Finite Group Databasebeta

← #13077935

Subgroups — #13077935

Order 1408.

712 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67043C211yesmaximal, characteristic, complemented
2C2×#66971C211yesmaximal, characteristic, complemented
3C2×#66969C211yesmaximal, characteristic, complemented
4#10623160C211yesmaximal, characteristic, complemented
5C11×#452C211yesmaximal, characteristic, complemented
6#10622851C211yesmaximal, characteristic, complemented
7#10622799C211yesmaximal, characteristic, complemented
8#10622786C211yesmaximal, characteristic, complemented
9#10622663C211yesmaximal, characteristic, complemented
10#10622419C211yesmaximal, characteristic, complemented
11D11×#103C211yesmaximal, characteristic, complemented
12#10622394C211yesmaximal, characteristic, complemented
13#10622384C211yesmaximal, characteristic, complemented
14#10622351C211yesmaximal, characteristic, complemented
15#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17#67043—24no—
18#67043—24no—
19C2×#4343C2211yescharacteristic
20C2×Q8×D11C2211yescharacteristic
21C2×Q8×D11C2211yescharacteristic
22C2×#4341—21no—
23C2×#4341—21no—
24C2×#4341C2211yescharacteristic
25C2×#4341C2211yescharacteristic
26C2×#4339—21no—
27C2×#4339C2211yescharacteristic
28C22×Dic22—21no—
29C22×Dic22C2211yescharacteristic
30C2×C11×Q16C2211yescharacteristic
31C2×C11×SD16C2211yescharacteristic
32C11×C22⋊Q8C2211yescharacteristic
33#66999C2211yescharacteristic
34C2×#4326C2211yescharacteristic
35C2×#4326C2211yescharacteristic
36C2×#4325C2211yescharacteristic
37C2×#4323C2211yescharacteristic
38#66983C2211yescharacteristic
39#66971—24no—
40#66969—24no—
41C2×#4314C2211yescharacteristic
42C2×#4314C2211yescharacteristic
43C2×#4313C2211yescharacteristic
44C2×C8×D11C2211yescharacteristic
45#66949—21no—
46#66948—21no—
47#66948C2211yescharacteristic
48C4⋊C4×D11C2211yescharacteristic
49#66937—21no—
50#66937—21no—
51C11×#103C2211yescharacteristic
52C11×#102C2211yescharacteristic
53C11×C22⋊C8C2211yescharacteristic
54#66899C2211yescharacteristic
55#66896C2211yescharacteristic
56C22⋊(C11⋊C8)C2211yescharacteristic
57(C2×D11)⋊C8C2211yescharacteristic
58(C2×D11)⋊C8C2211yescharacteristic
59#66880C2211yescharacteristic
60#66880C2211yescharacteristic
61#66874C2211yescharacteristic
62#66874C2211yescharacteristic
63C11×#41—22no—
64C11×#41—22no—
65C2×Q8×C11C2311yescharacteristic
66C2×Q8×C11C2311yescharacteristic
67C2×D4×C11—21no—
68C2×D4×C11C2311yescharacteristic
69C22×C4×C11—21no—
70C22×C4×C11C2311yescharacteristic
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11—21no—
74C2×C22⋊D11D411yescharacteristic
75C2×C22⋊D11D411yescharacteristic
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79#4343—22no—
80#4343—22no—
81Q8×D11—22no—
82Q8×D11—22no—
83Q8×D11—22no—
84Q8×D11D414yescomplemented
85#4341—28no—
86#4341—28no—
87#4341—22no—
88#4341—22no—
89#4341—22no—
90#4341D414yescomplemented
91#4339—28no—
92#4339—22no—
93#4339—22no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44D411yescharacteristic
97C2×D44C2311yescharacteristic
98C2×C4×D11—21no—
99C2×C4×D11—21no—
100C2×C4×D11—21no—
101C2×C4×D11—21no—
102C2×C4×D11C2311yescharacteristic
103C2×C4×D11C2311yescharacteristic
104C2×Dic22—28no—
105C2×Dic22—21no—
106C2×Dic22—21no—
107C2×Dic22—22no—
108C2×Dic22—22no—
109C2×Dic22—21no—
110C2×Dic22D411yescharacteristic
111C2×Dic22C2311yescharacteristic
112C2×Dic22C2311yescharacteristic
113C11×Q16—22no—
114C11×SD16—22no—
115C2×C8×C11C2311yescharacteristic
