Finite Group Databasebeta

← C2×#10592454 #11867961

Subgroups — C2×#10592454 #11867961

Order 1152.

1344 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3756C211yesmaximal, characteristic, complemented
2C2×#64151C211yesmaximal, characteristic
3C2×#64118C211yesmaximal, characteristic
4C2×#64116C211yesmaximal, characteristic
5C2×C32×#101C211yesmaximal, characteristic, complemented
6C2×#63651C211yesmaximal, characteristic, complemented
7C2×#63649C211yesmaximal, characteristic, complemented
8#10592454C218yesmaximal, direct product factor
9C2×#4755—34nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3756—21no—
16C2×#3756—21no—
17C2×#3756—21no—
18C2×#3756—22no—
19C2×#3756C2214yescomplemented
20#64151—22no—
21#64151C2214yes—
22C2×#3755—21no—
23C2×#3748C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#64118—22no—
26#64118C2214yes—
27#64116—22no—
28#64116C2214yes—
29C2×#3746—21no—
30C2×#3744—21no—
31C2×#3743—21no—
32C2×C8×C3⋊D3—21no—
33C32×#101C2214yescomplemented
34#63651C2214yescomplemented
35#63649C2214yescomplemented
36C22×#216—34no—
37C2×#942—34no—
38C2×#909—34no—
39C2×#907—34no—
40C2×C3×#101D314yescomplemented
41C2×#824—34no—
42C2×#822—34no—
43#4755—332no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8C2312yes—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×#638—21no—
53C22×C3⋊Dic3—21no—
54#3828—21no—
55#3828—21no—
56#3828D412yes—
57#3828C2312yes—
58C2×C4⋊(C3⋊D3)D411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634—21no—
61C2×#634—21no—
62C2×#634—21no—
63C2×#634—21no—
64C2×#634—21no—
65C2×#634D411yescharacteristic
66C2×#634C2312yes—
67C32×M16—21no—
68C32×M16—21no—
69C32×M16C2312yes—
70C32×M16C2312yes—
71C2×C32×C8—21no—
72C2×C32×C8—21no—
73#3756—24no—
74#3756—24no—
75#3756—24no—
76#3755—24no—
77#3748—21no—
78#3748C2312yes—
79C2×C3⋊(C3⋊C8)—21no—
80C2×C3⋊(C3⋊C8)D411yescharacteristic
81C2×C3⋊(C3⋊C8)D411yescharacteristic
82C2×C3⋊(C3⋊C8)D412yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84#3746—24no—
85#3744—24no—
86#3743—24no—
87C8×C3⋊D3—24no—
88C2×#473—91noSylow
89C22×C3×Q8C2×D314yes—
90C2×#235—34no—
91C22×Dic6—34no—
92C2×C3×M16C2×D314yes—
93C2×C3×M16C2×D314yes—
94C2×#216—316no—
95C2×#216—64no—
96C2×#216—64no—
97C2×#216—68no—
98C2×#216—64no—
99#942—316no—
100#942—68no—
101C2×#215—64no—
102C2×#208—34no—
103C22×C3⋊C8—34no—
104#909—316no—
105#909—68no—
106#907—316no—
107#907—68no—
108C2×Dic12—64no—
109C2×#204—64no—
110C2×ΓL(1,𝔽25)—64no—
111C2×D3×C8—64no—
112C3×#101C2×D3116yescomplemented
113#824—316no—
114#822—316no—
115C23×C32#4111yescharacteristic
116C22×C3⋊D3—21no—
117C32×Q8—22no—
118C32×Q8—22no—
119C32×Q8—41no—
120C32×Q8—41no—
121C2×C32×C4—22no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4C2411yescharacteristic
130#638—22no—
131#638—22no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C4⋊(C3⋊D3)—21no—
137C4⋊(C3⋊D3)C2×D412yes—
