Finite Group Databasebeta

← #29573185

Subgroups — #29573185

Order 15616.

432 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454786C211yesmaximal, characteristic
2#21445839C211yesmaximal, characteristic
3C4×#14519710C211yesmaximal, characteristic, complemented
4#21444574C211yesmaximal, characteristic, complemented
5#21443722C211yesmaximal, characteristic, complemented
6#21443720C211yesmaximal, characteristic, complemented
7C61×#1806C211yesmaximal, characteristic
8#16839893C411yescharacteristic, complemented
9#16839893C411yescharacteristic, complemented
10#16839840C411yescharacteristic, complemented
11#16839840C411yescharacteristic, complemented
12#16839834—21no—
13#16839834—21no—
14#16839815—21no—
15#16839815C2211yescharacteristic
16C2×#14519710—21no—
17#16839786C2211yescharacteristic
18C2×#14519704—21no—
19C4×#11758194—21no—
20C2×C4×#92418C2211yescharacteristic
21C4×C4⋊Dic61C2211yescharacteristic
22#16839524—21no—
23#16839521—21no—
24#16839512—21no—
25#16839512—21no—
26C4×#41×C61C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C2×#104×C61—21no—
29C4×C4⋊C4×C61C2211yescharacteristic
30C61×#339—21no—
31C2×#11758194—21no—
32C2×#11758194—21no—
33C2×#11758194—21no—
34C22×#92418D411yescharacteristic
35C22×#92418D411yescharacteristic
36C2×C4⋊Dic61—21no—
37C2×C4×Dic61—21no—
38#14519710—24no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418C2×C411yescharacteristic
44C4⋊#92418C2×C411yescharacteristic
45#14519704—42no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48C22⋊#92418—21no—
49#14519688—21no—
50#14519688—21no—
51C4×#92418—21no—
52C4×#92418C2×C411yescharacteristic
53C4×#92418C2×C411yescharacteristic
54C4×#92418D411yescharacteristic
55C4×#92418D411yescharacteristic
56#14519684—21no—
57C2×#41×C61D411yescharacteristic
58C2×M16×C61—21no—
59C4×Q8×C61C2×C411yescharacteristic
60C4×Q8×C61Q811yescharacteristic
61C4×D4×C61—21no—
62C4×D4×C61—21no—
63C4×D4×C61C2×C411yescharacteristic
64C4×D4×C61Q811yescharacteristic
65#117×C61—21no—
66#117×C61D411yescharacteristic
67C2×C4⋊C4×C61—21no—
68C2×C42×C61—21no—
69C2×C42×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73#104×C61—42no—
74#95×C61—21no—
75#41×C61—21no—
76#41×C61—21no—
77#41×C61—21no—
78#41×C61—21no—
79C2×Q8×C61C4⋊C411yescharacteristic
80C2×D4×C61—21no—
81C2×D4×C61C4⋊C411yescharacteristic
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—41no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×Dic61—41no—
90M16×C61—41no—
91M16×C61—41no—
92C2×C8×C61—41no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61C4⋊C411yescharacteristic
98C4⋊C4×C61C4⋊C411yescharacteristic
99C22⋊C4×C61—21no—
100C22⋊C4×C61—21no—
101C22⋊C4×C61—21no—
102C42×C61—21no—
103C42×C61—21no—
104C42×C61—21no—
105C42×C61—41no—
106C42×C61—41no—
107C42×C61C22×C411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×Q811yescharacteristic
110C42×C61#4111yescharacteristic
111C4⋊Dic61—22no—
112C4⋊Dic61—41no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115#11758194—42no—
116#11758194—42no—
117#11758194—41no—
118#11758194—41no—
119C2×#92418—22no—
120C2×#92418—21no—
121C2×#92418—21no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418C22⋊C411yescharacteristic
125C2×#92418C22⋊C411yescharacteristic
126C2×#92418C22⋊C411yescharacteristic
127C2×#92418C22⋊C411yescharacteristic
128C23×C61—21no—
129C23×C61#12111yescharacteristic
130Q8×C61—21no—
131Q8×C61—21no—
132D4×C61—21no—
133D4×C61—21no—
134D4×C61—41no—
135D4×C61—41no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—42no—
148C2×C4×C61—81no—
149C2×C4×C61—81no—
150C2×C4×C61C2×C22⋊C411yescharacteristic
151C2×C4×C61C2×C4⋊C411yescharacteristic
152C2×C4×C61#11711yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61C22⋊Q811yescharacteristic
155C2×C4×C61C22⋊Q811yescharacteristic
156C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C61#13711yescharacteristic
159C2×C4×C61#13711yescharacteristic
160C2×Dic61—42no—
161C2×Dic61—81no—
162C2×Dic61—81no—
163C8×C61—81no—
164#92418—21no—
165#92418—21no—
166#92418—21no—
167#92418—41no—
168#92418—41no—
169#92418—81no—
170#92418#10412yescomplemented
171#8668—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61#38011yescharacteristic
178C22×C61#46911yescharacteristic
179C22×C61#47011yescharacteristic
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—82no—
187C4×C61C2×#10411yescharacteristic
188C4×C61#42111yescharacteristic
189C4×C61#42811yescharacteristic
190C4×C61#42811yescharacteristic
191C4×C61#46811yescharacteristic
