Finite Group Databasebeta

← #14672097

Subgroups — #14672097

Order 2816.

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

normal subgroups only

This group has 472 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#13073602C211yesmaximal, characteristic
2C2×#10622186C211yesmaximal, characteristic
3C2×#10622116C211yesmaximal, characteristic
4C2×#10622116C211yesmaximal, characteristic
5#13068610C211yesmaximal, characteristic
6#101×Dic11C211yesmaximal, characteristic
7C2×C11×#356C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×Q8×Dic11C2211yescharacteristic
10C2×#66997C411yescharacteristic
11C2×#66997C2211yescharacteristic
12C2×C11×#101C2211yescharacteristic
13C2×C11×#101C2211yescharacteristic
14#10622843C411yescharacteristic
15C2×#66900C2211yescharacteristic
16C2×#66900C2211yescharacteristic
17#10622731—21no—
18M16×Dic11—21no—
19#10622597—21no—
20#10622597—21no—
21#10622585—21no—
22#10622585—21no—
23C4×Dic11⋊C4C411yescharacteristic
24#10622542C411yescharacteristic
25C11×#356—22no—
26#10622192—21no—
27#10622192—21no—
28#10622186—22no—
29#10622116—22no—
30#10622116—22no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×Q8×C11C2311yescharacteristic
33C22×Dic22C2×C411yescharacteristic
34C2×C11×M16—21no—
35C2×C11×M16—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11C2×C411yescharacteristic
43Q8×Dic11—41no—
44Q8×Dic11—41no—
45#66997—21no—
46#66997—21no—
47#66997—21no—
48#66997—21no—
49#66997—41no—
50#66997—41no—
51C2×C4⋊Dic11C2×C411yescharacteristic
52C2×C4⋊Dic11D411yescharacteristic
53C2×C4⋊Dic11D411yescharacteristic
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×Dic11⋊C4—21no—
59C2×C4×Dic11C2×C411yescharacteristic
60C2×C4×Dic11C2×C411yescharacteristic
61C2×C4×Dic11D411yescharacteristic
62C2×C4×Dic11D411yescharacteristic
63C2×#4318—21no—
64C2×#4318—21no—
65C11×#101—21no—
66C11×#101—21no—
67C11×#101—21no—
68C11×#101D412yes—
69#66900—21no—
70#66900—21no—
71#66900—21no—
72#66900D412yes—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—21no—
77C11⋊#95—21no—
78#66879—41no—
79Dic11⋊C8—41no—
80Dic11⋊C8—41no—
81C8×Dic11—41no—
82#13227—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—41no—
86C2×Q8×C11—41no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11C2×D411yescharacteristic
90C2×Q8×C11C2×D411yescharacteristic
91C2×Q8×C11#4111yescharacteristic
92C2×Q8×C11#4111yescharacteristic
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102C22×Dic11C22⋊C411yescharacteristic
103C22×Dic11C22⋊C411yescharacteristic
104C2×Dic22—21no—
105C2×Dic22—21no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C11×M16—22no—
109C11×M16—41no—
110C11×M16—41no—
111C11×M16—41no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C42×C11—21no—
119C42×C11—21no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123Dic11⋊C4—24no—
124Dic11⋊C4—42no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130Dic11⋊C4—41no—
131C4×Dic11—21no—
132C4×Dic11—21no—
133C4×Dic11—21no—
134C4×Dic11—21no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—21no—
138C4×Dic11—21no—
139#4318—22no—
140#4318—41no—
141#4318—41no—
142#4318—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145#2546—111no—
146C2×#356—111no—
147C2×#356—111no—
148C2×#356—111no—
149C2×#356D1111yescharacteristic
150#1801—111no—
151C4×#101—111no—
152C23×C11C2×C22⋊C411yescharacteristic
153Q8×C11—41no—
154Q8×C11—41no—
155Q8×C11—41no—
156Q8×C11—41no—
157Q8×C11—81no—
158Q8×C11—81no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11C4×D411yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12411yescharacteristic
176C2×C4×C11#12711yescharacteristic
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11#9911yescharacteristic
191C2×Dic11#9911yescharacteristic
192Dic22—81no—
193Dic22—81no—
194C8×C11—42no—
195C8×C11—81no—
196C11⋊C8—42no—
197C11⋊C8—81no—
198C2×C4⋊Q8—111no—
199C2×C4⋊Q8—111no—
200C2×C4⋊Q8C2×D1111yescharacteristic
