Finite Group Databasebeta

← #14671320

Subgroups — #14671320

Order 2816.

676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C22×#66900C211yesmaximal, characteristic
2#13072256C211yesmaximal, characteristic
3C2×#10622116C212yesmaximal, complemented
4#13066742C212yesmaximal, complemented
5C11×#1784C211yesmaximal, characteristic
6C23×Q8×C11C2211yescharacteristic
7C2×#66997C411yescharacteristic
8C2×#66997C2211yescharacteristic
9C2×#66977C411yescharacteristic
10C22×#4318—21no—
11C2×C11×#101—21no—
12C2×C11×#101C2212yes—
13C11×#407—21no—
14#10622843C411yescharacteristic
15#10622843C2211yescharacteristic
16#10622842—21no—
17#10622842—21no—
18C2×#66900—21no—
19C2×#66900—24no—
20C2×#66900C2212yes—
21#10622823—21no—
22#10622823—21no—
23C4×C22⋊Dic11C411yescharacteristic
24#10622116—24no—
25C22×Q8×C11—22no—
26C22×Q8×C11—22no—
27C22×Q8×C11—41no—
28C22×Q8×C11—41no—
29C22×Q8×C11—42no—
30C22×Q8×C11C2×C411yescharacteristic
31C22×Q8×C11D411yescharacteristic
32C22×Q8×C11D411yescharacteristic
33C22×Q8×C11C2311yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C22×Dic22C2×C411yescharacteristic
38C2×C11×M16—22no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41#66997—22no—
42#66997—22no—
43#66997—42no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45#66977—41no—
46#66977—41no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×C4×Dic11C2×C411yescharacteristic
53C2×C4×Dic11C2×C411yescharacteristic
54C2×#4318—24no—
55C2×#4318—22no—
56C2×#4318—41no—
57C2×#4318—42no—
58C22×C11⋊C8—41no—
59C11×#101—22no—
60C11×#101—22no—
61C11×#101—42no—
62C11×C22⋊C8—41no—
63C11×C22⋊C8—41no—
64#66900—24no—
65#66900—22no—
66#66900D414yes—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72#13094—111nomaximal, Sylow
73C24×C11C22⋊C411yescharacteristic
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×Q8×C11—44no—
87C2×Q8×C11—44no—
88C2×Q8×C11—44no—
89C2×Q8×C11—44no—
90C2×Q8×C11C2×D412yes—
91C2×Q8×C11#4112yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C22⋊C411yescharacteristic
106C22×C4×C11C22⋊C411yescharacteristic
107C22×C4×C11C22⋊C411yescharacteristic
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C2×Dic22—22no—
116C2×Dic22—41no—
117C2×Dic22—41no—
118C11×M16—42no—
119C11×M16—42no—
120C2×C8×C11—42no—
121C22⋊Dic11—24no—
122C22⋊Dic11—41no—
123C22⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—42no—
126Dic11⋊C4—42no—
127Dic11⋊C4—42no—
128Dic11⋊C4—41no—
129Dic11⋊C4—42no—
130Dic11⋊C4—41no—
131C4×Dic11—22no—
132C4×Dic11—41no—
133#4318—24no—
134#4318—44no—
135#4318—42no—
136C2×C11⋊C8—44no—
137C2×C11⋊C8—42no—
138C22×#101—111no—
139#2434—111no—
140C2×#356—112no—
141#1784D1111yescharacteristic
142#1394—112no—
143C23×C11—22no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—41no—
147C23×C11#9911yescharacteristic
148C23×C11#9911yescharacteristic
149C23×C11C2×C22⋊C411yescharacteristic
150Q8×C11—42no—
151Q8×C11—42no—
152Q8×C11—44no—
153Q8×C11—44no—
154Q8×C11—42no—
155Q8×C11—42no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11#9912yes—
179C2×C4×C11C4×D412yes—
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12112yes—
182C2×C4×C11#12311yescharacteristic
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—42no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194Dic22—82no—
195C8×C11—82no—
196C11⋊C8—44no—
197C23×Q8C2×D1111yescharacteristic
198C22×M16—221no—
199C2×C4⋊Q8—111no—
200C2×C4⋊Q8—111no—
201C2×C22⋊Q8—111no—
202C2×#101—21no—
203C2×#101—112no—
204C2×#101—224no—
205C2×#101—221no—
206C2×#101C2×D1112yes—
207#407—21no—
208#395—221no—
209#395—221no—
210#391—111no—
211#391—111no—
212#385—221no—
213#385—221no—
214C4×C22⋊C4—111no—
215#356—224no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—42no—
224C22×C11—42no—
225C22×C11#35612yescomplemented
226C22×C11#38611yescharacteristic
227C22×C11C2×#9911yescharacteristic
