Finite Group Databasebeta

← #29574647

Subgroups — #29574647

Order 15616.

488 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454937C211yesmaximal, characteristic
2C4×#14519808C211yesmaximal, characteristic
3#21444214C211yesmaximal, characteristic, complemented
4#21444202C211yesmaximal, characteristic
5#21443669C211yesmaximal, characteristic, complemented
6#21443656C211yesmaximal, characteristic, complemented
7C61×#1984C211yesmaximal, characteristic, complemented
8C2×#14519808C411yescharacteristic
9C4×#11758222C2211yescharacteristic
10#16839889—21no—
11#16839867—21no—
12#16839860—21no—
13C4×#11758202—21no—
14C4×#11758201—21no—
15#16839839—21no—
16#16839833—22no—
17#16839818—21no—
18#16839815C2211yescharacteristic
19#16839815C2211yescharacteristic
20#16839802C411yescharacteristic
21#16839784—21no—
22#16839771C411yescharacteristic
23#16839761C411yescharacteristic
24C4×#11758194C2211yescharacteristic
25#16839494—21no—
26Q8⋊#92418—21no—
27Q8⋊#92418—21no—
28#16839491—21no—
29C2×C4×Q8×C61C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×C4×C8×C61C2211yescharacteristic
32C61×#336—22no—
33C2×#11758222C2×C411yescharacteristic
34#14519808—22no—
35#14519808—22no—
36C2×#11758202—21no—
37C2×#11758201—21no—
38C2×#11758194C2×C411yescharacteristic
39C2×#11758194C2×C411yescharacteristic
40C2×#11758189—22no—
41C4×Dic122D411yescharacteristic
42C4×Dic122D411yescharacteristic
43C4×D244D411yescharacteristic
44C4×D244D411yescharacteristic
45C4×C22⋊D61—21no—
46C4×C22⋊D61—21no—
47#14519736C2×C411yescharacteristic
48#14519734—21no—
49C42×D61—21no—
50#14519710—21no—
51#14519708—21no—
52C4⋊#92418—21no—
53C4⋊#92418D411yescharacteristic
54C4⋊#92418D411yescharacteristic
55#14519706—22no—
56#14519701—21no—
57#14519701—21no—
58#14519700—21no—
59#14519697—21no—
60C22⋊#92418—21no—
61C22⋊#92418—21no—
62#14519689—22no—
63#14519688—21no—
64#14519687—22no—
65C4×#92418—21no—
66C4×#92418—21no—
67C4×#92418—21no—
68C22×Q8×C61C2×C411yescharacteristic
69C22×C8×C61—21no—
70C22×C8×C61D412yes—
71C4×Q8×C61—21no—
72C4×Q8×C61—21no—
73C4×Q8×C61—21no—
74C4×Q8×C61—21no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61C2×C411yescharacteristic
77C2×C42×C61—21no—
78C2×C42×C61C2311yescharacteristic
79C4⋊C8×C61—21no—
80C4⋊C8×C61—21no—
81C4×C8×C61—21no—
82C4×C8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×Q8×C61M1612yescomplemented
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61C22×C411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C2×C22⋊D61—21no—
95#11758222—21no—
96#11758222—21no—
97#11758222—21no—
98#11758222—21no—
99C2×D244C22⋊C411yescharacteristic
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×Dic122C22⋊C411yescharacteristic
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C2×C8×C61—42no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C42×C61—41no—
114C42×C61—41no—
115C42×C61C2×D411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61C2×D411yescharacteristic
118C42×C61#4111yescharacteristic
119C22⋊Dic61—21no—
120#11758202—24no—
121#11758201—24no—
122#11758198—21no—
123#11758198—21no—
124C4⋊Dic61C22⋊C411yescharacteristic
125C4⋊Dic61C22⋊C411yescharacteristic
126#11758196—21no—
127#11758196—21no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131#11758194—21no—
132#11758194—21no—
133#11758194—21no—
134#11758194M1612yescomplemented
135C2×#92418—21no—
136C2×#92418—21no—
137C2×#92418—21no—
138C2×#92418—21no—
139C2×#92418—41no—
140#11758189—82no—
141C23×C61C4×D411yescharacteristic
142C22×D61—21no—
143Q8×C61—22no—
144Q8×C61—22no—
145Q8×C61—41no—
146Q8×C61—41no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—22no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—41no—
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×C4×C61C2×M1611yescharacteristic
162C2×C4×C61C2×M1611yescharacteristic
163C2×C4×C61#13111yescharacteristic
164C2×C4×C61#13111yescharacteristic
165C22⋊D61—41no—
166C22⋊D61—41no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170D244—21no—
171D244—21no—
172C4×D61—41no—
173C4×D61—41no—
174C4×D61—41no—
175C4×D61—41no—
176C4×D61—81no—
177Dic122—21no—
178Dic122—21no—
179C8×C61—42no—
180C8×C61—42no—
181#92418—22no—
182#92418—41no—
183#92418—41no—
184#92418—41no—
185#92418—81no—
186#8955—611nomaximal, Sylow
187C22×C61—21no—
188C22×C61—21no—
189C22×C61#38611yescharacteristic
190C22×C61#43511yescharacteristic
191C22×C61#43611yescharacteristic
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—42no—
199C4×C61—81no—
200C4×C61#40711yescharacteristic
201C4×C61#40811yescharacteristic
202C4×C61#43511yescharacteristic
203C4×C61#43611yescharacteristic
204C4×C61#45511yescharacteristic
205C4×C61#45611yescharacteristic
206Dic61—41no—
207Dic61—41no—
208Dic61—41no—
209#2989—611no—
