Finite Group Databasebeta

← #14780316

Subgroups — #14780316

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071900C211yesmaximal, characteristic
2#13069554C212yesmaximal, complemented
3#13069232C212yesmaximal, complemented
4#13069226C212yesmaximal, complemented
5#13068909C211yesmaximal, characteristic
6#13068799C212yesmaximal, complemented
7#13068793C212yesmaximal, complemented
8#13068734C212yesmaximal, complemented
9C11×#1870C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C23×C11⋊C8C2211yescharacteristic
13C2×C4×Dic22C2211yescharacteristic
14C2×C11×C22⋊C8C2211yescharacteristic
15C2×C11×C22⋊C8C2212yes—
16#10622835C412yes—
17C4×C22⋊Dic11C2212yes—
18C4×C22⋊Dic11C2212yes—
19C2×C22⋊(C11⋊C8)C2212yes—
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21C2×#66879C2212yes—
22C2×Dic11⋊C8C2212yes—
23C2×Dic11⋊C8C2212yes—
24C2×Dic11⋊C8C2212yes—
25#10622595C412yes—
26#10622566C411yescharacteristic
27#10622566C411yescharacteristic
28#10622560C411yescharacteristic
29#10622560C411yescharacteristic
30#10622545C2211yescharacteristic
31C11×#336C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622188C2212yes—
36#10622162C2212yes—
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×Dic22C2×C411yescharacteristic
41C2×C11×M16—41no—
42C2×C11×M16—42no—
43C22×C8×C11C2312yes—
44C22×C8×C11C2312yes—
45C4×D4×C11—41no—
46C4×D4×C11—41no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4C2×C411yescharacteristic
49C2×C11×C22⋊C4C2×C411yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11C2×C412yes—
52C2×C22⋊Dic11C2×C412yes—
53C2×C22⋊Dic11C2×C412yes—
54C2×C22⋊Dic11C2×C412yes—
55C2×C4⋊Dic11C2×C411yescharacteristic
56C2×Dic11⋊C4C2×C412yes—
57C2×C4×Dic11C2312yes—
58C2×C4×Dic11C2312yes—
59C22×C11⋊C8—41no—
60C22×C11⋊C8—42no—
61C22×C11⋊C8C2312yes—
62C22×C11⋊C8C2312yes—
63C4×Dic22—41no—
64C4×Dic22—41no—
65C11×C22⋊C8—42no—
66C11×C22⋊C8—41no—
67C11⋊#95C2×C411yescharacteristic
68C11⋊#95C2×C411yescharacteristic
69C11⋊#95C2×C412yes—
70C11⋊#95C2×C412yes—
71C11⋊#95C2×C412yes—
72C11⋊#95C2×C412yes—
73C11⋊#95C2×C412yes—
74C22⋊(C11⋊C8)—42no—
75C22⋊(C11⋊C8)—41no—
76#66879—42no—
77Dic11⋊C8—42no—
78Dic11⋊C8—42no—
79Dic11⋊C8—42no—
80#23354—111nomaximal, Sylow
81C24×C11C22×C411yescharacteristic
82C24×C11C22×C411yescharacteristic
83C2×D4×C11—22no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×Dic11C22×C412yes—
100C22×Dic11C22×C412yes—
101C22×Dic11C22×C412yes—
102C22×Dic11C22×C412yes—
103C2×Dic22—41no—
104C2×Dic22—42no—
105C11×M16—44no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—21no—
116C42×C11—21no—
117C22⋊Dic11—24no—
118C22⋊Dic11—42no—
119C22⋊Dic11—42no—
120C22⋊Dic11—42no—
121C4⋊Dic11—41no—
122Dic11⋊C4—42no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125C4×Dic11—22no—
126C4×Dic11—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—44no—
134#2398—111no—
135#1985—112no—
136#1924—112no—
137#1924—112no—
138#1870D1111yescharacteristic
139#1869—111no—
140#1851—112no—
141#1850—112no—
142#1832—112no—
143C23×C11—21no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—22no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—22no—
152C23×C11#13112yes—
153C23×C11C23×C411yescharacteristic
154D4×C11—44no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—21no—
162C2×C4×C11—22no—
163C2×C4×C11—21no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11H(5,𝔽2)12yes—
171C2×C4×C11H(5,𝔽2)11yescharacteristic
172C2×C4×C11H(5,𝔽2)11yescharacteristic
173C2×C4×C112−1+412yes—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186Dic22—44no—
187C8×C11—42no—
188C8×C11—42no—
189C11⋊C8—42no—
190C11⋊C8—42no—
191C22×M16C2×D1111yescharacteristic
192C23×C8—111no—
193C2×C4×Q8—111no—
194C2×C4×D4C2×D1111yescharacteristic
195C2×C4⋊C8—112no—
196C2×C4⋊C8—112no—
197C2×C4⋊C8—112no—
198C2×C22⋊C8—112no—
199C2×C22⋊C8—111no—
200C2×C22⋊C8C2×D1112yes—
201C2×C22⋊C8C2×D1111yescharacteristic
202C2×#97—112no—
203#400—112no—
204#397—111no—
205#397—111no—
206#394—112no—
207#393—111no—
208#393—111no—
209C4×C22⋊C4—112no—
210C4×C22⋊C4—112no—
211#376—111no—
