Finite Group Databasebeta

← #29662384

Subgroups — #29662384

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456330C211yesmaximal, characteristic
2#21455860C212yesmaximal
3C8×Q8×D61C211yesmaximal, characteristic
4#21445220C211yesmaximal, characteristic, complemented
5#21445214C211yesmaximal, characteristic, complemented
6#21445213C211yesmaximal, characteristic, complemented
7#21445204C212yesmaximal, complemented
8#21445203C212yesmaximal, complemented
9#21444566C211yesmaximal, characteristic
10#21444473C212yesmaximal
11C61×#1676C211yesmaximal, characteristic, complemented
12#16840317C2212yes—
13C4×Q8×D61C2211yescharacteristic
14#16840167C2211yescharacteristic
15#16840163—21no—
16#16840163—21no—
17#16840158C2212yes—
18#16840099—22no—
19#16840054C2212yes—
20#16839973C2212yes—
21#16839972C2212yes—
22#16839919—22no—
23Q8×#92418C2211yescharacteristic
24C8×Dic122—21no—
25C8×Dic122C2211yescharacteristic
26#16839886—21no—
27#16839886C2211yescharacteristic
28#16839856—22no—
29#16839854—22no—
30#16839814C2212yes—
31#16839799—21no—
32#16839799—21no—
33C4⋊C8×D61—21no—
34C4⋊C8×D61C2211yescharacteristic
35C4×C8×D61—21no—
36C4×C8×D61C2211yescharacteristic
37#16839515C2211yescharacteristic
38#16839512C2212yes—
39#16839511C2212yes—
40#16839509C2212yes—
41#16839507C2212yes—
42C61×#500C2211yescharacteristic
43C61×#477C2212yes—
44C8×Q8×C61C2211yescharacteristic
45C61×#335C2211yescharacteristic
46C61×#333C2212yes—
47C2×Q8×D61D411yescharacteristic
48C2×Dic244—22no—
49C2×#11758202—22no—
50C2×C8×D61—21no—
51C2×C8×D61D411yescharacteristic
52C2×C8×D61D411yescharacteristic
53#14519777C2312yes—
54#14519768—22no—
55#14519757—22no—
56#14519753—22no—
57Q8×Dic61—22no—
58Q8×Dic61D411yescharacteristic
59C4×Dic122—21no—
60C4×Dic122C2311yescharacteristic
61#14519742—21no—
62#14519742—22no—
63#14519742D411yescharacteristic
64#14519735—22no—
65C4⋊C4×D61—21no—
66C4⋊C4×D61D411yescharacteristic
67C42×D61—21no—
68C42×D61C2311yescharacteristic
69#14519711—21no—
70#14519711—21no—
71#14519710—22no—
72#14519708—22no—
73#14519708—22no—
74C4⋊#92418—21no—
75C4⋊#92418C2312yes—
76C4⋊#92418C2311yescharacteristic
77#14519706—21no—
78#14519706—21no—
79#14519706—21no—
80#14519702—22no—
81#14519700—22no—
82#14519700—22no—
83#14519689—22no—
84C4×#92418—21no—
85C4×#92418C2311yescharacteristic
86C8×Dic61—21no—
87C8×Dic61—22no—
88C8×Dic61—21no—
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×C61C2312yes—
98C4⋊C8×C61C2311yescharacteristic
99#103×C61—22no—
100C4×C8×C61—21no—
101C4×C8×C61C2311yescharacteristic
102C2×Q8×C61—22no—
103C2×Q8×C61C2×D411yescharacteristic
104Q8×D61—22no—
105Q8×D61—22no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61C2×D411yescharacteristic
109C2×C4×D61C2×D411yescharacteristic
110C2×C4×D61#4111yescharacteristic
111C2×Dic122—21no—
112C2×Dic122—22no—
113C2×Dic122C2×D411yescharacteristic
114C2×C8×C61—21no—
115C2×C8×C61—22no—
116C2×C8×C61C2×D411yescharacteristic
117C2×C8×C61C2×D411yescharacteristic
118C4⋊C4×C61—21no—
119C4⋊C4×C61—22no—
120C4⋊C4×C61—22no—
121C4⋊C4×C61C2×D411yescharacteristic
122C42×C61—21no—
123C42×C61C2411yescharacteristic
124#11758202—44no—
125#11758198—42no—
126C4⋊Dic61—21no—
127C4⋊Dic61—22no—
128C4⋊Dic61—22no—
