Finite Group Databasebeta

← #29575488

Subgroups — #29575488

Order 15616.

514 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#21454775C211yesmaximal, characteristic
2C4×#14519810C211yesmaximal, characteristic
3#21444204C211yesmaximal, characteristic
4C2×#16839492C211yesmaximal, characteristic, complemented
5#21444142C211yesmaximal, characteristic, complemented
6#21443657C211yesmaximal, characteristic, complemented
7C61×#1283C211yesmaximal, characteristic, complemented
8C2×#14519810C411yescharacteristic
9C4×#11758222C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11#16839886—21no—
12#16839870—21no—
13#16839864—21no—
14C4×Dic244—21no—
15C4×#11758190—21no—
16#16839827—21no—
17#16839825—22no—
18#16839815C2211yescharacteristic
19#16839813—21no—
20#16839804C411yescharacteristic
21#16839772C411yescharacteristic
22#16839764C411yescharacteristic
23C2×C4×#92418C2211yescharacteristic
24C4×C8×D61—21no—
25#16839492—21no—
26#16839492—21no—
27#16839492—21no—
28#16839489—21no—
29#16839487—22no—
30C61×#431C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C4×M16×C61C2211yescharacteristic
33C2×#11758222C2×C411yescharacteristic
34C22×Dic122C2×C411yescharacteristic
35#14519810—22no—
36#14519810C814yescomplemented
37C2×Dic244—21no—
38C2×#11758190—21no—
39C22×#92418—21no—
40C2×C8×D61—22no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×Dic122D411yescharacteristic
46C4×Dic122D411yescharacteristic
47C4×D244D411yescharacteristic
48C4×D244D411yescharacteristic
49C4×C22⋊D61—21no—
50C4×C22⋊D61—21no—
51#14519736C2×C411yescharacteristic
52#14519734—21no—
53C2×C4⋊Dic61C2×C411yescharacteristic
54C2×#11758196—21no—
55C2×C4×Dic61—21no—
56C42×D61—21no—
57#14519711—21no—
58#14519709—21no—
59C4⋊#92418—21no—
60#14519706—22no—
61#14519702—21no—
62#14519702—21no—
63#14519702—21no—
64#14519699—21no—
65C22⋊#92418—21no—
66#14519689—22no—
67C4×#92418—21no—
68C4×#92418—21no—
69C4×#92418D411yescharacteristic
70C4×#92418D411yescharacteristic
71C8×Dic61—22no—
72C2×M16×C61C2×C411yescharacteristic
73C2×M16×C61C2×C411yescharacteristic
74C22×C8×C61—21no—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61—21no—
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C22⋊C8×C61D412yes—
80#97×C61—21no—
81C4×C8×C61—21no—
82C4×C8×C61—21no—
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C2×C22⋊D61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89#11758222—21no—
90#11758222—21no—
91#11758222C2×C812yes—
92#11758222M1612yes—
93C2×D244C22⋊C411yescharacteristic
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×Dic122—21no—
98C2×Dic122—21no—
99C2×Dic122—21no—
100C2×Dic122—21no—
101C2×Dic122—21no—
102C2×Dic122C22⋊C411yescharacteristic
103C2×Dic122C2×C812yescomplemented
104M16×C61—21no—
105M16×C61—21no—
106M16×C61—21no—
107M16×C61C2×C812yescomplemented
108C2×C8×C61—21no—
109C2×C8×C61—21no—
110C2×C8×C61—22no—
111C2×C8×C61—41no—
112C2×C8×C61—81no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117C22⋊Dic61—21no—
118#11758198—21no—
119#11758198—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61C22⋊C411yescharacteristic
123C4⋊Dic61C22⋊C411yescharacteristic
124#11758196—21no—
125#11758196—21no—
126#11758196—41no—
127#11758196—41no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—41no—
