Finite Group Databasebeta

← C2×#10593494 #11869469

Subgroups — C2×#10593494 #11869469

Order 1152.

846 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#63980C211yesmaximal, characteristic
2C2×#63957C211yesmaximal, characteristic, complemented
3C2×C22⋊#622C211yesmaximal, characteristic, complemented
4C2×#63743C211yesmaximal, characteristic, complemented
5C2×#63742C211yesmaximal, characteristic, complemented
6#10593494C218yesmaximal, direct product factor
7C2×#63739C211yesmaximal, characteristic, complemented
8C2×#63739C211yesmaximal, characteristic, complemented
9C23×C3⋊Dic3C2211yescharacteristic
10C22×C3×#67—21no—
11C22×#625C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C22×#622C2211yescharacteristic
14C2×C3×#217—21no—
15#63980—22no—
16#63980C2214yes—
17C2×#3724C2211yescharacteristic
18C2×#3724C2211yescharacteristic
19C2×#3724C2211yescharacteristic
20C2×(C2×D3)⋊Dic3—21no—
21#63957—22no—
22#63957C2214yescomplemented
23C2×Dic32—21no—
24C22⋊#622C2214yescomplemented
25#63743C2214yescomplemented
26#63742C2214yescomplemented
27#63739C2214yescomplemented
28#63739C2214yescomplemented
29C2×#939—61no—
30C2×#877—61no—
31C24×C32D411yescharacteristic
32C23×C3×D3—21no—
33C22×C3⋊Dic3—22no—
34C22×C3⋊Dic3—22no—
35C22×C3⋊Dic3D411yescharacteristic
36C22×C3⋊Dic3D412yes—
37C22×C3⋊Dic3C2312yes—
38C22×C3⋊Dic3C2311yescharacteristic
39C2×C3×#67—24no—
40C2×C3×#67—44no—
41C22×C3×Dic3—21no—
42C22×C3×Dic3—21no—
43C22×C3×Dic3—21no—
44C2×#625—22no—
45C2×#625—22no—
46C2×#625—21no—
47C2×#625C2312yes—
48C2×#622—22no—
49C2×#622—22no—
50C2×#622C2312yes—
51C2×#622C2312yes—
52C3×#217—24no—
53#3724—21no—
54#3724—21no—
55#3724—21no—
56#3724C2312yes—
57#3724C2312yes—
58#3724C2312yes—
59(C2×D3)⋊Dic3—24no—
60Dic32—24no—
61C2×#482—91nomaximal, Sylow
62C22×C3×D4—61no—
63C22×#67—21no—
64C22×#67—61no—
65C23×Dic3—61no—
66C23×Dic3—61no—
67C2×C3×C22⋊C4—61no—
68C2×#217—21no—
69C2×#217—61no—
70#939—64no—
71#939—64no—
72C2×(C2×D3)⋊C4—61no—
73C2×Dic3⋊C4—61no—
74C2×Dic3⋊C4—61no—
75C2×Dic3⋊C4—61no—
76C2×C4×Dic3—61no—
77C2×C4×Dic3—61no—
78#877—64no—
79#877—64no—
80C23×C32—22no—
81C23×C32—22no—
82C23×C32—22no—
83C23×C32C2×D412yes—
84C23×C32C2×D411yescharacteristic
85C22×C3×D3—22no—
86C22×C3×D3—42no—
87C22×C3×D3—42no—
88C22×C3×D3—42no—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—24no—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3C2×D412yes—
94C2×C3⋊Dic3C2×D411yescharacteristic
95C2×C3⋊Dic3#4112yes—
96C2×C3⋊Dic3#4112yes—
97C2×C3⋊Dic3C2411yescharacteristic
98C3×#67—48no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—42no—
103C2×C3×Dic3—42no—
104C2×C3×Dic3—42no—
105#625—22no—
106#625—22no—
107#625—42no—
108#622—22no—
109#622—22no—
110C2×#121—91no—
111C2×#117—91no—
112#482—98no—
113C2×#107—91no—
