Finite Group Databasebeta

← C2×#10593808 #11857635

Subgroups — C2×#10593808 #11857635

Order 1152.

1646 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 1646 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×#64283C212yesmaximal, complemented
3C2×#63788C212yesmaximal, complemented
4#10593808C218yesmaximal, direct product factor
5C2×#63780C212yesmaximal, complemented
6C23×C32×C4C411yescharacteristic
7C22×#638C411yescharacteristic
8C22×#638C2211yescharacteristic
9C2×#3828—22no—
10C2×#3828—22no—
11C2×#3828—24no—
12C2×#3828C414yes—
13C2×#3828C2214yes—
14C22×C4⋊(C3⋊D3)C411yescharacteristic
15C22×C4×C3⋊D3C411yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#634C2211yescharacteristic
18C2×#3792C2214yes—
19#64283—24no—
20#64283C2218yescomplemented
21C2×#3788—22no—
22C2×#3787—22no—
23#63788C2218yescomplemented
24#63780C2218yescomplemented
25C22×#235—62no—
26C24×C32C2×C411yescharacteristic
27C23×C3⋊D3C2×C411yescharacteristic
28C23×C3⋊D3C2×C411yescharacteristic
29C22×C32×C4—22no—
30C22×C32×C4—21no—
31C22×C32×C4—21no—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C414yes—
34C22×C32×C4C2×C411yescharacteristic
35C2×#638—22no—
36C2×#638—22no—
37C2×#638—22no—
38C2×#638—22no—
39C2×#638C2×C412yes—
40C2×#638C2×C414yes—
41C2×#638C2312yes—
42C22×C3⋊Dic3C2×C411yescharacteristic
43C22×C3⋊Dic3C2311yescharacteristic
44#3828—28no—
45#3828—28no—
46#3828—28no—
47#3828—28no—
48C2×C4⋊(C3⋊D3)—22no—
49C2×C4⋊(C3⋊D3)—22no—
50C2×C4⋊(C3⋊D3)C2×C414yes—
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3C2×C414yes—
55C2×C4×C3⋊D3C2×C412yes—
56C2×C4×C3⋊D3D412yes—
57C2×C4×C3⋊D3D412yes—
58C2×C4×C3⋊D3D414yes—
59C2×C4×C3⋊D3C2312yes—
60C2×#634—22no—
61C2×#634—22no—
62C2×#634C2×C412yes—
63C2×#634C2312yes—
64#3792—24no—
65#3792C2318yes—
66C2×#622—24no—
67#3788—28no—
68#3787—28no—
69C2×#413—91nomaximal, Sylow
70C23×C3×C4—22no—
71C22×#67—62no—
72C22×#67—62no—
73C2×#235—68no—
74C2×#235—68no—
75C2×#235—68no—
76C2×#235—616no—
77C2×#235—68no—
78C22×D12—62no—
79C22×C4×D3—62no—
80C22×C4×D3—62no—
81C22×Dic6—62no—
82C23×C32—21no—
83C23×C32—21no—
84C23×C32—42no—
85C23×C32C22×C411yescharacteristic
86C23×C32C22×C412yes—
87C22×C3⋊D3—21no—
88C22×C3⋊D3—21no—
89C22×C3⋊D3—42no—
90C22×C3⋊D3—42no—
91C22×C3⋊D3C22⋊C412yes—
92C22×C3⋊D3C22⋊C412yes—
93C22×C3⋊D3C22×C412yes—
94C22×C3⋊D3C22×C412yes—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4—24no—
98C2×C32×C4—24no—
99C2×C32×C4C22⋊C412yes—
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4C22×C412yes—
103C2×C32×C4C22×C412yes—
104#638—28no—
105#638—24no—
106#638—24no—
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3C22×C412yes—
110C2×C3⋊Dic3C22×C411yescharacteristic
111C2×C3⋊Dic3C2×D412yes—
112C2×C3⋊Dic3C2×D412yes—
113C2×C3⋊Dic3C2411yescharacteristic
114C4⋊(C3⋊D3)—28no—
115C4×C3⋊D3—24no—
116C4×C3⋊D3—24no—
