Finite Group Databasebeta

← #14672921

Subgroups — #14672921

Order 2816.

540 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 75 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#13076602C211yesmaximal, characteristic, complemented
2#13068575C211yesmaximal, characteristic
3#13068575C211yesmaximal, characteristic
4#13066743C211yesmaximal, characteristic, complemented
5#13066742C211yesmaximal, characteristic, complemented
6#13066742C211yesmaximal, characteristic, complemented
7C11×#1793C211yesmaximal, characteristic
8C2×C11×2−1+4C2211yescharacteristic
9C2×C11×#104—21no—
10C11×#417—21no—
11C2×C11×#101C2211yescharacteristic
12C11×#391C2211yescharacteristic
13C2×#66901—21no—
14C2×#66901—21no—
15#10622845—21no—
16#10622845—21no—
17#10622843C2211yescharacteristic
18#10622843C2211yescharacteristic
19C2×#66900C2211yescharacteristic
20C2×#66900C2211yescharacteristic
21#10622597—21no—
22#10622546—21no—
23#10622273—21no—
24#10622270—21no—
25#10622267—21no—
26#10622260—21no—
27C11×2−1+4—21no—
28C11×2−1+4—21no—
29C11×2−1+4—21no—
30C11×2−1+4—42no—
31C11×2−1+4Q812yes—
32C2×C11×#41—21no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—41no—
36C22×Q8×C11—41no—
37C22×Q8×C11C2311yescharacteristic
38C2×C11×M16—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C2×#4318—21no—
51C2×#4318—21no—
52C11×#104—42no—
53C11×#103—41no—
54C11×#102—41no—
55C11×#101—21no—
56C11×#101—21no—
57C11×#95—21no—
58C11×#95—21no—
59#66901—42no—
60#66901—42no—
61#66900—21no—
62#66900—21no—
63#66900—21no—
64#66900—21no—
65#66899—41no—
66#66899—41no—
67#66896—41no—
68#66896—41no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76#13379—111nomaximal, Sylow
77C11×#41—22no—
78C11×#41—22no—
79C11×#41—22no—
80C11×#41—22no—
81C11×#41—22no—
82C11×#41—22no—
83C11×#41—41no—
84C11×#41—41no—
85C11×#41—41no—
86C11×#41—42no—
87C11×#41—42no—
88C11×#41—42no—
89C11×#41—42no—
90C11×#41—41no—
91C11×#41—41no—
92C11×#41—41no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—41no—
97C2×Q8×C11—41no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C2×Q8×C11C2×Q811yescharacteristic
103C2×Q8×C11#4111yescharacteristic
104C2×Q8×C11#4111yescharacteristic
105C2×Q8×C11#4111yescharacteristic
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—41no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—41no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C11×M16—41no—
123C11×M16—41no—
124C2×C8×C11—41no—
125C11×C4⋊C4—41no—
126C42×C11—41no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4⋊Dic11—42no—
130Dic11⋊C4—42no—
131Dic11⋊C4—42no—
132Dic11⋊C4—81no—
133Dic11⋊C4—81no—
134C4×Dic11—41no—
135C4×Dic11—41no—
136#4318—41no—
137#4318—41no—
138#4318—41no—
139#4318—41no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8—41no—
142#2809—111no—
143#1793—111no—
144#1793—111no—
145#1793D1111yescharacteristic
146#1394—111no—
147#1394—111no—
148#1394—111no—
149C23×C11—41no—
150C23×C11#12011yescharacteristic
151Q8×C11—22no—
152Q8×C11—22no—
153Q8×C11—22no—
154Q8×C11—41no—
155Q8×C11—41no—
156Q8×C11—41no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—41no—
161D4×C11—22no—
162D4×C11—22no—
163D4×C11—22no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—41no—
167D4×C11—42no—
168D4×C11—42no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11C22⋊Q811yescharacteristic
189C2×C4×C11C22⋊Q811yescharacteristic
190C2×C4×C11C22⋊Q811yescharacteristic
191C2×C4×C11#12411yescharacteristic
192C2×C4×C11#12411yescharacteristic
193C2×C4×C11#12411yescharacteristic
194C2×Dic11—22no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C8×C11—81no—
206C11⋊C8—81no—
207C11⋊C8—81no—
208C2×2−1+4C2×D1111yescharacteristic
209C2×#104—21no—
210C2×#104—221no—
211C2×#104—221no—
212#417—21no—
213#417—221no—
214#417—221no—
215C2×#101—111no—
216C2×#101—111no—
217C2×#101C2×D1111yescharacteristic
218#400—221no—
219#398—221no—
220#398—221no—
221#391—111no—
222#391—111no—
223#391C2×D1111yescharacteristic
224#389—221no—
225#387—221no—