201C2×C4×Q8—111no—
202#423—221no—
203C2×#101—111no—
204C2×#101—111no—
205C2×#101C2×D1111yescharacteristic
206C2×#101C2×D1111yescharacteristic
207C4×M16—221no—
208#398—221no—
209#398—221no—
210#391—111no—
211#391—111no—
212#389—221no—
213#389—221no—
214C4×C4⋊C4—111no—
215#356—22no—
216#356—222no—
217#356—222no—
218#356—222no—
219#343—221no—
220#343—221no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11#39011yescharacteristic
224C22×C11C2×#9911yescharacteristic
225C22×C11#41011yescharacteristic
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—81no—
234Dic11—21no—
235Dic11—42no—
236Dic11—41no—
237Dic11—41no—
238Dic11—41no—
239Dic11—81no—
240Dic11#35612yescomplemented
241C22×Q8—111no—
242C22×Q8C4×D1111yescharacteristic
243C22×Q8C22×D1111yescharacteristic
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—221no—
247C2×M16—221no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—221no—
253C4⋊Q8—221no—
254C4⋊Q8—221no—
255C4⋊Q8—221no—
256C4⋊Q8—441no—
257C4⋊Q8—441no—
258C4×Q8—441no—
259C4×Q8—441no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C42—111no—
271C2×C42—111no—
272C2×C42—111no—
273C2×C42—111no—
274C2×C42C4×D1111yescharacteristic
275C4⋊C8—441no—
276C4⋊C8—441no—
277#101—21no—
278#101—21no—
279#101—21no—
280#101—112no—
281#101—221no—
282#101—221no—
283#101—221no—
284#101C22⋊D1112yes—
285#97—441no—
286C4×C8—441no—
287#95—221no—
288#95—221no—
289#95—221no—
290#95—221no—
291#95—221no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11#196411yescharacteristic
295C2×C11C2×#35611yescharacteristic
296C2×C11#213511yescharacteristic
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—221no—
304C2×Q8—221no—
305C2×Q8—441no—
306C2×Q8—441no—
307C2×Q8#433911yescharacteristic
308C2×Q8D4×D1111yescharacteristic
309C2×Q8#434111yescharacteristic
310C2×Q8C2×C22⋊D1111yescharacteristic
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—111no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322M16—22no—
323M16—41no—
324M16—41no—
325M16—41no—
326M16—222no—
327M16—441no—
328M16—441no—
329M16—441no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—441no—
333C2×C8—441no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—224no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C4⋊C4—442no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C42—21no—
350C42—21no—
351C42—221no—
352C42—221no—
353C42—221no—
354C42—221no—
355C42—221no—
356C42—221no—
357C42—221no—
358C42—221no—
359C11#1322711yescharacteristic, complemented, Sylow
360C23C22⋊C4×D1111yescharacteristic
361Q8—41no—
362Q8—41no—
363Q8—41no—
364Q8—41no—
365Q8—81no—
366Q8—81no—
367Q8—881no—
368Q8—881no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—111no—
382C2×C4—111no—
383C2×C4—222no—
384C2×C4—222no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4(C22⋊D11)⋊C411yescharacteristic
397C2×C4#6693711yescharacteristic
398C2×C4#6693811yescharacteristic
399C2×C4C4×C22⋊D1111yescharacteristic
400C2×C4#6699211yescharacteristic
401C2×C4#6699311yescharacteristic
402C8—42no—
403C8—81no—
404C8—442no—
405C8—881no—
406C22—21no—
407C22—21no—
408C22#1062235311yescharacteristic
409C22D11×#9911yescharacteristic
410C22#1062257011yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—42no—
418C4—81no—
419C4—112no—
420C4—221no—
421C4—442no—
422C4—441no—
423C4—441no—
424C4—441no—
425C4—881no—
426C2—21no—
427C2—21no—
428C2#1306945011yescharacteristic
429C2D11×#35611yescharacteristic
430C2#1307030911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC2×C11×#356C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC22×Q8×C11C23
hypercenterC2×#356D11
hypocenterC11#13227
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
240. Dic11#356semidirect
359. C11#13227semidirect

Maximal subgroups

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

subgroupindex
#130736022
C2×#106221862
C2×#106221162
#130686102
#101×Dic112
C2×C11×#3562
#1322711