129C4⋊Dic61—42no—
130C4⋊Dic61C2×D411yescharacteristic
131#11758196—21no—
132#11758196—21no—
133#11758196—21no—
134#11758196—42no—
135C4×Dic61—21no—
136C4×Dic61—21no—
137C4×Dic61—21no—
138C4×Dic61—42no—
139C4×Dic61C2×D411yescharacteristic
140C4×Dic61C2×D411yescharacteristic
141C4×Dic61#4111yescharacteristic
142C2×#92418—21no—
143C2×#92418—22no—
144C2×#92418C2×D411yescharacteristic
145C2×#92418C2×D411yescharacteristic
146Dic244—44no—
147C8×D61—22no—
148C8×D61—42no—
149C8×D61Q1614yescomplemented
150C22×D61#12111yescharacteristic
151Q8×C61—21no—
152Q8×C61—82no—
153Q8×C61#13512yes—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—42no—
157C2×C4×C61C22×D411yescharacteristic
158C2×C4×C61C22×D411yescharacteristic
159C2×C4×C61C2×#4111yescharacteristic
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—42no—
163C2×Dic61#12111yescharacteristic
164C2×Dic61#12111yescharacteristic
165C2×Dic61#12111yescharacteristic
166C4×D61—24no—
167C4×D61—21no—
168C4×D61—21no—
169C4×D61—41no—
170C4×D61—42no—
171C4×D61C2×Q1612yes—
172C4×D61#13712yes—
173Dic122—24no—
174Dic122—21no—
175Dic122—42no—
176Dic122—42no—
177Dic122#13512yes—
178C8×C61—21no—
179C8×C61—42no—
180C8×C61—41no—
181C8×C61C2×Q1612yes—
182#92418—21no—
183#92418—42no—
184#92418—41no—
185#92418C2×Q1612yes—
186#19118—611nomaximal, Sylow
187C22×C61C2×#12111yescharacteristic
188C2×D61—21no—
189C2×D61—21no—
190C2×D61#46212yes—
191C4×C61—22no—
192C4×C61—21no—
193C4×C61—41no—
194C4×C61—82no—
195C4×C61C22×Q1611yescharacteristic
196C4×C61C2×#13511yescharacteristic
197C4×C61C2×#13511yescharacteristic
198C4×C61C2×#13711yescharacteristic
199Dic61—21no—
200Dic61—22no—
201Dic61—21no—
202Dic61—41no—
203Dic61—82no—
204Dic61#46212yes—
205#3160—611no—
206#3104—612no—
207C2×C8×Q8—611no—
208#1676—611no—
209#1676D6111yescharacteristic, complemented
210#1674—611no—
211#1674—611no—
212#1672—612no—
213#1672—612no—
214#1564—611no—
215#1542—612no—
216C2×C61C2×#46211yescharacteristic
217C2×C61#305011yescharacteristic
218C2×C61#306711yescharacteristic
219D61—22no—
220#533—612no—
221C2×C4×Q8—611no—
222#500—611no—
223#500C2×D6111yescharacteristic
224#499—1221no—
225#499—1221no—
226#498—612no—
227#484—1222no—
228#477—612no—
229#477C2×D6112yes—
230#462—612no—
231#462—612no—
232#451—1222no—
233C8×Q8—611no—
234C8×Q8—611no—
235C8×Q8—611no—
236C8×Q8—1221no—
237C8×Q8—1221no—
238C8×Q8C2×D6111yescharacteristic
239C4×Q16—1222no—
240C4×Q16—1222no—
241#431—612no—
242#427—1221no—
243#427—1221no—
244C2×C4⋊C8—611no—
245C2×C4⋊C8—1221no—
246C2×C4×C8—611no—
247C2×C4×C8—1221no—
248#335—611no—
249#335C2×D6111yescharacteristic
250#334—612no—
251#333—612no—
252#333C2×D6112yes—
253#332—612no—
254#332—612no—
255C61#1911811yescharacteristic, complemented, Sylow
256C22×Q8—611no—
257C2×Q16—1222no—
258C2×Q16—1222no—
259C22×C8—611no—
260C22×C8—611no—
261C22×C8—1221no—
262C4⋊Q8—612no—
263C4⋊Q8C22×D6112yes—
264#125—1222no—
265C22⋊Q8—1222no—
266C22⋊Q8—1222no—
267C4×Q8—611no—
268C4×Q8—611no—
269C4×Q8—611no—
270C4×Q8—1221no—
271C4×Q8—1221no—
272C4×Q8—1222no—
273C4×Q8—1222no—
274C4×Q8C22×D6111yescharacteristic
275#117—1222no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—1221no—
278C2×C42—611no—
279C2×C42—1221no—
280#107—21no—
