Finite Group Databasebeta

← C2×#10592903 #11867958

Subgroups — C2×#10592903 #11867958

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
1C2×C32×#137C211yesmaximal, characteristic
2C2×#64160C211yesmaximal, characteristic
3C2×#64157C211yesmaximal, characteristic
4C22×#3756C211yesmaximal, characteristic, complemented
5C2×#63663C211yesmaximal, characteristic, complemented
6#10592903C218yesmaximal, direct product factor
7C2×#63651C211yesmaximal, characteristic, complemented
8C2×#63649C211yesmaximal, characteristic, complemented
9C2×#5204—34nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C32×#137—22no—
14C32×#137C2214yes—
15C2×C32×Q16—21no—
16C2×C32×SD16—21no—
17C2×C32×M16C2211yescharacteristic
18#64160—22no—
19#64160C2214yes—
20#64157—22no—
21#64157C2214yes—
22C2×#3756—21no—
23C2×#3756—21no—
24C2×#3756—21no—
25C2×#3756—22no—
26C2×#3756C2214yescomplemented
27C2×#3754—21no—
28C2×#3748—21no—
29C2×#3748C2211yescharacteristic
30C2×#3748C2211yescharacteristic
31C22×C3⋊(C3⋊C8)—21no—
32C22×C3⋊(C3⋊C8)C2211yescharacteristic
33#63663C2214yescomplemented
34#63651C2214yescomplemented
35#63649C2214yescomplemented
36C2×C3×#137D314yes—
37C2×#951—34no—
38C2×#948—34no—
39C22×#216—34no—
40C2×#836—34no—
41#5204—332no—
42C2×#824—34no—
43C2×#822—34no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41D412yes—
47C32×#41C2312yes—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8D411yescharacteristic
54C2×C32×Q8C2312yes—
55C2×C32×D4—21no—
56C2×C32×D4D411yescharacteristic
57C22×C32×C4—21no—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C2×#634—21no—
62C2×#634—21no—
63C2×#634—21no—
64C2×#634—21no—
65C2×#634—21no—
66C2×#634C2312yes—
67C32×Q16—24no—
68C32×SD16—24no—
69C32×M16—21no—
70C32×M16C2312yes—
71C2×C32×C8—21no—
72#3756—24no—
73#3756—24no—
74#3756—24no—
75#3754—24no—
76#3748—21no—
77#3748—21no—
78#3748—24no—
79#3748C2312yes—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C2×C3⋊(C3⋊C8)—21no—
83C2×C3⋊(C3⋊C8)—24no—
84C2×C3⋊(C3⋊C8)D411yescharacteristic
85C2×C3⋊(C3⋊C8)D411yescharacteristic
86C2×C3⋊(C3⋊C8)D412yes—
87C2×C3⋊(C3⋊C8)C2312yes—
88C2×#473—91noSylow
89C2×C3×#41C2×D314yes—
90C22×C3×Q8C2×D314yes—
91C22×Dic6—34no—
92C3×#137—28no—
93C3×#137C2×D3116yes—
94C2×C3×Q16—24no—
95C2×C3×SD16—24no—
96C2×C3×M16C2×D314yes—
97#951—316no—
98#951—68no—
99#948—316no—
100#948—68no—
101C2×#216—316no—
102C2×#216—64no—
103C2×#216—64no—
104C2×#216—68no—
105C2×#216—64no—
106C2×#214—64no—
107C2×#208—34no—
108C2×#208—34no—
109C2×#208—64no—
110C22×C3⋊C8—34no—
111C22×C3⋊C8—64no—
112#836—316no—
113#824—316no—
114#822—316no—
115C23×C32—21no—
116C23×C32#4111yescharacteristic
117C32×Q8—21no—
118C32×Q8—22no—
119C32×Q8—22no—
120C32×Q8—41no—
121C32×Q8—41no—
122C32×Q8C2×D412yes—
123C32×D4—22no—
124C32×D4—22no—
125C32×D4—21no—
126C32×D4C2×D412yes—
