Finite Group Databasebeta

← #14651594

Subgroups — #14651594

Order 2816.

726 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 93 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#13071947C211yesmaximal, characteristic
2#13071216C211yesmaximal, characteristic, complemented
3#13068560C211yesmaximal, characteristic
4#13066945C211yesmaximal, characteristic, complemented
5#13066470C211yesmaximal, characteristic, complemented
6#13066469C211yesmaximal, characteristic, complemented
7C11×#1789C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C2×#66988—21no—
10C22×Dic11⋊C4C2211yescharacteristic
11C2×C11×#104—22no—
12C11×#407C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14C2×#66901—22no—
15#10622842C412yescomplemented
16#10622835C412yescomplemented
17#10622833—21no—
18#10622824C2211yescharacteristic
19#10622823—22no—
20C4×C22⋊Dic11C2211yescharacteristic
21#10622820C2211yescharacteristic
22#10622556—21no—
23#10622555—21no—
24#10622546—22no—
25#10622265—22no—
26#10622107—22no—
27C2×C11×#41—21no—
28C2×C11×#41—21no—
29C2×C11×#41—21no—
30C2×C11×#41—21no—
31C2×C11×#41—44no—
32C22×Q8×C11C2×C411yescharacteristic
33C22×D4×C11—21no—
34C22×D4×C11C2×C411yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11D411yescharacteristic
38C23×Dic11D411yescharacteristic
39C2×C11×M16—21no—
40C2×C11×C22⋊C4—21no—
41C2×C42×C11D412yes—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—22no—
45C2×C22⋊Dic11—22no—
46#66988—44no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—22no—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4C2×C412yes—
54C2×Dic11⋊C4D412yes—
55C2×C4×Dic11D412yes—
56C2×#4318—21no—
57C11×#104—44no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61#66901—44no—
62C11⋊#95—22no—
63C11⋊#95—24no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—22no—
67C11⋊#95C2×C412yes—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#9480—111nomaximal, Sylow
71C24×C11—21no—
72C24×C11C2×D411yescharacteristic
73C11×#41—24no—
74C11×#41—24no—
75C11×#41—42no—
76C11×#41—42no—
77C11×#41—42no—
78C11×#41—42no—
79C11×#41—42no—
80C11×#41—42no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—42no—
84C2×D4×C11—24no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—22no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—42no—
111C22×Dic11—42no—
112C22×Dic11C22⋊C412yes—
113C22×Dic11C22⋊C412yes—
114C11×M16—42no—
115C2×C8×C11—41no—
116C11×C22⋊C4—42no—
117C42×C11—42no—
118C22⋊Dic11—42no—
119C22⋊Dic11—44no—
120C22⋊Dic11—42no—
121C22⋊Dic11—44no—
122Dic11⋊C4—22no—
123Dic11⋊C4—22no—
124Dic11⋊C4—22no—
125Dic11⋊C4—22no—
126Dic11⋊C4—44no—
127Dic11⋊C4—82no—
128C4×Dic11—42no—
129#4318—42no—
130C2×C11⋊C8—41no—
131#2406—111no—
132#2313—111no—
133#1789—111no—
134#1789D1111yescharacteristic
135#1463—111no—
136#1284—111no—
137#1284—111no—
138C23×C11—22no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11C2×C22⋊C411yescharacteristic
147C23×C11#12011yescharacteristic
148C23×C11#12311yescharacteristic
149Q8×C11—22no—
150Q8×C11—22no—
151Q8×C11—41no—
152Q8×C11—41no—
153D4×C11—22no—
154D4×C11—22no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—44no—
158D4×C11—44no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—44no—
167C2×C4×C11—44no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11C4×D411yescharacteristic
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—81no—
192C8×C11—81no—
193C11⋊C8—81no—
194C22×#41C2×D1111yescharacteristic
195C2×#123—221no—
196C22×C4⋊C4—111no—
197C2×#104—22no—
198C2×#104—222no—
199#407—111no—
200#407C2×D1111yescharacteristic
201#395—112no—
202#394—112no—
203#387—222no—
204#387—222no—
205#386—221no—
206#385—222no—
207#381—111no—
208#381—221no—
209#380—221no—
210C4×C22⋊C4—111no—
211C4×C22⋊C4C2×D1111yescharacteristic
212#324—222no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—44no—
