Finite Group Databasebeta

← #14764133

Subgroups — #14764133

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622333C212yesmaximal
2#13071099C211yesmaximal, characteristic
3#13069338C212yesmaximal, complemented
4#13069336C212yesmaximal, complemented
5#13069333C212yesmaximal, complemented
6#13069331C212yesmaximal, complemented
7#13068598C212yesmaximal
8#13068596C211yesmaximal, characteristic
9C11×#1797C211yesmaximal, characteristic
10C22×C42×C11C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×C22⋊C8C2212yes—
16#10622823C412yes—
17#10622823C412yes—
18C2×C22⋊(C11⋊C8)C2212yes—
19C2×#66879C2212yes—
20C2×Dic11⋊C8C2212yes—
21C2×Dic11⋊C8C2212yes—
22C2×Dic11⋊C8C2212yes—
23C2×Dic11⋊C8C2212yes—
24C2×C8×Dic11C2212yes—
25C4×Dic11⋊C4C2212yes—
26C4×Dic11⋊C4C2212yes—
27#10622541C411yescharacteristic
28#10622541C411yescharacteristic
29#10622541C411yescharacteristic
30#10622541C411yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622333—28no—
34C11×#336C2212yes—
35#10622188C2212yes—
36#10622188C2212yes—
37#10622162C2212yes—
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C8×C11C2312yes—
42C22×C8×C11C2312yes—
43C2×C42×C11—41no—
44C2×C42×C11—41no—
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11C2×C412yes—
50C2×C22⋊Dic11C2×C412yes—
51#66979—41no—
52#66979—41no—
53#66979D414yes—
54#66979Q814yes—
55C2×C4⋊Dic11C2×C411yescharacteristic
56C2×C4⋊Dic11C2×C411yescharacteristic
57C2×C4⋊Dic11C2×C411yescharacteristic
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×Dic11⋊C4C2×C412yes—
60C2×Dic11⋊C4C2×C412yes—
61C2×Dic11⋊C4C2×C412yes—
62C2×Dic11⋊C4C2×C412yes—
63C2×C4×Dic11C2312yes—
64C2×C4×Dic11C2312yes—
65C22×C11⋊C8C2312yes—
66C22×C11⋊C8C2312yes—
67C11×C4⋊C8—41no—
68C11×C4⋊C8—41no—
69C11×C22⋊C8—24no—
70C11⋊#95C2×C412yes—
71C11⋊#95C2×C412yes—
72C11⋊#95C2×C412yes—
73C11⋊#95C2×C412yes—
74C22⋊(C11⋊C8)—24no—
75#66879—24no—
76Dic11⋊C8—24no—
77Dic11⋊C8—24no—
78Dic11⋊C8—42no—
79Dic11⋊C8—42no—
80C8×Dic11—24no—
81C4⋊(C11⋊C8)—41no—
82C4⋊(C11⋊C8)—41no—
83#21957—111nomaximal, Sylow
84C24×C11C22×C411yescharacteristic
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×Q812yes—
102C22×C4×C11C2411yescharacteristic
103C22×Dic11C22×C412yes—
104C22×Dic11C22×C412yes—
105C22×Dic11C22×C412yes—
106C22×Dic11C22×C412yes—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C42×C11—21no—
114C42×C11—21no—
115C42×C11—21no—
116C42×C11—21no—
117C42×C11—41no—
118C42×C11—41no—
119C22⋊Dic11—42no—
120C22⋊Dic11C4⋊C418yes—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11C4⋊C414yes—
124C4⋊Dic11C4⋊C414yes—
125Dic11⋊C4—24no—
126Dic11⋊C4—24no—
127Dic11⋊C4—42no—
128Dic11⋊C4—42no—
129C4×Dic11—22no—
130C4×Dic11—22no—
131C4×Dic11C2×D414yes—
132C4×Dic11C2×Q814yes—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×#433—112no—
140#2296—111no—
141#1940—112no—
142#1940—112no—
143#1939—112no—
144#1939—112no—
145#1798—112no—
146#1797—111no—
147#1797D1111yescharacteristic
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11C2×C4⋊C412yes—
155C23×C11C23×C411yescharacteristic
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
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—44no—
173C2×C4×C11—44no—
174C2×C4×C11C2×C4⋊C412yes—
175C2×C4×C11#13112yes—
176C2×C4×C11#13112yes—
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C22×Q811yescharacteristic
179C2×C4×C11H(5,𝔽2)11yescharacteristic
180C2×C4×C11H(5,𝔽2)11yescharacteristic
181C2×C4×C112−1+411yescharacteristic
182C2×C4×C112−1+411yescharacteristic
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11C2×C4⋊C414yes—
194C2×Dic11C2×C4⋊C414yes—
195C8×C11—42no—
196C8×C11—42no—
197C11⋊C8—42no—
198C11⋊C8—42no—
199C2×#117—111no—
200C2×#117—111no—
201C22×C42C2×D1111yescharacteristic
202#433—228no—
203C2×C4⋊C8—112no—
204C2×C4⋊C8—112no—
205C2×C4⋊C8—112no—
206C2×C4⋊C8—112no—
207C2×C4⋊C8—111no—
208C2×C4⋊C8—111no—
209C2×C4⋊C8C2×D1111yescharacteristic
210C2×C4⋊C8C2×D1111yescharacteristic
211C2×C22⋊C8—112no—
212C2×C22⋊C8C2×D1112yes—
213C2×#97—112no—
214C2×C4×C8—112no—
215#389—111no—
216#389—111no—
217#389—111no—
218#389—111no—
219#385—112no—
220#385—112no—
221C4×C4⋊C4—112no—
222C4×C4⋊C4—112no—
223#336—112no—
224#336—112no—
225#336—112no—
226#336C2×D1112yes—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11C22×C4⋊C411yescharacteristic
235C22×C11#51811yescharacteristic
236C22×C11#51911yescharacteristic
