Finite Group Databasebeta

← #14648854

Subgroups — #14648854

Order 2816.

516 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 95 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#13077700C211yesmaximal, characteristic, complemented
2#13071900C211yesmaximal, characteristic
3C4×#66888C211yesmaximal, characteristic, complemented
4#13067059C211yesmaximal, characteristic
5#13066510C211yesmaximal, characteristic, complemented
6#13066508C211yesmaximal, characteristic, complemented
7C11×#1490C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12#10622835C411yescharacteristic
13#10622835C411yescharacteristic
14C4×C22⋊Dic11—21no—
15C4×C22⋊Dic11—21no—
16C2×#66888—21no—
17#10622595C411yescharacteristic
18#10622595C411yescharacteristic
19#10622566—21no—
20#10622560—21no—
21#10622545C2211yescharacteristic
22#10622539C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622441—22no—
25#10622332—21no—
26#10622331—21no—
27#10622314—22no—
28C11×D4⋊C8—22no—
29#10622192—21no—
30D4⋊(C11⋊C8)—22no—
31C22×D4×C11C2×C411yescharacteristic
32C23×C4×C11—21no—
33C22×Dic22D411yescharacteristic
34C2×C11×M16—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×Dic11⋊C4C2×C411yescharacteristic
48C2×Dic11⋊C4C2×C411yescharacteristic
49C2×C4×Dic11—21no—
50C2×C4×Dic11D411yescharacteristic
51C2×C4×Dic11D411yescharacteristic
52C2×#4318—21no—
53C4×Dic22—21no—
54C4×Dic22—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C11×C4⋊C8D412yes—
58C11×C22⋊C8—21no—
59C11×#97—21no—
60C11×#97—21no—
61C4×C8×C11—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95C2×C411yescharacteristic
68C11⋊#95C2×C411yescharacteristic
69C22⋊(C11⋊C8)—21no—
70#66888—24no—
71#66879—22no—
72Dic11⋊C8—22no—
73Dic11⋊C8—22no—
74C8×Dic11—22no—
75C4⋊(C11⋊C8)D412yes—
76#66867—21no—
77#66867—21no—
78C4×C11⋊C8—21no—
79#9032—111nomaximal, Sylow
80C24×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—42no—
84C22×C4×C11—21no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11C22⋊C411yescharacteristic
95C22×Dic11C22⋊C411yescharacteristic
96C22×Dic11C22⋊C411yescharacteristic
97C22×Dic11C22⋊C411yescharacteristic
98C2×Dic22—22no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—41no—
102C11×M16—22no—
103C11×M16—41no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114C22⋊Dic11—42no—
115C22⋊Dic11—42no—
116C22⋊Dic11—42no—
117C22⋊Dic11—42no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122Dic11⋊C4—21no—
123Dic11⋊C4—21no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—42no—
129#4318—22no—
130#4318—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—41no—
133#2983—111no—
134#2398—111no—
135C4×#101—111no—
136#1490—111no—
137#1490D1111yescharacteristic
138#1300—111no—
139#1300—111no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11C2×C22⋊C411yescharacteristic
148D4×C11—22no—
149D4×C11—22no—
150D4×C11—41no—
151D4×C11—41no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—82no—
160C2×C4×C11—82no—
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12311yescharacteristic
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11#10412yes—
183Dic22—42no—
184Dic22—42no—
185C8×C11—42no—
186C8×C11—42no—
187C11⋊C8—42no—
188C11⋊C8—42no—
189C2×C4×Q8—111no—
190C2×C4×D4C2×D1111yescharacteristic
191#446—222no—
192#446—222no—
193#432—111no—
194#432—221no—
195#432C2×D1111yescharacteristic
196#431—221no—
197C2×#101—221no—
198C4×M16—111no—
199C4×M16C2×D1111yescharacteristic
200#400—111no—
201#400—111no—
202#397—221no—
203#394—111no—
204#394—111no—
205#393—221no—
206C4×C22⋊C4—221no—
207C4×C22⋊C4—221no—