138C4×C3⋊D3—22no—
139C4×C3⋊D3—22no—
140#634—21no—
141#634—22no—
142#634—22no—
143#634—41no—
144#634—41no—
145#634C2×D412yes—
146C32×C8—22no—
147C32×C8—22no—
148C3⋊(C3⋊C8)—22no—
149C3⋊(C3⋊C8)C2×D412yes—
150C3⋊(C3⋊C8)C2×D412yes—
151C2×#137—91no—
152C2×#137—91no—
153C22×Q16—91no—
154C2×#131—91no—
155#473—98no—
156C2×#108—91no—
157C2×#101—91no—
158C2×#101C3⋊D311yescharacteristic, complemented
159C2×C3×Q8—24no—
160C2×C3×Q8—24no—
161C2×C3×Q8—24no—
162C2×C3×Q8—24no—
163C2×C3×Q8—24no—
164C2×C3×Q8C22×D318yes—
165C22×C3×C4—24no—
166C22×C3×C4C22×D314yes—
167C2×#67—64no—
168C22×Dic3—64no—
169#235—38no—
170#235—38no—
171#235—64no—
172#235—64no—
173C2×D12—34no—
174C2×C4×D3—64no—
175C2×Dic6—34no—
176C2×Dic6—38no—
177C2×Dic6—64no—
178C2×Dic6—64no—
179C2×Dic6—64no—
180C2×Dic6—64no—
181C2×Dic6—64no—
182C3×M16—24no—
183C3×M16—24no—
184C3×M16C22×D318yes—
185C3×M16C22×D318yes—
186C2×C3×C8—24no—
187C2×C3×C8—24no—
188#216—616no—
189#216—616no—
190#216—616no—
191#215—616no—
192#208—38no—
193#208—64no—
194C2×C3⋊C8—34no—
195C2×C3⋊C8—34no—
196C2×C3⋊C8—38no—
197C2×C3⋊C8—38no—
198C2×C3⋊C8—64no—
199Dic12—616no—
200#204—616no—
201ΓL(1,𝔽25)—616no—
202D3×C8—616no—
203C22×C32—22no—
204C22×C32#12111yescharacteristic
205C22×C32#12111yescharacteristic
206C22×C32C2×#4111yescharacteristic
207C2×C3⋊D3—22no—
208C2×C3⋊D3—42no—
209C32×C4—42no—
210C32×C4#12111yescharacteristic
211C32×C4#12111yescharacteristic
212C32×C4C22×D411yescharacteristic
213C32×C4C22×D411yescharacteristic
214C3⋊Dic3—22no—
215C3⋊Dic3—42no—
216C2×#41—91no—
217C22×Q8—91no—
218C22×Q8C2×C3⋊D311yescharacteristic
219#137—94no—
220#137—94no—
221#137—182no—
222#137—182no—
223C2×Q16—94no—
224C2×Q16—181no—
225C2×Q16—181no—
226C2×Q16—181no—
227C2×Q16—182no—
228C2×Q16—181no—
229C2×SD16—181no—
230C2×SD16—181no—
231#131—94no—
232#131—182no—
233C2×M16—91no—
234C2×M16—181no—
235C2×M16C2×C3⋊D311yescharacteristic
236C2×M16C2×C3⋊D311yescharacteristic
237C22×C8—91no—
238C22×C8—181no—
239#108—94no—
240#101—94no—
241#101C2×C3⋊D314yescomplemented
242C23×C3#23514yes—
243C22×D3—64no—
244C3×Q8—28no—
245C3×Q8—28no—
246C3×Q8—44no—
247C3×Q8—44no—
248C2×C3×C4—28no—
249C2×C3×C4—44no—
250C2×C3×C4—44no—
251C2×C3×C4#23514yes—
252C2×C3×C4D3×D414yes—
253C2×C3×C4D3×D414yes—
254C2×C3×C4D3×D414yes—
255C2×C3×C4D3×D414yes—
256C2×C3×C4C23×D314yes—
257#67—68no—
258#67—68no—
259C2×Dic3—64no—
260C2×Dic3—68no—
261C2×Dic3—124no—
262C2×Dic3—124no—
263D12—38no—
264D12—64no—
265C4×D3—68no—
266C4×D3—68no—
267Dic6—38no—
268Dic6—64no—
269Dic6—68no—
270Dic6—68no—
271Dic6—124no—
272Dic6—124no—
273C3×C8—28no—
274C3×C8—28no—
275C3⋊C8—38no—
276C3⋊C8—38no—
277C3⋊C8—68no—
278C2×C32—21no—
279C2×C32—21no—
280C2×C32#47312yescomplemented
281C2×C32C2×#12111yescharacteristic
282C3⋊D3—42no—
283#41—92no—
284#41—92no—
285#41—181no—
286#41—181no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—92no—
293C2×Q8—91no—
