Finite Group Databasebeta

← C2×#10593824 #11857636

Subgroups — C2×#10593824 #11857636

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×#3830C211yesmaximal, characteristic
2C22×#3792C212yesmaximal, complemented
3C2×#63788C212yesmaximal, complemented
4#10593824C218yesmaximal, direct product factor
5C2×#63780C212yesmaximal, complemented
6C22×C32×D4C411yescharacteristic
7C22×#638C411yescharacteristic
8C22×#638C2211yescharacteristic
9C23×C3⋊Dic3C411yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C2×#3830—22no—
12C2×#3830—22no—
13C2×#3830—24no—
14C2×#3830C414yes—
15C2×#3830C2214yes—
16C22×C4×C3⋊D3C411yescharacteristic
17C22×#634C2211yescharacteristic
18C2×#3792—22no—
19C2×#3792—24no—
20C2×#3792C2214yes—
21C2×#3792C2218yescomplemented
22C22×#622—22no—
23#63788C2218yescomplemented
24#63780C2218yescomplemented
25C22×#237—62no—
26C24×C32C2×C411yescharacteristic
27C24×C32C2×C411yescharacteristic
28C23×C3⋊D3C2×C411yescharacteristic
29C2×C32×D4—22no—
30C2×C32×D4—22no—
31C2×C32×D4C2×C414yes—
32C22×C32×C4C2×C411yescharacteristic
33C2×#638—22no—
34C2×#638—22no—
35C2×#638—22no—
36C2×#638—22no—
37C2×#638C2×C412yes—
38C2×#638C2×C414yes—
39C2×#638C2312yes—
40C22×C3⋊Dic3—22no—
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3C2×C411yescharacteristic
44C22×C3⋊Dic3C2×C414yes—
45C22×C3⋊Dic3C2×C411yescharacteristic
46C22×C3⋊Dic3C2×C412yes—
47C22×C3⋊Dic3D412yes—
48C22×C3⋊Dic3D412yes—
49C22×C3⋊Dic3D414yes—
50C22×C3⋊Dic3C2311yescharacteristic
51C22×C3⋊Dic3C2312yes—
52#3830—28no—
53#3830—28no—
54#3830—28no—
55#3830—28no—
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3C2×C414yes—
60C2×#634—22no—
61C2×#634—22no—
62C2×#634C2×C412yes—
63C2×#634C2312yes—
64#3792—24no—
65#3792—28no—
66#3792C2318yes—
67C2×#622—24no—
68C2×#622—28no—
69C2×#413—91nomaximal, Sylow
70C22×C3×D4—22no—
71C22×#67—62no—
72C22×#67—62no—
73C23×Dic3—62no—
74C23×Dic3—62no—
75C2×#237—68no—
76C2×#237—68no—
77C2×#237—68no—
78C2×#237—616no—
79C2×#237—68no—
80C22×C4×D3—62no—
81C22×Dic6—62no—
82C23×C32—21no—
83C23×C32—21no—
84C23×C32—42no—
85C23×C32—42no—
86C23×C32C22⋊C412yes—
87C23×C32C22⋊C412yes—
88C23×C32C22×C411yescharacteristic
89C23×C32C22×C412yes—
90C23×C32C22×C412yes—
91C22×C3⋊D3—21no—
92C22×C3⋊D3—21no—
93C22×C3⋊D3—42no—
94C22×C3⋊D3C22×C412yes—
95C32×D4—28no—
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4C22×C412yes—
99#638—28no—
100#638—24no—
101#638—24no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—24no—
105C2×C3⋊Dic3—24no—
106C2×C3⋊Dic3C22⋊C412yes—
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C2×C3⋊Dic3C22⋊C414yes—
110C2×C3⋊Dic3C22⋊C414yes—
111C2×C3⋊Dic3C22×C412yes—
112C2×C3⋊Dic3C22×C411yescharacteristic
113C2×C3⋊Dic3C22×C412yes—
114C2×C3⋊Dic3C2×D412yes—
115C2×C3⋊Dic3C2×D414yes—
116C2×C3⋊Dic3C2×D412yes—
117C2×C3⋊Dic3C2×D414yes—
118C2×C3⋊Dic3C2411yescharacteristic
119C4×C3⋊D3—24no—
120C4×C3⋊D3—24no—
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—
130C24×C3—22no—
131C23×D3—62no—
132C2×C3×D4—28no—
133C2×C3×D4—28no—
134C2×C3×D4—28no—
135C22×C3×C4—22no—
136C2×#67—64no—
137C2×#67—68no—
138C2×#67—64no—
139C2×#67—68no—
140C2×#67—68no—
141C2×#67—68no—
142C2×#67—68no—
143C22×Dic3—62no—
144C22×Dic3—62no—
145C22×Dic3—62no—
146C22×Dic3—64no—
147C22×Dic3—68no—
148C22×Dic3—64no—
149C22×Dic3—68no—
150C22×Dic3—64no—
151C22×Dic3—64no—
152C22×Dic3—68no—
153C22×Dic3—64no—
154C22×Dic3—64no—
155#237—632no—
156#237—632no—
157#237—632no—
158#237—632no—
159C2×C4×D3—68no—
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—24no—
170C22×C32—42no—
171C22×C32—42no—
172C22×C32—42no—
173C22×C32—42no—
174C22×C32—42no—
175C22×C32C2×C22⋊C411yescharacteristic
176C22×C32C2×C22⋊C414yes—
177C22×C32C2×C22⋊C411yescharacteristic
178C22×C32C23×C411yescharacteristic
179C2×C3⋊D3—22no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3—42no—
183C32×C4—22no—
184C3⋊Dic3—22no—
185C3⋊Dic3C2×C22⋊C412yes—
186C3⋊Dic3C2×C22⋊C412yes—
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#15711yescharacteristic
