Finite Group Databasebeta

← #14658135

Subgroups — #14658135

Order 2816.

464 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069085C211yesmaximal, characteristic, complemented
2#13069055C211yesmaximal, characteristic
3#13068820C211yesmaximal, characteristic, complemented
4#13067188C211yesmaximal, characteristic, complemented
5#13066976C211yesmaximal, characteristic
6#13066521C211yesmaximal, characteristic, complemented
7C11×#3193C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C22×#4318C2211yescharacteristic
11C11×#484—21no—
12C11×#480—21no—
13C11×#468—21no—
14C11×#468—21no—
15C11×#450—21no—
16C11×#448—21no—
17C11×#407C2211yescharacteristic
18C2×#66900—21no—
19C2×#66896—21no—
20#10622825C2211yescharacteristic
21#10622820C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×#66886—21no—
24#10622196—21no—
25#10622176—22no—
26#10622168—21no—
27#10622167—21no—
28#10622163—22no—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C2×C11×SD16—21no—
34C2×C11×SD16—21no—
35C2×C11×M16D411yescharacteristic
36C2×C11×M16D411yescharacteristic
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C22⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×#4318—21no—
53C2×#4318—21no—
54C2×#4318—21no—
55C2×#4318—42no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8—21no—
58C11×#107—21no—
59C11×#107—21no—
60C11×#103—21no—
61C11×#103—21no—
62C11×#102—21no—
63C11×#102—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66#66900—42no—
67#66896—42no—
68C11⋊#95—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)D412yes—
73#66886—42no—
74#10561—111nomaximal, Sylow
75C24×C11—21no—
76C24×C11#4111yescharacteristic
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—82no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×Dic11—41no—
100C11×SD16—81no—
101C11×SD16—81no—
102C11×M16—41no—
103C11×M16—41no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C22⋊Dic11—81no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119#4318—22no—
120#4318—22no—
121#4318—41no—
122#4318—41no—
123#4318—41no—
124#4318—41no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#3193D1111yescharacteristic
133#1901—111no—
134#1895—111no—
135#1855—111no—
136#1520—111no—
137#1471—111no—
138#1305—111no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11#12111yescharacteristic
149C23×C11#12311yescharacteristic
150C23×C11#12411yescharacteristic
151Q8×C11—41no—
152Q8×C11—41no—
153Q8×C11—81no—
154D4×C11—42no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—82no—
158D4×C11—82no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12311yescharacteristic
178C2×Dic11—81no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181C8×C11—41no—
182C8×C11—41no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C11⋊C8—81no—
186C22×M16—111no—
187C2×C22⋊Q8C2×D1111yescharacteristic
188C2×#121C2×D1111yescharacteristic
189#484—21no—
190#480—21no—
191#468—21no—
192#468—21no—
193#450—21no—
194#448—21no—
195C2×#108—221no—
196C2×#102—221no—
197C2×#101—221no—
198#407—111no—
199#407C2×D1111yescharacteristic
200C2×C22⋊C8—111no—
201#380—111no—
202#343—221no—
203#341—221no—
204#340—221no—
205#328—222no—
206#323—222no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—161no—
221C22×C11—161no—
222C22×C11#39411yescharacteristic
223C22×C11#47111yescharacteristic
224C22×C11#47311yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11B(4,𝔽2)11yescharacteristic
232C4×C11#45811yescharacteristic
233Dic11—161no—
234C22×Q8C22⋊D1111yescharacteristic
235C22×D4—21no—
236C22×D4C22⋊D1111yescharacteristic
237C23×C4C22×D1111yescharacteristic
238C2×SD16—21no—
239C2×SD16—21no—
240C2×M16—221no—
241C2×M16—221no—
242C2×M16—221no—
243C2×M16—442no—
244C2×M16C22⋊D1111yescharacteristic
245C2×M16C22⋊D1111yescharacteristic
246C22×C8—221no—
247C22×C8—221no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252#121—21no—
253#121—21no—
254#121—21no—
255#121—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4C22⋊D1111yescharacteristic
259C2×C4⋊C4C22⋊D1111yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—221no—
263#108—442no—
264#107—21no—
265#107—21no—
266#103—21no—
267#103—21no—
268#102—21no—
269#102—21no—
270#102—442no—
271#101—442no—
272C22⋊C8—21no—
273C22⋊C8—21no—
274C22⋊C8—112no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277C22⋊C8—221no—
278#95—221no—
279C2×C11—21no—
280C2×C11—21no—
281C2×C11—41no—
282C2×C11—41no—
283C2×C11—161no—
284C2×C11#204411yescharacteristic
285C2×C11#204811yescharacteristic
286C2×C11#205211yescharacteristic
287C24—21no—
288C24#434111yescharacteristic
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—82no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—441no—
306C22×C4D4×D1111yescharacteristic
307C22×C4#434111yescharacteristic
308C22×C4#434111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310C22×C4C2×C22⋊D1111yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312SD16—81no—
313SD16—81no—
314M16—41no—
315M16—41no—
316M16—222no—
317M16—222no—
318M16—441no—
319M16—441no—
320M16—441no—
321M16—441no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—441no—
327C2×C8—441no—
328C2×C8—441no—
329C2×C8—441no—
330C2×C8—441no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—881no—
344C11#1056111yescharacteristic, complemented, Sylow
345C23—21no—
346C23—21no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—81no—
353C23—81no—
354C23#6698811yescharacteristic
355C23#6698911yescharacteristic
356C23#6699211yescharacteristic
357Q8—41no—
358Q8—41no—
359Q8—81no—
360D4—42no—
361D4—41no—
362D4—41no—
363D4—82no—
364D4—82no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—881no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4#6698811yescharacteristic
384C2×C4#6699111yescharacteristic
385C2×C4#6699211yescharacteristic
386C2×C4#6700611yescharacteristic
387C8—41no—
388C8—41no—
389C8—442no—
390C8—442no—
391C8—881no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—161no—
406C22—161no—
407C22#1062281611yescharacteristic
408C22#1062281711yescharacteristic
409C22#1062283511yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—81no—
414C4—81no—
415C4—81no—
416C4—1761no—
417C4#1062285611yescharacteristic
418C4#1062285711yescharacteristic
419C2—21no—
420C2—21no—
421C2—41no—
422C2—41no—
423C2—161no—
424C2#1306986411yescharacteristic
425C2#1306988611yescharacteristic
426C2#1306991211yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3193C2
socleC22×C11#394
prime radicalC2×C11×#121C22
hypercenter#3193D11
hypocenterC11#10561
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3193

Complements

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

NH ≅ G/Ntype
1. #13069085C2semidirect
3. #13068820C2semidirect
4. #13067188C2semidirect
6. #13066521C2semidirect
344. C11#10561semidirect

Maximal subgroups

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

subgroupindex
#130690852
#130690552
#130688202
#130671882
#130669762
#130665212
C11×#31932
#1056111