Finite Group Databasebeta

← C2×#10590049 #11783245

Subgroups — C2×#10590049 #11783245

Order 1152.

890 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#157C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4#10590049C214yesmaximal, direct product factor
5C23×#157—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#624—21no—
8C2×C4⋊#157—22no—
9C2×C4⋊#157—21no—
10C2×C4⋊#157C414yescomplemented
11C2×C4⋊#157C2212yes—
12C2×C3×C4⋊Dic3—21no—
13C22×C3×C3⋊C8—21no—
14C2×#3724C412yescomplemented
15#63900—21no—
16#63900—21no—
17#63900C412yescomplemented
18#63900C2212yes—
19C2×#3710—21no—
20C2×#3710—22no—
21C2×#3710C414yescomplemented
22C2×#3710C2212yes—
23C22×D3×C8—61no—
24C2×D3×C4⋊C4—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—24no—
27C22×#157—22no—
28C22×#157—42no—
29C22×#157—42no—
30C22×C32×C4D411yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3C2×C412yes—
34C2×C4×C3⋊D3C2×C412yes—
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D412yes—
38C2×C4×C3⋊D3Q812yes—
39C2×C4×C3⋊D3C2311yescharacteristic
40C22×C3×Dic3—22no—
41C2×#624—22no—
42C2×#624—22no—
43C2×#624—42no—
44C2×#624—42no—
45C4⋊#157—24no—
46C4⋊#157—22no—
47C4⋊#157C2×C414yescomplemented
48C3×C4⋊Dic3—22no—
49C3×C4⋊Dic3—22no—
50C2×C3×C3⋊C8—24no—
51C2×C3×C3⋊C8—22no—
52#3724—22no—
53#3724C2×C414yescomplemented
54#3710—24no—
55#3710—22no—
56#3710C2×C414yescomplemented
57C2×#340—91nomaximal, Sylow
58C22×C4×D3—61no—
59C22×C4×D3—61no—
60C22×C4×D3—62no—
61C22×C3×C8—61no—
62C2×C3×C4⋊C4—61no—
63C2×C4⋊Dic3—21no—
64C2×Dic3⋊C4—62no—
65C22×C3⋊C8—21no—
66C2×D3×C8—64no—
67C2×D3×C8—62no—
68C2×D3×C8—62no—
69C2×D3×C8—64no—
70D3×C4⋊C4—62no—
71D3×C4⋊C4—62no—
72D3×C4⋊C4—62no—
73D3×C4⋊C4—62no—
74C23×C32C22⋊C411yescharacteristic
75C22×C3⋊D3C22⋊C411yescharacteristic
76C22×C3⋊D3C22⋊C412yes—
77C22×C3⋊D3C4⋊C412yes—
78C22×C3⋊D3D812yes—
79C22×C3⋊D3SD1612yes—
80C22×C3⋊D3SD1612yes—
81C22×C3⋊D3Q1612yes—
82C22×C3⋊D3C2×D411yescharacteristic
83C2×#157—24no—
84C2×#157—48no—
85C2×#157—42no—
86C2×#157—42no—
87C2×C32×C4C22⋊C411yescharacteristic
88C2×C32×C4C22⋊C412yes—
89C2×C32×C4C4⋊C412yes—
90C2×C32×C4C2×D411yescharacteristic
91C2×C3⋊Dic3C4212yes—
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C4⋊C412yes—
94C2×C3⋊Dic3C22×C411yescharacteristic
95C4×C3⋊D3C4212yes—
96C4×C3⋊D3C22⋊C412yes—
97C4×C3⋊D3C22⋊C412yes—
98C4×C3⋊D3C4⋊C412yes—
99C4×C3⋊D3C4⋊C412yes—
100C4×C3⋊D3C4⋊C412yes—
101C4×C3⋊D3C22×C411yescharacteristic
102C4×C3⋊D3C22×C411yescharacteristic
103C4×C3⋊D3C2×D411yescharacteristic
104C4×C3⋊D3C2×Q811yescharacteristic
105C2×C3×Dic3—24no—
106C2×C3×Dic3—44no—
107#624—44no—
108#624—42no—
109#624—42no—
110C3×C3⋊C8—24no—
111C23×C8—91no—
112C22×C4⋊C4—91no—
113C22×C4⋊C4—91no—
114#340—94no—
115C23×D3—61no—
116C23×D3—61no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—62no—
120C22×Dic3—22no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—62no—
128C2×C4×D3—61no—
