Finite Group Databasebeta

← #14654467

Subgroups — #14654467

Order 2816.

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

normal subgroups only

This group has 698 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#13079437C211yesmaximal, characteristic
2C2×#10622841C211yesmaximal, characteristic
3#13068540C211yesmaximal, characteristic
4#13066980C211yesmaximal, characteristic
5#13066979C211yesmaximal, characteristic
6#13066504C211yesmaximal, characteristic
7C2×C11×#451C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C22×C11×Q16—21no—
10C2×C11×C22⋊Q8C2211yescharacteristic
11C22×#4326—21no—
12C2×#66977C2211yescharacteristic
13C11×#451—22no—
14C11×#451—22no—
15C2×C11×#103—21no—
16C2×C11×C22⋊C8C2211yescharacteristic
17#10622841—22no—
18#10622841—21no—
19#10622841—22no—
20C2×#66900—22no—
21C2×#66899—21no—
22#10622820C2211yescharacteristic
23#10622820C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622665—22no—
26#10622663—21no—
27#10622656—21no—
28#10622584—21no—
29#10622166—22no—
30#10622107—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—44no—
37C22×Q8×C11D411yescharacteristic
38C22×Q8×C11D412yes—
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C22×Dic22D411yescharacteristic
42C2×C11×Q16—24no—
43C2×C11×Q16—44no—
44C22×C8×C11—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C22⋊Dic11—21no—
53C2×#4326—24no—
54C2×#4326—22no—
55C2×#4326—44no—
56C2×C4⋊Dic11D411yescharacteristic
57#66977—21no—
58#66977—21no—
59#66977—21no—
60#66977—21no—
61C2×Dic11⋊C4—21no—
62C2×#4318—21no—
63C2×#4318D412yes—
64C22×C11⋊C8—21no—
65C11×#103—24no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8D412yes—
68#66900—44no—
69#66899—24no—
70#66899—22no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yes—
77#66874—22no—
78#66872—22no—
79#9991—111nomaximal, Sylow
80C24×C11#4111yescharacteristic
81C2×Q8×C11—24no—
82C2×Q8×C11—24no—
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—44no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×Q8×C11—44no—
94C2×Q8×C11—44no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—42no—
101C22×C4×C11—44no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—21no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22—42no—
115C11×Q16—48no—
116C2×C8×C11—22no—
117C2×C8×C11—42no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C22⋊Dic11—41no—
125C22⋊Dic11—41no—
126#4326—48no—
127#4326—82no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132#4318—42no—
133#4318—42no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—42no—
137C2×C11⋊C8—41no—
138#3195—111no—
139C2×#451—111no—
140C2×#451D1111yescharacteristic
141#1784—111no—
142#1472—111no—
143#1472—111no—
144#1298—111no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—41no—
148C23×C11#12111yescharacteristic
149C23×C11#12111yescharacteristic
150C23×C11#12111yescharacteristic
151Q8×C11—24no—
152Q8×C11—24no—
153Q8×C11—42no—
154Q8×C11—42no—
155Q8×C11—44no—
156Q8×C11—42no—
157Q8×C11—44no—
158Q8×C11—42no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—24no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—44no—
168C2×C4×C11—44no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—81no—
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12711yescharacteristic
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181C2×Dic11—81no—
182Dic22—42no—
183Dic22—42no—
184C8×C11—42no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C11⋊C8—81no—
188C23×Q8C2×D1111yescharacteristic
189C22×Q16—21no—
190C22×Q16—221no—
191C2×C22⋊Q8—111no—
192C2×C22⋊Q8C2×D1111yescharacteristic
193#483—221no—
194#483—221no—
195#470—222no—
196#451—22no—
197#451—22no—
198#451—222no—
199#451—221no—
200#451—221no—
201#451—222no—
202C2×#103—21no—
