Finite Group Databasebeta

← #14736182

Subgroups — #14736182

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078939C211yesmaximal, characteristic
2#13078655C211yesmaximal, characteristic, complemented
3#13078647C211yesmaximal, characteristic
4#13068074C212yesmaximal, complemented
5#13068060C212yesmaximal, complemented
6#13068046C212yesmaximal, complemented
7#13068032C212yesmaximal, complemented
8#13067364C211yesmaximal, characteristic, complemented
9#13067274C211yesmaximal, characteristic, complemented
10#13067266C211yesmaximal, characteristic
11C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13#10623008C2211yescharacteristic
14#10623001C2211yescharacteristic
15C8×Q8×C11—21no—
16C8×Q8×C11—21no—
17C8×Q8×C11C2212yes—
18C8×Q8×C11C2212yes—
19C2×C11×C4⋊C8—21no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C4×C8×C11—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622841—21no—
24#10622840—21no—
25#10622726—21no—
26#10622726—21no—
27#10622644C2212yes—
28C4×#4326—22no—
29#10622640C2212yes—
30C4×#4325—22no—
31#10622634C2212yes—
32#10622633C2212yes—
33#10622583—21no—
34#10622581—21no—
35#10622538C2211yescharacteristic
36#10622538C2211yescharacteristic
37#10622310—21no—
38#10622310—21no—
39#10622307C2211yescharacteristic
40#10622307C2211yescharacteristic
41#10622294C2211yescharacteristic
42#10622294C2211yescharacteristic
43#10622124C2212yes—
44#10622123C2212yes—
45#10622120C2212yes—
46#10622119C2212yes—
47#10622096C2212yes—
48#10622095C2212yes—
49C22×Q8×C11D411yescharacteristic
50C2×#4339—21no—
51C22×C8×C11—21no—
52C22×C8×C11D411yescharacteristic
53C22×C8×C11D411yescharacteristic
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11D412yes—
57C4×Q8×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63C2×#4325—22no—
64#66983—21no—
65#66983—21no—
66#66979—21no—
67#66977—21no—
68#66977—21no—
69#66928—21no—
70#66927C2311yescharacteristic
71C4×D44—21no—
72C4×D44—21no—
73#66923—21no—
74#66922C2311yescharacteristic
75#66922C2311yescharacteristic
76#66922C2311yescharacteristic
77C4×Dic22—21no—
78C4×Dic22—21no—
79C11×C4⋊C8—22no—
80C11×C4⋊C8—22no—
81C11×C4⋊C8—21no—
82C11×C4⋊C8C2312yes—
83C4×C8×C11—22no—
84C4×C8×C11—22no—
85C4×C8×C11D411yescharacteristic
86C4×C8×C11D411yescharacteristic
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89#66899—22no—
90#66899—22no—
91C22⋊(C11⋊C8)—21no—
92C22⋊(C11⋊C8)—21no—
93#66885—21no—
94#66885—21no—
95#66885—21no—
96#66885—21no—
97#66880—21no—
98#66880—21no—
99#66880—21no—
100#66880—21no—
101#66874—22no—
102#66873—22no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2312yes—
107C4×C11⋊C8—21no—
108C4×C11⋊C8—21no—
109#19123—111nomaximal, Sylow
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11C2×D412yes—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C2×C22⋊D11—41no—
119#4339—42no—
120#4339—42no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×C4×D11—41no—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—42no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4C2×D412yes—
140C42×C11—22no—
141C42×C11—22no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146C22⋊Dic11—41no—
147#4326—44no—
148#4325—44no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159C4×Dic11—41no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162#3131—111no—
163#3104—111no—
164#3103—111no—
165C2×C8×Q8D1111yescharacteristic, complemented
166#1684—112no—
167#1682—112no—
168#1680—112no—
169#1678—112no—
170#1564—111no—
171#1542—111no—
172#1540—111no—
173C23×C11#12111yescharacteristic
174C22×D11—41no—
175Q8×C11—24no—
176Q8×C11—22no—
177Q8×C11#13514yes—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#13512yes—
188C2×C4×C11#13712yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C22⋊D11—82no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196D44—42no—
197D44—41no—
198D44—41no—
199D44—81no—
200C4×D11—82no—
201Dic22—42no—
202Dic22—41no—
203Dic22—41no—
204Dic22—81no—
205C8×C11—21no—
206C8×C11—21no—
207C8×C11—21no—
208C8×C11—21no—
209C8×C11—42no—
210C11⋊C8—42no—
211C11⋊C8—42no—
212#533—111no—
213#532—111no—
214C2×C4×Q8C2×D1111yescharacteristic
215#488—221no—
216#488—221no—
217#487—111no—
218#487—111no—
219#486—111no—
220#486—111no—
221#484—221no—
222#481—221no—
223#477—112no—
224#475—112no—
225#462—112no—
226#460—112no—
227#451—221no—
228#448—221no—
229C8×Q8—21no—
230C8×Q8—21no—
231C8×Q8C2×D1112yes—
232C8×Q8C2×D1112yes—
233C4×Q16—222no—
234C4×SD16—222no—
235#431—111no—
236#431—111no—
237C2×C4⋊C8—21no—
238C2×C4⋊C8C2×D1111yescharacteristic
239#416—221no—
240#416—221no—
241C2×C4×C8—21no—
242C2×C4×C8C2×D1111yescharacteristic