192C4×C61#46811yescharacteristic
193Dic61—82no—
194#2965—611no—
195#1806—611no—
196#1806D6111yescharacteristic
197C4×#107—611no—
198#1566—611no—
199#1303—611no—
200#1303—611no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—81no—
204C2×C61#180611yescharacteristic
205C2×C61#180911yescharacteristic
206C2×C61#181411yescharacteristic
207C4×#41C2×D6111yescharacteristic
208#446—611no—
209#446—611no—
210#436—611no—
211#436—611no—
212#435—1221no—
213#435—1221no—
214#431—611no—
215#431—1221no—
216C2×#107—1221no—
217#423—611no—
218#423C2×D6111yescharacteristic
219C2×#104—21no—
220C2×#104—1221no—
221C4×M16—1221no—
222C2×C4×C8—611no—
223C4×C4⋊C4—611no—
224C4×C4⋊C4C2×D6111yescharacteristic
225#340—1221no—
226#339—21no—
227#339—1221no—
228#334—1221no—
229#334—1221no—
230C61#866811yescharacteristic, complemented, Sylow
231C2×#41C22⋊D6111yescharacteristic
232C2×M16—21no—
233C2×M16—1221no—
234C2×M16—1221no—
235C2×M16—1221no—
236C22×C8—611no—
237C22×C8—611no—
238C4×Q8Dic12211yescharacteristic
239C4×Q8C4×D6111yescharacteristic
240C4×D4—21no—
241C4×D4—21no—
242C4×D4Dic12211yescharacteristic
243C4×D4C4×D6111yescharacteristic
244#117—21no—
245#117C22⋊D6111yescharacteristic
246C2×C4⋊C4—21no—
247C2×C4⋊C4—1221no—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42—1221no—
251C2×C42C22×D6111yescharacteristic
252#107—1224no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—611no—
256C4⋊C8—611no—
257C4⋊C8—1221no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261#104—42no—
262#104—2442no—
263C22⋊C8—1221no—
264C22⋊C8—1221no—
265C22⋊C8—1221no—
266#97—1221no—
267#97—1221no—
268C4×C8—611no—
269C4×C8—611no—
270C4×C8—611no—
271C4×C8—611no—
272C4×C8—1221no—
273#95—21no—
274#95—1221no—
275#41—21no—
276#41—21no—
277#41—21no—
278#41—21no—
279C2×Q8#1175819611yescharacteristic
280C2×D4—21no—
281C2×D4#1175819611yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—2441no—
287C22×C4D4×D6111yescharacteristic
288C22×C4#1175822411yescharacteristic
289C22×C4C2×C22⋊D6111yescharacteristic
290M16—41no—
291M16—41no—
292M16—2442no—
293M16—2442no—
294M16—2441no—
295M16—2441no—
296C2×C8—41no—
297C2×C8—611no—
298C2×C8—611no—
299C2×C8—611no—
300C2×C8—611no—
301C2×C8—1222no—
302C2×C8—1221no—
303C2×C8—1221no—
304C2×C8—2441no—
305C2×C8—2441no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—1222no—
311C4⋊C4—2441no—
312C4⋊C4#1175819611yescharacteristic
313C4⋊C4#1175819611yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—41no—
321C42—41no—
322C42—2441no—
323C42—2441no—
324C42C2×Dic12211yescharacteristic
325C42C2×C4×D6111yescharacteristic
326C42D4×D6111yescharacteristic
327C42#1175822411yescharacteristic
328C23—21no—
329C23#1451974911yescharacteristic
330Q8—21no—
331Q8—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—4881no—
351C2×C4—4881no—
352C2×C4—2442no—
353C2×C4C22⋊C4×D6111yescharacteristic
354C2×C4C2×#1175819611yescharacteristic
355C2×C4#1451973311yescharacteristic
356C2×C4#1451974911yescharacteristic
357C2×C4#1451975411yescharacteristic
358C2×C4#1451975411yescharacteristic
359C2×C4#1451980211yescharacteristic
360C2×C4#1451980311yescharacteristic
361C2×C4#1451980711yescharacteristic
362C2×C4#1451980811yescharacteristic
363C8—81no—
364C8—612no—
365C8—1221no—
366C8—1221no—
367C8—1221no—
368C8—4881no—
369C8—2441no—
370C8—2441no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22#1683962011yescharacteristic
377C22#1684001311yescharacteristic
378C22#1684001811yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—82no—
386C4—4882no—
387C4#104×D6111yescharacteristic
388C4#1683977711yescharacteristic
389C4#1683980211yescharacteristic
390C4#1683980511yescharacteristic
391C4#1684000611yescharacteristic
392C4#1684001011yescharacteristic
393C2—21no—
394C2—21no—
395C2—81no—
396C2#2144583711yescharacteristic
397C2#2144585011yescharacteristic
398C2#2144587111yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1806C2
socleC22×C61#380
prime radicalC2×#41×C61D4
cosocleC2×C42×C61C23
hypercenter#1806D61
hypocenterC61#8668
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
3. C4×#14519710C2semidirect
4. #21444574C2semidirect
5. #21443722C2semidirect
6. #21443720C2semidirect
8. #16839893C4semidirect
9. #16839893C4semidirect
10. #16839840C4semidirect
11. #16839840C4semidirect
170. #92418#104semidirect
230. C61#8668semidirect

Maximal subgroups

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

subgroupindex
#214547862
#214458392
C4×#145197102
#214445742
#214437222
#214437202
C61×#18062
#866861