114C2×#106—91no—
115C2×#102—91no—
116C2×#102—91no—
117C2×C22⋊C8—91no—
118C24×C3—21no—
119C24×C3—21no—
120C24×C3—61no—
121C23×D3—21no—
122C2×C3×D4—64no—
123C2×C3×D4—124no—
124C22×C3×C4—61no—
125C22×C3×C4—61no—
126C22×C3×C4—61no—
127C2×#67—24no—
128C2×#67—44no—
129C2×#67—62no—
130C2×#67—62no—
131C2×#67—122no—
132C2×#67—122no—
133C22×Dic3—21no—
134C22×Dic3—21no—
135C22×Dic3—21no—
136C22×Dic3—62no—
137C22×Dic3—62no—
138C22×Dic3—61no—
139C22×Dic3—61no—
140C22×Dic3—61no—
141C22×Dic3—61no—
142C22×Dic3—62no—
143C22×Dic3—62no—
144C22×Dic3—64no—
145C22×Dic3—64no—
146C22×Dic3—122no—
147C22×Dic3—122no—
148C3×C22⋊C4—64no—
149#217—24no—
150#217—64no—
151(C2×D3)⋊C4—64no—
152Dic3⋊C4—62no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156Dic3⋊C4—62no—
157Dic3⋊C4—62no—
158C4×Dic3—64no—
159C4×Dic3—64no—
160C22×C32—22no—
161C22×C32—22no—
162C22×C32—22no—
163C22×C32—44no—
164C22×C32#12312yes—
165C22×C32#13512yes—
166C22×C32AGL(1,ℤ/8)12yes—
167C22×C32C22×D411yescharacteristic
168C2×C3×D3—42no—
169C2×C3×D3—42no—
170C2×C3×D3—42no—
171C2×C3×D3—84no—
172C3⋊Dic3—22no—
173C3⋊Dic3#12312yes—
174C3⋊Dic3C2×#4111yescharacteristic
175C3⋊Dic3C2×#4111yescharacteristic
176C3×Dic3—42no—
177C3×Dic3—42no—
178C3×Dic3—42no—
179C22×D4—61no—
180C22×D4—91no—
181C23×C4—91no—
182C22×C8—91no—
183C22×C8—91no—
184#121—94no—
185#121—182no—
186#117—94no—
187#117—182no—
188C2×C4⋊C4—91no—
189C2×C4⋊C4—91no—
190C2×C4⋊C4—91no—
191C2×C22⋊C4—61no—
192C2×C22⋊C4—181no—
193C2×C42—181no—
194#107—94no—
195#106—94no—
196#102—94no—
197#102—94no—
198C22⋊C8—94no—
199C23×C3—24no—
200C23×C3—24no—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—42no—
206C23×C3—42no—
207C23×C3—42no—
208C23×C3—42no—
209C23×C3—62no—
210C23×C3—122no—
211C23×C3—122no—
212C23×C3—122no—
213C22×D3—22no—
214C22×D3—42no—
215C22×D3—42no—
216C22×D3—42no—
217C3×D4—128no—
218C2×C3×C4—62no—
219C2×C3×C4—62no—
220C2×C3×C4—62no—
221C2×C3×C4—122no—
222C2×C3×C4—122no—
223C2×C3×C4—122no—
224#67—48no—
225#67—122no—
226#67—122no—
227#67—124no—
228C2×Dic3—22no—
229C2×Dic3—22no—
230C2×Dic3—22no—
231C2×Dic3—42no—
232C2×Dic3—42no—
233C2×Dic3—42no—
234C2×Dic3—62no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—62no—
244C2×Dic3—68no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—124no—
249C2×Dic3—122no—
250C2×Dic3—122no—
251C2×Dic3—122no—
252C2×C32—42no—
253C2×C32#48214yescomplemented
254C2×C32C2×#12311yescharacteristic
255C2×C32C2×#13511yescharacteristic
256C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
257C3×D3—82no—
258C24—61no—
259C24GO+(4,𝔽2)11yescharacteristic
260C2×D4—64no—
261C2×D4—92no—
262C2×D4—124no—
263C2×D4—182no—
264C2×D4—182no—
265C2×D4—181no—
266C22×C4—61no—
267C22×C4—61no—
268C22×C4—61no—
269C22×C4—91no—
270C22×C4—92no—
271C22×C4—92no—
