Finite Group Databasebeta

← C2×#10594631 #11900330

Subgroups — C2×#10594631 #11900330

Order 1152.

3889 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#897C212yesmaximal, complemented
5C2×#63921C212yesmaximal
6C2×#63900C212yesmaximal, complemented
7C2×#63899C214yesmaximal, complemented
8C2×#63856C212yesmaximal, complemented
9#10594631C2116yesmaximal, direct product factor
10C2×D3×C22⋊Q8—32nomaximal
11C23×D32C2211yescharacteristic
12C22×C4×C3⋊D3C2212yes—
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×C3×Dic6C2212yescomplemented
16C22×#627C2212yescomplemented
17C22×#624C2212yes—
18C22×#624C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×C4×D32—28no—
21C2×C4×D32C2218yes—
22C2×#3797—28no—
23C2×#3797C2218yescomplemented
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26C2×#3750C2212yescomplemented
27C4⋊C4×C3⋊D3C2218yescomplemented
28C2×C3×(C2×D3)⋊C4C2214yes—
29C2×C3×C4⋊Dic3C2214yescomplemented
30C3×#897C22116yescomplemented
31C2×#3724C2214yescomplemented
32C2×(C2×D3)⋊Dic3C2214yes—
33#63921C22116yes—
34#63900C22116yescomplemented
35#63899C22132yescomplemented
36#63856C22116yescomplemented
37C22×D3×Q8—32no—
38C23×C4×D3—32no—
39C2×C3×C22⋊Q8—32no—
40C2×#946—32no—
41C2×#924—32no—
42D3×C22⋊Q8—332no—
43C2×#897D312yescomplemented
44C2×#896—34no—
45C2×D3×C4⋊C4—32no—
46C2×D3×C4⋊C4—34no—
47C2×D3×C4⋊C4—61no—
48C2×D3×C22⋊C4—34no—
49C2×#878—34no—
50C23×C3⋊D3C2311yescharacteristic
51C23×C3×D3C2312yes—
52C22×D32—24no—
53C22×D32—24no—
54C22×D32Q818yescomplemented
55C22×D32C2314yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4×C3⋊D3—28no—
61C2×C4×C3⋊D3D418yes—
62C2×C4×C3⋊D3C2318yes—
63C2×C4×C3⋊D3C2314yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2314yes—
66C2×C3×C4×D3—28no—
67C2×C3×C4×D3C2318yes—
68C2×C3×Dic6—28no—
69C2×C3×Dic6C2318yescomplemented
70C2×#627—28no—
71C2×#627C2318yescomplemented
72C2×#624—28no—
73C2×#624—24no—
74C2×#624C2318yes—
75C2×#624C2314yes—
76C2×D3×Dic3—28no—
77C2×D3×Dic3C2318yes—
78C4×D32—232no—
79#3797—232no—
80C32×C4⋊C4C2314yescomplemented
81C4⋊(C3⋊Dic3)C2314yescomplemented
82#3750C2318yescomplemented
83C3×(C2×D3)⋊C4C23116yes—
84C3×C4⋊Dic3C23116yescomplemented
85#3724C23116yescomplemented
86(C2×D3)⋊Dic3C23116yes—
87C22×C22⋊Q8—91noSylow
88C24×D3—32no—
89C22×C3×Q8—32no—
90C23×C3×C4—32no—
91C23×Dic3—32no—
92C2×D3×Q8—316no—
93C2×D3×Q8—616no—
94C22×C4×D3—32no—
95C22×C4×D3—32no—
96C22×C4×D3—34no—
97C22×C4×D3—32no—
98C22×C4×D3—34no—
99C22×C4×D3—316no—
100C22×C4×D3—61no—
101C22×C4×D3—62no—
102C22×C4×D3—616no—
103C22×C4×D3C2×D312yes—
104C22×Dic6—34no—
105C22×Dic6C2×D312yescomplemented
106C3×C22⋊Q8—316no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—34no—
109C2×C3×C4⋊C4C2×D312yescomplemented
110C2×C3×C22⋊C4—34no—
111C2×#217—34no—
112#946—316no—
113C2×(C2×D3)⋊C4—34no—
114C2×(C2×D3)⋊C4C2×D314yes—
115C2×C4⋊Dic3—32no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3C2×D314yescomplemented
118#924—316no—