132C4×Dic61—41no—
133C2×#92418—21no—
134C2×#92418—21no—
135C2×#92418—42no—
136C2×#92418—41no—
137Dic244—24no—
138#11758190—24no—
139C8×D61—44no—
140C23×C61C4×D411yescharacteristic
141C22×D61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61C2×C22⋊C411yescharacteristic
146C2×C4×C61C4×D411yescharacteristic
147C2×C4×C61#12011yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12311yescharacteristic
151C2×C4×C61C22×C811yescharacteristic
152C2×C4×C61C2×M1611yescharacteristic
153C2×C4×C61#13111yescharacteristic
154C2×C4×C61#13111yescharacteristic
155C22⋊D61—22no—
156C22⋊D61—22no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—22no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—81no—
165D244—21no—
166D244C22⋊C812yes—
167C4×D61—22no—
168C4×D61—22no—
169C4×D61—42no—
170C4×D61—41no—
171C4×D61—41no—
172Dic122—21no—
173Dic122—22no—
174Dic122—22no—
175Dic122—41no—
176Dic122—41no—
177Dic122C22⋊C812yes—
178C8×C61—22no—
179C8×C61—42no—
180C8×C61—41no—
181C8×C61—81no—
182#92418—22no—
183#92418—41no—
184#92418—81no—
185#9096—611nomaximal, Sylow
186C22×C61—21no—
187C22×C61—21no—
188C22×C61#38611yescharacteristic
189C22×C61C8×D411yescharacteristic
190C22×C61#43511yescharacteristic
191C2×D61—22no—
192C2×D61—41no—
193C2×D61—41no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61C2×C22⋊C811yescharacteristic
198C4×C61#40811yescharacteristic
199C4×C61C8×D411yescharacteristic
200C4×C61#43511yescharacteristic
201C4×C61#47111yescharacteristic
202C4×C61#47311yescharacteristic
203Dic61—22no—
204Dic61—42no—
205Dic61—41no—
206Dic61—41no—
207Dic61—81no—
208C8×#41—611no—
209C4×#137—611no—
210#1477—611no—
211C2×Q8⋊C8—611no—
212#1461—611no—
213#1283D6111yescharacteristic, complemented
214#1278—611no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61#186911yescharacteristic
218C2×C61#190611yescharacteristic
219C2×C61#190811yescharacteristic
220D61—42no—
221C2×#137—611no—
222C4×#41—611no—
223C2×C4×Q8—611no—
224C8×Q8—1221no—
225#441—1221no—
226#440—1221no—
227C4×Q16—1221no—
228C4×SD16—1221no—
229C8×D4—1221no—
230C8×D4—1222no—
231#431—611no—
232#431—1221no—
233#431C2×D6111yescharacteristic
234#428—611no—
235C2×C4⋊C8C2×D6111yescharacteristic
236#419—611no—
237#417—611no—
238C4×M16C2×D6111yescharacteristic
239C2×C4×C8—611no—
240C2×C4×C8—1221no—
241Q8⋊C8—1221no—
242Q8⋊C8—1221no—
243Q8⋊C8—1221no—
244D4⋊C8—1221no—
245#324—1222no—
246C61#909611yescharacteristic, complemented, Sylow
247C2×#41—611no—
248C22×Q8—611no—
249#137—614no—
250#137—1222no—
251C2×Q16—1221no—
252C2×SD16—1221no—
253C2×M16C4×D6111yescharacteristic
254C2×M16C4×D6111yescharacteristic
255C22×C8—21no—
256C22×C8—1222no—
257C22×C8—1221no—
258C4×Q8—611no—
259C4×Q8—611no—
260C4×Q8—1221no—
261C4×Q8—1221no—
262C4×Q8—1221no—
263C4×Q8—1221no—
264C4×D4—611no—
265C4×D4—611no—
266C4×D4—1221no—
267C4×D4—1221no—
268#117—611no—
269#117—1221no—
270C2×C4⋊C4—611no—
271C2×C4⋊C4—1221no—
272C2×C42—1221no—
273C2×C42—1221no—
274C2×C42C22×D6111yescharacteristic
275#107—1221no—
276#106—1221no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—1222no—
281C4⋊C8—1221no—
282#103—1221no—
283#103—1221no—
284#103—1221no—
285#102—1221no—
286C22⋊C8—1222no—
287C22⋊C8—1221no—
288C22⋊C8D24412yes—
289#97—21no—
