Finite Group Databasebeta

← #11785334

Subgroups — #11785334

Order 1152.

564 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×#3805C211yesmaximal, characteristic
2#10593805C211yesmaximal, characteristic, complemented
3C2×#63741C212yesmaximal
4#10591257C211yesmaximal, characteristic, complemented
5#10590074C212yesmaximal, complemented
6C2×#3805C2211yescharacteristic
7C2×#3792C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×C4×#67—21no—
10#67⋊Dic3—21no—
11C2×#3724—21no—
12#63957C2211yescharacteristic
13C2×Dic32C2212yes—
14C4×#627C411yescharacteristic, complemented
15#63902C411yescharacteristic, complemented
16C4×#625C411yescharacteristic, complemented
17#63878—21no—
18C4×D3×Dic3—21no—
19#63838C411yescharacteristic, complemented
20#63779—21no—
21C4⋊#622—21no—
22#63741—24no—
23C3×C3⋊#95—21no—
24C4×#237—61no—
25#4649—61no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C2×C3×#67—21no—
30C22×C3×Dic3—22no—
31C2×C3×C4×D3—21no—
32C2×#627C2×C411yescharacteristic
33C2×#625C2×C411yescharacteristic
34#3805—21no—
35#3805—21no—
36#3805D412yes—
37#3805Q812yes—
38C2×D3×Dic3—21no—
39C2×D3×Dic3—21no—
40#3792—22no—
41#3792—22no—
42C2×#622—22no—
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C3×#217—21no—
48C3×(C2×D3)⋊C4—21no—
49C3×Dic3⋊C4—21no—
50C3×C4×Dic3—21no—
51#3724—24no—
52#3724C2×C411yescharacteristic
53#3724C2×C411yescharacteristic
54Dic3⋊Dic3—21no—
55(C2×D3)⋊Dic3—21no—
56Dic32—21no—
57Dic32—21no—
58Dic32—22no—
59Dic32—22no—
60#1806—91nomaximal, Sylow
61C2×#237—61no—
62C3×C4×D4—61no—
63D4×Dic3—61no—
64C4×#67—21no—
65C4×#67—61no—
66C2×Dic3⋊C4—62no—
67C2×C4×Dic3—61no—
68C2×C4×Dic3—61no—
69C2×C4×Dic3—62no—
70C2×C4×Dic3—61no—
71#892—61no—
72#887—61no—
73#67⋊C4—61no—
74#67⋊C4—61no—
75#877—61no—
76#877—61no—
77C42×D3—61no—
78C4×Dic6—61no—
79C3×#95—61no—
80C3⋊#95—21no—
81C23×C32C2×D411yescharacteristic
82C22×C3×D3—21no—
83C2×C32×C4—41no—
84C2×C32×C4C22⋊C411yescharacteristic
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3C22⋊C411yescharacteristic
89C2×C3⋊Dic3C22×C411yescharacteristic
90C2×C3⋊Dic3C2×D411yescharacteristic
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3C2×Q811yescharacteristic
93C2×C3⋊Dic3#4111yescharacteristic
94C2×C3⋊Dic3#4111yescharacteristic
95C3×#67—22no—
96C3×#67—22no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—21no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—42no—
103C3×C4×D3—42no—
104#627—21no—
105#627C4⋊C412yescomplemented
106#625—21no—
107#625C4⋊C412yescomplemented
108D3×Dic3—22no—
109D3×Dic3—22no—
110D3×Dic3—42no—
111#622—42no—
112C4×#41—91no—
113#423—91no—
114C2×#104—92no—
115C4×C4⋊C4—91no—
116#339—92no—
117C2×C3×D4—61no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—61no—
121C22×C3×C4—62no—
122C2×#67—21no—
123C2×#67—61no—
124C22×Dic3—22no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131#237—62no—
132#237—62no—
133#237—62no—
134#237—62no—
135C2×C4×D3—21no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×Dic6—61no—
139C3×C4⋊C4—61no—
140C3×C22⋊C4—61no—
141C3×C22⋊C4—61no—
142C3×C42—61no—
143#217—21no—
144#217—61no—
145(C2×D3)⋊C4—21no—
146(C2×D3)⋊C4—61no—
147C4⋊Dic3—61no—
148Dic3⋊C4—21no—
149Dic3⋊C4—61no—
150Dic3⋊C4—61no—
151Dic3⋊C4—61no—
152Dic3⋊C4—68no—
153C4×Dic3—21no—
154C4×Dic3—61no—
155C4×Dic3—61no—
156C4×Dic3—61no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—61no—
161C4×Dic3—61no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—122no—
167C4×Dic3—122no—
168C22×C32—21no—
169C22×C32—21no—
170C22×C32C2×C22⋊C411yescharacteristic
171C22×C32#12111yescharacteristic
172C22×C32C22⋊Q811yescharacteristic
173C2×C3×D3—22no—
174C2×C3×D3—41no—
175C2×C3×D3—41no—
176C32×C4—21no—
177C32×C4—21no—
178C3⋊Dic3—21no—
179C3⋊Dic3#10412yescomplemented
180C3⋊Dic3C2×C4⋊C411yescharacteristic
181C3⋊Dic3#11711yescharacteristic
182C3⋊Dic3#12111yescharacteristic
183C3⋊Dic3C22⋊Q811yescharacteristic
184C3×Dic3—22no—
185C3×Dic3—44no—