228C22×C11C2×#9911yescharacteristic
229C4×C11—22no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—41no—
235C4×C11—41no—
236Dic11—42no—
237Dic11—42no—
238Dic11—81no—
239Dic11—81no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—41no—
243C22×Q8—41no—
244C22×Q8—42no—
245C22×Q8—111no—
246C22×Q8C4×D1111yescharacteristic
247C22×Q8D4411yescharacteristic
248C22×Q8C22⋊D1111yescharacteristic
249C22×Q8C22×D1111yescharacteristic
250C23×C4C4×D1111yescharacteristic
251C23×C4D4411yescharacteristic
252C23×C4C22⋊D1111yescharacteristic
253C2×M16—22no—
254C2×M16—224no—
255C2×M16—222no—
256C2×M16—441no—
257C2×M16—442no—
258C22×C8—441no—
259C4⋊Q8—222no—
260C4⋊Q8—222no—
261C4⋊Q8—442no—
262C22⋊Q8—441no—
263C22⋊Q8—441no—
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×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C42—111no—
273C2×C42—111no—
274#101—22no—
275#101—22no—
276#101—42no—
277#101—114no—
278#101—224no—
279#101—222no—
280C22⋊C8—41no—
281C22⋊C8—41no—
282#95—221no—
283#95—221no—
284#95—221no—
285#95—221no—
286#95—221no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—22no—
290C2×C11—41no—
291C2×C11#189811yescharacteristic
292C2×C11C2×#35611yescharacteristic
293C2×C11#213311yescharacteristic
294C24(C2×D11)⋊C411yescharacteristic
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—22no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—44no—
308C2×Q8—44no—
309C2×Q8—44no—
310C2×Q8—44no—
311C2×Q8—222no—
312C2×Q8—441no—
313C2×Q8—441no—
314C2×Q8D4×D1112yes—
315C2×Q8#434112yes—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—221no—
332C22×C4—221no—
333C22×C4(C2×D11)⋊C411yescharacteristic
334C22×C4(C2×D11)⋊C411yescharacteristic
335C22×C4(C2×D11)⋊C411yescharacteristic
336C22×C4C2×C4×D1111yescharacteristic
337C22×C4C2×D4411yescharacteristic
338C22×C4C2×C22⋊D1111yescharacteristic
339M16—42no—
340M16—42no—
341M16—224no—
342M16—444no—
343M16—442no—
344C2×C8—42no—
345C2×C8—444no—
346C2×C8—442no—
347C4⋊C4—441no—
348C4⋊C4—442no—
349C4⋊C4—442no—
350C4⋊C4—442no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C4⋊C4—442no—
354C22⋊C4—224no—
355C22⋊C4—441no—
356C22⋊C4—441no—
357C42—222no—
358C42—441no—
359C11#1309411yescharacteristic, complemented, Sylow
360C23—21no—
361C23—21no—
362C23—22no—
363C23—41no—
364C23#6687011yescharacteristic
365C23#6687011yescharacteristic
366C23C2×(C2×D11)⋊C411yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—44no—
370Q8—44no—
371Q8—42no—
372Q8—42no—
373Q8—882no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—442no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4#6687012yes—
408C2×C4(C22⋊D11)⋊C412yes—
409C2×C4#6693511yescharacteristic
410C2×C4#6693911yescharacteristic
411C2×C4#6699212yes—
412C8—82no—
413C8—444no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—42no—
422C22—42no—
423C22#1062211612yescomplemented
424C22C2×#6687011yescharacteristic
425C22C2×#6687011yescharacteristic
426C22#1062257111yescharacteristic
427C4—22no—
428C4—21no—
429C4—22no—
430C4—21no—
431C4—22no—
432C4—41no—
433C4—41no—
434C4—442no—
435C4—442no—
436C4—881no—
437C4—881no—
438C2—21no—
439C2—21no—
440C2—22no—
441C2—41no—
442C2#1306906711yescharacteristic
443C2C2×#1062211611yescharacteristic
444C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#1784C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC22×Q8×C11C23
hypercenter#1784D11
hypocenterC11#13094
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ #1784

Complements

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

NH ≅ G/Ntype
3. C2×#10622116C2semidirect
4. #13066742C2semidirect
225. C22×C11#356semidirect
359. C11#13094semidirect
423. C22#10622116semidirect

Maximal subgroups

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

subgroupindex
C22×#669002
#130722562
C2×#106221162
#130667422
C11×#17842
#1309411