116C2×C8×C11C2311yescharacteristic
117C11×C4⋊C4—21no—
118C11×C4⋊C4C2311yescharacteristic
119C11×C22⋊C4—21no—
120#4326—22no—
121#4326—22no—
122#4325—22no—
123#4323—22no—
124(C2×D11)⋊C4—21no—
125(C2×D11)⋊C4—21no—
126(C2×D11)⋊C4—21no—
127C4⋊Dic11C2311yescharacteristic
128Dic11⋊C4—21no—
129Dic11⋊C4—21no—
130C2×C11⋊C8C2311yescharacteristic
131C2×C11⋊C8C2311yescharacteristic
132#4314—22no—
133#4314—22no—
134#4313—22no—
135C8×D11—22no—
136#3013—111nomaximal, Sylow
137C23×C11—21no—
138C23×C11C2×D411yescharacteristic
139C22×D11—21no—
140C22×D11C2×D411yescharacteristic
141C22×D11C2×D411yescharacteristic
142Q8×C11—21no—
143Q8×C11—21no—
144Q8×C11—21no—
145Q8×C11C2×D412yes—
146D4×C11—24no—
147D4×C11—21no—
148D4×C11C2×D412yes—
149C2×C4×C11—24no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11C2×D411yescharacteristic
156C2×C4×C11C2411yescharacteristic
157C22⋊D11—24no—
158C22⋊D11—22no—
159C22⋊D11—24no—
160C22⋊D11—22no—
161C22⋊D11—81no—
162C2×Dic11—24no—
163C2×Dic11—24no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—24no—
167C2×Dic11—21no—
168C2×Dic11C2×D411yescharacteristic
169C2×Dic11C2×D411yescharacteristic
170D44—22no—
171D44—21no—
172D44—21no—
173D44—42no—
174D44—81no—
175C4×D11—24no—
176C4×D11—24no—
177C4×D11—21no—
178C4×D11—21no—
179C4×D11—42no—
180C4×D11—81no—
181C4×D11C2×D412yes—
182C4×D11C2×D412yes—
183Dic22—24no—
184Dic22—24no—
185Dic22—21no—
186Dic22—21no—
187Dic22—22no—
188Dic22—24no—
189Dic22C2×D412yes—
190Dic22C2×D412yes—
191C8×C11—21no—
192C8×C11—21no—
193C11⋊C8—21no—
194C11⋊C8—21no—
195C2×2−1+4—111no—
196C2×#137—111no—
197C2×#135—111no—
198#537—111no—
199#452—111no—
200#452D1111yescharacteristic, complemented
201#451—111no—
202#451—111no—
203#449—111no—
204#449—111no—
205#448—111no—
206#448—111no—
207#417—111no—
208C2×#103—111no—
209#408—111no—
210C22×C11—21no—
211C22×C11—22no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11C22×D411yescharacteristic
217C2×D11—21no—
218C2×D11—21no—
219C2×D11—21no—
220C2×D11—21no—
221C2×D11—21no—
222C2×D11—41no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11#12012yes—
226C4×C11—21no—
227C4×C11—22no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11C22×D411yescharacteristic
231C4×C11C22×D411yescharacteristic
232Dic11—21no—
233Dic11—22no—
234Dic11—22no—
235Dic11—41no—
236Dic11#12012yes—
2372−1+4—224no—
2382−1+4—224no—
239C2×#41—111no—
240C2×#41—111no—
241C2×#41—111no—
242C2×#41—111no—
243C2×#41—221no—
244C2×#41—221no—
245C2×#41—221no—
246C2×#41C2×D1111yescharacteristic
247C22×Q8—111no—
248C22×Q8—111no—
249C22×Q8—111no—
250C22×Q8—221no—
251#137—224no—
252#135—224no—
253C2×Q16—111no—
254C2×Q16—111no—
255C2×Q16C2×D1111yescharacteristic
256C2×SD16—111no—
257C2×SD16—111no—
258C2×SD16—111no—
259C2×SD16C2×D1111yescharacteristic
260C2×D8—111no—
261C2×M16—111no—
262C22×C8—111no—
263C22⋊Q8—111no—
264C22⋊Q8—221no—
265C22⋊Q8C2×D1111yescharacteristic
266#121—111no—
267#121—111no—
268#121—221no—
269#121—221no—
270#121—221no—
271C2×C4⋊C4—111no—
272#103—111no—
273#103—111no—
274#103—111no—
275#103—111no—
276#103—111no—
277#103C2×D1111yescharacteristic
278#102—111no—
279#102C2×D1111yescharacteristic
280C22⋊C8—111no—
281C22⋊C8—111no—
282C22⋊C8—111no—
283C22⋊C8C2×D1111yescharacteristic
284C2×C11—41no—
285C2×C11—42no—
286C2×C11C2×#12011yescharacteristic
287C2×C11#57711yescharacteristic
288C2×C11#57811yescharacteristic
289D11—22no—
290D11—41no—
291D11—81no—
292#41—22no—
293#41—22no—
294#41—114no—
295#41—222no—
296#41—222no—
