Finite Group Databasebeta

← #14754137

Subgroups — #14754137

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66954C211yesmaximal, characteristic
2#13068762C212yesmaximal, complemented
3#13068741C211yesmaximal, characteristic, complemented
4#13068739C211yesmaximal, characteristic, complemented
5#13068719C212yesmaximal
6#13068663C211yesmaximal, characteristic
7#13068659C211yesmaximal, characteristic
8#13068495C211yesmaximal, characteristic, complemented
9#13068417C212yesmaximal
10#13068371C212yesmaximal, complemented
11C11×#1772C211yesmaximal, characteristic, complemented
12C2×#66954C2211yescharacteristic
13C2×#66954C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C2×C11×#108C2211yescharacteristic
16C11×#427C2211yescharacteristic
17C11×#405C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19#10622745C2212yes—
20C2×#66883C2211yescharacteristic
21#10622719C2211yescharacteristic
22#10622714C2212yes—
23#10622714C2211yescharacteristic
24#10622714C2211yescharacteristic
25#10622619C2212yes—
26C4×#4318C2211yescharacteristic
27#10622302C412yescomplemented
28#10622302C412yescomplemented
29C4×#4313C412yescomplemented
30C4×C8×D11C412yescomplemented
31C11×#339C2212yes—
32C11⋊#338C2212yes—
33#10622197C2212yes—
34#10622195C2212yes—
35#10622171C2212yes—
36#10622169C2212yes—
37#10622169C2212yes—
38#10622161C2212yes—
39C2×#4339C2311yescharacteristic
40C2×C11×M16C2312yes—
41C22×C8×C11C2311yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C11×#117C2312yes—
44C2×C42×C11C2311yescharacteristic
45C4×C22⋊D11—22no—
46#66979C2312yes—
47#66979C2311yescharacteristic
48C2×#4318C2312yes—
49C2×#4318C2311yescharacteristic
50C2×#4318C2311yescharacteristic
51#66954—21no—
52#66954—21no—
53#66954—21no—
54#66954—21no—
55#66954—21no—
56#66954—21no—
57#66954—21no—
58#66954—21no—
59C2×#4313C2×C412yes—
60C2×#4313C2×C412yes—
61C2×C8×D11C2×C412yes—
62C2×C8×D11C2×C412yes—
63C4×D44—21no—
64#66925C2×C412yes—
65C42×D11C2×C412yes—
66C4×Dic22—21no—
67C11×#108—21no—
68C11×#108—21no—
69C11×#107—21no—
70C11×#106—21no—
71C11×#97—22no—
72C4×C8×C11—22no—
73C4×C8×C11C2×C411yescharacteristic
74C4×C8×C11C2×C411yescharacteristic
75C4×C8×C11C2×C411yescharacteristic
76C4×C8×C11C2×C411yescharacteristic
77#66888—22no—
78#66887—22no—
79#66883—21no—
80#66883—21no—
81#66882—21no—
82#66881—21no—
83#66879—22no—
84#66879C2×C412yes—
85#66879C2×C412yes—
86C8×Dic11—22no—
87C8×Dic11C2×C412yes—
88C8×Dic11C2×C412yes—
89#66870—24no—
90#66867C2×C412yes—
91C4×C11⋊C8C2×C412yes—
92#20787—111nomaximal, Sylow
93C22×C4×C11—21no—
94C22×C4×C11C2411yescharacteristic
95C2×C22⋊D11#4112yes—
96#4339—21no—
97#4339—21no—
98#4339—21no—
99#4339—21no—
100C2×D44#4111yescharacteristic
101C2×C4×D11—22no—
102C2×C4×D11C22×C412yes—
103C2×Dic22#4111yescharacteristic
104C11×M16—22no—
105C11×M16—22no—
106C2×C8×C11—22no—
107C2×C8×C11C22×C411yescharacteristic
108C2×C8×C11C22×C411yescharacteristic
109C2×C8×C11C22×C411yescharacteristic
110C2×C8×C11C22×C411yescharacteristic
111C2×C8×C11#4111yescharacteristic
112C2×C8×C11#4111yescharacteristic
113C2×C8×C11#4111yescharacteristic
114C2×C8×C11#4111yescharacteristic
115C2×C8×C11#4111yescharacteristic
116C2×C8×C11#4111yescharacteristic
117C2×C8×C11#4111yescharacteristic
118C2×C8×C11#4111yescharacteristic
119C11×C4⋊C4—22no—
120C11×C22⋊C4—22no—
121C42×C11—21no—
122C42×C11—22no—
123C42×C11C22×C411yescharacteristic