208#376—111no—
209#343—221no—
210D4⋊C8—22no—
211D4⋊C8—222no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11#38611yescharacteristic
222C22×C11C2×#10411yescharacteristic
223C22×C11#42111yescharacteristic
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—81no—
230C4×C11#45412yes—
231Dic11—22no—
232Dic11—41no—
233Dic11—41no—
234Dic11—41no—
235Dic11—81no—
236Dic11—81no—
237C22×Q8—111no—
238C22×D4C4×D1111yescharacteristic
239C23×C4—21no—
240C2×M16—21no—
241C2×M16—221no—
242C4×Q8—221no—
243C4×Q8—221no—
244C4×Q8—221no—
245C4×Q8—221no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4C4×D1111yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C42—111no—
260C2×C42—111no—
261C2×C42—221no—
262C2×C42C22×D1111yescharacteristic
263C4⋊C8—112no—
264C4⋊C8—222no—
265C4⋊C8—222no—
266C4⋊C8C22⋊D1112yes—
267#101—224no—
268C22⋊C8—21no—
269C22⋊C8—221no—
270#97—21no—
271#97—21no—
272#97—222no—
273#97—221no—
274#97—221no—
275C4×C8—21no—
276C4×C8—222no—
277C4×C8—221no—
278#95—111no—
279#95—111no—
280#95—221no—
281#95—221no—
282#95—221no—
283#95—221no—
284#95—221no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—82no—
288C2×C11#187111yescharacteristic
289C2×C11#188811yescharacteristic
290C2×C11#189111yescharacteristic
291C24—21no—
292C2×Q8—222no—
293C2×Q8—221no—
294C2×Q8—221no—
295C2×Q8—441no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—42no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4C2×C4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C22×C4D4×D1111yescharacteristic
313M16—22no—
314M16—41no—
315M16—222no—
316M16—441no—
317C2×C8—22no—
318C2×C8—41no—
319C2×C8—222no—
320C2×C8—441no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—442no—
332C22⋊C4—442no—
333C22⋊C4—442no—
334C22⋊C4—442no—
335C42—221no—
336C42—221no—
337C42—221no—
338C42—221no—
339C42—442no—
340C42#433911yescharacteristic
341C42D4×D1111yescharacteristic
342C42#434111yescharacteristic
343C42C2×C22⋊D1111yescharacteristic
344C11#903211yescharacteristic, complemented, Sylow
345C23—22no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23C22⋊C4×D1111yescharacteristic
353Q8—442no—
354Q8—442no—
355D4—22no—
356D4—22no—
357D4—41no—
358D4—41no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—112no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4(C22⋊D11)⋊C411yescharacteristic
385C2×C4#6693611yescharacteristic
386C2×C4#6693711yescharacteristic
387C2×C4C4×C22⋊D1111yescharacteristic
388C2×C4#6699011yescharacteristic
389C2×C4#6699111yescharacteristic
390C8—42no—
391C8—42no—
392C8—442no—
393C8—442no—
394C22—21no—
395C22—21no—
396C22—42no—
397C22—42no—
398C22—42no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22D11×#10411yescharacteristic
404C22#1062243411yescharacteristic
405C22#1062256911yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—81no—
412C4—222no—
413C4—441no—
414C4—441no—
415C4—441no—
416C4—881no—
417C4—881no—
418C4#1062281412yes—
419C2—21no—
420C2—21no—
421C2—82no—
422C2#1306891511yescharacteristic
423C2#1306901611yescharacteristic
424C2#1306903111yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1490C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1490D11
hypocenterC11#9032
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
1. #13077700C2semidirect
3. C4×#66888C2semidirect
5. #13066510C2semidirect
6. #13066508C2semidirect
344. C11#9032semidirect

Maximal subgroups

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

subgroupindex
#130777002
#130719002
C4×#668882
#130670592
#130665102
#130665082
C11×#14902
#903211