Finite Group Databasebeta

← #14738604

Subgroups — #14738604

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079983C212yesmaximal
2#13077591C211yesmaximal, characteristic
3#13068119C212yesmaximal, complemented
4#13068112C212yesmaximal, complemented
5#13068017C211yesmaximal, characteristic, complemented
6#13068012C211yesmaximal, characteristic, complemented
7#13068007C211yesmaximal, characteristic, complemented
8#13068002C211yesmaximal, characteristic, complemented
9#13067375C211yesmaximal, characteristic, complemented
10#13067346C212yesmaximal, complemented
11C11×#3160C211yesmaximal, characteristic, complemented
12C11×#533C2212yes—
13#10623010C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#500C2211yescharacteristic
16C11×#499—21no—
17C11×#499—21no—
18C11×#498C2212yes—
19C11×#427—21no—
20C11×#427—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23C8×C22⋊D11—21no—
24#10622704C2212yes—
25#10622703C2212yes—
26#10622697C2212yes—
27#10622696C2212yes—
28#10622665—22no—
29#10622662—22no—
30#10622641—22no—
31#10622635—22no—
32#10622539C2211yescharacteristic
33#10622537C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622184C2212yes—
43#10622184C2212yes—
44#10622096C2212yes—
45#10622096C2211yescharacteristic
46#10622096C2211yescharacteristic
47C22×C8×C11D411yescharacteristic
48C22×C8×C11D411yescharacteristic
49C11×C4⋊Q8C2312yes—
50C11×C4⋊Q8C2312yes—
51C11×#125—22no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C11×#117—22no—
57C2×C42×C11C2311yescharacteristic
58C2×#4326—22no—
59C2×#4325—22no—
60#66983D411yescharacteristic
61#66982—21no—
62C4×C22⋊D11—21no—
63#66977D411yescharacteristic
64C2×#4318—22no—
65C2×#4313—21no—
66C2×C8×D11—21no—
67#66929—21no—
68#66928D411yescharacteristic
69C4×D44C2311yescharacteristic
70#66925—21no—
71#66923D411yescharacteristic
72C4×Dic22C2311yescharacteristic
73C11×#107—21no—
74C11×#107—21no—
75C11×#107—21no—
76C11×#107—21no—
77C11×#106—22no—
78C11×#106—22no—
79C4×C8×C11D411yescharacteristic
80C4×C8×C11D411yescharacteristic
81C4×C8×C11C2311yescharacteristic
82C4×C8×C11C2311yescharacteristic
83#66899—22no—
84#66899—22no—
85C22⋊(C11⋊C8)—21no—
86(C2×D11)⋊C8—21no—
87(C2×D11)⋊C8—21no—
88#66879—21no—
89Dic11⋊C8—21no—
90Dic11⋊C8—21no—
91C8×Dic11—21no—
92#66874—22no—
93#66873—22no—
94#66872—22no—
95#66871—22no—
96C4⋊(C11⋊C8)—22no—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101#66867—21no—
102#19361—111nomaximal, Sylow
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—21no—
109C2×D44C2×D411yescharacteristic
110C2×C4×D11—21no—
111C2×Dic22C2×D411yescharacteristic
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—42no—
124C11×C22⋊C4—42no—
125C42×C11—42no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C42×C11C2411yescharacteristic
130C22⋊Dic11—21no—
131#4326—82no—
132#4325—82no—
133(C2×D11)⋊C4—21no—
134(C2×D11)⋊C4—21no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—21no—
137C4⋊Dic11C2×D411yescharacteristic
138C4⋊Dic11C2×D411yescharacteristic
139Dic11⋊C4—21no—
140Dic11⋊C4—21no—
141Dic11⋊C4—21no—
142Dic11⋊C4—21no—
143C4×Dic11—21no—
144#4318—82no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149#4313—42no—
150C8×D11—42no—
151#3252—112no—
152#3160D1111yescharacteristic, complemented
153#2966—111no—
154#1692—112no—
155#1691—112no—
156#1676—111no—
157#1675—111no—
158#1674—111no—
159#1673—111no—
160#1567—111no—
161#1559—112no—
162C23×C11#12111yescharacteristic
163C22×D11—21no—
164Q8×C11—42no—
165Q8×C11—42no—
166Q8×C11—82no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C2×#4111yescharacteristic
180C22⋊D11—42no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184D44—21no—
185D44—21no—
186C4×D11—41no—
187C4×D11—41no—
188Dic22—21no—
189Dic22—21no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11#13712yes—
193C8×C11#13712yes—
194C11⋊C8—41no—
195C11⋊C8—41no—
196C11⋊C8—42no—
197C11⋊C8—42no—
198#533C2×D1112yes—
199#529—111no—
200#500C2×D1111yescharacteristic
201#500C2×D1111yescharacteristic
202#499—21no—
203#499—21no—
204#498C2×D1112yes—
205#479—222no—
206#477—112no—
207#476—112no—
208#470—222no—
209#468—222no—
210#464—222no—
211#462—112no—
212#461—112no—
213#446—111no—
214C8×Q8—111no—
215#436—111no—
216#435—221no—
217C8×D4—111no—
218C8×D4—221no—
219#433—221no—
220#432—111no—
221#427—21no—
222#427—21no—
223#423—112no—
224#405—221no—
225C2×C4×C8C2×D1111yescharacteristic