210C4×#137—611no—
211#1984D6111yescharacteristic, complemented
212#1479—611no—
213#1476—611no—
214#1283—611no—
215#1278—611no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61#187011yescharacteristic
219C2×C61#188111yescharacteristic
220C2×C61#188211yescharacteristic
221D61—81no—
222C2×#137—611no—
223C4×#41—611no—
224C2×C4×Q8C2×D6111yescharacteristic
225#446—1221no—
226#441—1221no—
227#440—1221no—
228C4×Q16—1221no—
229C4×SD16—1221no—
230#436—1221no—
231#435—1222no—
232#432—1221no—
233#431—611no—
234#431—611no—
235#428—611no—
236#423—1221no—
237C2×C4⋊C8C2×D6111yescharacteristic
238#419—611no—
239#417—611no—
240C4×M16—611no—
241C2×C4×C8C2×D6111yescharacteristic
242#336—22no—
243Q8⋊C8—1221no—
244Q8⋊C8—1221no—
245Q8⋊C8—1221no—
246D4⋊C8—1221no—
247C61#895511yescharacteristic, complemented, Sylow
248C2×#41—611no—
249C22×Q8C4×D6111yescharacteristic
250#137—1222no—
251#137—1222no—
252C2×Q16—1221no—
253C2×SD16—1221no—
254C2×M16—611no—
255C2×M16—611no—
256C2×M16—1222no—
257C22×C8—21no—
258C22×C8C22⋊D6112yes—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8—611no—
264C4×Q8—611no—
265C4×D4—611no—
266C4×D4—611no—
267C4×D4—1221no—
268C4×D4—1221no—
269#117—611no—
270#117—1221no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4C4×D6111yescharacteristic
273C2×C42—21no—
274C2×C42—1221no—
275C2×C42C22×D6111yescharacteristic
276#107—1221no—
277#106—1221no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—611no—
281C4⋊C8—611no—
282C4⋊C8—1222no—
283C4⋊C8—1221no—
284#103—1221no—
285#103—1221no—
286#103—1221no—
287#102—1221no—
288C22⋊C8—1222no—
289C22⋊C8—1221no—
290C22⋊C8—1221no—
291#97—1222no—
292#97—1221no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8—1221no—
296C4×C8—1221no—
297C4×C8—1221no—
298#41—1221no—
299#41—1221no—
300#41—1221no—
301#41—1221no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—611no—
308C2×Q8#1175818912yescomplemented
309C2×D4—611no—
310C2×D4—1221no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4C2×C4×D6111yescharacteristic
317C22×C4#1175822211yescharacteristic
318C22×C4C2×C22⋊D6111yescharacteristic
319Q16—1224no—
320SD16—1224no—
321M16—612no—
322M16—1221no—
323M16—1221no—
324M16—1221no—
325M16—4882no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—42no—
331C2×C8—1221no—
332C2×C8—1221no—
333C2×C8—1221no—
334C2×C8—1221no—
335C2×C8—2441no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—611no—
341C4⋊C4—611no—
342C4⋊C4—1221no—
343C4⋊C4—1221no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C22⋊C4—1221no—
347C42—41no—
348C42—41no—
349C42—1221no—
350C42—1221no—
351C42—1221no—
352C42D4×D6111yescharacteristic
353C42D4×D6111yescharacteristic
354C42D4×D6111yescharacteristic
355C42#1175822411yescharacteristic
356C23—1221no—
357C23C4×C22⋊D6111yescharacteristic
358Q8—22no—
359Q8—22no—
360Q8—41no—
361Q8—41no—
362Q8—1221no—
363Q8—1221no—
364D4—1221no—
365D4—1221no—
366D4—2441no—
367D4—2441no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—4881no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4C22⋊C4×D6111yescharacteristic
385C2×C4#1451973711yescharacteristic
386C2×C4#1451974511yescharacteristic
387C2×C4#1451974811yescharacteristic
388C2×C4#1451975011yescharacteristic
389C2×C4#1451975911yescharacteristic
390C2×C4M16×D6111yescharacteristic
391C2×C4C2×#1175818911yescharacteristic
392C2×C4#1451978311yescharacteristic
393C2×C4#1451978511yescharacteristic
394C8—42no—
395C8—42no—
396C8—1222no—
397C8—4881no—
398C8—2441no—
399C8—2441no—
400C8—2441no—
401C22—21no—
402C22—21no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22#1683963811yescharacteristic
407C22#1683983311yescharacteristic
408C22#1683983811yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—42no—
413C4—81no—
414C4—2441no—
415C4—2441no—
416C4—2441no—
417C4#1683972411yescharacteristic
418C4#1683972711yescharacteristic
419C4#1683983011yescharacteristic
420C4#1683983711yescharacteristic
421C4#1683993911yescharacteristic
422C4#1683994411yescharacteristic
423C2—21no—
424C2—21no—
425C2—4881no—
426C2#2144611311yescharacteristic
427C2#2144618411yescharacteristic
428C2#2144619111yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1984C2
socleC22×C61#386
prime radicalC2×#11758222C2×C4
cosocleC2×C42×C61C23
hypercenter#1984D61
hypocenterC61#8955
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
3. #21444214C2semidirect
5. #21443669C2semidirect
6. #21443656C2semidirect
7. C61×#1984C2semidirect
88. C2×Q8×C61M16semidirect
134. #11758194M16semidirect
211. #1984D61semidirect
247. C61#8955semidirect
308. C2×Q8#11758189semidirect

Maximal subgroups

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

subgroupindex
#214549372
C4×#145198082
#214442142
#214442022
#214436692
#214436562
C61×#19842
#895561