221C22×C11—44no—
222C22×C11—42no—
223C22×C11—82no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11#38611yescharacteristic
227C22×C11#42112yes—
228C22×C11B(4,𝔽2)12yes—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—42no—
234C4×C11—82no—
235Dic11—42no—
236Dic11—42no—
237Dic11—82no—
238Dic11—82no—
239C2×#41—21no—
240C2×#41—21no—
241C2×#41—21no—
242C2×#41—21no—
243C2×#41—44no—
244C22×Q8C4×D1111yescharacteristic
245C22×D4—21no—
246C22×D4C4×D1111yescharacteristic
247C23×C4—21no—
248C23×C4—111no—
249C23×C4—111no—
250C23×C4C22×D1111yescharacteristic
251C2×M16—21no—
252C2×M16—221no—
253#123—444no—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—222no—
261C2×C4⋊C4—222no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—222no—
264C2×C22⋊C4—222no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C42—112no—
268C2×C42C22⋊D1112yes—
269#104—44no—
270#104—444no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—221no—
274C22⋊C8—221no—
275#95—21no—
276#95—112no—
277#95—222no—
278#95—222no—
279#95—224no—
280#95—221no—
281#95—221no—
282C2×C11—22no—
283C2×C11—22no—
284C2×C11—41no—
285C2×C11—82no—
286C2×C11#188911yescharacteristic
287C2×C11#189711yescharacteristic
288C2×C11#191211yescharacteristic
289C24—21no—
290C24D4×D1111yescharacteristic
291#41—24no—
292#41—24no—
293#41—42no—
294#41—42no—
295#41—42no—
296#41—42no—
297#41—42no—
298#41—42no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—42no—
302C2×D4—24no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—112no—
317C22×C4—112no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—222no—
323C22×C4—222no—
324C22×C4—442no—
325C22×C4—442no—
326C22×C4C2×C4×D1111yescharacteristic
327C22×C4#433911yescharacteristic
328C22×C4D4×D1111yescharacteristic
329C22×C4D4×D1111yescharacteristic
330C22×C4#434111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332M16—42no—
333M16—442no—
334C2×C8—41no—
335C2×C8—441no—
336C4⋊C4—222no—
337C4⋊C4—222no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—444no—
341C4⋊C4—882no—
342C22⋊C4—42no—
343C22⋊C4—444no—
344C22⋊C4—444no—
345C22⋊C4—442no—
346C22⋊C4—442no—
347C42—42no—
348C42—442no—
349C11#948011yescharacteristic, complemented, Sylow
350C23—22no—
351C23—22no—
352C23—22no—
353C23—41no—
354C23—41no—
355C23—42no—
356C23—41no—
357C23—42no—
358C23C22⋊C4×D1111yescharacteristic
359C23#6693611yescharacteristic
360C23#6699011yescharacteristic
361Q8—22no—
362Q8—22no—
363Q8—41no—
364Q8—41no—
365D4—22no—
366D4—22no—
367D4—41no—
368D4—41no—
369D4—44no—
370D4—44no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—881no—
400C2×C4(C22⋊D11)⋊C411yescharacteristic
401C2×C4#6693711yescharacteristic
402C2×C4C4×C22⋊D1111yescharacteristic
403C2×C4#6699111yescharacteristic
404C8—81no—
405C8—881no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—44no—
414C22—44no—
415C22—42no—
416C22—82no—
417C22—81no—
418C22—81no—
419C22#1062243412yes—
420C22#1062256911yescharacteristic
421C22#1062264512yes—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—42no—
427C4—82no—
428C4—442no—
429C4—442no—
430C4—882no—
431C4—882no—
432C2—22no—
433C2—22no—
434C2—41no—
435C2—82no—
436C2#1306902111yescharacteristic
437C2#1306906111yescharacteristic
438C2#1306915011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1789C2
socleC22×C11#386
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenter#1789D11
hypocenterC11#9480
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #13071216C2semidirect
4. #13066945C2semidirect
5. #13066470C2semidirect
6. #13066469C2semidirect
15. #10622842C4semidirect
16. #10622835C4semidirect
349. C11#9480semidirect

Maximal subgroups

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

subgroupindex
#130719472
#130712162
#130685602
#130669452
#130664702
#130664692
C11×#17892
#948011