Finite Group Databasebeta

← #14670595

Subgroups — #14670595

Order 2816.

472 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 89 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#13071788C211yesmaximal, characteristic
2C2×#10622115C211yesmaximal, characteristic
3#13069019C211yesmaximal, characteristic
4#13068831C211yesmaximal, characteristic, complemented
5#13066743C211yesmaximal, characteristic, complemented
6#13066742C211yesmaximal, characteristic, complemented
7C11×#1857C211yesmaximal, characteristic, complemented
8C11×#519C2211yescharacteristic
9C2×#67000C2211yescharacteristic
10C11×#428—21no—
11C2×C11×#101C2211yescharacteristic
12C11×#391C2211yescharacteristic
13#10622843C2211yescharacteristic
14C2×#66900C2211yescharacteristic
15C2×#66900C2211yescharacteristic
16#10622614—21no—
17#10622608—21no—
18#10622602—21no—
19#10622553—21no—
20#10622282—21no—
21#10622281—21no—
22#10622278—21no—
23#10622263—21no—
24C11×#339—21no—
25#10622170—21no—
26#10622170—21no—
27#10622115C414yescomplemented
28C22×Q8×C11C2311yescharacteristic
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C2×C11×M16—21no—
32C4×Q8×C11—41no—
33C4×Q8×C11—41no—
34C11×#117—21no—
35C11×#117—21no—
36C11×#117—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39#67000—21no—
40#67000—21no—
41#67000C2×C412yes—
42#67000Q812yes—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11D411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11D411yescharacteristic
52C2×C4×Dic11D411yescharacteristic
53C2×#4318—21no—
54C2×#4318—21no—
55C11×#107—41no—
56C11×#106—41no—
57C11×#101—21no—
58C11×#101C2×C412yescomplemented
59C11×#95—21no—
60C11×#95—21no—
61#66900—21no—
62#66900—21no—
63#66900—21no—
64#66900C2×C412yescomplemented
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69#66873—41no—
70#66873—41no—
71#66872—41no—
72#66871—41no—
73#12970—111nomaximal, Sylow
74C23×D11—21no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11C22×C411yescharacteristic
78C2×Q8×C11C2×Q811yescharacteristic
79C2×Q8×C11#4111yescharacteristic
80C2×Q8×C11#4111yescharacteristic
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C2×D44—21no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44C4⋊C412yes—
93C2×C4×D11—81no—
94C2×C4×D11—81no—
95C2×C4×D11—81no—
96C11×M16—22no—
97C11×M16—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11—41no—
110C42×C11—41no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—81no—
116(C2×D11)⋊C4—81no—
117(C2×D11)⋊C4—81no—
118C4⋊Dic11—41no—
119Dic11⋊C4—81no—
120Dic11⋊C4—81no—
121C4×Dic11—21no—
122C4×Dic11—41no—
123C4×Dic11C4⋊C412yes—
124#4318—22no—
125#4318—41no—
126#4318—41no—
127#4318—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130#2379—111no—
131C2×#355—111no—
132#1888—111no—
133#1857—111no—
134#1857D1111yescharacteristic, complemented
135#1394—111no—
136#1394—111no—
137C23×C11#12011yescharacteristic
138C22×D11—22no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145Q8×C11—41no—
146Q8×C11—41no—
147Q8×C11—41no—
148Q8×C11—41no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11C2×C4⋊C411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11C4×D411yescharacteristic
166C2×C4×C11C22⋊Q811yescharacteristic
167C2×C4×C11C22⋊Q811yescharacteristic
168C2×C4×C11#12311yescharacteristic
169C2×Dic11—22no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178D44—42no—
179D44—81no—
180C4×D11—84no—
181C8×C11—42no—
182C11⋊C8—42no—
183C11⋊C8—81no—
184C2×#124—111no—
185#519C2×D1111yescharacteristic
186#428—21no—
187#428—221no—
188#418—221no—
189C2×#101—111no—
190C2×#101—111no—
191C2×#101C2×D1111yescharacteristic
192#391—111no—
193#391C2×D1111yescharacteristic
194#388—221no—
195#388—221no—
196#386—221no—
197#385—221no—
198#385—221no—
199#382—221no—
200#355—114no—
201#339—21no—
202#339—221no—
203#339—221no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#38511yescharacteristic
207C22×C11B(4,𝔽2)11yescharacteristic