243#335—112no—
244#334—112no—
245#333—112no—
246#332—112no—
247#332—112no—
248#331—112no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11#46412yes—
252C22×C11C2×#12111yescharacteristic
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C4×C11—24no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—42no—
261C4×C11#46412yes—
262C4×C11C2×#13512yes—
263C4×C11C2×#13511yescharacteristic
264C4×C11C2×#13711yescharacteristic
265Dic11—81no—
266Dic11—81no—
267Dic11—81no—
268C2×#41—221no—
269C22×Q8D4411yescharacteristic
270C2×Q16—222no—
271C2×SD16—222no—
272C22×C8—21no—
273C22×C8C22⋊D1111yescharacteristic
274C22×C8C22⋊D1111yescharacteristic
275C4⋊Q8—111no—
276C4⋊Q8—111no—
277C4⋊Q8—111no—
278#127—111no—
279#125—221no—
280#124—221no—
281C22⋊Q8—221no—
282C22⋊Q8—221no—
283#121—221no—
284#121—221no—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×Q8—221no—
288C4×Q8—221no—
289C4×Q8D4412yes—
290C4×Q8C22×D1112yes—
291C4×D4—221no—
292C4×D4—221no—
293#117—221no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4D4411yescharacteristic
296C2×C42—21no—
297C2×C42C22×D1111yescharacteristic
298#107—222no—
299#106—222no—
300C4⋊C8—22no—
301C4⋊C8—22no—
302C4⋊C8—21no—
303C4⋊C8—112no—
304C4⋊C8—112no—
305C4⋊C8C22×D1112yes—
306#103—222no—
307#103—222no—
308#103—221no—
309#103—221no—
310#103—221no—
311#103—221no—
312#103—222no—
313#102—221no—
314#102—221no—
315#102—221no—
316#102—221no—
317#102—222no—
318C22⋊C8—221no—
319C22⋊C8—221no—
320C4×C8—22no—
321C4×C8—22no—
322C4×C8—221no—
323C4×C8—221no—
324C4×C8C22⋊D1111yescharacteristic
325C4×C8C22⋊D1111yescharacteristic
326C4×C8C22×D1111yescharacteristic
327C4×C8C22×D1111yescharacteristic
328C2×C11—22no—
329C2×C11C2×#46411yescharacteristic
330C2×C11#305011yescharacteristic
331C2×C11#306711yescharacteristic
332D11—161no—
333#41—442no—
334#41—442no—
335C2×Q8—24no—
336C2×Q8—21no—
337C2×Q8—221no—
338C2×Q8—221no—
339C2×Q8—221no—
340C2×Q8C2×D4412yes—
341C2×D4—221no—
342C2×D4—221no—
343C2×D4—221no—
344C2×D4—441no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—441no—
348C22×C4C2×D4411yescharacteristic
349C22×C4#433911yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351Q16—444no—
352SD16—444no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—42no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8C2×C22⋊D1111yescharacteristic
360C2×C8C2×C22⋊D1111yescharacteristic
361C2×C8C2×C22⋊D1111yescharacteristic
362C2×C8C2×C22⋊D1111yescharacteristic
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—441no—
373C4⋊C4—441no—
374C4⋊C4C2×D4412yes—
375C22⋊C4—441no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C42—22no—
379C42—22no—
380C42—441no—
381C42C2×D4411yescharacteristic
382C42#433911yescharacteristic
383C42C2×C22⋊D1111yescharacteristic
384C42C23×D1111yescharacteristic
385C11#1912311yescharacteristic, complemented, Sylow
386C23—441no—
387C23#6698311yescharacteristic
388Q8—24no—
389Q8—22no—
390Q8—442no—
391Q8—441no—
392Q8—441no—
393Q8—881no—
394Q8#6695714yes—
395D4—442no—
396D4—441no—
397D4—441no—
398D4—881no—
399D4—882no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—882no—
410C2×C4#6698311yescharacteristic
411C2×C4#6698311yescharacteristic
412C2×C4#6698311yescharacteristic
413C2×C4#6699512yes—
414C2×C4#6700312yes—
415C2×C4C22×D4411yescharacteristic
416C2×C4C2×#433911yescharacteristic
417C2×C4C22×C22⋊D1111yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—21no—
422C8—42no—
423C8—442no—
424C8—442no—
425C22—21no—
426C22—21no—
427C22—881no—
428C22—881no—
429C22—881no—
430C22#1062264112yes—
431C22C2×#6698311yescharacteristic
432C4—21no—
433C4—21no—
434C4—24no—
435C4—21no—
436C4—42no—
437C4—881no—
438C4—881no—
439C4—881no—
440C4#1062264112yes—
441C4C2×#6695712yes—
442C4C2×#6699511yescharacteristic
443C4C2×#6700311yescharacteristic
444C2—22no—
445C2—1761no—
446C2C2×#1062264111yescharacteristic
447C2#1307819711yescharacteristic
448C2#1307833611yescharacteristic
subgroupG/H
centerC2×C4#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C8×Q8×C11C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×C8×Q8D11
hypocenterC11#19123
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #13078655C2semidirect
4. #13068074C2semidirect
5. #13068060C2semidirect
6. #13068046C2semidirect
7. #13068032C2semidirect
8. #13067364C2semidirect
9. #13067274C2semidirect
11. C2×C8×Q8×C11C2semidirect
165. C2×C8×Q8D11semidirect
385. C11#19123semidirect

Maximal subgroups

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

subgroupindex
#130789392
#130786552
#130786472
#130680742
#130680602
#130680462
#130680322
#130673642
#130672742
#130672662
C2×C8×Q8×C112
#1912311