119C2×Dic3⋊C4—34no—
120C2×Dic3⋊C4—34no—
121C2×Dic3⋊C4—34no—
122C2×Dic3⋊C4—62no—
123#897C2×D3116yescomplemented
124#896—332no—
125D3×C4⋊C4—316no—
126D3×C4⋊C4—332no—
127D3×C4⋊C4—68no—
128D3×C22⋊C4—332no—
129#878—332no—
130C23×C32C2411yescharacteristic
131C22×C3⋊D3C2×D414yes—
132C22×C3⋊D3C2×Q814yes—
133C22×C3⋊D3#4114yes—
134C22×C3⋊D3C2412yes—
135C22×C3×D3—24no—
136C22×C3×D3—24no—
137C22×C3×D3C2×Q818yescomplemented
138C22×C3×D3C2414yes—
139C2×D32—232no—
140C2×D32—28no—
141C2×D32—28no—
142C2×D32C2×Q8116yescomplemented
143C2×C32×C4—24no—
144C2×C32×C4C2×D414yes—
145C2×C32×C4C2414yes—
146C2×C32×C4C2412yes—
147C2×C3⋊Dic3—24no—
148C2×C3⋊Dic3C2×D414yes—
149C2×C3⋊Dic3C2414yes—
150C2×C3⋊Dic3C2412yes—
151C4×C3⋊D3—216no—
152C4×C3⋊D3C2×D4116yes—
153C2×C3×Dic3—24no—
154C2×C3×Dic3—28no—
155C2×C3×Dic3C2418yes—
156C2×C3×Dic3C2414yes—
157C3×C4×D3—216no—
158C3×Dic6—216no—
159#627—216no—
160#624—216no—
161#624—28no—
162D3×Dic3—216no—
163C23×Q8—91no—
164C24×C4—91no—
165C2×C22⋊Q8—32no—
166C2×C22⋊Q8—94no—
167C2×C22⋊Q8—916no—
168C2×C22⋊Q8—92no—
169C22×C4⋊C4—92no—
170C22×C4⋊C4—91no—
171C22×C22⋊C4—92no—
172C24×C3—32no—
173C23×D3—32no—
174C23×D3—316no—
175C23×D3—38no—
176C23×D3—61no—
177C23×D3—68no—
178C23×D3—68no—
179C23×D3C22×D312yes—
180C2×C3×Q8—38no—
181C2×C3×Q8—68no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—32no—
185C22×C3×C4—34no—
186C22×C3×C4—38no—
187C22×C3×C4—68no—
188C22×C3×C4C22×D314yes—
189C22×C3×C4C22×D312yes—
190C22×Dic3—32no—
191C22×Dic3—34no—
192C22×Dic3—38no—
193C22×Dic3—61no—
194C22×Dic3—62no—
195C22×Dic3—68no—
196C22×Dic3C22×D312yes—
197C22×Dic3C22×D314yes—
198D3×Q8—664no—
199C2×C4×D3—28no—
200C2×C4×D3—316no—
201C2×C4×D3—38no—
202C2×C4×D3—38no—
203C2×C4×D3—316no—
204C2×C4×D3—316no—
205C2×C4×D3—38no—
206C2×C4×D3—64no—
207C2×C4×D3—68no—
208C2×C4×D3—68no—
209C2×C4×D3—664no—
210C2×C4×D3—68no—
211C2×C4×D3—616no—
212C2×C4×D3—68no—
213C2×C4×D3—616no—
214C2×C4×D3—128no—
215C2×C4×D3C22×D318yes—
216C2×Dic6—28no—
217C2×Dic6—316no—
218C2×Dic6—616no—
219C2×Dic6C22×D318yescomplemented
220C3×C4⋊C4—24no—
221C3×C4⋊C4—316no—
222C3×C4⋊C4C22×D318yescomplemented
223C3×C22⋊C4—316no—
224#217—316no—
225(C2×D3)⋊C4—316no—
226(C2×D3)⋊C4C22×D3116yes—
227C4⋊Dic3—38no—
228C4⋊Dic3—64no—
229C4⋊Dic3C22×D3116yescomplemented
230Dic3⋊C4—316no—
231Dic3⋊C4—316no—
232Dic3⋊C4—316no—
233Dic3⋊C4—68no—
234C22×C32C22×D412yes—
235C22×C32C22×Q812yes—
236C22×C32C2×#4112yes—
237C22×C32C2511yescharacteristic
238C2×C3⋊D3C22⋊Q8116yescomplemented
239C2×C3⋊D3C22×D414yes—
240C2×C3⋊D3C22×Q814yes—
241C2×C3⋊D3C2×#4114yes—
242C2×C3×D3—216no—
243C2×C3×D3—24no—
244C2×C3×D3—24no—
245C2×C3×D3C22×Q818yescomplemented
246D32—232no—
247C32×C4—24no—
248C32×C4C22×D414yes—
249C3⋊Dic3—24no—
250C3⋊Dic3C22×D414yes—
251C3×Dic3—24no—
252C3×Dic3—28no—
253C25—91no—
254C22×Q8—32no—
255C22×Q8—92no—
256C22×Q8—98no—
257C22×Q8—188no—
258C23×C4—32no—
259C23×C4—92no—
260C23×C4—91no—
261C23×C4—98no—
262C23×C4—92no—
