Finite Group Databasebeta

← C2×#10593411 #11808198

Subgroups — C2×#10593411 #11808198

Order 1152.

1542 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 1542 conjugacy classes of subgroups — too many to draw. Only its 199 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×#3797C211yesmaximal, characteristic
2C22×#3773C212yesmaximal
3C2×#63883C211yesmaximal, characteristic
4C2×#63781C211yesmaximal, characteristic
5C2×#63737C212yesmaximal
6#10593411C218yesmaximal, direct product factor
7C23×#157C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×C3×Dic6—21no—
10C22×#627—21no—
11C22×#624C2211yescharacteristic
12C22×#624C2212yes—
13C22×#624C2211yescharacteristic
14C2×#3797—22no—
15C2×#3797—28no—
16C2×#3797C2214yes—
17C2×#3773—28no—
18C2×#3773C2218yes—
19C2×C3×Dic3⋊C4—21no—
20C2×Dic3⋊Dic3—21no—
21#63883—22no—
22#63883C2214yes—
23#63781C2214yes—
24#63737C2218yes—
25C22×D3×Q8—61no—
26C2×D3×C4⋊C4—61no—
27C23×C3⋊D3C2311yescharacteristic
28C22×#157—24no—
29C22×#157—24no—
30C22×#157Q818yescomplemented
31C22×#157C2314yes—
32C22×C32×C4D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C2×C4×C3⋊D3—24no—
35C2×C4×C3⋊D3D412yes—
36C2×C4×C3⋊D3C2312yes—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—22no—
39C22×C3×Dic3—21no—
40C2×C3×Dic6—28no—
41C2×C3×Dic6—24no—
42C2×#627—28no—
43C2×#627—24no—
44C2×#624—22no—
45C2×#624—24no—
46C2×#624—21no—
47C2×#624—22no—
48C2×#624—24no—
49C2×#624—21no—
50C2×#624D418yes—
51C2×#624Q814yescomplemented
52C2×#624C2312yes—
53C2×#624C2314yes—
54C2×#624C2312yes—
55#3797—216no—
56#3797—216no—
57#3773—216no—
58C3×Dic3⋊C4—24no—
59Dic3⋊Dic3—24no—
60C2×#395—91nomaximal, Sylow
61C22×C3×Q8—61no—
62C2×D3×Q8—64no—
63C2×D3×Q8—616no—
64C2×D3×Q8—64no—
65C22×C4×D3—62no—
66C22×C4×D3—61no—
67C22×C4×D3—61no—
68C22×C4×D3—61no—
69C22×C4×D3—61no—
70C22×Dic6—21no—
71C22×Dic6—62no—
72C2×C3×C4⋊C4—61no—
73C2×C4⋊Dic3—61no—
74C2×Dic3⋊C4—21no—
75C2×Dic3⋊C4—61no—
76D3×C4⋊C4—64no—
77D3×C4⋊C4—64no—
78C23×C32C2×D411yescharacteristic
79C22×C3⋊D3C2×D411yescharacteristic
80C22×C3⋊D3C2×D414yes—
81C22×C3⋊D3C2×Q814yes—
82C22×C3⋊D3C2×Q812yes—
83C22×C3⋊D3#4112yes—
84C22×C3⋊D3C2411yescharacteristic
85C2×#157—216no—
86C2×#157—24no—
87C2×#157—24no—
88C2×#157C2×Q818yescomplemented
89C2×C32×C4—22no—
90C2×C32×C4C2×D412yes—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3C2×D412yes—
93C4×C3⋊D3—24no—
94C4×C3⋊D3—24no—
95C2×C3×Dic3—28no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—42no—
101C3×Dic6—216no—
102#627—216no—
103#624—28no—
104#624—24no—
105#624—24no—
106#624—22no—
107#624—24no—
108#624—42no—
109#624C2×D418yes—
110#624C2×Q814yescomplemented
111C23×Q8—91no—
112C22×C4⋊C4—91no—
113C22×C4⋊C4—92no—