198C23×C4—91no—
199C23×C4—91no—
200C23×C4—91no—
201C2×M16—94no—
202C2×M16—98no—
203C2×M16—184no—
204C2×M16—182no—
205C22×C8—182no—
206#101—98no—
207#100—98no—
208C23×C3—24no—
209C23×C3—24no—
210C23×C3—22no—
211C23×C3—24no—
212C23×C3—24no—
213C23×C3—24no—
214C23×C3—24no—
215C23×C3—48no—
216C23×C3—48no—
217C22×D3—64no—
218C22×D3—64no—
219C22×D3—64no—
220C22×D3—128no—
221C3×D4—232no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225#67—616no—
226#67—616no—
227#67—632no—
228C2×Dic3—64no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C2×Dic3—68no—
232C2×Dic3—68no—
233C2×Dic3—62no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3—68no—
239C2×Dic3—68no—
240C2×Dic3—62no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—616no—
244C2×Dic3—616no—
245C4×D3—616no—
246C4×D3—616no—
247Dic6—616no—
248Dic6—616no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32—24no—
252C2×C32—42no—
253C2×C32#41312yescomplemented
254C2×C32C22×C22⋊C411yescharacteristic
255C3⋊D3—42no—
256C24—91no—
257C24C2×#15711yescharacteristic
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—22no—
268C2×D4—22no—
269C2×D4—92no—
270C2×D4—92no—
271C2×D4—94no—
272C2×D4—182no—
273C2×D4—182no—
274C2×D4—182no—
275C2×D4—182no—
276C2×D4C2×#15714yes—
277C22×C4—91no—
278C22×C4—92no—
279C22×C4—91no—
280C22×C4—92no—
281C22×C4—92no—
282C22×C4—94no—
283C22×C4—92no—
284C22×C4—91no—
285C22×C4—94no—
286C22×C4—94no—
287C22×C4—182no—
288C22×C4—181no—
289C22×C4—181no—
290C22×C4—182no—
291C22×C4—181no—
292C22×C4—181no—
293C22×C4C2×#15711yescharacteristic
294M16—98no—
295M16—184no—
296M16—188no—
297C2×C8—188no—
298C2×C8—184no—
299C22×C3—28no—
300C22×C3—28no—
301C22×C3—22no—
302C22×C3—28no—
303C22×C3—22no—
304C22×C3—22no—
305C22×C3—48no—
306C22×C3—48no—
307C22×C3—48no—
308C22×C3—48no—
309C22×C3—48no—
310C22×C3—48no—
311C2×D3—68no—
312C2×D3—128no—
313C2×D3—128no—
314C2×D3—128no—
315C3×C4—28no—
316Dic3—64no—
317Dic3—64no—
318Dic3—64no—
319Dic3—64no—
320Dic3—68no—
321C32C2×#41311yescharacteristic, complemented, Sylow
322C23—21no—
323C23—21no—
324C23—42no—
325C23—42no—
326C23—92no—
327C23—181no—
328C23—181no—
329C23—362no—
330C23C22⋊#15712yes—
331C23C22⋊#15712yes—
332C23C22×#15711yescharacteristic
333C23C22×#15712yes—
334C23C22×#15712yes—
335Q8—184no—
336Q8—184no—
337D4—28no—
338D4—184no—
339D4—184no—
340D4—188no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—94no—
344C2×C4—92no—
345C2×C4—94no—
346C2×C4—92no—
347C2×C4—94no—
348C2×C4—94no—
349C2×C4—92no—
350C2×C4—91no—
351C2×C4—91no—
352C2×C4—91no—
353C2×C4—92no—
354C2×C4—91no—
355C2×C4—92no—
356C2×C4—184no—
357C2×C4—184no—
358C2×C4—184no—
359C2×C4—184no—
360C2×C4—181no—
361C2×C4—181no—
362C2×C4C22×#15712yes—
363C8—188no—
364C2×C3—24no—
365C2×C3—24no—
366C2×C3—24no—
367C2×C3—22no—
368C2×C3—48no—
369C2×C3—48no—
370D3—128no—
371C22—22no—
372C22—24no—
373C22—22no—
374C22—42no—
375C22—42no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—182no—
380C22—362no—
381C22—362no—
382C22—362no—
383C22C2×C22⋊#15711yescharacteristic
384C22C2×C22⋊#15714yes—
385C22C2×C22⋊#15711yescharacteristic
386C22C23×#15711yescharacteristic
387C4—22no—
388C4—92no—
389C4—92no—
390C4—92no—
391C4—92no—
392C4—182no—
393C3—22no—
394C2—21no—
395C2—21no—
396C2—24no—
397C2—42no—
398C2—362no—
399C2#1059382412yesdirect product factor
400C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC22×C32×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×#3830C2
cosocleC2×C3⋊Dic3C24
hypercenterC22×D4#157
hypocenterC32C2×#413
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×#3792C2semidirect
3. C2×#63788C2semidirect
4. #10593824C2direct (N × H)
5. C2×#63780C2semidirect
21. C2×#3792C22semidirect
23. #63788C22semidirect
24. #63780C22semidirect
253. C2×C32#413semidirect
321. C32C2×#413semidirect
399. C2#10593824direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×#37922
C2×#637882
#105938242
C2×#637802
C2×#4139