Finite Group Databasebeta

← C2×#10590156 #11783442

Subgroups — C2×#10590156 #11783442

Order 1152.

718 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3792C211yesmaximal, characteristic
2C22×#3792C211yesmaximal, characteristic
3C2×#64086C211yesmaximal, characteristic
4#10590156C214yesmaximal, direct product factor
5C23×C3⋊Dic3C2211yescharacteristic
6C2×#3792—21no—
7C2×#3792—21no—
8C2×#3792—21no—
9C2×#3792—21no—
10C2×#3792—21no—
11C2×#3792—21no—
12C2×#3792—21no—
13C2×#3792C412yescomplemented
14C2×#3792C412yescomplemented
15C2×#3792C412yescomplemented
16C2×#3792C2212yes—
17C2×#3792C2212yes—
18C22×#622—21no—
19C22×#622C412yescomplemented
20C2×C32×C22⋊C4C411yescharacteristic
21C2×#3757C411yescharacteristic
22C2×#3750—21no—
23C2×C4×C3⋊Dic3—21no—
24#64086—21no—
25#64086—21no—
26#64086C412yes—
27#64086C2212yes—
28C2×#877—62no—
29C24×C32C2×C411yescharacteristic
30C22×C32×C4—21no—
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3⋊Dic3D411yescharacteristic
43C22×C3⋊Dic3Q811yescharacteristic
44C22×C3⋊Dic3Q811yescharacteristic
45C22×C3⋊Dic3C2311yescharacteristic
46#3792—22no—
47#3792—22no—
48#3792—22no—
49#3792—22no—
50#3792—22no—
51#3792—22no—
52#3792—22no—
53#3792C2×C414yescomplemented
54C2×#622—22no—
55C2×#622—22no—
56C2×#622—22no—
57C2×#622—22no—
58C2×#622—22no—
59C2×#622C2×C414yescomplemented
60C32×C22⋊C4—21no—
61C32×C22⋊C4C2×C412yes—
62#3757—21no—
63#3757C2×C412yes—
64#3750—22no—
65#3750—22no—
66C4×C3⋊Dic3—22no—
67C4×C3⋊Dic3—22no—
68C2×#344—91nomaximal, Sylow
69C23×Dic3—62no—
70C2×C3×C22⋊C4—22no—
71C2×#217—62no—
72C2×Dic3⋊C4—64no—
73C2×C4×Dic3—64no—
74#877—64no—
75#877—64no—
76#877—64no—
77#877—64no—
78C23×C32—42no—
79C23×C32C4211yescharacteristic
80C23×C32C4211yescharacteristic
81C23×C32C22⋊C411yescharacteristic
82C23×C32C22⋊C411yescharacteristic
83C23×C32C4⋊C411yescharacteristic
84C23×C32C4⋊C411yescharacteristic
85C23×C32C22×C411yescharacteristic
86C2×C32×C4—22no—
87C2×C32×C4—42no—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—42no—
90C2×C3⋊Dic3C4211yescharacteristic
91C2×C3⋊Dic3C4211yescharacteristic
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C22⋊C411yescharacteristic
94C2×C3⋊Dic3C22⋊C411yescharacteristic
95C2×C3⋊Dic3C22⋊C411yescharacteristic
96C2×C3⋊Dic3C22⋊C411yescharacteristic
97C2×C3⋊Dic3C22⋊C411yescharacteristic
98C2×C3⋊Dic3C22⋊C411yescharacteristic
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C4⋊C411yescharacteristic
103C2×C3⋊Dic3C4⋊C411yescharacteristic
104C2×C3⋊Dic3C4⋊C411yescharacteristic
105C2×C3⋊Dic3C4⋊C411yescharacteristic
106C2×C3⋊Dic3C4⋊C411yescharacteristic
107C2×C3⋊Dic3C4⋊C411yescharacteristic
108C2×C3⋊Dic3C4⋊C411yescharacteristic
109C2×C3⋊Dic3C4⋊C411yescharacteristic
110C2×C3⋊Dic3C4⋊C411yescharacteristic
111C2×C3⋊Dic3C4⋊C411yescharacteristic
112C2×C3⋊Dic3C22×C411yescharacteristic
113C2×C3⋊Dic3C22×C411yescharacteristic
114C2×C3⋊Dic3C2×D411yescharacteristic
115C2×C3⋊Dic3C2×D411yescharacteristic
116C2×C3⋊Dic3C2×D411yescharacteristic
117C2×C3⋊Dic3C2×Q811yescharacteristic
118#622—24no—
119#622—24no—
120C22×M16—91no—
121C22×M16—91no—
122C2×#117—91no—
123#344—94no—
124C24×C3—22no—
125C22×C3×C4—24no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128C22×Dic3—62no—
129C22×Dic3—62no—
130C22×Dic3—62no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133C22×Dic3—62no—
134C22×Dic3—62no—
135C22×Dic3—62no—
136C22×Dic3—62no—
137C22×Dic3—62no—
138C22×Dic3—62no—
139C22×Dic3—62no—
140C22×Dic3—64no—
141C3×C22⋊C4—24no—
142C3×C22⋊C4—24no—
143#217—64no—
144#217—64no—
145Dic3⋊C4—68no—
146Dic3⋊C4—68no—
147C4×Dic3—68no—
148C4×Dic3—68no—
149C22×C32—22no—
150C22×C32—22no—
151C22×C32—22no—
152C22×C32—41no—
153C22×C32—41no—
154C22×C32—41no—
155C22×C32—41no—
156C22×C32#9511yescharacteristic
157C22×C32#9511yescharacteristic
158C22×C32#9511yescharacteristic
159C22×C32#9511yescharacteristic
160C22×C32C2×C4211yescharacteristic
161C22×C32C2×C22⋊C411yescharacteristic
162C22×C32C2×C4⋊C411yescharacteristic
163C32×C4—42no—
164C3⋊Dic3—42no—
165C3⋊Dic3#9511yescharacteristic
