Finite Group Databasebeta

← C2×#10596029 #11903113

Subgroups — C2×#10596029 #11903113

Order 1152.

3756 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×#64147C211yesmaximal, characteristic, complemented
3C2×#64147C211yesmaximal, characteristic, complemented
4C2×#64138C212yesmaximal, complemented
5C2×C4×#638C212yesmaximal, complemented
6#10596029C2116yesmaximal, direct product factor
7C2×#64101C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
9C2×#64093C212yesmaximal, complemented
10C2×#64088C212yesmaximal, complemented
11C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
12C2×#64079C211yesmaximal, characteristic, complemented
13C2×#5558—34nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2212yes—
16C22×#638C2212yes—
17C22×#638C2212yes—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2212yes—
22C32×C4×D4C2218yescomplemented
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2212yes—
25C2×C32×C42C2211yescharacteristic
26C2×#3757C2212yes—
27C2×#3757C2212yes—
28#64147C2218yescomplemented
29#64147C2218yescomplemented
30#64138C22116yescomplemented
31C4×#638C22116yescomplemented
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2212yes—
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
37C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
38C2×#3750C2212yes—
39C2×#3750C2212yes—
40C2×#3750C2212yes—
41C2×C4×C3⋊Dic3C2212yes—
42#64101C2218yescomplemented
43C4⋊C4×C3⋊D3C2218yescomplemented
44#64093C22116yescomplemented
45#64088C22116yescomplemented
46C4×C4⋊(C3⋊D3)C2218yescomplemented
47#64079C2218yescomplemented
48C2×C3×C4×D4D314yescomplemented
49C2×#938—34no—
50C2×#938—34no—
51C2×#929—38no—
52C2×C4×#67—38no—
53#5558—364no—
54C2×#892—34no—
55C2×D3×C4⋊C4—34no—
56C2×#884—38no—
57C2×#879—38no—
58C2×C4×D12—34no—
59C2×#870—34no—
60C24×C32C2312yes—
61C23×C3⋊D3C2311yescharacteristic
62C23×C3⋊D3C2311yescharacteristic
63C2×C32×D4—24no—
64C2×C32×D4C2314yes—
65C22×C32×C4—44no—
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2318yes—
70C22×C32×C4C2311yescharacteristic
71C2×#638—28no—
72C2×#638—44no—
73C2×#638C2318yes—
74C2×#638C2318yes—
75C22×C3⋊Dic3C2312yes—
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C2×C4⋊(C3⋊D3)—24no—
80C2×C4⋊(C3⋊D3)C2314yes—
81C2×C4×C3⋊D3—24no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—44no—
84C2×C4×C3⋊D3C2314yes—
85C2×C4×C3⋊D3C2314yes—
86C2×C4×C3⋊D3C2318yes—
87C32×C4⋊C4C2314yes—
88C32×C22⋊C4C2318yes—
89C32×C42C2314yes—
90#3757C2318yes—
91#3757C2318yes—
92#3752C2314yes—
93#3752C2314yes—
94#3752C2318yes—
95C4⋊(C3⋊Dic3)C2314yes—
96C4⋊(C3⋊Dic3)C2314yes—
97C4⋊(C3⋊Dic3)C2314yes—
98#3750C2318yes—
99#3750C2318yes—
100#3750C2318yes—
101C4×C3⋊Dic3C2318yes—
102C2×#553—91noSylow
103C22×C3×D4C2×D314yes—
104C23×C3×C4C2×D318yes—
