Finite Group Databasebeta

← #14738412

Subgroups — #14738412

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079623C211yesmaximal, characteristic
2#13079176C211yesmaximal, characteristic
3#13077551C211yesmaximal, characteristic, complemented
4#13068168C212yesmaximal, complemented
5#13068158C212yesmaximal, complemented
6#13068000C212yesmaximal, complemented
7#13067966C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067346C211yesmaximal, characteristic, complemented
10#13067339C211yesmaximal, characteristic
11C11×#3237C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#533C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#501—21no—
16C11×#491—21no—
17C11×#485—22no—
18C11×#477C2212yes—
19C11×#475C2212yes—
20C11×#432C2211yescharacteristic
21#10622702—21no—
22#10622701C2211yescharacteristic
23#10622699—21no—
24#10622698C2211yescharacteristic
25#10622694C2211yescharacteristic
26#10622692C2211yescharacteristic
27#10622661—21no—
28#10622661—21no—
29#10622660—22no—
30#10622644C2212yes—
31#10622640C2212yes—
32C4×#4325—21no—
33C4×#4325—21no—
34#10622637—21no—
35#10622637C2212yes—
36Q8×C11⋊C8—21no—
37Q8×C11⋊C8C2212yes—
38#10622612—21no—
39#10622610—21no—
40#10622539C2211yescharacteristic
41#10622537C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yes—
44#10622184C2212yes—
45#10622123C2212yes—
46#10622120C2212yes—
47#10622118C2212yes—
48#10622117C2212yes—
49C2×#4339—21no—
50C11×C4⋊Q8D411yescharacteristic
51C11×C4⋊Q8D411yescharacteristic
52C11×C4⋊Q8C2311yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×#125—21no—
55C11×#125—21no—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8D412yes—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11C2312yes—
64C11×#117—21no—
65C11×#117—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4326—22no—
68C2×#4325—22no—
69C2×#4325—21no—
70C2×#4325—21no—
71#66983—21no—
72#66983—21no—
73C2×#4318—21no—
74C22×C11⋊C8D411yescharacteristic
75C22×C11⋊C8D411yescharacteristic
76#66928—21no—
77#66927C2311yescharacteristic
78C4×D44—21no—
79C4×D44—21no—
80#66922C2311yescharacteristic
81C11×#107—22no—
82C11×#106—22no—
83C11×C4⋊C8C2312yes—
84C11×#103—22no—
85C11×#103—22no—
86C11×C22⋊C8—21no—
87C11×#97—21no—
88#66899—21no—
89#66899—21no—
90C22⋊(C11⋊C8)—21no—
91#66874—22no—
92#66873—22no—
93#66873—21no—
94#66873—21no—
95#66872—21no—
96#66872—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102#66867—21no—
103#66867—22no—
104C4×C11⋊C8—22no—
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#19340—111nomaximal, Sylow
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C2×C22⋊D11—41no—
118#4339—82no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×C4×D11—41no—
123C2×Dic22—21no—
124C2×C8×C11—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4C2×D412yes—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—41no—
139C42×C11—22no—
140C42×C11—41no—
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11#4111yescharacteristic
144C42×C11C2411yescharacteristic
145#4326—82no—
146#4325—42no—
147#4325—42no—
148#4325—82no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153#4318—42no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—41no—
158C2×C11⋊C8C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162#3237D1111yescharacteristic, complemented
163#3216—111no—
164#3167—111no—
165#2960—111no—
166#1700—112no—
167#1698—112no—
168#1672—112no—
169#1666—112no—
170#1568—111no—
171#1559—111no—
172#1557—111no—
173C23×C11#12111yescharacteristic
174C22×D11—41no—
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—42no—
178Q8×C11—41no—
179Q8×C11—41no—
180Q8×C11—81no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C22⋊D11—82no—
196C2×Dic11—41no—
197D44—41no—
198D44—41no—
199D44—42no—
200D44—81no—
201C4×D11—82no—
202Dic22—42no—
203C8×C11—42no—
204C11⋊C8—21no—
205C11⋊C8—21no—
206C11⋊C8—21no—
207C11⋊C8—42no—
208C11⋊C8—42no—
209C11⋊C8#13712yes—
210#533C2×D1111yescharacteristic
211#533C2×D1111yescharacteristic
212#532—111no—
213#501—21no—
214#498—111no—
215#497—221no—
216#492—111no—
217#491—21no—
218#489—221no—
219#487—111no—
220#486—111no—
221#485—22no—
222#477C2×D1112yes—
223#475C2×D1112yes—
224#465—221no—
225#465—221no—
226#462—112no—
227#460—112no—
228#452—222no—
229#446—112no—
230#446—221no—
231C8×Q8—112no—
232C8×Q8—221no—