166C3⋊Dic3#9511yescharacteristic
167C3⋊Dic3#9511yescharacteristic
168C3⋊Dic3#9511yescharacteristic
169C3⋊Dic3C2×C22⋊C411yescharacteristic
170C3⋊Dic3C2×C22⋊C411yescharacteristic
171C3⋊Dic3C2×C4⋊C411yescharacteristic
172C3⋊Dic3C2×C4⋊C411yescharacteristic
173C23×C4—91no—
174C2×M16—92no—
175C2×M16—92no—
176C2×M16—92no—
177C2×M16—92no—
178C2×M16—92no—
179C2×M16—181no—
180C2×M16—181no—
181C2×M16—181no—
182C2×M16—181no—
183C2×M16—181no—
184C2×M16—181no—
185C2×M16—181no—
186C22×C8—92no—
187C22×C8—181no—
188#117—92no—
189#117—92no—
190#117—181no—
191#117—181no—
192C2×C4⋊C4—181no—
193C2×C22⋊C4—91no—
194C2×C22⋊C4#15711yescharacteristic
195C2×C42—181no—
196C23×C3—22no—
197C23×C3—22no—
198C23×C3—22no—
199C23×C3—22no—
200C23×C3—22no—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—48no—
204C2×C3×C4—28no—
205C2×C3×C4—48no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—68no—
235C2×Dic3—128no—
236C2×C32—21no—
237C2×C32—21no—
238C2×C32—21no—
239C2×C32—21no—
240C2×C32—21no—
241C2×C32—21no—
242C2×C32#34412yescomplemented
243C2×C32C2×#9511yescharacteristic
244C24C2×#15711yescharacteristic
245C22×C4—21no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—91no—
253C22×C4—91no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—91no—
260C22×C4—181no—
261M16—94no—
262M16—182no—
263M16—182no—
264M16—182no—
265M16—182no—
266M16—182no—
267M16—182no—
268M16—182no—
269C2×C8—94no—
270C2×C8—182no—
271C2×C8—182no—
272C2×C8—182no—
273C2×C8—182no—
274C2×C8—182no—
275C4⋊C4—182no—
276C4⋊C4—182no—
277C22⋊C4—21no—
278C22⋊C4—92no—
279C22⋊C4—181no—
280C22⋊C4C2×#15712yes—
281C42—182no—
282C42—182no—
283C22×C3—28no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—44no—
292C22×C3—44no—
293C22×C3—44no—
294C22×C3—44no—
295C22×C3—44no—
296C22×C3—44no—
297C3×C4—48no—
298Dic3—62no—
299Dic3—62no—
300Dic3—62no—
301Dic3—62no—
302Dic3—62no—
303Dic3—62no—
304Dic3—62no—
305Dic3—62no—
306Dic3—128no—
307C32C2×#34411yescharacteristic, complemented, Sylow
308C23—42no—
309C23C4×#15711yescharacteristic
310C23C4×#15711yescharacteristic
311C23C4⋊#15711yescharacteristic
312C23C4⋊#15711yescharacteristic
313C23C22⋊#15711yescharacteristic
314C23C22⋊#15711yescharacteristic
315C23C22×#15711yescharacteristic
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—91no—
319C2×C4—91no—
320C2×C4—91no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—91no—
326C2×C4—91no—
327C2×C4—91no—
328C2×C4—91no—
329C2×C4—91no—
330C2×C4—91no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—91no—
335C2×C4—91no—
336C2×C4—91no—
337C2×C4—91no—
338C2×C4—91no—
339C2×C4—91no—
340C2×C4—91no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—91no—
344C2×C4—91no—
345C2×C4—91no—
346C2×C4—182no—
347C2×C4—362no—
348C8—184no—
349C8—184no—
350C2×C3—24no—
351C2×C3—24no—
352C2×C3—22no—
353C2×C3—24no—
354C2×C3—42no—
355C2×C3—42no—
356C2×C3—42no—
357C2×C3—42no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22#6378111yescharacteristic
366C22#6378111yescharacteristic
367C22#6378111yescharacteristic
368C22#6378111yescharacteristic
369C22C2×C4×#15711yescharacteristic
370C22C2×C4⋊#15711yescharacteristic
371C22C2×C22⋊#15711yescharacteristic
372C4—42no—
373C4—91no—
374C4—91no—
375C4—91no—
376C4—91no—
377C4—91no—
378C4—91no—
379C4—91no—
380C4—91no—
381C4—362no—
382C3—22no—
383C2—21no—
384C2—21no—
385C2—21no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2#1059015612yesdirect product factor
390C2C2×#6378111yescharacteristic
subgroupG/H
centerC22#63781
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC2×C32×C22⋊C4C4
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32C2×#344
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590156C2direct (N × H)
13. C2×#3792C4semidirect
14. C2×#3792C4semidirect
15. C2×#3792C4semidirect
19. C22×#622C4semidirect
53. #3792C2×C4semidirect
59. C2×#622C2×C4semidirect
242. C2×C32#344semidirect
307. C32C2×#344semidirect
389. C2#10590156direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37922
C2×#640862
#105901562
C2×#3449