114#395—98no—
115C2×#95—91no—
116C2×#95—92no—
117C23×D3—61no—
118C23×D3—61no—
119C2×C3×Q8—68no—
120C2×C3×Q8—64no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—61no—
124C22×C3×C4—62no—
125C22×C3×C4—61no—
126C22×Dic3—21no—
127C22×Dic3—22no—
128C22×Dic3—21no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131D3×Q8—632no—
132D3×Q8—632no—
133C2×C4×D3—62no—
134C2×C4×D3—68no—
135C2×C4×D3—64no—
136C2×C4×D3—64no—
137C2×C4×D3—62no—
138C2×C4×D3—62no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—64no—
144C2×C4×D3—64no—
145C2×C4×D3—68no—
146C2×C4×D3—68no—
147C2×C4×D3—62no—
148C2×C4×D3—124no—
149C2×C4×D3—124no—
150C2×Dic6—28no—
151C2×Dic6—24no—
152C2×Dic6—68no—
153C2×Dic6—616no—
154C3×C4⋊C4—64no—
155C4⋊Dic3—64no—
156Dic3⋊C4—24no—
157Dic3⋊C4—64no—
158C22×C32#12012yes—
159C22×C32C22⋊Q812yes—
160C22×C32C4⋊Q812yes—
161C22×C32C22×D411yescharacteristic
162C2×C3⋊D3#12012yes—
163C2×C3⋊D3C22⋊Q818yes—
164C2×C3⋊D3C22⋊Q812yes—
165C2×C3⋊D3C4⋊Q818yes—
166C2×C3⋊D3C4⋊Q812yes—
167C2×C3⋊D3C22×D412yes—
168C2×C3⋊D3C22×Q812yes—
169C2×C3⋊D3C22×Q811yescharacteristic
170C2×C3⋊D3C2×#4111yescharacteristic
171#157—28no—
172C32×C4—22no—
173C3⋊Dic3—22no—
174C3×Dic3—28no—
175C3×Dic3—24no—
176C3×Dic3—42no—
177C22×Q8—61no—
178C22×Q8—94no—
179C22×Q8—181no—
180C22×Q8—188no—
181C22×Q8—182no—
182C23×C4—92no—
183C23×C4—91no—
184C23×C4—91no—
185C23×C4—92no—
186C23×C4—91no—
187C2×C4⋊C4—61no—
188C2×C4⋊C4—94no—
189C2×C4⋊C4—98no—
190C2×C4⋊C4—182no—
191C2×C4⋊C4—181no—
192C2×C4⋊C4—188no—
193#95—94no—
194#95—98no—
195C23×C3—21no—
196C23×C3—21no—
197C22×D3—61no—
198C22×D3—61no—
199C22×D3—64no—
200C22×D3—64no—
201C22×D3—62no—
202C22×D3—62no—
203C22×D3—64no—
204C22×D3—64no—
205C22×D3—62no—
206C22×D3—62no—
207C22×D3—61no—
208C22×D3—61no—
209C3×Q8—616no—
210C2×C3×C4—24no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—42no—
214C2×C3×C4—62no—
215C2×C3×C4—64no—
216C2×C3×C4—68no—
217C2×C3×C4—64no—
218C2×C3×C4—62no—
219C2×C3×C4—122no—
220C2×Dic3—22no—
221C2×Dic3—24no—
222C2×Dic3—28no—
223C2×Dic3—24no—
224C2×Dic3—22no—
225C2×Dic3—42no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—64no—
229C2×Dic3—122no—
230C4×D3—68no—
231C4×D3—64no—
232C4×D3—68no—
233C4×D3—64no—
234C4×D3—616no—
235C4×D3—68no—
236C4×D3—68no—
237C4×D3—68no—
238C4×D3—124no—
239C4×D3—124no—
240C4×D3—124no—
241C4×D3—124no—
242Dic6—216no—
243Dic6—632no—
244C2×C32#39514yescomplemented
245C2×C32C2×#12011yescharacteristic
246C2×C32C2×C22⋊Q811yescharacteristic
247C2×C32C2×C4⋊Q811yescharacteristic
248C3⋊D3#39514yescomplemented
249C3⋊D3C2×C22⋊Q812yes—
250C3⋊D3C2×C4⋊Q812yes—
251C24—91no—
252C2×Q8—68no—
253C2×Q8—64no—
254C2×Q8—184no—
255C2×Q8—188no—
256C2×Q8—1816no—
257C2×Q8—1816no—
