Finite Group Databasebeta

← C22×#63948 #11918710

Subgroups — C22×#63948 #11918710

Order 1152.

3077 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
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic
3C22×#3755C211yesmaximal, characteristic, complemented
4C22×C3×#216C211yesmaximal, characteristic, complemented
5C2×#63948C2124yesmaximal, direct product factor
6C22×#3718C211yesmaximal, characteristic, complemented
7C22×#3717C211yesmaximal, characteristic, complemented
8C22×#3711C211yesmaximal, characteristic, complemented
9C22×#942—31nomaximal
10C22×#918—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×D3×Q8—26no—
14C2×C3×D3×Q8C22112yescomplemented
15C22×C3×C4×D3—21no—
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×Dic6—21no—
18C22×C3×Dic6C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#626—21no—
21C22×#624—21no—
22C2×#3799—26no—
23C2×#3799C22112yes—
24C2×#3755C22112yescomplemented
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26C2×C3×#216C22112yescomplemented
27C22×C3×C3⋊C8C2211yescharacteristic
28#63948C22164yesdirect product factor
29C2×#3718C22112yescomplemented
30C2×#3717C22112yescomplemented
31C2×#3711C22112yescomplemented
32C23×C3×Q8—31no—
33C22×#239—31no—
34C22×D3×Q8D311yescharacteristic, complemented
35C22×#235—31no—
36C22×C3×Q16—31no—
37C22×#216—31no—
38C22×#216—31no—
39C22×#216D311yescharacteristic, complemented
40C2×#942—324no—
41C22×#215—31no—
42C22×#215—31no—
43C22×#215—31no—
44C22×#215—61no—
45C22×#208—31no—
46C2×#918—324no—
47C22×#204—31no—
48C22×ΓL(1,𝔽25)—31no—
49C23×C3⋊D3—21no—
50C23×C3×D3D411yescharacteristic
51C2×C32×Q8—23no—
52C2×C32×Q8C2316yes—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—23no—
56C2×C4⋊(C3⋊D3)C2316yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C3×D3×Q8—224no—
61C3×D3×Q8C23116yescomplemented
62C2×C3×C4×D3—212no—
63C2×C3×C4×D3D416yes—
64C2×C3×C4×D3C2316yes—
65C2×C3×Dic6—23no—
66C2×C3×Dic6—23no—
67C2×C3×Dic6—212no—
68C2×C3×Dic6C2316yes—
69C2×C3×Dic6C2316yes—
70C2×#626—212no—
71C2×#624—212no—
72#3799—224no—
73#3799C23116yes—
74#3755C23116yescomplemented
75C2×C3⋊(C3⋊C8)C2316yes—
76C3×#216C23116yescomplemented
77C2×C3×C3⋊C8C2316yes—
78#3718C23116yescomplemented
79#3717C23116yescomplemented
80#3711C23116yescomplemented
81C22×#137—91noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8—312no—
84C22×C3×Q8—31no—
85C22×C3×Q8—31no—
86C22×C3×Q8—61no—
87C22×C3×Q8—66no—
88C22×C3×Q8C2×D311yescharacteristic
89C22×C3×Q8C2×D311yescharacteristic
90C23×C3×C4—31no—
91C23×C3×C4—61no—
92C22×#67—61no—
93C2×#239—312no—
94C2×#239—66no—
95C2×D3×Q8—26no—
96C2×D3×Q8C2×D3112yescomplemented
97C2×#235—312no—
98C2×#235—66no—
99C22×D12—31no—