129C2×C4×D3—62no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—61no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—62no—
139C2×C4×D3—64no—
140C2×C4×D3—64no—
141C2×C4×D3—124no—
142C2×C4×D3—124no—
143C2×C3×C8—62no—
144C2×C3×C8—64no—
145C3×C4⋊C4—62no—
146C3×C4⋊C4—62no—
147C4⋊Dic3—22no—
148C4⋊Dic3—22no—
149Dic3⋊C4—64no—
150Dic3⋊C4—64no—
151C2×C3⋊C8—22no—
152C2×C3⋊C8—24no—
153D3×C8—64no—
154D3×C8—68no—
155D3×C8—64no—
156C22×C32#9512yes—
157C22×C32#10212yes—
158C22×C32#10312yes—
159C22×C32C2×C22⋊C411yescharacteristic
160C2×C3⋊D3#9512yes—
161C2×C3⋊D3#10212yes—
162C2×C3⋊D3#10214yes—
163C2×C3⋊D3#10312yes—
164C2×C3⋊D3#10314yes—
165C2×C3⋊D3#10614yes—
166C2×C3⋊D3#10714yes—
167C2×C3⋊D3C2×C22⋊C411yescharacteristic
168C2×C3⋊D3C2×C4⋊C411yescharacteristic
169C2×C3⋊D3C2×D811yescharacteristic
170C2×C3⋊D3C2×SD1611yescharacteristic
171C2×C3⋊D3C2×SD1611yescharacteristic
172C2×C3⋊D3C2×Q1611yescharacteristic
173#157—44no—
174C32×C4#9512yes—
175C32×C4C2×C22⋊C411yescharacteristic
176C32×C4C2×C4⋊C411yescharacteristic
177C3⋊Dic3#9512yes—
178C3⋊Dic3C2×C4211yescharacteristic
179C3⋊Dic3C2×C4⋊C411yescharacteristic
180C3×Dic3—44no—
181C23×C4—91no—
182C23×C4—181no—
183C23×C4—181no—
184C22×C8—61no—
185C22×C8—92no—
186C22×C8—94no—
187C22×C8—181no—
188C22×C8—182no—
189C2×C4⋊C4—61no—
190C2×C4⋊C4—92no—
191C2×C4⋊C4—92no—
192C2×C4⋊C4—92no—
193C2×C4⋊C4—94no—
194C2×C4⋊C4—92no—
195C2×C4⋊C4—181no—
196C2×C4⋊C4—181no—
197C2×C4⋊C4—181no—
198C2×C4⋊C4—182no—
199C23×C3—21no—
200C23×C3—21no—
201C22×D3—61no—
202C22×D3—61no—
203C22×D3—62no—
204C22×D3—62no—
205C22×D3—62no—
206C22×D3—62no—
207C22×D3—62no—
208C22×D3—62no—
209C22×D3—62no—
210C22×D3—62no—
211C22×D3—62no—
212C22×D3—62no—
213C22×D3—62no—
214C22×D3—62no—
215C22×D3—61no—
216C22×D3—61no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—22no—
222C2×C3×C4—21no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—64no—
226C2×C3×C4—124no—
227C2×Dic3—24no—
228C2×Dic3—44no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C4×D3—62no—
238C4×D3—62no—
239C4×D3—62no—
240C4×D3—62no—
241C4×D3—62no—
242C4×D3—62no—
243C4×D3—62no—
244C4×D3—62no—
245C4×D3—62no—
246C4×D3—62no—
247C4×D3—62no—
248C4×D3—62no—
249C4×D3—61no—
250C4×D3—61no—
251C4×D3—61no—
252C4×D3—61no—
253C4×D3—61no—
254C4×D3—61no—
255C4×D3—61no—
256C4×D3—61no—
257C4×D3—128no—
258C4×D3—124no—
259C4×D3—124no—
260C3×C8—64no—
261C3⋊C8—24no—
262C2×C32#34014yescomplemented
263C2×C32C2×#9511yescharacteristic
264C2×C32C2×#10211yescharacteristic
265C2×C32C2×#10311yescharacteristic
266C3⋊D3#34014yescomplemented
267C3⋊D3C2×#10211yescharacteristic
268C3⋊D3C2×#10311yescharacteristic
269C3⋊D3C2×#10611yescharacteristic
270C3⋊D3C2×#10711yescharacteristic
271C24—91no—
272C22×C4—62no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—91no—
278C22×C4—92no—
279C22×C4—92no—
280C22×C4—92no—
281C22×C4—92no—
282C22×C4—182no—
283C22×C4—182no—
284C22×C4—182no—
285C22×C4—184no—
286C22×C4—362no—
287C22×C4—362no—
288C22×C4—362no—
289C22×C4—362no—