117C4×C3⋊D3C22⋊C414yes—
118C4×C3⋊D3C22⋊C414yes—
119C4×C3⋊D3C2×D414yes—
120C4×C3⋊D3C2×D414yes—
121#634—24no—
122#634—24no—
123#622—28no—
124C22×#41—91no—
125C22×M16—92no—
126#413—98no—
127C2×#101—92no—
128C2×#100—92no—
129C24×C3—22no—
130C23×D3—62no—
131C23×D3—62no—
132C22×C3×C4—28no—
133C22×C3×C4—24no—
134C22×C3×C4—24no—
135C22×C3×C4—22no—
136C22×C3×C4—28no—
137C22×C3×C4—22no—
138C2×#67—64no—
139C2×#67—68no—
140C2×#67—64no—
141C2×#67—68no—
142C2×#67—68no—
143C2×#67—68no—
144C2×#67—68no—
145C22×Dic3—62no—
146C22×Dic3—62no—
147#235—632no—
148#235—632no—
149#235—632no—
150#235—632no—
151C2×D12—68no—
152C2×D12—68no—
153C2×D12—68no—
154C2×C4×D3—64no—
155C2×C4×D3—68no—
156C2×C4×D3—64no—
157C2×C4×D3—68no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C2×C4×D3—68no—
161C2×C4×D3—64no—
162C2×C4×D3—64no—
163C2×Dic6—64no—
164C2×Dic6—64no—
165C2×Dic6—68no—
166C2×Dic6—68no—
167C22×C32—22no—
168C22×C32—22no—
169C22×C32—42no—
170C22×C32—42no—
171C22×C32—42no—
172C22×C32C2×C22⋊C411yescharacteristic
173C22×C32C2×C22⋊C411yescharacteristic
174C22×C32C23×C411yescharacteristic
175C2×C3⋊D3—22no—
176C2×C3⋊D3—24no—
177C2×C3⋊D3—42no—
178C2×C3⋊D3—42no—
179C2×C3⋊D3—42no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3C2×C22⋊C414yes—
183C32×C4—22no—
184C32×C4C2×C22⋊C412yes—
185C32×C4C2×C22⋊C412yes—
186C3⋊Dic3—22no—
187C3⋊Dic3C2×C22⋊C412yes—
188C3⋊Dic3C22×D412yes—
189C2×#41—94no—
190C2×#41—94no—
191C2×#41—182no—
192C2×#41—184no—
193C2×#41—182no—
194C22×Q8—91no—
195C22×D4—91no—
196C22×D4—91no—
197C22×D4—91no—
198C23×C4—91no—
199C23×C4—91no—
200C23×C4#15711yescharacteristic
201C2×M16—98no—
202C2×M16—94no—
203C2×M16—182no—
204C2×M16—184no—
205C22×C8—182no—
206#101—98no—
207#100—98no—
208C23×C3—24no—
209C23×C3—24no—
210C23×C3—22no—
211C23×C3—24no—
212C23×C3—48no—
213C22×D3—64no—
214C22×D3—64no—
215C22×D3—64no—
216C22×D3—64no—
217C22×D3—64no—
218C22×D3—64no—
219C22×D3—128no—
220C22×D3—128no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—216no—
224C2×C3×C4—216no—
225C2×C3×C4—24no—
226C2×C3×C4—24no—
227C2×C3×C4—22no—
228C2×C3×C4—24no—
229C2×C3×C4—22no—
230#67—616no—
231#67—616no—
232#67—632no—
233C2×Dic3—62no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—62no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240D12—632no—
241C4×D3—68no—
242C4×D3—68no—
243C4×D3—68no—
244C4×D3—68no—
245C4×D3—616no—
246C4×D3—616no—
247Dic6—616no—
248Dic6—616no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32—42no—
252C2×C32#41312yescomplemented
253C2×C32C22×C22⋊C411yescharacteristic
254C3⋊D3—24no—
255C3⋊D3—42no—
256C24—91no—
257C24—91no—
258C24C2×#15711yescharacteristic
259#41—188no—
260#41—188no—
261#41—188no—
262#41—188no—
263C2×Q8—92no—
264C2×Q8—92no—
265C2×Q8—182no—
266C2×Q8—182no—
267C2×D4—92no—
268C2×D4—92no—
269C2×D4—94no—
