Finite Group Databasebeta

← #14654270

Subgroups — #14654270

Order 2816.

744 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079388C211yesmaximal, characteristic
2C2×#10622841C211yesmaximal, characteristic
3#13069601C211yesmaximal, characteristic
4#13068551C211yesmaximal, characteristic
5#13067188C211yesmaximal, characteristic
6#13066464C211yesmaximal, characteristic
7C11×#2434C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C2×C11×C4⋊Q8—21no—
10C2×C11×C22⋊Q8C2211yescharacteristic
11C22×#4326—21no—
12C2×#66977C2211yescharacteristic
13C11×#395—22no—
14C11×#391—21no—
15C11×#385—22no—
16C4×C11×C22⋊C4C2211yescharacteristic
17#10622841—22no—
18#10622841—21no—
19#10622841—22no—
20C2×#66899—21no—
21C2×#66899—22no—
22#10622825C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622664—22no—
26#10622663—21no—
27#10622657—21no—
28#10622583—21no—
29#10622176—22no—
30#10622165—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
42C11×C4⋊Q8—44no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C2×C11×C4⋊C4—24no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4D412yes—
52C2×C42×C11—21no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—21no—
55C2×#4326—24no—
56C2×#4326—22no—
57C2×#4326—44no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11D411yescharacteristic
60#66977—21no—
61#66977—21no—
62#66977—21no—
63#66977—21no—
64C2×Dic11⋊C4—21no—
65C22×C11⋊C8—21no—
66C22×C11⋊C8D412yes—
67C11×#95—24no—
68C11×#95—21no—
69#66899—24no—
70#66899—22no—
71#66899—44no—
72C11⋊#95—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yes—
77#66874—22no—
78#66871—22no—
79#9957—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C2×Q8×C11—24no—
82C2×Q8×C11—24no—
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
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—22no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—42no—
102C22×C4×C11—44no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—41no—
114C2×Dic22—21no—
115C2×Dic22—21no—
116C2×Dic22—42no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—48no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4Q1614yescomplemented
126C42×C11—42no—
127C22⋊Dic11—41no—
128C22⋊Dic11—41no—
129C22⋊Dic11—42no—
130#4326—48no—
131#4326—82no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—42no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—42no—
140C2×C11⋊C8—42no—
141#3189—111no—
142C2×#451—111no—
143#2434D1111yescharacteristic
144#1996—111no—
145#1787—111no—
146#1520—111no—
147#1282—111no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11#12011yescharacteristic
151C23×C11#12111yescharacteristic
152C23×C11#12711yescharacteristic
153C23×C11C2×Q1612yes—
154C23×C11#13712yes—
155Q8×C11—24no—
156Q8×C11—24no—
157Q8×C11—42no—
158Q8×C11—42no—
159Q8×C11—44no—
160Q8×C11—44no—
161Q8×C11—42no—
162Q8×C11—81no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—44no—
175C2×C4×C11—44no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—81no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191C2×Dic11—81no—
192Dic22—42no—
193Dic22—42no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C23×Q8C2×D1111yescharacteristic
197C22×Q16—221no—
198C2×C4⋊Q8—21no—
199C2×C22⋊Q8—111no—
200C2×C22⋊Q8C2×D1111yescharacteristic
201#484—221no—
202#484—221no—
203#467—222no—
204#451—222no—
205#451—221no—
206#451—221no—
207#451—222no—
208C2×#103—221no—
209C2×#103—222no—
210C2×C22⋊C8—111no—
211C2×C22⋊C8—111no—
212#395—22no—
213#391—21no—
214#385—22no—
215#380—111no—
216C4×C22⋊C4C2×D1111yescharacteristic
217#342—222no—
218#328—222no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11#39211yescharacteristic
228C22×C11#45112yes—
229C22×C11#46212yes—
230C22×C11#49411yescharacteristic
231C22×C11#49711yescharacteristic
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—44no—