226#387—221no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—42no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11#39311yescharacteristic
233C22×C11B(4,𝔽2)11yescharacteristic
234C22×C11B(4,𝔽2)11yescharacteristic
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—42no—
242C4×C11—81no—
243C4×C11—81no—
244Dic11—42no—
245Dic11—81no—
246Dic11—81no—
247Dic11—81no—
2482−1+4—21no—
2492−1+4—21no—
2502−1+4—21no—
2512−1+4—42no—
2522−1+4Dic2212yes—
253C2×#41—21no—
254C2×#41—21no—
255C2×#41—21no—
256C2×#41—41no—
257C22×Q8—41no—
258C22×Q8C22×D1111yescharacteristic
259C2×M16—21no—
260C2×M16—221no—
261C2×M16—221no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4C22⋊D1111yescharacteristic
270C2×C42—111no—
271C2×C42—111no—
272C2×C42C22⋊D1111yescharacteristic
273#104—42no—
274#104—442no—
275#104—442no—
276#103—41no—
277#103—441no—
278#103—441no—
279#102—41no—
280#102—441no—
281#102—441no—
282#101—21no—
283#101—21no—
284#101—221no—
285#101—221no—
286#101—221no—
287#101—221no—
288#95—21no—
289#95—21no—
290#95—221no—
291#95—221no—
292#95—221no—
293#95—221no—
294#95—221no—
295#95—221no—
296#95—221no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—82no—
300C2×C11#202911yescharacteristic
301C2×C11#220311yescharacteristic
302C2×C11#220411yescharacteristic
303#41—22no—
304#41—22no—
305#41—22no—
306#41—22no—
307#41—22no—
308#41—22no—
309#41—41no—
310#41—41no—
311#41—41no—
312#41—42no—
313#41—42no—
314#41—42no—
315#41—42no—
316#41—41no—
317#41—41no—
318#41—41no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—41no—
323C2×Q8—41no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×Q8—42no—
327C2×Q8—42no—
328C2×Q8C2×Dic2211yescharacteristic
329C2×Q8#433911yescharacteristic
330C2×Q8#434111yescharacteristic
331C2×Q8#434111yescharacteristic
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—41no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4D4×D1111yescharacteristic
346C22×C4D4×D1111yescharacteristic
347C22×C4C2×C22⋊D1111yescharacteristic
348M16—41no—
349M16—41no—
350M16—441no—
351M16—441no—
352M16—441no—
353M16—441no—
354C2×C8—41no—
355C2×C8—441no—
356C2×C8—441no—
357C4⋊C4—41no—
358C4⋊C4—441no—
359C4⋊C4—441no—
360C4⋊C4—442no—
361C4⋊C4—442no—
362C4⋊C4—442no—
363C4⋊C4—881no—
364C4⋊C4—881no—
365C42—41no—
366C42—441no—
367C42—441no—
368C11#1337911yescharacteristic, complemented, Sylow
369C23—41no—
370C23#6699011yescharacteristic
371Q8—22no—
372Q8—22no—
373Q8—22no—
374Q8—41no—
375Q8—41no—
376Q8—41no—
377Q8—41no—
378Q8—41no—
379Q8—41no—
380Q8—41no—
381D4—22no—
382D4—22no—
383D4—22no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—42no—
388D4—42no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—222no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—442no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4#6693111yescharacteristic
420C2×C4#6693111yescharacteristic
421C2×C4#6693811yescharacteristic
422C2×C4#6693811yescharacteristic
423C2×C4#6697711yescharacteristic
424C2×C4#6698911yescharacteristic
425C8—81no—
426C8—881no—
427C8—881no—
428C22—21no—
429C22—21no—
430C22—42no—
431C22—81no—
432C22—81no—
433C22#1062256011yescharacteristic
434C22#1062264511yescharacteristic
435C22#1062264511yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—42no—
443C4—81no—
444C4—81no—
445C4—442no—
446C4—881no—
447C4—881no—
448C4—881no—
449C2—21no—
450C2—21no—
451C2—82no—
452C2#1306978011yescharacteristic
453C2#1307063511yescharacteristic
454C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#1793C2
socleC22×C11B(4,𝔽2)
prime radicalC2×C11×2−1+4C22
hypercenter#1793D11
hypocenterC11#13379
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1793

Complements

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

NH ≅ G/Ntype
1. #13076602C2semidirect
4. #13066743C2semidirect
5. #13066742C2semidirect
6. #13066742C2semidirect
368. C11#13379semidirect

Maximal subgroups

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

subgroupindex
#130766022
#130685752
#130667432
#130667422
C11×#17932
#1337911