127C2×C32×C4—21no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142#634—22no—
143#634—22no—
144#634—41no—
145#634—41no—
146C32×C8—22no—
147C3⋊(C3⋊C8)—22no—
148C3⋊(C3⋊C8)—22no—
149C3⋊(C3⋊C8)C2×D412yes—
150C3⋊(C3⋊C8)C2×D412yes—
151C2×#137—91no—
152C2×#137C3⋊D311yescharacteristic
153C22×Q16—91no—
154C2×#131—91no—
155#473—98no—
156C2×#108—91no—
157C2×#101—91no—
158C2×#101—91no—
159C3×#41—24no—
160C3×#41—24no—
161C3×#41#6718yes—
162C3×#41C22×D318yes—
163C2×C3×Q8—24no—
164C2×C3×Q8—24no—
165C2×C3×Q8—24no—
166C2×C3×Q8—24no—
167C2×C3×Q8—24no—
168C2×C3×Q8#6714yes—
169C2×C3×Q8C22×D318yes—
170C2×C3×D4—24no—
171C2×C3×D4#6714yes—
172C22×C3×C4—24no—
173C22×C3×C4—24no—
174C22×C3×C4C22×D314yes—
175C22×Dic3—64no—
176C2×Dic6—38no—
177C2×Dic6—64no—
178C2×Dic6—64no—
179C2×Dic6—64no—
180C2×Dic6—64no—
181C2×Dic6—64no—
182C3×Q16—216no—
183C3×SD16—216no—
184C3×M16—24no—
185C3×M16C22×D318yes—
186C2×C3×C8—24no—
187#216—616no—
188#216—616no—
189#216—616no—
190#214—616no—
191#208—38no—
192#208—38no—
193#208—616no—
194#208—64no—
195#208—64no—
196C2×C3⋊C8—34no—
197C2×C3⋊C8—34no—
198C2×C3⋊C8—38no—
199C2×C3⋊C8—38no—
200C2×C3⋊C8—616no—
201C2×C3⋊C8—64no—
202C2×C3⋊C8—64no—
203C22×C32—22no—
204C22×C32—22no—
205C22×C32—42no—
206C22×C32#12111yescharacteristic
207C22×C32#12111yescharacteristic
208C22×C32C2×#4111yescharacteristic
209C32×C4—22no—
210C32×C4—42no—
211C32×C4#12111yescharacteristic
212C32×C4#12111yescharacteristic
213C32×C4C22×D411yescharacteristic
214C32×C4C22×D411yescharacteristic
215C3⋊Dic3—42no—
216C2×#41C2×C3⋊D311yescharacteristic
217C22×Q8—91no—
218C22×Q8C2×C3⋊D311yescharacteristic
219#137—22no—
220#137—94no—
221#137—182no—
222#137C2×C3⋊D314yes—
223C2×Q16—21no—
224C2×Q16—94no—
225C2×Q16—181no—
226C2×Q16—181no—
227C2×Q16—182no—
228C2×Q16—181no—
229C2×SD16—21no—
230C2×SD16—181no—
231#131—94no—
232#131—182no—
233C2×M16—91no—
234C2×M16—91no—
235C2×M16—181no—
236C2×M16C2×C3⋊D311yescharacteristic
237C22×C8—91no—
238C22×C8—181no—
239#108—94no—
240#101—94no—
241#101—94no—
242C23×C3—24no—
243C23×C3#23714yes—
244C3×Q8—24no—
245C3×Q8—28no—
246C3×Q8—28no—
247C3×Q8—44no—
248C3×Q8—44no—
249C3×Q8C2×#6718yes—
250C3×D4—28no—
251C3×D4—28no—
252C3×D4—24no—
253C3×D4C2×#6718yes—
254C2×C3×C4—24no—
255C2×C3×C4—28no—
256C2×C3×C4—28no—
257C2×C3×C4—28no—
258C2×C3×C4—44no—
259C2×C3×C4—44no—
260C2×C3×C4D3×D414yes—
261C2×C3×C4D3×D414yes—
262C2×C3×C4#23714yes—
263C2×C3×C4C2×#6714yes—
264C2×C3×C4C2×#6714yes—
265C2×C3×C4C23×D314yes—
266C2×Dic3—68no—
267C2×Dic3—124no—
268C2×Dic3—124no—
269Dic6—68no—
270Dic6—68no—
271Dic6—124no—
272Dic6—124no—
273C3×C8—28no—
274C3⋊C8—38no—
275C3⋊C8—38no—
276C3⋊C8—68no—
277C3⋊C8—68no—
278C2×C32—21no—
279C2×C32—21no—
280C2×C32—42no—
281C2×C32#47312yescomplemented
282C2×C32C2×#12111yescharacteristic
283#41—21no—
284#41—21no—
285#41#63812yes—
286#41C22×C3⋊D312yes—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—92no—