226#335—111no—
227#335—111no—
228#335—112no—
229#333—112no—
230#333—112no—
231#332—112no—
232#332—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11C2×#12111yescharacteristic
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—41no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—82no—
245C4×C11—82no—
246C4×C11C2×#13711yescharacteristic
247C4×C11C2×#13711yescharacteristic
248C4×C11#57611yescharacteristic
249C4×C11#57811yescharacteristic
250Dic11—41no—
251Dic11—41no—
252Dic11—41no—
253C2×Q16—222no—
254C2×SD16—222no—
255C2×M16—222no—
256C2×M16—221no—
257C22×C8—221no—
258C22×C8C22⋊D1111yescharacteristic
259C22×C8C22⋊D1111yescharacteristic
260C4⋊Q8C22×D1112yes—
261C4⋊Q8C22×D1112yes—
262#126—221no—
263#125—22no—
264#125—111no—
265#124—111no—
266#123—221no—
267C22⋊Q8—22no—
268C22⋊Q8—22no—
269C22⋊Q8—111no—
270#121—111no—
271C4×Q8—22no—
272C4×Q8—22no—
273C4×Q8—111no—
274C4×D4—111no—
275C4×D4—221no—
276#117—22no—
277#117—221no—
278C2×C42C22×D1111yescharacteristic
279#107—21no—
280#107—21no—
281#107—21no—
282#107—21no—
283#107—222no—
284#106—22no—
285#106—22no—
286#106—222no—
287C4⋊C8—111no—
288C4⋊C8—111no—
289C4⋊C8—112no—
290C4⋊C8—112no—
291C4⋊C8—221no—
292C4⋊C8—221no—
293C4⋊C8—222no—
294#103—222no—
295#103—222no—
296#103—222no—
297#102—222no—
298C22⋊C8—221no—
299C22⋊C8—221no—
300C22⋊C8—221no—
301#97—221no—
302#97—221no—
303C4×C8—221no—
304C4×C8C22⋊D1111yescharacteristic
305C4×C8C22⋊D1111yescharacteristic
306C4×C8C22×D1111yescharacteristic
307C4×C8C22×D1111yescharacteristic
308C2×C11—41no—
309C2×C11#303911yescharacteristic
310C2×C11#306111yescharacteristic
311C2×C11#306711yescharacteristic
312D11—81no—
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—111no—
316C2×D4—111no—
317C2×D4—221no—
318C22×C4—221no—
319C22×C4D4×D1111yescharacteristic
320C22×C4#434111yescharacteristic
321C22×C4C2×C22⋊D1111yescharacteristic
322Q16—882no—
323SD16—882no—
324M16—442no—
325M16—882no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—221no—
331C2×C8—221no—
332C2×C8—442no—
333C2×C8C2×C22⋊D1111yescharacteristic
334C2×C8C2×C22⋊D1111yescharacteristic
335C2×C8C2×C22⋊D1111yescharacteristic
336C2×C8C2×C22⋊D1111yescharacteristic
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—111no—
344C4⋊C4—111no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C22⋊C4—42no—
350C22⋊C4—221no—
351C22⋊C4—221no—
352C22⋊C4—221no—
353C22⋊C4—221no—
354C22⋊C4—221no—
355C42—42no—
356C42—221no—
357C42D4×D1111yescharacteristic
358C42#434111yescharacteristic
359C42C2×C22⋊D1111yescharacteristic
360C42C23×D1111yescharacteristic
361C11#1936111yescharacteristic, complemented, Sylow
362C23—221no—
363C23#6699111yescharacteristic
364Q8—42no—
365Q8—42no—
366Q8—82no—
367Q8—221no—
368Q8—221no—
369D4—221no—
370D4—221no—
371D4—442no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4#6699111yescharacteristic
385C2×C4#6699111yescharacteristic
386C2×C4#6699111yescharacteristic
387C2×C4C2×D4×D1111yescharacteristic
388C2×C4C2×#434111yescharacteristic
389C2×C4C22×C22⋊D1111yescharacteristic
390C8—21no—
391C8—21no—
392C8—442no—
393C8—442no—
394C8—441no—
395C8—441no—
396C8#6699512yes—
397C8#6699512yes—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—441no—
402C22—441no—
403C22—441no—
404C22C2×#6699111yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—82no—
410C4—82no—
411C4—441no—
412C4—441no—
413C4—441no—
414C4#1062330011yescharacteristic
415C4#1062330211yescharacteristic
416C4C2×#6699511yescharacteristic
417C4C2×#6699511yescharacteristic
418C2—41no—
419C2—881no—
420C2#1307809911yescharacteristic
421C2#1307828211yescharacteristic
422C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3160C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#3160D11
hypocenterC11#19361
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3160

Complements

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

NH ≅ G/Ntype
3. #13068119C2semidirect
4. #13068112C2semidirect
5. #13068017C2semidirect
6. #13068012C2semidirect
7. #13068007C2semidirect
8. #13068002C2semidirect
9. #13067375C2semidirect
10. #13067346C2semidirect
11. C11×#3160C2semidirect
152. #3160D11semidirect
361. C11#19361semidirect

Maximal subgroups

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

subgroupindex
#130799832
#130775912
#130681192
#130681122
#130680172
#130680122
#130680072
#130680022
#130673752
#130673462
C11×#31602
#1936111