203C2×#103—221no—
204C2×#101—222no—
205#407—111no—
206#407—111no—
207C2×C22⋊C8—111no—
208C2×C22⋊C8C2×D1111yescharacteristic
209#324—222no—
210#324—222no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—44no—
219C22×C11#39211yescharacteristic
220C22×C11#47312yes—
221C22×C11#47312yes—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—44no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11B(4,𝔽2)12yes—
229Dic11—81no—
230Dic11—81no—
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—21no—
234C22×Q8—21no—
235C22×Q8—21no—
236C22×Q8—44no—
237C22×Q8—111no—
238C22×Q8C22⋊D1111yescharacteristic
239C22×Q8C22⋊D1112yes—
240C23×C4—21no—
241C23×C4C22×D1111yescharacteristic
242C2×Q16—24no—
243C2×Q16—44no—
244C2×Q16—224no—
245C2×Q16—222no—
246C2×Q16—444no—
247C2×M16—112no—
248C2×M16—221no—
249C22×C8—21no—
250C22×C8—221no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—221no—
256C22⋊Q8—221no—
257C22⋊Q8—221no—
258C22⋊Q8—221no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4C22⋊D1111yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—221no—
265#106—222no—
266#103—24no—
267#103—222no—
268#103—224no—
269#103—222no—
270#101—444no—
271C22⋊C8—21no—
272C22⋊C8—112no—
273C22⋊C8—221no—
274C22⋊C8—221no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277C22⋊C8—221no—
278C22⋊C8C22⋊D1112yes—
279C2×C11—22no—
280C2×C11—22no—
281C2×C11—41no—
282C2×C11#202011yescharacteristic
283C2×C11#202011yescharacteristic
284C2×C11#202111yescharacteristic
285C24#434111yescharacteristic
286C2×Q8—24no—
287C2×Q8—24no—
288C2×Q8—24no—
289C2×Q8—22no—
290C2×Q8—21no—
291C2×Q8—22no—
292C2×Q8—21no—
293C2×Q8—44no—
294C2×Q8—42no—
295C2×Q8—42no—
296C2×Q8—42no—
297C2×Q8—42no—
298C2×Q8—44no—
299C2×Q8—44no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—221no—
303C2×Q8—221no—
304C2×Q8—442no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—44no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4D4×D1111yescharacteristic
315C22×C4D4×D1111yescharacteristic
316C22×C4D4×D1111yescharacteristic
317C22×C4C2×C22⋊D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320Q16—48no—
321Q16—448no—
322Q16—882no—
323M16—442no—
324M16—442no—
325C2×C8—22no—
326C2×C8—42no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—442no—
330C2×C8—441no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C11#999111yescharacteristic, complemented, Sylow
344C23—22no—
345C23—22no—
346C23—41no—
347C23#6699111yescharacteristic
348C23#6699211yescharacteristic
349C23#6699211yescharacteristic
350Q8—24no—
351Q8—24no—
352Q8—42no—
353Q8—42no—
354Q8—44no—
355Q8—42no—
356Q8—44no—
357Q8—42no—
358Q8—442no—
359Q8—442no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—442no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—881no—
379C2×C4#6699011yescharacteristic
380C2×C4#6699011yescharacteristic
381C2×C4#6699311yescharacteristic
382C2×C4#6700611yescharacteristic
383C8—42no—
384C8—442no—
385C8—442no—
386C8—881no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—44no—
395C22#1062280512yes—
396C22#1062281712yes—
397C22#1062283611yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—44no—
402C4—81no—
403C4—81no—
404C4—881no—
405C4—881no—
406C4#1062264512yes—
407C2—22no—
408C2—22no—
409C2—41no—
410C2#1306973411yescharacteristic
411C2#1306973511yescharacteristic
412C2#1306973911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#451C2
socleC22×C11#392
prime radicalC24×C11#41
hypercenterC2×#451D11
hypocenterC11#9991
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
343. C11#9991semidirect

Maximal subgroups

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

subgroupindex
#130794372
C2×#106228412
#130685402
#130669802
#130669792
#130665042
C2×C11×#4512
#999111