236C4×C11—44no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11B(4,𝔽2)12yes—
240Dic11—81no—
241Dic11—81no—
242Dic11—161no—
243C22×Q8—21no—
244C22×Q8—21no—
245C22×Q8—21no—
246C22×Q8—21no—
247C22×Q8—21no—
248C22×Q8—44no—
249C22×Q8—111no—
250C22×Q8C22⋊D1111yescharacteristic
251C22×Q8C22⋊D1112yes—
252C23×C4—21no—
253C23×C4C22×D1111yescharacteristic
254C2×Q16—224no—
255C2×Q16—222no—
256C2×Q16—444no—
257C22×C8—112no—
258C22×C8—221no—
259C4⋊Q8—44no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—221no—
265C22⋊Q8—221no—
266C22⋊Q8—221no—
267C22⋊Q8—221no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4C22⋊D1111yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4C22⋊D1112yes—
278C2×C42—21no—
279#107—222no—
280#103—222no—
281#103—224no—
282#103—222no—
283#103—444no—
284C22⋊C8—112no—
285C22⋊C8—221no—
286C22⋊C8—221no—
287C22⋊C8—221no—
288#95—24no—
289#95—21no—
290#95—221no—
291C2×C11—21no—
292C2×C11—22no—
293C2×C11—22no—
294C2×C11—21no—
295C2×C11#200911yescharacteristic
296C2×C11#201611yescharacteristic
297C2×C11#202111yescharacteristic
298C24C2×C22⋊D1111yescharacteristic
299C2×Q8—24no—
300C2×Q8—24no—
301C2×Q8—24no—
302C2×Q8—22no—
303C2×Q8—21no—
304C2×Q8—22no—
305C2×Q8—21no—
306C2×Q8—44no—
307C2×Q8—42no—
308C2×Q8—42no—
309C2×Q8—42no—
310C2×Q8—42no—
311C2×Q8—44no—
312C2×Q8—44no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—221no—
316C2×Q8—221no—
317C2×Q8—442no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—42no—
323C22×C4—44no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—441no—
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4#434111yescharacteristic
333C22×C4C2×C22⋊D1111yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335Q16—448no—
336Q16—882no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8—442no—
340C2×C8—442no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—48no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C4⋊C4—442no—
349C4⋊C4—441no—
350C4⋊C4—441no—
351C22⋊C4—22no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C22⋊C4—442no—
357C22⋊C4#432614yescomplemented
358C42—42no—
359C11#995711yescharacteristic, complemented, Sylow
360C23—41no—
361C23—41no—
362C23#6699111yescharacteristic
363C23#6699311yescharacteristic
364C23#6699512yes—
365C23C2×#432612yes—
366C23#6700611yescharacteristic
367Q8—24no—
368Q8—24no—
369Q8—42no—
370Q8—42no—
371Q8—44no—
372Q8—44no—
373Q8—42no—
374Q8—81no—
375Q8—442no—
376Q8—442no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—881no—
398C2×C4—881no—
399C2×C4—881no—
400C2×C4—881no—
401C2×C4—881no—
402C2×C4#6699011yescharacteristic
403C2×C4#6699011yescharacteristic
404C2×C4#6699211yescharacteristic
405C2×C4#6699211yescharacteristic
406C8—442no—
407C8—442no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—42no—
415C22—42no—
416C22#1062269911yescharacteristic
417C22#1062270312yes—
418C22#1062270511yescharacteristic
419C22#1062283611yescharacteristic
420C22#1062284112yes—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—44no—
425C4—44no—
426C4—81no—
427C4—81no—
428C4—881no—
429C4—881no—
430C4—1761no—
431C4#1062264512yes—
432C2—22no—
433C2—21no—
434C2—22no—
435C2—21no—
436C2#1306967611yescharacteristic
437C2#1306971611yescharacteristic
438C2#1306973911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2434C2
socleC22×C11#392
prime radicalC24×C11C2×D4
hypercenter#2434D11
hypocenterC11#9957
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2434

Complements

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

NH ≅ G/Ntype
125. C11×C22⋊C4Q16semidirect
357. C22⋊C4#4326semidirect
359. C11#9957semidirect

Maximal subgroups

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

subgroupindex
#130793882
C2×#106228412
#130696012
#130685512
#130671882
#130664642
C11×#24342
#995711