208C22×C11#45811yescharacteristic
209C2×D11—42no—
210C2×D11—42no—
211C2×D11—42no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11—81no—
226Dic11—42no—
227Dic11—81no—
228Dic11—81no—
229C22×Q8C22×D1111yescharacteristic
230C22×D4—111no—
231C23×C4—221no—
232C2×M16—21no—
233C2×M16—221no—
234C2×M16—221no—
235#124—112no—
236#124—112no—
237#124—221no—
238#124—221no—
239C4×Q8—41no—
240C4×Q8—41no—
241#117—21no—
242#117—21no—
243#117—21no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4C22⋊D1111yescharacteristic
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C42—111no—
254C2×C42—111no—
255C2×C42C22⋊D1111yescharacteristic
256#107—41no—
257#107—441no—
258#106—41no—
259#106—441no—
260#102—441no—
261#102—441no—
262#101—21no—
263#101—112no—
264#101—221no—
265#101—221no—
266#101—221no—
267#101C4×D1112yescomplemented
268#95—21no—
269#95—21no—
270#95—221no—
271#95—221no—
272#95—221no—
273#95—221no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11#186711yescharacteristic
277C2×C11#220211yescharacteristic
278C2×C11#220311yescharacteristic
279D11—82no—
280C24—221no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8C2×C4×D1111yescharacteristic
284C2×Q8#433911yescharacteristic
285C2×Q8Q8×D1111yescharacteristic
286C2×Q8#434311yescharacteristic
287C2×D4—112no—
288C2×D4—221no—
289C2×D4—441no—
290C2×D4—441no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—881no—
297C22×C4—881no—
298C22×C4—881no—
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4C2×C22⋊D1111yescharacteristic
302M16—22no—
303M16—41no—
304M16—222no—
305M16—441no—
306M16—441no—
307M16—441no—
308C2×C8—41no—
309C2×C8—441no—
310C2×C8—441no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—441no—
319C4⋊C4—881no—
320C4⋊C4—881no—
321C22⋊C4—41no—
322C22⋊C4—222no—
323C22⋊C4—222no—
324C22⋊C4—222no—
325C22⋊C4—222no—
326C22⋊C4—881no—
327C22⋊C4—881no—
328C22⋊C4—881no—
329C42—41no—
330C42—41no—
331C42—41no—
332C42—41no—
333C42—112no—
334C42—221no—
335C42—441no—
336C11#1297011yescharacteristic, complemented, Sylow
337C23—222no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23—441no—
342C23—441no—
343C23—441no—
344C23#6699011yescharacteristic
345Q8—41no—
346Q8—41no—
347Q8—41no—
348Q8—41no—
349D4—442no—
350D4—881no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—222no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—884no—
375C2×C4C4⋊C4×D1111yescharacteristic
376C2×C4#6694611yescharacteristic
377C2×C4#6694711yescharacteristic
378C2×C4#6694911yescharacteristic
379C2×C4C4×C22⋊D1111yescharacteristic
380C2×C4#6699911yescharacteristic
381C8—42no—
382C8—442no—
383C8—881no—
384C22—21no—
385C22—21no—
386C22—442no—
387C22—442no—
388C22—442no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22—881no—
393C22#1062260211yescharacteristic
394C22#1062264511yescharacteristic
395C22#1062266611yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—81no—
406C4—442no—
407C4—881no—
408C4—881no—
409C2—21no—
410C2—21no—
411C2—882no—
412C2#1306889511yescharacteristic
413C2#1307063211yescharacteristic
414C2#1307063511yescharacteristic
subgroupG/H
centerC22#10622645
commutatorC2×Q8×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#1857C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D44D4
cosocleC22×Q8×C11C23
hypercenter#1857D11
hypocenterC11#12970
LCSG ▷ C2×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

Complements

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

NH ≅ G/Ntype
4. #13068831C2semidirect
5. #13066743C2semidirect
6. #13066742C2semidirect
7. C11×#1857C2semidirect
27. #10622115C4semidirect
58. C11×#101C2×C4semidirect
64. #66900C2×C4semidirect
134. #1857D11semidirect
267. #101C4×D11semidirect
336. C11#12970semidirect

Maximal subgroups

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

subgroupindex
#130717882
C2×#106221152
#130690192
#130688312
#130667432
#130667422
C11×#18572
#1297011