263C23×C4—91no—
264C23×C4—92no—
265C23×C4—188no—
266C22⋊Q8—316no—
267C22⋊Q8—932no—
268C22⋊Q8—916no—
269C2×C4⋊C4—34no—
270C2×C4⋊C4—916no—
271C2×C4⋊C4—94no—
272C2×C4⋊C4—92no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—98no—
275C2×C4⋊C4D3211yescharacteristic, complemented
276C2×C22⋊C4—34no—
277C2×C22⋊C4—916no—
278C2×C22⋊C4—94no—
279C23×C3—21no—
280C23×C3—38no—
281C23×C3—34no—
282C23×C3—64no—
283C23×C3—64no—
284C23×C3C23×D312yes—
285C22×D3—24no—
286C22×D3—24no—
287C22×D3—38no—
288C22×D3—38no—
289C22×D3—38no—
290C22×D3—34no—
291C22×D3—332no—
292C22×D3—64no—
293C22×D3—64no—
294C22×D3—64no—
295C22×D3—62no—
296C22×D3—616no—
297C22×D3—616no—
298C22×D3—664no—
299C22×D3D3×Q818yescomplemented
300C22×D3C23×D314yes—
301C3×Q8—616no—
302C2×C3×C4—28no—
303C2×C3×C4—22no—
304C2×C3×C4—24no—
305C2×C3×C4—24no—
306C2×C3×C4—34no—
307C2×C3×C4—38no—
308C2×C3×C4—44no—
309C2×C3×C4—68no—
310C2×C3×C4—64no—
311C2×C3×C4—616no—
312C2×C3×C4D3×D418yes—
313C2×C3×C4C23×D318yes—
314C2×C3×C4C23×D314yes—
315C2×Dic3—28no—
316C2×Dic3—24no—
317C2×Dic3—38no—
318C2×Dic3—34no—
319C2×Dic3—38no—
320C2×Dic3—64no—
321C2×Dic3—62no—
322C2×Dic3—64no—
323C2×Dic3—616no—
324C2×Dic3—68no—
325C2×Dic3—124no—
326C2×Dic3C23×D314yes—
327C2×Dic3C23×D318yes—
328C4×D3—216no—
329C4×D3—332no—
330C4×D3—616no—
331C4×D3—616no—
332C4×D3—632no—
333C4×D3—616no—
334C4×D3—632no—
335C4×D3—1216no—
336Dic6—216no—
337Dic6—632no—
338C2×C32C2×C22⋊Q814yescomplemented
339C2×C32C23×D411yescharacteristic
340C2×C32C23×Q811yescharacteristic
341C2×C32C22×#4111yescharacteristic
342C3⋊D3C2×C22⋊Q818yescomplemented
343C3×D3—28no—
344C24—32no—
345C24—94no—
346C24—98no—
347C24—91no—
348C24—184no—
349C24—184no—
350C2×Q8—38no—
351C2×Q8—68no—
352C2×Q8—98no—
353C2×Q8—188no—
354C2×Q8—1832no—
355C22×C4—34no—
356C22×C4—32no—
357C22×C4—38no—
358C22×C4—68no—
359C22×C4—98no—
360C22×C4—94no—
361C22×C4—98no—
362C22×C4—91no—
363C22×C4—94no—
364C22×C4—98no—
365C22×C4—92no—
366C22×C4—98no—
367C22×C4—188no—
368C22×C4—1832no—
369C22×C4—184no—
370C22×C4—188no—
371C22×C4—188no—
372C22×C4C2×D3212yes—
373C22×C4C2×D3211yescharacteristic
374C4⋊C4—316no—
375C4⋊C4—916no—
376C4⋊C4—98no—
377C4⋊C4—94no—
378C4⋊C4C2×D3214yescomplemented
379C22⋊C4—316no—
380C22⋊C4—916no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—38no—
386C22×C3—64no—
387C22×C3—64no—
388C22×C3—616no—
389C22×C3C2×D3×D414yes—
390C22×C3C2×D3×Q814yes—
391C22×C3D3×#4114yes—
392C22×C3C24×D312yes—
393C2×D3—24no—
394C2×D3—24no—
395C2×D3—216no—
396C2×D3—38no—
397C2×D3—38no—
398C2×D3—38no—
399C2×D3—332no—
400C2×D3—64no—
401C2×D3—64no—
402C2×D3—616no—
403C2×D3—64no—
404C2×D3—664no—
405C2×D3C2×D3×Q818yescomplemented
406C3×C4—28no—
407C3×C4—24no—
408C3×C4—44no—
409C3×C4—68no—
410C3×C4—64no—
411C3×C4C2×D3×D418yes—
412Dic3—28no—
413Dic3—24no—
414Dic3—38no—
415Dic3—64no—
416Dic3—68no—
417Dic3—124no—
418C32C22×C22⋊Q811yescharacteristic, complemented, Sylow
419C23—38no—
420C23—34no—
