Finite Group Databasebeta

← #29575498

Subgroups — #29575498

Order 15616.

488 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454780C211yesmaximal, characteristic
2C4×#14519808C211yesmaximal, characteristic
3#21444207C211yesmaximal, characteristic
4C2×Q8⋊#92418C211yesmaximal, characteristic, complemented
5#21443668C211yesmaximal, characteristic, complemented
6#21443655C211yesmaximal, characteristic, complemented
7C61×#1461C211yesmaximal, 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#16839830—22no—
17#16839813—21no—
18#16839802C411yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20#16839771C411yescharacteristic
21#16839761C411yescharacteristic
22C4×#11758194C2211yescharacteristic
23C4×#11758189—21no—
24C2×C4×#92418C2211yescharacteristic
25#16839494—21no—
26Q8⋊#92418—21no—
27Q8⋊#92418—21no—
28#16839491—21no—
29C2×C4×Q8×C61C2211yescharacteristic
30C61×#431C2211yescharacteristic
31C61×#431C2211yescharacteristic
32C61×#324—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—
41C22×#92418—21no—
42C22×#92418—21no—
43C4×Dic122D411yescharacteristic
44C4×Dic122D411yescharacteristic
45C4×D244D411yescharacteristic
46C4×D244D411yescharacteristic
47C4×C22⋊D61—21no—
48C4×C22⋊D61—21no—
49#14519736C2×C411yescharacteristic
50#14519734—21no—
51C42×D61—21no—
52#14519710—21no—
53#14519708—21no—
54C4⋊#92418—21no—
55C4⋊#92418—21no—
56#14519706—22no—
57#14519701—21no—
58#14519701—21no—
59#14519700—21no—
60#14519697—21no—
61#14519689—22no—
62#14519688—21no—
63#14519687—22no—
64C4×#92418—21no—
65C4×#92418—21no—
66C4×#92418D411yescharacteristic
67C4×#92418D411yescharacteristic
68C22×Q8×C61C2×C411yescharacteristic
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71C4×Q8×C61—21no—
72C4×Q8×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61C2×C411yescharacteristic
75C2×C42×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61D412yes—
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—41no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C42×C61—41no—
111C42×C61—41no—
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61#4111yescharacteristic
116C22⋊Dic61—21no—
117#11758202—24no—
118#11758201—24no—
119#11758198—21no—
120#11758198—21no—
121C4⋊Dic61C22⋊C411yescharacteristic
122C4⋊Dic61C22⋊C411yescharacteristic
123#11758196—21no—
124#11758196—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128#11758194—21no—
129#11758194—21no—
130#11758194—21no—
131#11758194M1612yescomplemented
132C2×#92418—21no—
133C2×#92418—21no—
134C2×#92418—21no—
135C2×#92418—21no—
136C2×#92418—42no—
137C2×#92418—41no—
138C2×#92418—81no—
139#11758189—44no—
140C23×C61C4×D411yescharacteristic
141C22×D61—21no—
142Q8×C61—22no—
143Q8×C61—22no—
144Q8×C61—41no—
145Q8×C61—41no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—22no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—81no—
154C2×C4×C61C2×C22⋊C411yescharacteristic
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12311yescharacteristic
160C2×C4×C61C2×M1611yescharacteristic
161C2×C4×C61C2×M1611yescharacteristic
162C2×C4×C61#13111yescharacteristic
163C2×C4×C61#13111yescharacteristic
164C22⋊D61—41no—
165C22⋊D61—41no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169D244—21no—
170D244—21no—
171C4×D61—42no—
172C4×D61—41no—
173C4×D61—41no—
174C4×D61—41no—
175C4×D61—41no—
176Dic122—21no—
177Dic122—21no—
178C8×C61—42no—
179C8×C61—81no—
180#92418—22no—
181#92418—22no—
182#92418—41no—
183#92418—41no—
184#92418—81no—
185#9098—611nomaximal, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61#38611yescharacteristic
189C22×C61#43511yescharacteristic
190C22×C61#43611yescharacteristic
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—42no—
198C4×C61—81no—
199C4×C61#40711yescharacteristic
200C4×C61#40811yescharacteristic
201C4×C61#43511yescharacteristic
202C4×C61#43611yescharacteristic
203C4×C61#47111yescharacteristic
204C4×C61#47311yescharacteristic
205Dic61—41no—
206Dic61—41no—
207Dic61—41no—
208#2965—611no—
209C4×#137—611no—
210#1477—611no—
211C2×Q8⋊C8—611no—
212#1461D6111yescharacteristic, complemented
213#1283—611no—
214#1278—611no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61#187011yescharacteristic
218C2×C61#190611yescharacteristic
219C2×C61#190811yescharacteristic
220D61—81no—
221C2×#137—611no—
222C4×#41—611no—
223C2×C4×Q8C2×D6111yescharacteristic
224#446—1221no—
225#441—1221no—
