Finite Group Databasebeta

← #14653296

Subgroups — #14653296

Order 2816.

510 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#10622664C211yesmaximal, characteristic
2#13069602C211yesmaximal, characteristic
3#13069600C211yesmaximal, characteristic
4#13068639C211yesmaximal, characteristic
5#13068395C211yesmaximal, characteristic
6#13067189C211yesmaximal, characteristic
7C11×#1520C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×#4326C411yescharacteristic, complemented
10C2×#66977C2211yescharacteristic
11C23×C11⋊C8C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×#66899C411yescharacteristic, complemented
15#10622825C2211yescharacteristic
16C4×C22⋊Dic11C2211yescharacteristic
17C2×#66879—21no—
18#10622664—21no—
19#10622664—21no—
20#10622664—21no—
21#10622664—21no—
22C2×#66874C411yescharacteristic, complemented
23C2×#66872—21no—
24C2×#66871C411yescharacteristic, complemented
25C11×#328—22no—
26#10622188—21no—
27#10622167—21no—
28#10622165—22no—
29#10622164—22no—
30#10622105—22no—
31C22×Q8×C11C2×C411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×Dic22C2×C411yescharacteristic
34C22×C8×C11—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11D412yes—
47C2×#4326—21no—
48C2×#4326—21no—
49C2×#4326—42no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11C2×C411yescharacteristic
52#66977—21no—
53#66977—21no—
54#66977—21no—
55#66977—21no—
56C2×Dic11⋊C4—21no—
57C2×C4×Dic11—21no—
58C22×C11⋊C8—42no—
59C22×C11⋊C8C2×C411yescharacteristic
60C22×C11⋊C8C2×C411yescharacteristic
61C22×C11⋊C8D411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C22×C11⋊C8D411yescharacteristic
64C22×C11⋊C8D411yescharacteristic
65C11×C22⋊C8—21no—
66C11×C22⋊C8D412yes—
67C11×#95—21no—
68#66899—21no—
69#66899—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72#66879—42no—
73#66874—21no—
74#66874—21no—
75#66872—42no—
76#66871—21no—
77#66871—21no—
78#9784—111nomaximal, Sylow
79C24×C11C2×D411yescharacteristic
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—22no—
98C22×Dic11—41no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—42no—
115C22⋊Dic11—22no—
116C22⋊Dic11—22no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119C22⋊Dic11—42no—
120#4326—42no—
121#4326—42no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—41no—
129C4×Dic11—41no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8C22⋊C411yescharacteristic
137C2×C11⋊C8C22⋊C411yescharacteristic
138C2×C11⋊C8C22⋊C411yescharacteristic
139C2×C11⋊C8C22⋊C411yescharacteristic
140C2×#467—111no—
141#1996—111no—
142#1996—111no—
143#1807—111no—
144#1752—111no—
145#1520—111no—
146#1520D1111yescharacteristic
147C23×C11—41no—
148C23×C11—41no—
149C23×C11C4×D411yescharacteristic
150C23×C11#12111yescharacteristic
151C23×C11#12711yescharacteristic
152C23×C11#13712yes—
153C23×C11#13712yes—
154Q8×C11—41no—
155Q8×C11—41no—
156Q8×C11—81no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11C2×C22⋊C411yescharacteristic
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12411yescharacteristic
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11—81no—
183C2×Dic11—81no—
184C2×Dic11—81no—
185C2×Dic11—81no—
186C2×Dic11—81no—
187Dic22—41no—
188Dic22—41no—
189Dic22—81no—
190C8×C11—42no—
191C11⋊C8—21no—
192C11⋊C8—21no—
193C11⋊C8—21no—
194C11⋊C8#9912yes—
195C22×Q16—111no—
196C23×C8—111no—
197C2×C22⋊Q8—111no—
198C2×C22⋊Q8C2×D1111yescharacteristic
199#467—221no—
200#467—221no—
201#467—221no—
202#467—221no—
203C2×#107—111no—
204C2×#106—221no—
205C2×#103—111no—
206C2×#103—111no—
207C2×C22⋊C8C2×D1111yescharacteristic
208C2×#97—221no—
209#380—111no—
210#380C2×D1111yescharacteristic
211C4×C22⋊C4—111no—
212#342—222no—
213#342—222no—
214#340—221no—
215#336—221no—
216#328—22no—
217#328—222no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11#39011yescharacteristic
227C22×C11#44112yes—
228C22×C11#47012yes—
229C22×C11#49711yescharacteristic
230C22×C11#49711yescharacteristic