124C42×C11C22×C411yescharacteristic
125C22⋊Dic11—21no—
126C22⋊Dic11—22no—
127(C2×D11)⋊C4—22no—
128C4⋊Dic11—21no—
129C4⋊Dic11—22no—
130Dic11⋊C4—22no—
131C4×Dic11—22no—
132C4×Dic11—22no—
133C4×Dic11C22×C412yes—
134#4318—21no—
135#4318—21no—
136#4318—21no—
137#4318—21no—
138#4318—22no—
139#4318—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8C22×C412yes—
142C2×C11⋊C8C22×C412yes—
143#4313—22no—
144#4313—22no—
145#4313—22no—
146#4313—22no—
147C8×D11—22no—
148C8×D11—22no—
149C8×D11—22no—
150C8×D11—22no—
151C4×#131—111no—
152#1841—112no—
153#1833—111no—
154#1833—111no—
155#1827—112no—
156#1813—111no—
157#1812—111no—
158#1772—111no—
159#1772D1111yescharacteristic, complemented
160#1757—112no—
161#1747—112no—
162C23×C11C2×#4111yescharacteristic
163C22×D11#11712yes—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11C23×C411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C2×C4×C11C2×#4111yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174C22⋊D11—22no—
175C22⋊D11—22no—
176C2×Dic11—22no—
177C2×Dic11—42no—
178C2×Dic11#11712yes—
179D44—21no—
180D44—21no—
181C4×D11—22no—
182C4×D11—22no—
183C4×D11—44no—
184Dic22—21no—
185Dic22—21no—
186C8×C11—42no—
187C8×C11#11711yescharacteristic
188C8×C11#11711yescharacteristic
189C8×C11#11711yescharacteristic
190C8×C11#11711yescharacteristic
191C8×C11#11711yescharacteristic
192C8×C11#11711yescharacteristic
193C8×C11#11711yescharacteristic
194C8×C11#11711yescharacteristic
195C11⋊C8—22no—
196C11⋊C8—22no—
197C11⋊C8—42no—
198C2×#131—111no—
199C2×#131—111no—
200C4×#41—111no—
201C2×#108—111no—
202C2×#108C2×D1111yescharacteristic
203#427—111no—
204#427C2×D1111yescharacteristic
205#413—112no—
206#410—112no—
207#405—111no—
208#405—111no—
209#405—112no—
210#405—112no—
211#405—112no—
212#405C2×D1112yes—
213C4×M16—111no—
214C4×M16—112no—
215C2×C4×C8—112no—
216C2×C4×C8C2×D1111yescharacteristic
217#344—112no—
218#344—112no—
219#339—112no—
220#339C2×D1112yes—
221#338—112no—
222H(3,ℤ/4)—112no—
223H(3,ℤ/4)—112no—
224H(3,ℤ/4)—112no—
225C22×C11—41no—
226C22×C11C2×#11711yescharacteristic
227C22×C11#52911yescharacteristic
228C22×C11#52911yescharacteristic
229C2×D11—22no—
230C2×D11—42no—
231C4×C11—22no—
232C4×C11—41no—
233C4×C11—82no—
234C4×C11C2×#11711yescharacteristic
235C4×C11C2×#11711yescharacteristic
236C4×C11#52911yescharacteristic
237C4×C11#52911yescharacteristic
238Dic11—22no—
239Dic11—42no—
240Dic11—82no—
241C2×#41—111no—
242#131—221no—
243#131—221no—
244#131—221no—
245#131—221no—
246#131—221no—
247#131—221no—
248#131—221no—
249#131—221no—
250C2×M16—111no—
251C2×M16—111no—
252C2×M16—112no—
253C2×M16—112no—
254C2×M16—112no—
255C2×M16C22×D1112yes—
256C22×C8—112no—
257C22×C8—112no—
258C22×C8C22×D1111yescharacteristic
259C22×C8C22×D1111yescharacteristic
260C4×Q8—221no—
261C4×D4—221no—
262C4×D4—222no—
263#117—111no—
264#117—112no—
265#117—112no—
266#117C22×D1112yes—
267C2×C42—112no—
268C2×C42C22×D1111yescharacteristic
269#108—21no—
270#108—21no—
271#108—221no—
272#108—221no—
273#107—21no—
274#107—221no—
275#106—21no—
276#106—221no—
277#101—222no—
278#100—222no—
279#99—224no—
280#97—22no—
281#97—112no—
282#97—112no—
283#97—112no—
284#97—222no—
285C4×C8—22no—
286C4×C8—112no—
287C4×C8—112no—
288C4×C8—112no—
289C4×C8—222no—
290C4×C8C4×D1111yescharacteristic
291C4×C8C4×D1111yescharacteristic
292C4×C8C4×D1111yescharacteristic
293C4×C8C4×D1111yescharacteristic