212#336—112no—
213#336—112no—
214#336—112no—
215#336—112no—
216#336—112no—
217#336C2×D1112yes—
218C22×C11—22no—
219C22×C11—24no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—42no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11#51811yescharacteristic
229C22×C11#52012yes—
230C22×C11C2×#13111yescharacteristic
231C22×C11#56811yescharacteristic
232C22×C11#56812yes—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11H(3,𝔽4)11yescharacteristic
238C4×C11#56212yes—
239C4×C11#56311yescharacteristic
240Dic11—42no—
241Dic11—42no—
242Dic11—42no—
243Dic11—42no—
244C22×Q8—111no—
245C22×D4C4×D1111yescharacteristic
246C23×C4C22×D1111yescharacteristic
247C23×C4C22×D1111yescharacteristic
248C2×M16—42no—
249C2×M16—41no—
250C22×C8—112no—
251C22×C8—112no—
252C22×C8—442no—
253C22×C8—441no—
254C22×C8C22×D1112yes—
255C22×C8C22×D1112yes—
256C4×Q8—441no—
257C4×Q8—441no—
258C4×D4—41no—
259C4×D4—41no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4C4×D1111yescharacteristic
263C2×C22⋊C4—112no—
264C2×C22⋊C4—112no—
265C2×C22⋊C4—112no—
266C2×C22⋊C4—112no—
267C2×C22⋊C4C4×D1111yescharacteristic
268C2×C22⋊C4C4×D1111yescharacteristic
269C2×C42—112no—
270C2×C42—112no—
271C2×C42C22×D1111yescharacteristic
272C4⋊C8—442no—
273C4⋊C8—442no—
274C4⋊C8—442no—
275C22⋊C8—41no—
276C22⋊C8—42no—
277C22⋊C8—441no—
278C22⋊C8—442no—
279#97—442no—
280#95—111no—
281#95—111no—
282#95—112no—
283#95—112no—
284#95—112no—
285#95—112no—
286#95—112no—
287C2×C11—42no—
288C2×C11—81no—
289C2×C11#237911yescharacteristic
290C2×C11#297611yescharacteristic
291C2×C11#297811yescharacteristic
292C2×C11#299212yes—
293C2×C11#299512yes—
294C24C2×C4×D1111yescharacteristic
295C24C2×C4×D1111yescharacteristic
296C2×Q8—441no—
297C2×Q8—442no—
298C2×D4—22no—
299C2×D4—41no—
300C2×D4—41no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—112no—
310C22×C4—112no—
311C22×C4—112no—
312C22×C4—112no—
313C22×C4C2×C4×D1111yescharacteristic
314C22×C4C2×C4×D1111yescharacteristic
315C22×C4C2×C4×D1111yescharacteristic
316C22×C4C2×C4×D1111yescharacteristic
317C22×C4C23×D1111yescharacteristic
318M16—44no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—222no—
331C2×C8—444no—
332C4⋊C4—41no—
333C4⋊C4—442no—
334C4⋊C4—441no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—224no—
338C22⋊C4—442no—
339C22⋊C4—442no—
340C22⋊C4—442no—
341C42—21no—
342C42—21no—
343C42—222no—
344C42—222no—
345C42—222no—
346C42—222no—
347C11#2335411yescharacteristic, complemented, Sylow
348C23—21no—
349C23—21no—
350C23—22no—
351C23—22no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—22no—
356C23—22no—
357C23#6696012yes—
358C23C22×C4×D1111yescharacteristic
359Q8—444no—
360D4—44no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—222no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4#6703712yes—
389C2×C4#6703711yescharacteristic
390C2×C4#6703711yescharacteristic
391C2×C4#6704312yes—
392C8—42no—
393C8—42no—
394C8—442no—
395C8—442no—
396C22—22no—
397C22—24no—
398C22—42no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—42no—
406C22#1062301711yescharacteristic
407C22#1062307712yes—
408C22C2×#6696011yescharacteristic
409C22#1062327611yescharacteristic
410C22#1062328112yes—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—442no—
416C4—442no—
417C4—442no—
418C4—442no—
419C4#1062312511yescharacteristic
420C4#1062315212yes—
421C4#1062318211yescharacteristic
422C2—42no—
423C2—81no—
424C2#1307178611yescharacteristic
425C2#1307766611yescharacteristic
426C2#1307767411yescharacteristic
427C2#1307775612yes—
428C2#1307778012yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#23354
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #13069554C2semidirect
3. #13069232C2semidirect
4. #13069226C2semidirect
6. #13068799C2semidirect
7. #13068793C2semidirect
8. #13068734C2semidirect
347. C11#23354semidirect

Maximal subgroups

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

subgroupindex
#130719002
#130695542
#130692322
#130692262
#130689092
#130687992
#130687932
#130687342
C11×#18702
#2335411