100C22×D12—31no—
101C22×D12—61no—
102C22×D12—61no—
103C22×C4×D3—21no—
104C22×C4×D3—61no—
105C22×C4×D3—61no—
106C22×C4×D3C2×D311yescharacteristic
107C22×Dic6—21no—
108C22×Dic6C2×D311yescharacteristic
109C22×Dic6C2×D311yescharacteristic
110C2×C3×Q16—312no—
111C22×C3×C8—31no—
112C2×#216—312no—
113C2×#216—312no—
114C2×#216C2×D3112yescomplemented
115#942—364no—
116C2×#215—312no—
117C2×#215—312no—
118C2×#215—312no—
119C2×#215—612no—
120C2×#208—312no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—61no—
124C22×C3⋊C8C2×D311yescharacteristic
125#918—364no—
126C2×#204—312no—
127C2×ΓL(1,𝔽25)—312no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—26no—
130C22×C3⋊D3—44no—
131C22×C3×D3—24no—
132C22×C3×D3C2×D416yes—
133C32×Q8—26no—
134C32×Q8C2414yes—
135C2×C32×C4—26no—
136C2×C32×C4C2×D413yes—
137C2×C32×C4C2413yes—
138C4⋊(C3⋊D3)—26no—
139C4⋊(C3⋊D3)C2414yes—
140C2×C3×Dic3—26no—
141C2×C3×Dic3—26no—
142C2×C3×Dic3C2×D416yes—
143C3×C4×D3—216no—
144C3×C4×D3C2×D4112yes—
145C3×C4×D3C2414yes—
146C3×Dic6—26no—
147C3×Dic6—26no—
148C3×Dic6—216no—
149C3×Dic6C2414yes—
150C3×Dic6C2414yes—
151#626—216no—
152#624—216no—
153C3⋊(C3⋊C8)C2414yes—
154C3×C3⋊C8C2414yes—
155C22×#41—91no—
156C23×Q8—31no—
157C2×#137—924no—
158C22×Q16—31no—
159C22×Q16—91no—
160C22×SD16—91no—
161C22×SD16—91no—
162C22×M16—91no—
163C24×C3—31no—
164C23×D3—61no—
165C23×D3—61no—
166C23×D3—121no—
167C23×D3#6711yescharacteristic
168C2×C3×Q8—23no—
169C2×C3×Q8—23no—
170C2×C3×Q8—26no—
171C2×C3×Q8—316no—
172C2×C3×Q8—36no—
173C2×C3×Q8—36no—
174C2×C3×Q8—43no—
175C2×C3×Q8—612no—
176C2×C3×Q8—624no—
177C2×C3×Q8—63no—
178C2×C3×Q8—63no—
179C2×C3×Q8C22×D316yes—
180C2×C3×Q8C22×D316yes—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—31no—
185C22×C3×C4—36no—
186C22×C3×C4—36no—
187C22×C3×C4—41no—
188C22×C3×C4—612no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C2×#67—612no—
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3#6711yescharacteristic
197#239—316no—
198#239—624no—
199D3×Q8—224no—
200D3×Q8C22×D3116yescomplemented
201#235—316no—
202#235—624no—
203C2×D12—36no—
204C2×D12—36no—
205C2×D12—66no—
206C2×D12—612no—
207C2×D12—63no—
208C2×D12—63no—
209C2×D12—123no—
210C2×C4×D3—212no—
211C2×C4×D3—612no—
212C2×C4×D3—612no—
213C2×C4×D3#6716yes—
214C2×C4×D3C22×D316yes—
215C2×Dic6—23no—
216C2×Dic6—23no—
217C2×Dic6—212no—
218C2×Dic6C22×D316yes—
219C2×Dic6C22×D316yes—
220C3×Q16—316no—
221C2×C3×C8—36no—
222#216—316no—
223#216—316no—
224#216C22×D3116yescomplemented
225#215—316no—
226#215—316no—
227#215—316no—
228#215—616no—
229#208—316no—
230C2×C3⋊C8—36no—
231C2×C3⋊C8—36no—
232C2×C3⋊C8—66no—
233C2×C3⋊C8C22×D316yes—
234#204—316no—
235ΓL(1,𝔽25)—316no—
236C22×C32#13714yescomplemented