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11#228311yescharacteristic
298D11—42no—
299#41—221no—
300#41—221no—
301#41—221no—
302#41—221no—
303C2×Q8—111no—
304C2×D4—112no—
305C2×D4—111no—
306C22×C4—21no—
307C22×C4—112no—
308C22×C4—222no—
309C22×C4C23×D1111yescharacteristic
310M16—22no—
311M16—22no—
312M16—221no—
313M16—221no—
314M16—221no—
315M16—221no—
316M16—222no—
317M16—222no—
318M16—222no—
319M16—222no—
320M16—222no—
321M16—222no—
322C2×C8—22no—
323C2×C8—112no—
324C2×C8—112no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8C2×C4×D1111yescharacteristic
331C2×C8C2×C4×D1111yescharacteristic
332C2×C8C2×C4×D1111yescharacteristic
333C2×C8C2×C4×D1111yescharacteristic
334C2×C8#433911yescharacteristic
335C2×C8#433911yescharacteristic
336C2×C8#433911yescharacteristic
337C2×C8#433911yescharacteristic
338C2×C8#434111yescharacteristic
339C2×C8#434111yescharacteristic
340C2×C8#434311yescharacteristic
341C2×C8#434311yescharacteristic
342C4⋊C4—22no—
343C4⋊C4—222no—
344C4⋊C4—221no—
345C4⋊C4—222no—
346C22⋊C4—22no—
347C22⋊C4—222no—
348C22⋊C4—221no—
349C22⋊C4—222no—
350C42—21no—
351C42—22no—
352C42—112no—
353C42—222no—
354C42—222no—
355C42C2×C4×D1111yescharacteristic
356C42C2×C4×D1111yescharacteristic
357C11#2078711yescharacteristic, complemented, Sylow
358C23—112no—
359C23#41×D1111yescharacteristic
360Q8—221no—
361Q8—221no—
362D4—222no—
363D4—222no—
364D4—221no—
365D4—221no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—112no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—444no—
375C2×C4—442no—
376C2×C4C22×C4×D1111yescharacteristic
377C2×C4C2×#433911yescharacteristic
378C2×C4C2×#433911yescharacteristic
379C2×C4C2×#434111yescharacteristic
380C2×C4C2×#434311yescharacteristic
381C2×C4#41×D1111yescharacteristic
382C8—42no—
383C8—222no—
384C8—222no—
385C8—442no—
386C8#6692511yescharacteristic
387C8#6692511yescharacteristic
388C8#6692511yescharacteristic
389C8#6692511yescharacteristic
390C8#6694511yescharacteristic
391C8#6694511yescharacteristic
392C8#6694511yescharacteristic
393C8#6694511yescharacteristic
394C22—41no—
395C22—222no—
396C22—442no—
397C22D11×#11711yescharacteristic
398C22#1062308811yescharacteristic
399C22#1062311111yescharacteristic
400C4—22no—
401C4—41no—
402C4—82no—
403C4—222no—
404C4—442no—
405C4—882no—
406C4C2×#6692511yescharacteristic
407C4C2×#6694511yescharacteristic
408C4#1062308811yescharacteristic
409C4#1062311111yescharacteristic
410C2—21no—
411C2—21no—
412C2—21no—
413C2—442no—
414C2#1307101211yescharacteristic
subgroupG/H
centerC8#66945
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1772C2
socleC2×C11#2283
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#1772D11
hypocenterC11#20787
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #1772

Complements

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

NH ≅ G/Ntype
2. #13068762C2semidirect
3. #13068741C2semidirect
4. #13068739C2semidirect
8. #13068495C2semidirect
10. #13068371C2semidirect
11. C11×#1772C2semidirect
27. #10622302C4semidirect
28. #10622302C4semidirect
29. C4×#4313C4semidirect
30. C4×C8×D11C4semidirect
159. #1772D11semidirect
357. C11#20787semidirect

Maximal subgroups

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

subgroupindex
C4×#669542
#130687622
#130687412
#130687392
#130687192
#130686632
#130686592
#130684952
#130684172
#130683712
C11×#17722
#2078711