
343C42—1221no—
344C23—611no—
345C23—611no—
346C23—612no—
347C23—612no—
348C23—2441no—
349C23—2441no—
350C23C2×C4⋊#692311yescharacteristic
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—612no—
358C2×C4—612no—
359C2×C4—611no—
360C2×C4—612no—
361C2×C4—611no—
362C2×C4—612no—
363C2×C4—612no—
364C2×C4—612no—
365C2×C4—612no—
366C2×C4—612no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4C2×C22⋊#692311yescharacteristic
374C2×C4#1451985611yescharacteristic
375C2×C4D4×#692312yes—
376C2×C4Q8×#692312yes—
377C8—21no—
378C8—21no—
379C8—41no—
380C8—1221no—
381C8—1221no—
382C8—2444no—
383C8—2444no—
384C8—2441no—
385C22—21no—
386C22—21no—
387C22—611no—
388C22—612no—
389C22—611no—
390C22—1221no—
391C22—1221no—
392C22—1221no—
393C22—1221no—
394C22—2442no—
395C22—2442no—
396C22#1684070411yescharacteristic
397C22#1684071312yes—
398C4—41no—
399C4—41no—
400C4—611no—
401C4—612no—
402C4—611no—
403C4—2441no—
404C4—2441no—
405C4#1684071011yescharacteristic
406C4#1684071112yes—
407C4(C2×#6923)⋊Q811yescharacteristic
408C2—22no—
409C2—1221no—
410C2—1222no—
411C2—1221no—
412C2#2146100411yescharacteristic
413C2#2146170311yescharacteristic
414C2#2146170411yescharacteristic
subgroupG/H
centerC2×C4#14519856
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61#380
prime radicalC23×D61C2×Q8
cosocleC22×C4×D61C23
hypercenterC2×C4⋊C8#6923
hypocenterC61#11230
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
234. C61#11230semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1082
#214615242
#214615112
C2×#168406312
C2×#168397872
#1123061