294C2×Q8—181no—
295C2×Q8—181no—
296C2×Q8—181no—
297C2×Q8—181no—
298C2×Q8—181no—
299C2×Q8C22×C3⋊D312yes—
300C2×D4—91no—
301C2×D4—181no—
302C22×C4—21no—
303C22×C4—181no—
304C22×C4—181no—
305C22×C4C22×C3⋊D311yescharacteristic
306Q16—184no—
307Q16—184no—
308Q16—184no—
309Q16—184no—
310SD16—184no—
311SD16—184no—
312M16—21no—
313M16—21no—
314M16—92no—
315M16—184no—
316M16—181no—
317M16C22×C3⋊D312yes—
318M16C22×C3⋊D312yes—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—92no—
322C2×C8—91no—
323C2×C8—91no—
324C2×C8—92no—
325C2×C8—184no—
326C2×C8—181no—
327C22×C3—28no—
328C22×C3#88414yes—
329C22×C3#88414yes—
330C22×C3C2×#23514yes—
331C2×D3—68no—
332C2×D3—128no—
333C3×C4—48no—
334C3×C4#88414yes—
335C3×C4#88414yes—
336C3×C4C2×D3×D414yes—
337C3×C4C2×D3×D414yes—
338Dic3—68no—
339Dic3—128no—
340C32C2×#47311yescharacteristic, complemented, Sylow
341C23—181no—
342C23#382811yescharacteristic
343Q8—22no—
344Q8—22no—
345Q8—41no—
346Q8—41no—
347Q8—92no—
348Q8—181no—
349Q8—182no—
350Q8—182no—
351Q8—361no—
352Q8—361no—
353D4—92no—
354D4—182no—
355D4—182no—
356D4—181no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—181no—
361C2×C4—182no—
362C2×C4—182no—
363C2×C4—182no—
364C2×C4—361no—
365C2×C4—361no—
366C2×C4#382811yescharacteristic
367C2×C4D4×C3⋊D311yescharacteristic
368C2×C4D4×C3⋊D311yescharacteristic
369C2×C4D4×C3⋊D311yescharacteristic
370C2×C4D4×C3⋊D311yescharacteristic
371C2×C4C23×C3⋊D311yescharacteristic
372C8—22no—
373C8—22no—
374C8—92no—
375C8—92no—
376C8—182no—
377C2×C3—24no—
378C2×C3—24no—
379C2×C3#475518yescomplemented
380C2×C3C2×#88414yes—
381D3—128no—
382C22—22no—
383C22—182no—
384C22—362no—
385C22#6409311yescharacteristic
386C22#6409311yescharacteristic
387C22C2×#382811yescharacteristic
388C4—42no—
389C4—182no—
390C4—362no—
391C4#6409311yescharacteristic
392C4#6409311yescharacteristic
393C4C2×D4×C3⋊D311yescharacteristic
394C4C2×D4×C3⋊D311yescharacteristic
395C3C2×#475514yescomplemented
396C2—21no—
397C2—21no—
398C2—362no—
399C2#1059245412yesdirect product factor
400C2C2×#6409311yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#101C2
socleC22×C32#121
prime radicalC2×#3828C22
hypercenterC2×#101C3⋊D3
hypocenterC32C2×#473
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C22×#3756C2semidirect
5. C2×C32×#101C2semidirect
6. C2×#63651C2semidirect
7. C2×#63649C2semidirect
8. #10592454C2direct (N × H)
19. C2×#3756C22semidirect
33. C32×#101C22semidirect
34. #63651C22semidirect
35. #63649C22semidirect
40. C2×C3×#101D3semidirect
112. C3×#101C2×D3semidirect
158. C2×#101C3⋊D3semidirect
241. #101C2×C3⋊D3semidirect
280. C2×C32#473semidirect
340. C32C2×#473semidirect
379. C2×C3#4755semidirect
395. C3C2×#4755semidirect
399. C2#10592454direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37562
C2×#641512
C2×#641182
C2×#641162
C2×C32×#1012
C2×#636512
C2×#636492
#105924542
C2×#47553