237C22×C32C22×D413yes—
238C2×C3⋊D3—24no—
239C2×C3⋊D3—412no—
240C2×C3×D3—212no—
241C2×C3×D3C22×D414yes—
242C32×C4—24no—
243C32×C4C22×D413yes—
244C32×C4C2511yescharacteristic
245C3×Dic3—24no—
246C3×Dic3—24no—
247C3×Dic3C22×D414yes—
248C2×#41—912no—
249C2×#41—186no—
250C22×Q8—312no—
251C22×Q8—31no—
252C22×Q8—31no—
253C22×Q8—61no—
254C22×Q8—66no—
255C22×Q8D3211yescharacteristic
256C22×D4—91no—
257C22×D4—181no—
258C23×C4—31no—
259C23×C4—61no—
260C23×C4—181no—
261#137—964no—
262C2×Q16—312no—
263C2×Q16—912no—
264C2×SD16—912no—
265C2×SD16—912no—
266C2×M16—912no—
267C22×C8—31no—
268C22×C8—91no—
269C23×C3—21no—
270C23×C3—36no—
271C23×C3—64no—
272C23×C3D3×D411yescharacteristic
273C23×C3C2×#6711yescharacteristic
274C22×D3—24no—
275C22×D3—66no—
276C22×D3—66no—
277C22×D3—126no—
278C22×D3—124no—
279C22×D3—124no—
280C22×D3—244no—
281C22×D3C2×#6716yes—
282C3×Q8—26no—
283C3×Q8—26no—
284C3×Q8—24no—
285C3×Q8—34no—
286C3×Q8—34no—
287C3×Q8—46no—
288C3×Q8—616no—
289C3×Q8—66no—
290C3×Q8—66no—
291C3×Q8C23×D314yes—
292C3×Q8C23×D314yes—
293C2×C3×C4—26no—
294C2×C3×C4—26no—
295C2×C3×C4—23no—
296C2×C3×C4—23no—
297C2×C3×C4—36no—
298C2×C3×C4—312no—
299C2×C3×C4—34no—
300C2×C3×C4—46no—
301C2×C3×C4—616no—
302C2×C3×C4—66no—
303C2×C3×C4—66no—
304C2×C3×C4D3×D413yes—
305C2×C3×C4C2×#6713yes—
306C2×C3×C4C23×D313yes—
307C2×C3×C4C23×D313yes—
308#67—616no—
309C2×Dic3—26no—
310C2×Dic3—26no—
311C2×Dic3C2×#6716yes—
312D12—34no—
313D12—34no—
314D12—64no—
315D12—616no—
316D12—66no—
317D12—66no—
318D12—126no—
319C4×D3—216no—
320C4×D3—616no—
321C4×D3—616no—
322C4×D3C2×#67112yes—
323C4×D3C23×D314yes—
324Dic6—26no—
325Dic6—26no—
326Dic6—216no—
327Dic6C23×D314yes—
328Dic6C23×D314yes—
329C3×C8—34no—
330C3⋊C8—34no—
331C3⋊C8—34no—
332C3⋊C8—64no—
333C3⋊C8C23×D314yes—
334C2×C32C2×#13716yescomplemented
335C2×C32C23×D411yescharacteristic
336C3⋊D3—44no—
337C3×D3—24no—
338C24—31no—
339C24—181no—
340#41—916no—
341#41—1824no—
342C2×Q8—23no—
343C2×Q8—316no—
344C2×Q8—36no—
345C2×Q8—36no—
346C2×Q8—612no—
347C2×Q8—624no—
348C2×Q8—63no—
349C2×Q8—63no—
350C2×Q8C2×D3216yes—
351C2×D4—96no—
352C2×D4—1812no—
353C2×D4—183no—
354C22×C4—21no—
355C22×C4—31no—
356C22×C4—36no—
357C22×C4—36no—
358C22×C4—612no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—1812no—
362C22×C4C2×D3211yescharacteristic
363Q16—316no—
364Q16—916no—
365SD16—916no—
366SD16—916no—
367M16—916no—
368C2×C8—36no—
369C2×C8—96no—
370C22×C3—23no—
371C22×C3—24no—
372C22×C3—34no—
373C22×C3—612no—
374C22×C3#91814yescomplemented
375C22×C3#94214yescomplemented
376C22×C3C2×D3×D413yes—
377C22×C3C22×#6713yes—
378C2×D3—212no—
379C2×D3—64no—
380C2×D3—64no—
381C2×D3—124no—
382C2×D3—1212no—
383C2×D3—1212no—
384C2×D3—2412no—