237C22×C11C2×#13111yescharacteristic
238C22×C11C2×#13111yescharacteristic
239C22×C11#56811yescharacteristic
240C22×C11#56811yescharacteristic
241C4×C11—22no—
242C4×C11—22no—
243C4×C11—22no—
244C4×C11—41no—
245C4×C11—41no—
246C4×C11#53711yescharacteristic
247C4×C11#53711yescharacteristic
248C4×C11#54411yescharacteristic
249C4×C11#54411yescharacteristic
250Dic11—24no—
251Dic11—24no—
252Dic11—42no—
253Dic11—42no—
254C23×C4C4×D1111yescharacteristic
255C23×C4C4×D1111yescharacteristic
256C23×C4C22×D1111yescharacteristic
257C22×C8—112no—
258C22×C8—112no—
259C22×C8C22×D1112yes—
260C22×C8C22×D1112yes—
261#117—114no—
262#117—114no—
263#117—441no—
264#117—441no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—112no—
268C2×C4⋊C4—112no—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—112no—
273C2×C22⋊C4—112no—
274C2×C22⋊C4—112no—
275C2×C42—41no—
276C2×C42—41no—
277C2×C42—112no—
278C2×C42—112no—
279C2×C42C4×D1111yescharacteristic
280C2×C42C4×D1111yescharacteristic
281C2×C42C22×D1111yescharacteristic
282C2×C42C22×D1111yescharacteristic
283C4⋊C8—41no—
284C4⋊C8—41no—
285C4⋊C8—224no—
286C4⋊C8—224no—
287C4⋊C8—441no—
288C4⋊C8—441no—
289C4⋊C8—442no—
290C4⋊C8—442no—
291C22⋊C8—24no—
292C22⋊C8—224no—
293#97—224no—
294C4×C8—224no—
295#95—112no—
296#95—112no—
297#95—112no—
298#95—112no—
299C2×C11—42no—
300C2×C11#231611yescharacteristic
301C2×C11#290611yescharacteristic
302C2×C11#290611yescharacteristic
303C2×C11#297611yescharacteristic
304C2×C11#297611yescharacteristic
305C2×C11#298611yescharacteristic
306C2×C11#298711yescharacteristic
307C24C2×C4×D1111yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—112no—
319C22×C4—112no—
320C22×C4—112no—
321C22×C4—112no—
322C22×C4C2×C4×D1111yescharacteristic
323C22×C4C2×C4×D1111yescharacteristic
324C22×C4C2×C4×D1111yescharacteristic
325C22×C4C2×C4×D1111yescharacteristic
326C22×C4C2×C4×D1111yescharacteristic
327C22×C4D4×D1112yes—
328C22×C4Q8×D1112yes—
329C22×C4C23×D1111yescharacteristic
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—222no—
342C4⋊C4—114no—
343C4⋊C4—114no—
344C4⋊C4—224no—
345C4⋊C4—224no—
346C4⋊C4—441no—
347C4⋊C4—441no—
348C4⋊C4—442no—
349C4⋊C4—442no—
350C22⋊C4—118no—
351C22⋊C4—442no—
352C42—21no—
353C42—21no—
354C42—21no—
355C42—21no—
356C42—41no—
357C42—41no—
358C42—114no—
359C42—114no—
360C42—222no—
361C42—222no—
362C11#2195711yescharacteristic, complemented, Sylow
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23C4⋊C4×D1112yes—
370C23C22×C4×D1111yescharacteristic
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—114no—
390C2×C4—114no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—222no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4C4⋊C4×D1112yes—
402C2×C4#6695412yes—
403C2×C4#6696012yes—
404C2×C4C2×D4×D1111yescharacteristic
405C2×C4#6703711yescharacteristic
406C2×C4#6703711yescharacteristic
407C2×C4C2×Q8×D1111yescharacteristic
408C2×C4#6704311yescharacteristic
409C2×C4#6704311yescharacteristic
410C8—42no—
411C8—42no—
412C8—442no—
413C8—442no—
414C22—22no—
415C22—22no—
416C22—22no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22#1062301711yescharacteristic
422C22C2×C4⋊C4×D1111yescharacteristic
423C22#1062304711yescharacteristic
424C22C2×#6695411yescharacteristic
425C22C2×#6696011yescharacteristic
426C22#1062327611yescharacteristic
427C22#1062327611yescharacteristic
428C4—22no—
429C4—22no—
430C4—22no—
431C4—41no—
432C4—41no—
433C4—224no—
434C4—224no—
435C4—442no—
436C4—442no—
437C4#1062312811yescharacteristic
438C4#1062312811yescharacteristic
439C4#1062315411yescharacteristic
440C4#1062315411yescharacteristic
441C2—42no—
442C2#1307123311yescharacteristic
443C2#1307718111yescharacteristic
444C2#1307718511yescharacteristic
445C2#1307766111yescharacteristic
446C2#1307766611yescharacteristic
447C2#1307771711yescharacteristic
448C2#1307772111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1797C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1797D11
hypocenterC11#21957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #13069338C2semidirect
4. #13069336C2semidirect
5. #13069333C2semidirect
6. #13069331C2semidirect
362. C11#21957semidirect

Maximal subgroups

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

subgroupindex
C2×#106223332
#130710992
#130693382
#130693362
#130693332
#130693312
#130685982
#130685962
C11×#17972
#2195711