270C2×D4—94no—
271C2×D4—182no—
272C2×D4—182no—
273C2×D4—182no—
274C2×D4—182no—
275C2×D4—182no—
276C2×D4—182no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—91no—
281C22×C4—92no—
282C22×C4—92no—
283C22×C4—92no—
284C22×C4—94no—
285C22×C4—92no—
286C22×C4—91no—
287C22×C4—94no—
288C22×C4—182no—
289C22×C4—181no—
290C22×C4—181no—
291C22×C4C2×#15711yescharacteristic
292C22×C4C2×#15714yes—
293C22×C4C2×#15711yescharacteristic
294M16—98no—
295M16—188no—
296M16—184no—
297C2×C8—188no—
298C2×C8—184no—
299C22×C3—28no—
300C22×C3—28no—
301C22×C3—22no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—48no—
305C22×C3—48no—
306C22×C3—48no—
307C2×D3—68no—
308C2×D3—68no—
309C2×D3—128no—
310C2×D3—128no—
311C2×D3—128no—
312C2×D3—128no—
313C2×D3—128no—
314C2×D3—128no—
315C3×C4—28no—
316C3×C4—24no—
317C3×C4—24no—
318Dic3—64no—
319Dic3—64no—
320Dic3—68no—
321C32C2×#41311yescharacteristic, complemented, Sylow
322C23—21no—
323C23—21no—
324C23—42no—
325C23—92no—
326C23—92no—
327C23—92no—
328C23—92no—
329C23—181no—
330C23—181no—
331C23—362no—
332C23—362no—
333C23C22×#15711yescharacteristic
334C23C22×#15712yes—
335Q8—184no—
336Q8—184no—
337D4—188no—
338D4—184no—
339D4—184no—
340D4—188no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—92no—
346C2×C4—92no—
347C2×C4—91no—
348C2×C4—91no—
349C2×C4—94no—
350C2×C4—94no—
351C2×C4—94no—
352C2×C4—94no—
353C2×C4—92no—
354C2×C4—181no—
355C2×C4—181no—
356C2×C4—184no—
357C2×C4—184no—
358C2×C4C22⋊#15711yescharacteristic
359C2×C4C22⋊#15712yes—
360C2×C4C22⋊#15711yescharacteristic
361C2×C4C22×#15712yes—
362C2×C4C22×#15712yes—
363C8—188no—
364C2×C3—24no—
365C2×C3—24no—
366C2×C3—24no—
367C2×C3—22no—
368C2×C3—48no—
369D3—128no—
370D3—128no—
371C22—22no—
372C22—22no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—94no—
377C22—184no—
378C22—182no—
379C22—362no—
380C22—362no—
381C22—362no—
382C22—362no—
383C22—362no—
384C22C2×C22⋊#15711yescharacteristic
385C22C2×C22⋊#15711yescharacteristic
386C22C23×#15711yescharacteristic
387C4—22no—
388C4—92no—
389C4—92no—
390C4—182no—
391C4C2×C22⋊#15712yes—
392C4C2×C22⋊#15712yes—
393C3—22no—
394C2—21no—
395C2—21no—
396C2—42no—
397C2—184no—
398C2—362no—
399C2#1059380812yesdirect product factor
400C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC23×C32×C4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×#3828C2
cosocleC2×C3⋊Dic3C24
hypercenterC23×C4#157
hypocenterC32C2×#413
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64283C2semidirect
3. C2×#63788C2semidirect
4. #10593808C2direct (N × H)
5. C2×#63780C2semidirect
20. #64283C22semidirect
23. #63788C22semidirect
24. #63780C22semidirect
252. C2×C32#413semidirect
321. C32C2×#413semidirect
399. C2#10593808direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C2×#642832
C2×#637882
#105938082
C2×#637802
C2×#4139