258C22×C4—61no—
259C22×C4—62no—
260C22×C4—61no—
261C22×C4—92no—
262C22×C4—94no—
263C22×C4—98no—
264C22×C4—94no—
265C22×C4—92no—
266C22×C4—98no—
267C22×C4—94no—
268C22×C4—91no—
269C22×C4—92no—
270C22×C4—92no—
271C22×C4—184no—
272C22×C4—181no—
273C22×C4—182no—
274C22×C4—184no—
275C22×C4—182no—
276C22×C4—181no—
277C22×C4—184no—
278C22×C4—184no—
279C22×C4—184no—
280C22×C4GO+(4,𝔽2)11yescharacteristic
281C4⋊C4—64no—
282C4⋊C4—184no—
283C4⋊C4—1816no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—22no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—62no—
295C2×D3—61no—
296C2×D3—61no—
297C2×D3—62no—
298C2×D3—62no—
299C2×D3—68no—
300C2×D3—68no—
301C2×D3—62no—
302C2×D3—68no—
303C2×D3—68no—
304C2×D3—62no—
305C2×D3—62no—
306C2×D3—61no—
307C2×D3—62no—
308C2×D3—62no—
309C2×D3—61no—
310C3×C4—24no—
311C3×C4—42no—
312C3×C4—68no—
313C3×C4—64no—
314C3×C4—122no—
315Dic3—28no—
316Dic3—24no—
317Dic3—42no—
318Dic3—64no—
319Dic3—122no—
320C32C2×#39511yescharacteristic, complemented, Sylow
321C23—91no—
322C23—91no—
323C23—92no—
324C23—92no—
325C23—94no—
326C23—94no—
327C23C2×GO+(4,𝔽2)11yescharacteristic
328Q8—616no—
329Q8—1816no—
330C2×C4—22no—
331C2×C4—62no—
332C2×C4—64no—
333C2×C4—64no—
334C2×C4—68no—
335C2×C4—62no—
336C2×C4—98no—
337C2×C4—94no—
338C2×C4—98no—
339C2×C4—92no—
340C2×C4—122no—
341C2×C4—184no—
342C2×C4—184no—
343C2×C4—184no—
344C2×C4—188no—
345C2×C4—182no—
346C2×C4—184no—
347C2×C4—184no—
348C2×C4—184no—
349C2×C4—1816no—
350C2×C4—184no—
351C2×C4—182no—
352C2×C4—362no—
353C2×C4C2×GO+(4,𝔽2)12yes—
354C2×C3—24no—
355C2×C3—24no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362D3—62no—
363D3—62no—
364D3—62no—
365D3—62no—
366D3—64no—
367D3—64no—
368C22—98no—
369C22—98no—
370C22—91no—
371C22—91no—
372C22—92no—
373C22—92no—
374C22—92no—
375C22—92no—
376C22—92no—
377C22D32⋊Q812yes—
378C22#6422212yes—
379C22#6424112yes—
380C22C22×GO+(4,𝔽2)11yescharacteristic
381C4—22no—
382C4—64no—
383C4—68no—
384C4—122no—
385C4—188no—
386C4—182no—
387C3—21no—
388C3—21no—
389C2—92no—
390C2—94no—
391C2—92no—
392C2#1059341114yesdirect product factor
393C2C2×D32⋊Q811yescharacteristic
394C2C2×#6422211yescharacteristic
395C2C2×#6424111yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊D3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#395
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #10593411C2direct (N × H)
30. C22×#157Q8semidirect
51. C2×#624Q8semidirect
88. C2×#157C2×Q8semidirect
110. #624C2×Q8semidirect
244. C2×C32#395semidirect
248. C3⋊D3#395semidirect
320. C32C2×#395semidirect
392. C2#10593411direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×#37732
C2×#638832
C2×#637812
C2×#637372
#105934112
C2×#3959