293C2×Q8—181no—
294C2×Q8—181no—
295C2×Q8—181no—
296C2×Q8—181no—
297C2×Q8—181no—
298C2×Q8#63811yescharacteristic
299C2×Q8C22×C3⋊D312yes—
300C2×D4—21no—
301C2×D4#63811yescharacteristic
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—181no—
305C22×C4C22×C3⋊D311yescharacteristic
306Q16—24no—
307Q16—184no—
308Q16—184no—
309Q16—184no—
310SD16—24no—
311SD16—184no—
312M16—21no—
313M16—92no—
314M16—92no—
315M16—184no—
316M16—181no—
317M16—181no—
318M16C22×C3⋊D312yes—
319C2×C8—21no—
320C2×C8—92no—
321C2×C8—91no—
322C2×C8—91no—
323C2×C8—92no—
324C2×C8—184no—
325C2×C8—181no—
326C2×C8—181no—
327C22×C3—28no—
328C22×C3—28no—
329C22×C3—48no—
330C22×C3#93914yes—
331C22×C3#93914yes—
332C22×C3C2×#23714yes—
333C3×C4—28no—
334C3×C4—48no—
335C3×C4#93914yes—
336C3×C4#93914yes—
337C3×C4C2×D3×D414yes—
338C3×C4C22×#6714yes—
339Dic3—128no—
340C32C2×#47311yescharacteristic, complemented, Sylow
341C23—21no—
342C23#383011yescharacteristic
343Q8—21no—
344Q8—22no—
345Q8—22no—
346Q8—41no—
347Q8—41no—
348Q8—182no—
349Q8—182no—
350Q8—361no—
351Q8—361no—
352Q8C2×#63812yes—
353D4—22no—
354D4—22no—
355D4—21no—
356D4C2×#63812yes—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—182no—
364C2×C4—361no—
365C2×C4—361no—
366C2×C4D4×C3⋊D311yescharacteristic
367C2×C4D4×C3⋊D311yescharacteristic
368C2×C4#383011yescharacteristic
369C2×C4C2×#63811yescharacteristic
370C2×C4C2×#63811yescharacteristic
371C2×C4C23×C3⋊D311yescharacteristic
372C8—22no—
373C8—92no—
374C8—92no—
375C8—182no—
376C8—182no—
377C2×C3—24no—
378C2×C3—24no—
379C2×C3—48no—
380C2×C3#520418yescomplemented
381C2×C3C2×#93914yes—
382C22—22no—
383C22—22no—
384C22—42no—
385C22#6414811yescharacteristic
386C22#6414811yescharacteristic
387C22C2×#383011yescharacteristic
388C4—22no—
389C4—42no—
390C4—362no—
391C4#6414811yescharacteristic
392C4#6414811yescharacteristic
393C4C2×D4×C3⋊D311yescharacteristic
394C4C22×#63811yescharacteristic
395C3C2×#520414yescomplemented
396C2—21no—
397C2—21no—
398C2—42no—
399C2#1059290312yesdirect product factor
400C2C2×#6414811yescharacteristic
subgroupG/H
centerC22#64148
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#137C2
socleC22×C32#121
prime radicalC2×C32×#41C22
hypercenterC2×#137C3⋊D3
hypocenterC32C2×#473
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
4. C22×#3756C2semidirect
5. C2×#63663C2semidirect
6. #10592903C2direct (N × H)
7. C2×#63651C2semidirect
8. C2×#63649C2semidirect
26. C2×#3756C22semidirect
33. #63663C22semidirect
34. #63651C22semidirect
35. #63649C22semidirect
281. C2×C32#473semidirect
340. C32C2×#473semidirect
380. C2×C3#5204semidirect
395. C3C2×#5204semidirect
399. C2#10592903direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1372
C2×#641602
C2×#641572
C22×#37562
C2×#636632
#105929032
C2×#636512
C2×#636492
C2×#52043