105C22×#67—38no—
106C22×#67—38no—
107C22×D12—34no—
108C22×C4×D3—34no—
109C22×C4×D3—34no—
110C22×C4×D3—38no—
111C3×C4×D4C2×D3132yescomplemented
112C2×C3×C4⋊C4C2×D314yes—
113C2×C3×C22⋊C4C2×D318yes—
114C2×C3×C42C2×D314yes—
115C2×#217—38no—
116C2×#217—38no—
117#938—332no—
118#938—332no—
119#929—364no—
120C4×#67—364no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4—34no—
123C2×(C2×D3)⋊C4—38no—
124C2×C4⋊Dic3—34no—
125C2×C4⋊Dic3—34no—
126C2×C4⋊Dic3—34no—
127C2×Dic3⋊C4—38no—
128C2×Dic3⋊C4—38no—
129C2×Dic3⋊C4—38no—
130C2×C4×Dic3—38no—
131#892—332no—
132D3×C4⋊C4—332no—
133#884—364no—
134#879—364no—
135C4×D12—332no—
136#870—332no—
137C23×C32—24no—
138C23×C32—24no—
139C23×C32—24no—
140C23×C32C2414yes—
141C23×C32C2411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3#4114yes—
148C22×C3⋊D3C2412yes—
149C22×C3⋊D3C2412yes—
150C32×D4—28no—
151C2×C32×C4—22no—
152C2×C32×C4—24no—
153C2×C32×C4—22no—
154C2×C32×C4—48no—
155C2×C32×C4#4114yes—
156C2×C32×C4C2414yes—
157C2×C32×C4C2412yes—
158C2×C32×C4C2412yes—
159C2×C32×C4C2412yes—
160#638—216no—
161#638—48no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—24no—
165C2×C3⋊Dic3—24no—
166C2×C3⋊Dic3C2412yes—
167C2×C3⋊Dic3C2414yes—
168C2×C3⋊Dic3C2414yes—
169C2×C3⋊Dic3C2412yes—
170C4⋊(C3⋊D3)—28no—
171C4×C3⋊D3—28no—
172C4×C3⋊D3—28no—
173C4×C3⋊D3—48no—
174#553—916no—
175C2×#126—92no—
176C2×#125—91no—
177C2×#123—92no—
178C2×#121—91no—
179C2×#121—91no—
180C2×#121—92no—
181C2×C4×D4—92no—
182C2×C4×D4—91no—
183C2×C4×D4C3⋊D311yescharacteristic, complemented
184C2×#117—91no—
185C22×C4⋊C4—91no—
186C24×C3C22×D318yes—
187C23×D3—34no—
188C23×D3—34no—
189C2×C3×D4—216no—
190C2×C3×D4C22×D3116yes—
191C22×C3×C4—416no—
192C22×C3×C4C22×D318yes—
193C22×C3×C4C22×D314yes—
194C22×C3×C4C22×D314yes—
195C22×C3×C4C22×D3132yes—
196C22×C3×C4C22×D314yes—
197C2×#67—332no—
198C2×#67—332no—
199C2×#67—632no—
200C2×#67—1216no—
201C22×Dic3—34no—
202C22×Dic3—38no—
203C22×Dic3—38no—
204C22×Dic3—34no—
205C2×D12—316no—
206C2×D12—616no—
207C2×C4×D3—316no—
208C2×C4×D3—316no—
209C2×C4×D3—332no—
210C2×C4×D3—616no—
211C2×C4×D3—616no—
212C2×C4×D3—1216no—
213C3×C4⋊C4C22×D3116yes—
214C3×C22⋊C4C22×D3132yes—
215C3×C42C22×D3116yes—
216#217—332no—
217#217—332no—
218(C2×D3)⋊C4—316no—
219(C2×D3)⋊C4—316no—
220(C2×D3)⋊C4—332no—
221C4⋊Dic3—316no—
222C4⋊Dic3—316no—
223C4⋊Dic3—316no—
224Dic3⋊C4—332no—
225Dic3⋊C4—332no—
226Dic3⋊C4—332no—
227C4×Dic3—332no—
228C22×C32—24no—
229C22×C32—24no—
230C22×C32—24no—
231C22×C32—48no—
232C22×C32C2×#4112yes—
233C22×C32C2×#4112yes—
234C22×C32H(5,𝔽2)12yes—
235C22×C32C2511yescharacteristic
236C2×C3⋊D3—28no—
237C2×C3⋊D3—22no—
238C2×C3⋊D3—22no—
239C2×C3⋊D3—22no—
240C2×C3⋊D3—22no—
241C2×C3⋊D3—22no—
242C2×C3⋊D3—44no—
243C2×C3⋊D3C2×#4114yes—
244C32×C4—22no—