297#41—228no—
298#41—222no—
299#41—222no—
300#41—222no—
301#41—222no—
302#41—228no—
303#41—228no—
304#41—222no—
305C2×Q8—111no—
306C2×Q8—114no—
307C2×Q8—111no—
308C2×Q8—111no—
309C2×Q8—221no—
310C2×Q8—221no—
311C2×Q8—222no—
312C2×Q8—222no—
313C2×Q8—228no—
314C2×Q8—222no—
315C2×Q8—222no—
316C2×Q8—222no—
317C2×Q8—221no—
318C2×Q8C22×D1111yescharacteristic
319C2×Q8C22×D1111yescharacteristic
320C2×D4—21no—
321C2×D4—111no—
322C2×D4—111no—
323C2×D4—111no—
324C2×D4—111no—
325C2×D4—221no—
326C2×D4—221no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4C22×D1111yescharacteristic
331C22×C4—21no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4—221no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4C22×D1111yescharacteristic
342Q16—22no—
343Q16—222no—
344Q16—222no—
345SD16—22no—
346SD16—222no—
347SD16—222no—
348SD16—222no—
349D8—222no—
350M16—222no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8—222no—
354C2×C8C22×D1111yescharacteristic
355C2×C8C22×D1111yescharacteristic
356C4⋊C4—21no—
357C4⋊C4—111no—
358C4⋊C4—221no—
359C4⋊C4—221no—
360C4⋊C4C22×D1111yescharacteristic
361C22⋊C4—21no—
362C22⋊C4—221no—
363C22⋊C4—221no—
364C22⋊C4—221no—
365C11#301311yescharacteristic, complemented, Sylow
366C23—21no—
367C23—111no—
368C23—111no—
369C23—221no—
370C23D4×D1111yescharacteristic
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—112no—
375Q8—112no—
376Q8—222no—
377Q8—224no—
378Q8—224no—
379Q8—224no—
380Q8—221no—
381Q8—221no—
382Q8D4×D1112yes—
383D4—24no—
384D4—21no—
385D4—222no—
386D4—222no—
387D4—222no—
388D4—224no—
389D4—224no—
390D4—221no—
391D4—221no—
392D4—442no—
393D4—881no—
394D4—881no—
395D4D4×D1112yes—
396C2×C4—24no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—111no—
403C2×C4—112no—
404C2×C4—112no—
405C2×C4—111no—
406C2×C4—224no—
407C2×C4—224no—
408C2×C4—224no—
409C2×C4—224no—
410C2×C4—224no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—442no—
417C2×C4—881no—
418C2×C4D4×D1111yescharacteristic
419C2×C4C23×D1111yescharacteristic
420C8—21no—
421C8—21no—
422C8—221no—
423C8—221no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—112no—
431C22—221no—
432C22—221no—
433C22—221no—
434C22—221no—
435C22—221no—
436C22—441no—
437C22—441no—
438C22—441no—
439C22C2×D4×D1111yescharacteristic
440C4—21no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—112no—
445C4—221no—
446C4—222no—
447C4—222no—
448C4—441no—
449C4C2×D4×D1111yescharacteristic
450C4C2×D4×D1111yescharacteristic
451C2—41no—
452C2—42no—
453C2—222no—
454C2—441no—
455C2—881no—
456C2D11×#12011yescharacteristic
457C2#1062330111yescharacteristic
458C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
hypercenter#452D11
hypocenterC11#3013
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#67043C2semidirect
2. C2×#66971C2semidirect
3. C2×#66969C2semidirect
4. #10623160C2semidirect
5. C11×#452C2semidirect
6. #10622851C2semidirect
7. #10622799C2semidirect
8. #10622786C2semidirect
9. #10622663C2semidirect
10. #10622419C2semidirect
11. D11×#103C2semidirect
12. #10622394C2semidirect
13. #10622384C2semidirect
14. #10622351C2semidirect
15. #10622340C2semidirect
84. Q8×D11D4semidirect
90. #4341D4semidirect
200. #452D11semidirect
365. C11#3013semidirect

Maximal subgroups

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

subgroupindex
C2×#670432
C2×#669712
C2×#669692
#106231602
C11×#4522
#106228512
#106227992
#106227862
#106226632
#106224192
D11×#1032
#106223942
#106223842
#106223512
#106223402
#301311