290C22×C4GO+(4,𝔽2)11yescharacteristic
291C2×C8—62no—
292C2×C8—64no—
293C2×C8—94no—
294C2×C8—182no—
295C2×C8—184no—
296C4⋊C4—62no—
297C4⋊C4—62no—
298C4⋊C4—94no—
299C4⋊C4—94no—
300C4⋊C4—182no—
301C4⋊C4—182no—
302C4⋊C4—184no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
311C2×D3—62no—
312C2×D3—62no—
313C2×D3—61no—
314C2×D3—61no—
315C2×D3—61no—
316C2×D3—61no—
317C2×D3—62no—
318C2×D3—61no—
319C2×D3—61no—
320C2×D3—62no—
321C2×D3—64no—
322C2×D3—64no—
323C2×D3—62no—
324C2×D3—62no—
325C2×D3—64no—
326C2×D3—64no—
327C2×D3—64no—
328C2×D3—64no—
329C2×D3—64no—
330C2×D3—64no—
331C2×D3—61no—
332C2×D3—61no—
333C2×D3—61no—
334C2×D3—61no—
335C2×D3—61no—
336C2×D3—61no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—124no—
344Dic3—44no—
345Dic3—62no—
346Dic3—62no—
347Dic3—61no—
348Dic3—61no—
349Dic3—61no—
350Dic3—61no—
351C32C2×#34011yescharacteristic, complemented, Sylow
352C23—91no—
353C23—91no—
354C23—92no—
355C23—92no—
356C23—92no—
357C23—92no—
358C23—92no—
359C23—92no—
360C23D32⋊C411yescharacteristic
361C2×C4—64no—
362C2×C4—91no—
363C2×C4—91no—
364C2×C4—92no—
365C2×C4—92no—
366C2×C4—91no—
367C2×C4—91no—
368C2×C4—92no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—92no—
372C2×C4—92no—
373C2×C4—92no—
374C2×C4—92no—
375C2×C4—92no—
376C2×C4—124no—
377C2×C4—184no—
378C2×C4—362no—
379C2×C4—362no—
380C2×C4—364no—
381C2×C4—362no—
382C2×C4—362no—
383C2×C4—368no—
384C2×C4D32⋊C412yes—
385C2×C4D32⋊C411yescharacteristic
386C2×C4#377312yes—
387C2×C4C2×GO+(4,𝔽2)11yescharacteristic
388C8—64no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—24no—
394C2×C3—24no—
395C2×C3—21no—
396C2×C3—21no—
397D3—64no—
398D3—64no—
399D3—61no—
400D3—61no—
401D3—61no—
402D3—61no—
403D3—61no—
404D3—61no—
405D3—61no—
406D3—61no—
407C22—91no—
408C22—91no—
409C22—92no—
410C22—91no—
411C22—91no—
412C22—92no—
413C22—94no—
414C22—94no—
415C22—94no—
416C22—94no—
417C22—91no—
418C22—91no—
419C22—92no—
420C22#6372912yes—
421C22#6373012yes—
422C22#6373712yes—
423C22C2×D32⋊C411yescharacteristic
424C4—91no—
425C4—91no—
426C4—92no—
427C4—124no—
428C4—364no—
429C4#6373712yes—
430C4C2×D32⋊C411yescharacteristic
431C4C2×#377311yescharacteristic
432C3—21no—
433C3—21no—
434C2—91no—
435C2—91no—
436C2—91no—
437C2—94no—
438C2—91no—
439C2#1059004914yesdirect product factor
440C2C2×#6372911yescharacteristic
441C2C2×#6373011yescharacteristic
442C2C2×#6373711yescharacteristic
subgroupG/H
centerC23D32⋊C4
commutatorC3⋊Dic3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#340
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590049C2direct (N × H)
10. C2×C4⋊#157C4semidirect
14. C2×#3724C4semidirect
17. #63900C4semidirect
21. C2×#3710C4semidirect
47. C4⋊#157C2×C4semidirect
53. #3724C2×C4semidirect
56. #3710C2×C4semidirect
262. C2×C32#340semidirect
266. C3⋊D3#340semidirect
351. C32C2×#340semidirect
439. C2#10590049direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊#1572
C2×#639002
C22×#37102
#105900492
C2×#3409