226#440—1221no—
227C4×Q16—1221no—
228C4×SD16—1221no—
229#436—1221no—
230#435—1222no—
231#431—1221no—
232#431C2×D6111yescharacteristic
233#431C2×D6111yescharacteristic
234#428—611no—
235C2×C4⋊C8—611no—
236#419—611no—
237#417—611no—
238C4×M16—611no—
239C4×M16—1221no—
240C2×C4×C8—611no—
241Q8⋊C8—1221no—
242Q8⋊C8—1221no—
243Q8⋊C8—1221no—
244D4⋊C8—1221no—
245#324—22no—
246C61#909811yescharacteristic, complemented, Sylow
247C2×#41—611no—
248C22×Q8C4×D6111yescharacteristic
249#137—1222no—
250#137—1222no—
251C2×Q16—1221no—
252C2×SD16—1221no—
253C2×M16—611no—
254C2×M16—611no—
255C2×M16—1222no—
256C22×C8—1221no—
257C22×C8—1221no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—611no—
263C4×Q8—611no—
264C4×D4—611no—
265C4×D4—611no—
266C4×D4—1221no—
267C4×D4—1221no—
268#117—611no—
269#117—1221no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C4×D6111yescharacteristic
272C2×C42—21no—
273C2×C42—1221no—
274C2×C42C22×D6111yescharacteristic
275#107—1221no—
276#106—1221no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—1222no—
280C4⋊C8—1221no—
281C4⋊C8—1221no—
282#103—1221no—
283#103—1221no—
284#103—1221no—
285#102—1221no—
286C22⋊C8—21no—
287C22⋊C8—1222no—
288C22⋊C8C22⋊D6112yes—
289#97—1222no—
290#97—1221no—
291C4×C8—21no—
292C4×C8—21no—
293C4×C8—611no—
294C4×C8—611no—
295C4×C8—1221no—
296C4×C8—1221no—
297#41—1221no—
298#41—1221no—
299#41—1221no—
300#41—1221no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—611no—
307C2×Q8#1175818912yescomplemented
308C2×D4—611no—
309C2×D4—1221no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4C2×C4×D6111yescharacteristic
316C22×C4#1175822211yescharacteristic
317C22×C4C2×C22⋊D6111yescharacteristic
318Q16—1224no—
319SD16—1224no—
320M16—612no—
321M16—1221no—
322M16—1221no—
323M16—1221no—
324M16—2444no—
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—1221no—
328C2×C8—1221no—
329C2×C8—1221no—
330C2×C8—1221no—
331C2×C8—4881no—
332C2×C8—2442no—
333C2×C8—2441no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—611no—
339C4⋊C4—611no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C22⋊C4—1221no—
343C22⋊C4—1221no—
344C22⋊C4—1221no—
345C42—41no—
346C42—41no—
347C42—1221no—
348C42—1221no—
349C42—1221no—
350C42D4×D6111yescharacteristic
351C42D4×D6111yescharacteristic
352C42D4×D6111yescharacteristic
353C42#1175822411yescharacteristic
354C23—1221no—
355C23C4×C22⋊D6111yescharacteristic
356Q8—22no—
357Q8—22no—
358Q8—41no—
359Q8—41no—
360Q8—1221no—
361Q8—1221no—
362D4—1221no—
363D4—1221no—
364D4—2441no—
365D4—2441no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—2442no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4C22⋊C4×D6111yescharacteristic
383C2×C4#1451973711yescharacteristic
384C2×C4#1451974511yescharacteristic
385C2×C4#1451974811yescharacteristic
386C2×C4#1451975011yescharacteristic
387C2×C4#1451975911yescharacteristic
388C2×C4M16×D6111yescharacteristic
389C2×C4C2×#1175818911yescharacteristic
390C2×C4#1451978311yescharacteristic
391C2×C4#1451978511yescharacteristic
392C8—42no—
393C8—81no—
394C8—1222no—
395C8—1222no—
396C8—4881no—
397C8—2441no—
398C8—2441no—
399C22—21no—
400C22—21no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22#1683963811yescharacteristic
405C22#1683983311yescharacteristic
406C22#1683983811yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—42no—
411C4—81no—
412C4—2441no—
413C4—2441no—
414C4—2441no—
415C4#1683972411yescharacteristic
416C4#1683972711yescharacteristic
417C4#1683983011yescharacteristic
418C4#1683983711yescharacteristic
419C4#1684002811yescharacteristic
420C4#1684003611yescharacteristic
421C2—21no—
422C2—21no—
423C2—4881no—
424C2#2144611311yescharacteristic
425C2#2144631711yescharacteristic
426C2#2144633111yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1461C2
socleC22×C61#386
prime radicalC2×#11758222C2×C4
cosocleC2×C42×C61C23
hypercenter#1461D61
hypocenterC61#9098
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
4. C2×Q8⋊#92418C2semidirect
5. #21443668C2semidirect
6. #21443655C2semidirect
7. C61×#1461C2semidirect
88. C2×Q8×C61M16semidirect
131. #11758194M16semidirect
212. #1461D61semidirect
246. C61#9098semidirect
307. C2×Q8#11758189semidirect

Maximal subgroups

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

subgroupindex
#214547802
C4×#145198082
#214442072
C2×Q8⋊#924182
#214436682
#214436552
C61×#14612
#909861