245C32×C4—24no—
246C32×C4—22no—
247C32×C4C2×#4114yes—
248C3⋊Dic3—22no—
249C3⋊Dic3—22no—
250C3⋊Dic3—24no—
251C3⋊Dic3—24no—
252C22×D4—92no—
253C22×D4—92no—
254C22×D4—91no—
255C22×D4C2×C3⋊D311yescharacteristic
256C23×C4—91no—
257C23×C4—91no—
258C23×C4—92no—
259C23×C4C2×C3⋊D312yes—
260#126—916no—
261#125—98no—
262#123—916no—
263#121—98no—
264#121—98no—
265#121—916no—
266C4×D4—916no—
267C4×D4—98no—
268C4×D4C2×C3⋊D318yescomplemented
269#117—98no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—92no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—92no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—92no—
276C2×C4⋊C4—98no—
277C2×C4⋊C4C2×C3⋊D311yescharacteristic
278C2×C22⋊C4—92no—
279C2×C22⋊C4—92no—
280C2×C22⋊C4—92no—
281C2×C22⋊C4—91no—
282C2×C22⋊C4—91no—
283C2×C22⋊C4C2×C3⋊D312yes—
284C2×C42—92no—
285C2×C42C2×C3⋊D311yescharacteristic
286C23×C3—216no—
287C23×C3—216no—
288C23×C3—216no—
289C23×C3C23×D3116yes—
290C23×C3C23×D314yes—
291C22×D3—316no—
292C22×D3—38no—
293C22×D3—38no—
294C22×D3—68no—
295C22×D3—68no—
296C22×D3—68no—
297C22×D3—68no—
298C22×D3—68no—
299C3×D4—232no—
300C2×C3×C4—216no—
301C2×C3×C4—28no—
302C2×C3×C4—28no—
303C2×C3×C4—432no—
304C2×C3×C4#235116yes—
305C2×C3×C4C23×D3116yes—
306C2×C3×C4C23×D318yes—
307C2×C3×C4C23×D318yes—
308C2×C3×C4C23×D318yes—
309#67—664no—
310#67—1232no—
311C2×Dic3—38no—
312C2×Dic3—316no—
313C2×Dic3—316no—
314C2×Dic3—38no—
315C2×Dic3—68no—
316C2×Dic3—68no—
317C2×Dic3—616no—
318C2×Dic3—616no—
319D12—632no—
320C4×D3—632no—
321C4×D3—632no—
322C4×D3—1232no—
323C2×C32—44no—
324C2×C32#55314yescomplemented
325C2×C32C22×#4111yescharacteristic
326C2×C32C22×#4111yescharacteristic
327C2×C32C2×H(5,𝔽2)11yescharacteristic
328C3⋊D3—24no—
329C3⋊D3—42no—
330C24—91no—
331C24—91no—
332C24C22×C3⋊D312yes—
333C2×D4—24no—
334C2×D4—98no—
335C2×D4—98no—
336C2×D4—94no—
337C2×D4—184no—
338C2×D4—188no—
339C2×D4—364no—
340C2×D4C22×C3⋊D314yes—
341C22×C4—44no—
342C22×C4—91no—
343C22×C4—92no—
344C22×C4—91no—
345C22×C4—92no—
346C22×C4—94no—
347C22×C4—94no—
348C22×C4—98no—
349C22×C4—184no—
350C22×C4—184no—
351C22×C4—364no—
352C22×C4C22×C3⋊D312yes—
353C22×C4C22×C3⋊D311yescharacteristic
354C22×C4C22×C3⋊D311yescharacteristic
355C22×C4C22×C3⋊D318yes—
356C22×C4C22×C3⋊D311yescharacteristic
357C4⋊C4—94no—
358C4⋊C4—98no—
359C4⋊C4—94no—
360C4⋊C4—98no—
361C4⋊C4—94no—
362C4⋊C4—98no—
363C4⋊C4C22×C3⋊D314yes—
364C22⋊C4—98no—
365C22⋊C4—98no—
366C22⋊C4—98no—
367C22⋊C4—94no—
368C22⋊C4—94no—
369C22⋊C4C22×C3⋊D318yes—
370C42—98no—
371C42C22×C3⋊D314yes—
372C22×C3—216no—
373C22×C3—216no—
374C22×C3—216no—
375C22×C3—432no—
376C22×C3C2×#23518yes—
377C22×C3#100418yes—
378C22×C3D3×#4118yes—
379C22×C3C24×D314yes—
380C2×D3—316no—
381C2×D3—68no—
382C2×D3—68no—
383C2×D3—632no—