421C23—64no—
422C23—64no—
423C23—916no—
424C23—94no—
425C23—94no—
426C23—94no—
427C23—92no—
428C23—188no—
429C23—188no—
430C23—1832no—
431C23C22×D3211yescharacteristic
432Q8—616no—
433Q8—1816no—
434C2×C4—24no—
435C2×C4—38no—
436C2×C4—34no—
437C2×C4—64no—
438C2×C4—68no—
439C2×C4—616no—
440C2×C4—94no—
441C2×C4—92no—
442C2×C4—916no—
443C2×C4—94no—
444C2×C4—1816no—
445C2×C4—188no—
446C2×C4—1816no—
447C2×C4—1816no—
448C2×C4—184no—
449C2×C4#380214yes—
450C2×C4C22×D3214yes—
451C2×C4C22×D3212yes—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—24no—
455C2×C3—21no—
456C2×C3—68no—
457C2×C3D3×C22⋊Q818yescomplemented
458C2×C3C22×D3×D412yes—
459C2×C3C22×D3×Q812yes—
460C2×C3C2×D3×#4112yes—
461D3—28no—
462D3—316no—
463D3—68no—
464C22—38no—
465C22—64no—
466C22—64no—
467C22—616no—
468C22—94no—
469C22—94no—
470C22—916no—
471C22—94no—
472C22—1832no—
473C22C2×#380212yes—
474C22#6431212yes—
475C22D32×Q812yes—
476C22C23×D3211yescharacteristic
477C4—24no—
478C4—64no—
479C4—68no—
480C4—94no—
481C4—184no—
482C4C2×#380214yes—
483C3—21no—
484C3C2×D3×C22⋊Q812yescomplemented
485C2—68no—
486C2—98no—
487C2#1059463114yesdirect product factor
488C2C22×#380211yescharacteristic
489C2C2×#6431211yescharacteristic
490C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×D32C22
hypercenterC2×C4⋊C4D32
hypocenterC32C22×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#3797C2semidirect
3. C2×C4⋊C4×C3⋊D3C2semidirect
4. C2×C3×#897C2semidirect
6. C2×#63900C2semidirect
7. C2×#63899C2semidirect
8. C2×#63856C2semidirect
9. #10594631C2direct (N × H)
15. C22×C3×Dic6C22semidirect
16. C22×#627C22semidirect
23. C2×#3797C22semidirect
24. C2×C32×C4⋊C4C22semidirect
25. C2×C4⋊(C3⋊Dic3)C22semidirect
26. C2×#3750C22semidirect
27. C4⋊C4×C3⋊D3C22semidirect
29. C2×C3×C4⋊Dic3C22semidirect
30. C3×#897C22semidirect
31. C2×#3724C22semidirect
34. #63900C22semidirect
35. #63899C22semidirect
36. #63856C22semidirect
43. C2×#897D3semidirect
54. C22×D32Q8semidirect
69. C2×C3×Dic6C23semidirect
71. C2×#627C23semidirect
80. C32×C4⋊C4C23semidirect
81. C4⋊(C3⋊Dic3)C23semidirect
82. #3750C23semidirect
84. C3×C4⋊Dic3C23semidirect
85. #3724C23semidirect
105. C22×Dic6C2×D3semidirect
109. C2×C3×C4⋊C4C2×D3semidirect
117. C2×C4⋊Dic3C2×D3semidirect
123. #897C2×D3semidirect
137. C22×C3×D3C2×Q8semidirect
142. C2×D32C2×Q8semidirect
219. C2×Dic6C22×D3semidirect
222. C3×C4⋊C4C22×D3semidirect
229. C4⋊Dic3C22×D3semidirect
238. C2×C3⋊D3C22⋊Q8semidirect
245. C2×C3×D3C22×Q8semidirect
275. C2×C4⋊C4D32semidirect
299. C22×D3D3×Q8semidirect
338. C2×C32C2×C22⋊Q8semidirect
342. C3⋊D3C2×C22⋊Q8semidirect
378. C4⋊C4C2×D32semidirect
405. C2×D3C2×D3×Q8semidirect
418. C32C22×C22⋊Q8semidirect
457. C2×C3D3×C22⋊Q8semidirect
484. C3C2×D3×C22⋊Q8semidirect
487. C2#10594631direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D322
C22×#37972
C2×C4⋊C4×C3⋊D32
C2×C3×#8972
C2×#639212
C2×#639002
C2×#638992
C2×#638562
#105946312
C2×D3×C22⋊Q83