290C4×C8—21no—
291C4×C8—21no—
292C4×C8—611no—
293C4×C8—611no—
294C4×C8—1222no—
295C4×C8—1221no—
296C4×C8—1221no—
297#41—612no—
298#41—612no—
299#41—1221no—
300#41—1221no—
301C2×Q8—611no—
302C2×Q8—612no—
303C2×Q8—1221no—
304C2×Q8—1221no—
305C2×Q8—1221no—
306C2×Q8—1221no—
307C2×Q8—1221no—
308C2×D4—611no—
309C2×D4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4C2×C4×D6111yescharacteristic
316C22×C4C2×D24411yescharacteristic
317C22×C4#1175822211yescharacteristic
318Q16—1224no—
319SD16—1224no—
320M16—21no—
321M16—21no—
322M16—21no—
323M16C8×D6112yescomplemented
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—81no—
329C2×C8—1221no—
330C2×C8—1221no—
331C2×C8—2444no—
332C2×C8—2442no—
333C2×C8—2441no—
334C4⋊C4—611no—
335C4⋊C4—611no—
336C4⋊C4—1221no—
337C4⋊C4—1221no—
338C4⋊C4—1221no—
339C4⋊C4—1221no—
340C4⋊C4—2441no—
341C4⋊C4—2441no—
342C22⋊C4—1221no—
343C22⋊C4—1221no—
344C22⋊C4—1221no—
345C42—1221no—
346C42—1221no—
347C42—1221no—
348C42—2441no—
349C42—2441no—
350C42D4×D6111yescharacteristic
351C42D4×D6111yescharacteristic
352C42D4×D6111yescharacteristic
353C42#1175822611yescharacteristic
354C23—1221no—
355C23C4×D24411yescharacteristic
356Q8—612no—
357Q8—1221no—
358Q8—1222no—
359Q8—1222no—
360Q8—2441no—
361Q8—2441no—
362D4—612no—
363D4—1222no—
364D4—1222no—
365D4—1221no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—1221no—
370C2×C4—1222no—
371C2×C4—1222no—
372C2×C4—1222no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—4881no—
376C2×C4—2442no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4C22⋊C4×D6111yescharacteristic
383C2×C4#1451973911yescharacteristic
384C2×C4#1451974711yescharacteristic
385C2×C4#1451975011yescharacteristic
386C2×C4#1451975211yescharacteristic
387C2×C4#1451976211yescharacteristic
388C2×C4C2×C8×D6111yescharacteristic
389C2×C4M16×D6111yescharacteristic
390C2×C4#1451978311yescharacteristic
391C2×C4#1451978511yescharacteristic
392C8—22no—
393C8—42no—
394C8—41no—
395C8—81no—
396C8—1222no—
397C8—4881no—
398C8—2441no—
399C22—21no—
400C22—21no—
401C22—1222no—
402C22—2441no—
403C22—2441no—
404C22#1683964011yescharacteristic
405C22C8×D24411yescharacteristic
406C22#1683983511yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—1222no—
411C4—4881no—
412C4—2441no—
413C4—2441no—
414C4—2442no—
415C4C22⋊C8×D6111yescharacteristic
416C4#1683972711yescharacteristic
417C4#1683982711yescharacteristic
418C4#1683983211yescharacteristic
419C4#1684002411yescharacteristic
420C4#1684003611yescharacteristic
421C2—21no—
422C2—21no—
423C2—2442no—
424C2#2144611011yescharacteristic
425C2#2144632111yescharacteristic
426C2#2144633511yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1283C2
socleC22×C61#386
prime radicalC2×#11758222C2×C4
cosocleC2×C42×C61C23
hypercenter#1283D61
hypocenterC61#9096
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
4. C2×#16839492C2semidirect
5. #21444142C2semidirect
6. #21443657C2semidirect
7. C61×#1283C2semidirect
36. #14519810C8semidirect
103. C2×Dic122C2×C8semidirect
107. M16×C61C2×C8semidirect
213. #1283D61semidirect
246. C61#9096semidirect
323. M16C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214547752
C4×#145198102
#214442042
C2×#168394922
#214441422
#214436572
C61×#12832
#909661