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—81no—
235C4×C11—81no—
236C4×C11—161no—
237C4×C11C2×#9911yescharacteristic
238C4×C11#41011yescharacteristic
239Dic11—82no—
240Dic11—81no—
241Dic11—81no—
242Dic11—161no—
243C22×Q8—111no—
244C22×Q8C4×D1111yescharacteristic
245C23×C4C22×D1111yescharacteristic
246C2×Q16—221no—
247C2×Q16—221no—
248C2×Q16—442no—
249C22×C8—21no—
250C22×C8—111no—
251C22×C8—111no—
252C22×C8—111no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8—111no—
256C22×C8—442no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—221no—
262C22⋊Q8—221no—
263C22⋊Q8—221no—
264C22⋊Q8—221no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4C4×D1111yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—112no—
274C2×C22⋊C4—221no—
275C2×C22⋊C4—221no—
276C2×C42—221no—
277#107—221no—
278#107—221no—
279#106—442no—
280#103—221no—
281#103—221no—
282#103—221no—
283#103—221no—
284C22⋊C8—21no—
285C22⋊C8C22⋊D1112yes—
286#97—442no—
287#95—21no—
288#95—221no—
289#95—221no—
290C2×C11—22no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—22no—
294C2×C11#196411yescharacteristic
295C2×C11#197111yescharacteristic
296C2×C11#197611yescharacteristic
297C24D4×D1111yescharacteristic
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—221no—
303C2×Q8—221no—
304C2×Q8—441no—
305C2×Q8—441no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—222no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—441no—
315C22×C4C2×C4×D1111yescharacteristic
316C22×C4#433911yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C22×C4#434111yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321Q16—442no—
322Q16—442no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—111no—
327C2×C8—111no—
328C2×C8—111no—
329C2×C8—111no—
330C2×C8—222no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8—441no—
334C2×C8—441no—
335C2×C8—441no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—221no—
343C4⋊C4—221no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C4⋊C4—441no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—42no—
351C22⋊C4—222no—
352C22⋊C4—222no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C22⋊C4—442no—
356C42—441no—
357C42—441no—
358C11#978411yescharacteristic, complemented, Sylow
359C23—41no—
360C23—41no—
361C23(C22⋊D11)⋊C411yescharacteristic
362C23#6693711yescharacteristic
363C23#6696812yes—
364C23#6697112yes—
365C23#6699311yescharacteristic
366Q8—41no—
367Q8—41no—
368Q8—81no—
369Q8—441no—
370Q8—441no—
371Q8—881no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—442no—
393C2×C4—881no—
394C2×C4—881no—
395C2×C4—881no—
396C2×C4—881no—
397C2×C4—881no—
398C2×C4C22⋊C4×D1111yescharacteristic
399C2×C4#6693811yescharacteristic
400C2×C4C4×C22⋊D1111yescharacteristic
401C2×C4#6699211yescharacteristic
402C8—42no—
403C8—112no—
404C8—221no—
405C8—221no—
406C8—221no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—42no—
414C22—42no—
415C22#1062240212yes—
416C22#1062242912yes—
417C22#1062257011yescharacteristic
418C22#1062278011yescharacteristic
419C22#1062280311yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—81no—
424C4—81no—
425C4—161no—
426C4—882no—
427C4—881no—
428C4—881no—
429C4—1761no—
430C4#1062235311yescharacteristic
431C4D11×#9911yescharacteristic
432C2—21no—
433C2—22no—
434C2—21no—
435C2—22no—
436C2#1306945011yescharacteristic
437C2#1306948411yescharacteristic
438C2#1306951311yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1520C2
socleC22×C11#390
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1520D11
hypocenterC11#9784
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
9. C22×#4326C4semidirect
14. C2×#66899C4semidirect
22. C2×#66874C4semidirect
24. C2×#66871C4semidirect
358. C11#9784semidirect

Maximal subgroups

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

subgroupindex
C2×#106226642
#130696022
#130696002
#130686392
#130683952
#130671892
C11×#15202
#978411