272C22×C4—91no—
273C22×C4—182no—
274C22×C4—182no—
275C2×C8—92no—
276C2×C8—92no—
277C2×C8—182no—
278C2×C8—182no—
279C4⋊C4—92no—
280C4⋊C4—92no—
281C4⋊C4—92no—
282C4⋊C4—181no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C22⋊C4—64no—
286C22⋊C4—184no—
287C42—184no—
288C22×C3—24no—
289C22×C3—24no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—22no—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3—22no—
298C22×C3—42no—
299C22×C3—42no—
300C22×C3—42no—
301C22×C3—42no—
302C22×C3—48no—
303C22×C3—48no—
304C22×C3—122no—
305C22×C3—122no—
306C22×C3—122no—
307C22×C3—244no—
308C2×D3—42no—
309C2×D3—42no—
310C2×D3—42no—
311C2×D3—84no—
312C3×C4—122no—
313C3×C4—122no—
314C3×C4—122no—
315Dic3—42no—
316Dic3—42no—
317Dic3—42no—
318Dic3—62no—
319Dic3—61no—
320Dic3—61no—
321Dic3—62no—
322Dic3—61no—
323Dic3—61no—
324Dic3—64no—
325Dic3—122no—
326C32C2×#48211yescharacteristic, complemented, Sylow
327C23—22no—
328C23—22no—
329C23—22no—
330C23—62no—
331C23—122no—
332C23—122no—
333C23—122no—
334C23C2×GO+(4,𝔽2)12yes—
335C23C2×GO+(4,𝔽2)11yescharacteristic
336D4—128no—
337D4—182no—
338D4—182no—
339D4—362no—
340C2×C4—62no—
341C2×C4—62no—
342C2×C4—62no—
343C2×C4—91no—
344C2×C4—91no—
345C2×C4—92no—
346C2×C4—92no—
347C2×C4—92no—
348C2×C4—122no—
349C2×C4—122no—
350C2×C4—122no—
351C2×C4—182no—
352C2×C4—182no—
353C2×C4—184no—
354C2×C4—182no—
355C8—182no—
356C8—182no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—24no—
364C2×C3—24no—
365C2×C3—44no—
366C2×C3—44no—
367C2×C3—242no—
368D3—82no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—44no—
373C22—122no—
374C22—122no—
375C22—122no—
376C22—244no—
377C22#6423312yes—
378C22#6423612yes—
379C22#6423712yes—
380C22C22×GO+(4,𝔽2)11yescharacteristic
381C4—91no—
382C4—91no—
383C4—92no—
384C4—122no—
385C4—122no—
386C4—122no—
387C4—182no—
388C3—21no—
389C3—21no—
390C2—42no—
391C2—242no—
392C2#1059349414yesdirect product factor
393C2C2×#6423311yescharacteristic
394C2C2×#6423611yescharacteristic
395C2C2×#6423711yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC24×C32D4
socleC23×C32C2×D4
prime radicalC2×#63980C2
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×#482
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×#63957C2semidirect
3. C2×C22⋊#622C2semidirect
4. C2×#63743C2semidirect
5. C2×#63742C2semidirect
6. #10593494C2direct (N × H)
7. C2×#63739C2semidirect
8. C2×#63739C2semidirect
22. #63957C22semidirect
24. C22⋊#622C22semidirect
25. #63743C22semidirect
26. #63742C22semidirect
27. #63739C22semidirect
28. #63739C22semidirect
253. C2×C32#482semidirect
326. C32C2×#482semidirect
392. C2#10593494direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639802
C2×#639572
C2×C22⋊#6222
C2×#637432
C2×#637422
#105934942
C2×#637392
C2×#4829