233C4×SD16—221no—
234C4×SD16—221no—
235#432—111no—
236#432C2×D1111yescharacteristic
237#424—221no—
238#423—111no—
239#405—221no—
240C2×C4×C8—111no—
241#335—112no—
242#334—112no—
243#333—112no—
244#332—112no—
245#332—112no—
246#331—112no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11C2×#12111yescharacteristic
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—81no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—81no—
261C4×C11—81no—
262C4×C11C2×#13711yescharacteristic
263C4×C11#57511yescharacteristic
264C4×C11#57712yes—
265Dic11—81no—
266C2×#41—221no—
267C2×Q16—222no—
268C2×SD16—221no—
269C2×SD16—221no—
270C2×SD16—222no—
271C2×M16—221no—
272C22×C8—111no—
273C22×C8—111no—
274C4⋊Q8—111no—
275C4⋊Q8C22⋊D1111yescharacteristic
276C4⋊Q8C22⋊D1111yescharacteristic
277C4⋊Q8C22×D1111yescharacteristic
278C4⋊Q8C22×D1111yescharacteristic
279#127—111no—
280#125—21no—
281#125—21no—
282#124—221no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8C22⋊D1112yes—
287#121—221no—
288#121—221no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8C22×D1112yes—
293C4×D4—221no—
294C4×D4—221no—
295#117—21no—
296#117—21no—
297C2×C42C22×D1111yescharacteristic
298#107—22no—
299#106—22no—
300#106—221no—
301#106—221no—
302C4⋊C8—112no—
303C4⋊C8—112no—
304C4⋊C8—222no—
305C4⋊C8—222no—
306C4⋊C8—221no—
307C4⋊C8C22×D1112yes—
308#103—22no—
309#103—22no—
310#103—221no—
311#103—221no—
312#103—222no—
313#102—221no—
314#102—221no—
315#102—222no—
316C22⋊C8—21no—
317C22⋊C8—221no—
318#97—21no—
319#97—222no—
320#97—221no—
321C4×C8—111no—
322C4×C8—111no—
323C4×C8—111no—
324C4×C8—111no—
325C4×C8—222no—
326C2×C11—41no—
327C2×C11#303711yescharacteristic
328C2×C11#305711yescharacteristic
329C2×C11#306711yescharacteristic
330D11—161no—
331#41—882no—
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—221no—
336C2×Q8C2×C22⋊D1112yes—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C2×D4—441no—
341C22×C4—441no—
342C22×C4D4×D1111yescharacteristic
343C22×C4#434111yescharacteristic
344C22×C4C2×C22⋊D1111yescharacteristic
345Q16—882no—
346SD16—442no—
347SD16—442no—
348SD16—882no—
349M16—442no—
350C2×C8—22no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8—111no—
354C2×C8—111no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4C2×C22⋊D1112yes—
373C22⋊C4—22no—
374C22⋊C4—41no—
375C22⋊C4—441no—
376C22⋊C4—441no—
377C42—22no—
378C42—41no—
379C42D4×D1111yescharacteristic
380C42#434111yescharacteristic
381C42C2×C22⋊D1111yescharacteristic
382C42C23×D1111yescharacteristic
383C11#1934011yescharacteristic, complemented, Sylow
384C23—441no—
385C23#6699211yescharacteristic
386Q8—22no—
387Q8—22no—
388Q8—42no—
389Q8—41no—
390Q8—41no—
391Q8—81no—
392Q8—442no—
393D4—441no—
394D4—441no—
395D4—442no—
396D4—881no—
397D4—882no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—441no—
407C2×C4—882no—
408C2×C4#6699211yescharacteristic
409C2×C4#6699211yescharacteristic
410C2×C4#6699211yescharacteristic
411C2×C4C2×D4×D1111yescharacteristic
412C2×C4C2×#434111yescharacteristic
413C2×C4C22×C22⋊D1111yescharacteristic
414C8—42no—
415C8—112no—
416C8—221no—
417C8—221no—
418C8—221no—
419C8—442no—
420C8—442no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—881no—
425C22—881no—
426C22—881no—
427C22C2×#6699211yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—42no—
433C4—42no—
434C4—81no—
435C4—81no—
436C4—881no—
437C4D11×#13711yescharacteristic
438C4#1062330811yescharacteristic
439C4#1062336812yes—
440C2—41no—
441C2—1761no—
442C2#1307808511yescharacteristic
443C2#1307825711yescharacteristic
444C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3237C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3237D11
hypocenterC11#19340
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3237

Complements

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

NH ≅ G/Ntype
3. #13077551C2semidirect
4. #13068168C2semidirect
5. #13068158C2semidirect
6. #13068000C2semidirect
7. #13067966C2semidirect
8. #13067377C2semidirect
9. #13067346C2semidirect
11. C11×#3237C2semidirect
162. #3237D11semidirect
383. C11#19340semidirect

Maximal subgroups

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

subgroupindex
#130796232
#130791762
#130775512
#130681682
#130681582
#130680002
#130679662
#130673772
#130673462
#130673392
C11×#32372
#1934011