385C2×D3C22×#6714yes—
386C3×C4—24no—
387C3×C4—24no—
388C3×C4—23no—
389C3×C4—21no—
390C3×C4—34no—
391C3×C4—44no—
392C3×C4—64no—
393C3×C4—64no—
394C3×C4C2×D3×D413yes—
395C3×C4C22×#6713yes—
396C3×C4C24×D311yescharacteristic
397C3×C4C24×D311yescharacteristic
398Dic3—24no—
399Dic3—24no—
400Dic3C22×#6714yes—
401C32C22×#13711yescharacteristic, complemented, Sylow
402C23—36no—
403C23—64no—
404C23—186no—
405C23—364no—
406C23D3×#6711yescharacteristic
407Q8—26no—
408Q8—34no—
409Q8—34no—
410Q8—616no—
411Q8—66no—
412Q8—66no—
413Q8C22×D3214yes—
414D4—94no—
415D4—1816no—
416D4—186no—
417C2×C4—26no—
418C2×C4—36no—
419C2×C4—312no—
420C2×C4—34no—
421C2×C4—616no—
422C2×C4—66no—
423C2×C4—66no—
424C2×C4—1816no—
425C2×C4D3×#6713yes—
426C2×C4C22×D3213yes—
427C8—34no—
428C8—94no—
429C2×C3—26no—
430C2×C3—21no—
431C2×C3—64no—
432C2×C3C2×#91816yescomplemented
433C2×C3C2×#94216yescomplemented
434C2×C3C22×D3×D411yescharacteristic
435C2×C3C23×#6711yescharacteristic
436D3—24no—
437D3—124no—
438D3—124no—
439D3—244no—
440C22—34no—
441C22—612no—
442C22—184no—
443C22—3612no—
444C22#6394814yesdirect product factor
445C22C2×D3×#6713yes—
446C4—24no—
447C4—34no—
448C4—64no—
449C4—64no—
450C4C2×D3×#6713yes—
451C4C23×D3211yescharacteristic
452C3—21no—
453C3C22×#91811yescharacteristic, complemented
454C3C22×#94211yescharacteristic, complemented
455C2—64no—
456C2—364no—
457C2C2×#6394816yesdirect product factor
458C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×#3799C2
hypercenterC22×Q8D32
hypocenterC32C22×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×Q8C2semidirect
3. C22×#3755C2semidirect
4. C22×C3×#216C2semidirect
5. C2×#63948C2direct (N × H)
6. C22×#3718C2semidirect
7. C22×#3717C2semidirect
8. C22×#3711C2semidirect
14. C2×C3×D3×Q8C22semidirect
24. C2×#3755C22semidirect
26. C2×C3×#216C22semidirect
28. #63948C22direct (N × H)
29. C2×#3718C22semidirect
30. C2×#3717C22semidirect
31. C2×#3711C22semidirect
34. C22×D3×Q8D3semidirect
39. C22×#216D3semidirect
61. C3×D3×Q8C23semidirect
74. #3755C23semidirect
76. C3×#216C23semidirect
78. #3718C23semidirect
79. #3717C23semidirect
80. #3711C23semidirect
96. C2×D3×Q8C2×D3semidirect
114. C2×#216C2×D3semidirect
200. D3×Q8C22×D3semidirect
224. #216C22×D3semidirect
236. C22×C32#137semidirect
334. C2×C32C2×#137semidirect
374. C22×C3#918semidirect
375. C22×C3#942semidirect
401. C32C22×#137semidirect
432. C2×C3C2×#918semidirect
433. C2×C3C2×#942semidirect
444. C22#63948direct (N × H)
453. C3C22×#918semidirect
454. C3C22×#942semidirect
457. C2C2×#63948direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C22×#37992
C22×#37552
C22×C3×#2162
C2×#639482
C22×#37182
C22×#37172
C22×#37112
C22×#9423
C22×#9183