186C3×Dic3—41no—
187C3×Dic3—41no—
188C2×#41—91no—
189C2×M16—92no—
190C4×Q8—91no—
191C4×Q8—91no—
192C4×D4—61no—
193C4×D4—91no—
194C4×D4—91no—
195C4×D4—181no—
196#117—91no—
197#117—181no—
198C2×C4⋊C4—181no—
199C2×C42—91no—
200C2×C42—92no—
201C2×C42—181no—
202C4⋊C8—181no—
203C4⋊C8—181no—
204#104—184no—
205#95—61no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—61no—
209C22×D3—21no—
210C3×D4—62no—
211C3×D4—62no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—42no—
217C2×C3×C4—42no—
218C2×C3×C4—61no—
219C2×C3×C4—61no—
220C2×C3×C4—61no—
221C2×C3×C4—64no—
222C2×C3×C4—122no—
223C2×C3×C4—122no—
224C2×C3×C4—122no—
225#67—22no—
226#67—22no—
227#67—62no—
228#67—62no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—24no—
233C2×Dic3—42no—
234C2×Dic3—42no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—64no—
254C2×Dic3—122no—
255C2×Dic3—122no—
256C4×D3—42no—
257C4×D3—62no—
258C4×D3—62no—
259C4×D3—122no—
260Dic6—62no—
261Dic6—62no—
262C2×C32—21no—
263C2×C32—21no—
264C2×C32#38011yescharacteristic
265C2×C32C2×#10411yescharacteristic
266C2×C32#42111yescharacteristic
267C3×D3—42no—
268#41—92no—
269#41—92no—
270#41—181no—
271#41—181no—
272C2×Q8—91no—
273C2×D4—61no—
274C2×D4—91no—
275C22×C4—62no—
276C22×C4—61no—
277C22×C4—91no—
278C22×C4—91no—
279C22×C4—181no—
280C22×C4—181no—
281C22×C4GO+(4,𝔽2)11yescharacteristic
282M16—182no—
283M16—182no—
284C2×C8—182no—
285C4⋊C4—61no—
286C4⋊C4—91no—
287C4⋊C4—91no—
288C4⋊C4—181no—
289C4⋊C4—184no—
290C22⋊C4—61no—
291C22⋊C4—61no—
292C22⋊C4—181no—
293C42—61no—
294C42—91no—
295C42—91no—
296C42—91no—
297C42—91no—
298C42—181no—
299C42—181no—
300C42—182no—
301C42—182no—
302C22×C3—22no—
303C22×C3—22no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—62no—
313C22×C3—121no—
314C22×C3—121no—
315C2×D3—22no—
316C2×D3—41no—
317C2×D3—41no—
318C3×C4—22no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—62no—
323C3×C4—121no—
324C3×C4—124no—
325C3×C4—121no—
326Dic3—22no—
327Dic3—41no—
328Dic3—44no—
329Dic3—41no—
330Dic3—61no—
331Dic3—61no—
332Dic3—61no—
333Dic3—61no—
334Dic3—62no—
335Dic3—62no—
336Dic3—61no—
337Dic3—61no—
338Dic3—61no—
339Dic3—61no—
340Dic3—62no—
341Dic3—121no—
342C32#180611yescharacteristic, complemented, Sylow
343C23—61no—
344C23C2×GO+(4,𝔽2)11yescharacteristic
345Q8—92no—
346Q8—181no—
347D4—62no—
348D4—62no—
349D4—92no—
350D4—181no—
351C2×C4—41no—
352C2×C4—61no—
353C2×C4—64no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—91no—
357C2×C4—91no—
358C2×C4—91no—
359C2×C4—91no—
360C2×C4—91no—
361C2×C4—91no—
362C2×C4—91no—
363C2×C4—91no—
364C2×C4—122no—
365C2×C4—122no—
366C2×C4—122no—
367C2×C4—182no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4—362no—
371C2×C4D32⋊C411yescharacteristic
372C2×C4D32⋊C411yescharacteristic
373C8—362no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—41no—
383C2×C3—41no—
384C2×C3—122no—
385D3—42no—
386C22—21no—
387C22—21no—
388C22—62no—
389C22—121no—
390C22—121no—
391C22D32⋊Q811yescharacteristic
392C22#6423011yescharacteristic
393C22C2×D32⋊C411yescharacteristic
394C4—21no—
395C4—21no—
396C4—62no—
397C4—92no—
398C4—91no—
399C4—91no—
400C4—91no—
401C4—91no—
402C4—124no—
403C4—121no—
404C4—121no—
405C4—181no—
406C3—21no—
407C3—21no—
408C2—21no—
409C2—21no—
410C2—122no—
411C2#1059338011yescharacteristic
412C2#1059340311yescharacteristic
413C2#1059350611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3805C22
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1806
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593805C2semidirect
4. #10591257C2semidirect
5. #10590074C2semidirect
14. C4×#627C4semidirect
15. #63902C4semidirect
16. C4×#625C4semidirect
19. #63838C4semidirect
105. #627C4⋊C4semidirect
107. #625C4⋊C4semidirect
179. C3⋊Dic3#104semidirect
342. C32#1806semidirect

Maximal subgroups

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

subgroupindex
C4×#38052
#105938052
C2×#637412
#105912572
#105900742
#18069