384C2×D3—68no—
385C2×D3—68no—
386C2×D3—68no—
387C2×D3—1216no—
388C3×C4—216no—
389C3×C4—28no—
390C3×C4—28no—
391C3×C4C2×#235116yes—
392Dic3—68no—
393Dic3—68no—
394Dic3—616no—
395Dic3—616no—
396C32C2×#55311yescharacteristic, complemented, Sylow
397C23—24no—
398C23—24no—
399C23—24no—
400C23—94no—
401C23—92no—
402C23—92no—
403C23—182no—
404C23—182no—
405C23—182no—
406C23—182no—
407C23—182no—
408C23C23×C3⋊D314yes—
409C23C23×C3⋊D311yescharacteristic
410D4—28no—
411D4—188no—
412D4—1816no—
413D4—368no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—48no—
418C2×C4—92no—
419C2×C4—94no—
420C2×C4—92no—
421C2×C4—94no—
422C2×C4—182no—
423C2×C4—182no—
424C2×C4—184no—
425C2×C4—184no—
426C2×C4—188no—
427C2×C4—188no—
428C2×C4—368no—
429C2×C4#382814yes—
430C2×C4C23×C3⋊D314yes—
431C2×C4C23×C3⋊D312yes—
432C2×C4C23×C3⋊D312yes—
433C2×C4C23×C3⋊D312yes—
434C2×C3—416no—
435C2×C3#5558116yescomplemented
436C2×C3C22×#23514yes—
437C2×C3C2×#100414yes—
438C2×C3C2×D3×#4114yes—
439D3—616no—
440D3—128no—
441C22—24no—
442C22—24no—
443C22—24no—
444C22—48no—
445C22—94no—
446C22—182no—
447C22—182no—
448C22—188no—
449C22—182no—
450C22—182no—
451C22—182no—
452C22—364no—
453C22C2×#382812yes—
454C22#6436112yes—
455C22#41×C3⋊D312yes—
456C22C24×C3⋊D311yescharacteristic
457C4—22no—
458C4—24no—
459C4—22no—
460C4—182no—
461C4—182no—
462C4—184no—
463C4—184no—
464C4C2×#382814yes—
465C3C2×#555814yescomplemented
466C2—44no—
467C2—184no—
468C2—362no—
469C2#1059602914yesdirect product factor
470C2C22×#382811yescharacteristic
471C2C2×#6436111yescharacteristic
472C2C2×#41×C3⋊D311yescharacteristic
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
hypercenterC2×C4×D4C3⋊D3
hypocenterC32C2×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. C2×#64147C2semidirect
3. C2×#64147C2semidirect
4. C2×#64138C2semidirect
5. C2×C4×#638C2semidirect
6. #10596029C2direct (N × H)
7. C2×#64101C2semidirect
8. C2×C4⋊C4×C3⋊D3C2semidirect
9. C2×#64093C2semidirect
10. C2×#64088C2semidirect
11. C2×C4×C4⋊(C3⋊D3)C2semidirect
12. C2×#64079C2semidirect
22. C32×C4×D4C22semidirect
28. #64147C22semidirect
29. #64147C22semidirect
30. #64138C22semidirect
31. C4×#638C22semidirect
42. #64101C22semidirect
43. C4⋊C4×C3⋊D3C22semidirect
44. #64093C22semidirect
45. #64088C22semidirect
46. C4×C4⋊(C3⋊D3)C22semidirect
47. #64079C22semidirect
48. C2×C3×C4×D4D3semidirect
111. C3×C4×D4C2×D3semidirect
183. C2×C4×D4C3⋊D3semidirect
268. C4×D4C2×C3⋊D3semidirect
324. C2×C32#553semidirect
396. C32C2×#553semidirect
435. C2×C3#5558semidirect
465. C3C2×#5558semidirect
469. C2#10596029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×#641472
C2×#641382
C2×C4×#6382
#105960292
C2×#641012
C2×C4⋊C4×C3⋊D32
C2×#640932
C2×#640882
C2×C4×C4⋊(C3⋊D3)2
C2×#640792
C2×#55583