281#107—21no—
282#107—22no—
283#107—1222no—
284#107—1221no—
285#107—1221no—
286#106—1222no—
287#106—1222no—
288C4⋊C8—21no—
289C4⋊C8—611no—
290C4⋊C8—612no—
291C4⋊C8—1221no—
292C4⋊C8—1221no—
293C4⋊C8—1221no—
294C4⋊C8—1221no—
295C4⋊C8C22×D6111yescharacteristic
296C4⋊C8C22×D6112yes—
297#103—22no—
298#103—1222no—
299#103—1222no—
300#103—1222no—
301C22⋊C8—1222no—
302C4×C8—21no—
303C4×C8—611no—
304C4×C8—611no—
305C4×C8—611no—
306C4×C8—1221no—
307C4×C8—1222no—
308C4×C8—1221no—
309C4×C8—1221no—
310C4×C8C22×D6111yescharacteristic
311C2×Q8—22no—
312C2×Q8—611no—
313C2×Q8—1221no—
314C2×Q8—1222no—
315C2×Q8—1222no—
316C2×Q8—1222no—
317C2×Q8D4×D6111yescharacteristic
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—1221no—
322C22×C4—1221no—
323Q16—2444no—
324Q16—2444no—
325C2×C8—21no—
326C2×C8—22no—
327C2×C8—611no—
328C2×C8—614no—
329C2×C8—611no—
330C2×C8—1222no—
331C2×C8—1221no—
332C2×C8—1222no—
333C2×C8—2442no—
334C2×C8D4×D6111yescharacteristic
335C2×C8D4×D6111yescharacteristic
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—611no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C4⋊C4—1221no—
343C4⋊C4—1221no—
344C4⋊C4—1222no—
345C4⋊C4—1222no—
346C4⋊C4—2442no—
347C4⋊C4—2442no—
348C4⋊C4D4×D6111yescharacteristic
349C22⋊C4—2442no—
350C42—21no—
351C42—611no—
352C42—611no—
353C42—611no—
354C42—1221no—
355C42—1221no—
356C42—1221no—
357C42—2442no—
358C42C23×D6111yescharacteristic
359C23—611no—
360Q8—21no—
361Q8—82no—
362Q8—612no—
363Q8—1224no—
364Q8—1221no—
365Q8—2442no—
366Q8—2442no—
367Q8#1451980012yes—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—42no—
371C2×C4—611no—
372C2×C4—612no—
373C2×C4—612no—
374C2×C4—611no—
375C2×C4—611no—
376C2×C4—1224no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—2441no—
382C2×C4—2442no—
383C2×C4—2442no—
384C2×C4C2×D4×D6111yescharacteristic
385C2×C4C2×D4×D6111yescharacteristic
386C2×C4#41×D6111yescharacteristic
387C8—21no—
388C8—42no—
389C8—41no—
390C8—612no—
391C8—1221no—
392C8—2442no—
393C8—2441no—
394C8Q16×D6112yes—
395C22—612no—
396C22—1221no—
397C22—1221no—
398C22#121×D6111yescharacteristic
399C4—22no—
400C4—21no—
401C4—41no—
402C4—82no—
403C4—612no—
404C4—1221no—
405C4—1222no—
406C4—1221no—
407C4—4882no—
408C4—2441no—
409C4C2×Q16×D6111yescharacteristic
410C4#135×D6111yescharacteristic
411C4C2×#1451980011yescharacteristic
412C4#137×D6111yescharacteristic
413C2—1222no—
414C2#462×D6111yescharacteristic
415C2#2145540211yescharacteristic
416C2#2145553711yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1676C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1676D61
hypocenterC61#19118
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1676

Complements

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

NH ≅ G/Ntype
4. #21445220C2semidirect
5. #21445214C2semidirect
6. #21445213C2semidirect
7. #21445204C2semidirect
8. #21445203C2semidirect
11. C61×#1676C2semidirect
149. C8×D61Q16semidirect
209. #1676D61semidirect
255. C61#19118semidirect

Maximal subgroups

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

subgroupindex
#214563302
#214558602
C8×Q8×D612
#214452202
#214452142
#214452132
#214452042
#214452032
#214445662
#214444732
C61×#16762
#1911861