Finite Group Databasebeta

← #11775587

Subgroups — #11775587

Order 1152.

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

normal subgroups only

This group has 670 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
1C2×#63980C211yesmaximal, characteristic
2C2×C22⋊#622C211yesmaximal, characteristic, complemented
3#10591720C211yesmaximal, characteristic, complemented
4#10590071C214yesmaximal, complemented
5C23×C3⋊Dic3C2211yescharacteristic
6C22×C3×#67—21no—
7C22×#625C411yescharacteristic, complemented
8C22×#622—21no—
9C2×C3×#217—21no—
10#63980—21no—
11#63980—21no—
12#63980C412yescomplemented
13#63980C2212yes—
14C2×#3724—21no—
15C2×#3724C411yescharacteristic, complemented
16C2×(C2×D3)⋊Dic3—21no—
17C22⋊#622—21no—
18C22⋊#622C2212yescomplemented
19#63579C2212yescomplemented
20C2×#939—61no—
21#4942—61no—
22C24×C32D411yescharacteristic
23C23×C3×D3—21no—
24C22×C3⋊Dic3—42no—
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C2×C3×#67—22no—
32C2×C3×#67—22no—
33C2×C3×#67—42no—
34C2×C3×#67—42no—
35C22×C3×Dic3—21no—
36C22×C3×Dic3—22no—
37C2×#625—21no—
38C2×#625—42no—
39C2×#625C2×C412yes—
40C2×#622—22no—
41C2×#622—42no—
42C3×#217—42no—
43#3724—21no—
44#3724—42no—
45#3724C2×C412yes—
46(C2×D3)⋊Dic3—22no—
47(C2×D3)⋊Dic3—22no—
48#1519—91nomaximal, Sylow
49C22×C3×D4—61no—
50C22×#67—21no—
51C22×#67—61no—
52C23×Dic3—61no—
53C23×Dic3—61no—
54C2×C3×C22⋊C4—61no—
55C2×#217—21no—
56C2×#217—61no—
57#939—62no—
58#939—62no—
59#939—62no—
60#939—62no—
61C2×(C2×D3)⋊C4—61no—
62C2×Dic3⋊C4—61no—
63C2×Dic3⋊C4—62no—
64C3⋊#95—62no—
65C23×C32—41no—
66C23×C32—41no—
67C23×C32C22⋊C411yescharacteristic
68C23×C32C22⋊C411yescharacteristic
69C23×C32D812yes—
70C23×C32SD1612yes—
71C23×C32C2×D411yescharacteristic
72C22×C3×D3—22no—
73C22×C3×D3—42no—
74C22×C3×D3—42no—
75C22×C3×D3—42no—
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22×C411yescharacteristic
85C2×C3⋊Dic3C2×D411yescharacteristic
86C3×#67—44no—
87C3×#67—42no—
88C3×#67—42no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—42no—
94#625—42no—
95#625—42no—
96#622—42no—
97C2×#121—91no—
98C2×C22⋊C8—91no—
99#380—91no—
100#327—94no—
101C24×C3—21no—
102C24×C3—21no—
103C24×C3—61no—
104C23×D3—21no—
105C2×C3×D4—62no—
106C2×C3×D4—62no—
107C2×C3×D4—122no—
108C2×C3×D4—122no—
109C22×C3×C4—61no—
110C22×C3×C4—62no—
111C2×#67—22no—
112C2×#67—22no—
113C2×#67—42no—
114C2×#67—42no—
115C2×#67—62no—
116C2×#67—62no—
117C2×#67—124no—
118C22×Dic3—21no—
119C22×Dic3—22no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C22×Dic3—61no—
132C22×Dic3—124no—
133C22×Dic3—124no—
134C3×C22⋊C4—122no—
135#217—42no—
136#217—62no—
137#217—62no—
138(C2×D3)⋊C4—62no—
139(C2×D3)⋊C4—62no—
140Dic3⋊C4—62no—
141Dic3⋊C4—62no—
142Dic3⋊C4—124no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32—21no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32—21no—
149C22×C32—42no—
150C22×C32—42no—
151C22×C32#10212yes—
152C22×C32#10212yes—
153C22×C32C2×C22⋊C411yescharacteristic
154C22×C32C2×D811yescharacteristic
155C22×C32C2×SD1611yescharacteristic
156C2×C3×D3—42no—
157C2×C3×D3—42no—
158C2×C3×D3—42no—
159C2×C3×D3—84no—
160C3⋊Dic3—21no—
161C3⋊Dic3—21no—
162C3⋊Dic3—21no—
163C3⋊Dic3#9912yes—
164C3×Dic3—42no—
165C3×Dic3—82no—
166C22×D4—61no—
167C22×D4—91no—
168C23×C4—91no—
169C22×C8—181no—
170#121—92no—
171#121—92no—
172#121—181no—
173#121—181no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4—181no—
176C2×C22⋊C4—61no—
177C2×C22⋊C4—181no—
178C22⋊C8—92no—
179C22⋊C8—181no—
180#95—92no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—22no—
188C23×C3—22no—
189C23×C3—22no—
190C23×C3—22no—
191C23×C3—42no—
192C23×C3—42no—
193C23×C3—42no—
194C23×C3—42no—
195C23×C3—62no—
196C23×C3—122no—
197C23×C3—122no—
198C23×C3—122no—
199C22×D3—22no—
200C22×D3—42no—
201C22×D3—42no—
202C22×D3—42no—
203C3×D4—122no—
204C3×D4—122no—
205C3×D4—124no—
206C2×C3×C4—62no—
207C2×C3×C4—122no—
208C2×C3×C4—122no—
209C2×C3×C4—122no—
210C2×C3×C4—122no—
211#67—42no—
212#67—42no—
213#67—44no—
214#67—124no—
215#67—124no—
216C2×Dic3—22no—
217C2×Dic3—42no—
218C2×Dic3—42no—
219C2×Dic3—42no—
220C2×Dic3—42no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—64no—
230C2×Dic3—64no—
231C2×Dic3—122no—
232C2×Dic3—122no—
233C2×Dic3—122no—
234C2×Dic3—122no—
235C2×Dic3—122no—
236C2×Dic3—122no—
237C2×Dic3—122no—
238C2×Dic3—122no—
239C2×Dic3—122no—
240C2×Dic3—122no—
241C2×C32—21no—
242C2×C32—22no—
243C2×C32—21no—
244C2×C32—22no—
245C2×C32C2×#9911yescharacteristic
246C2×C32C2×#10211yescharacteristic
247C2×C32#42111yescharacteristic
248C3×D3—82no—
249C24—61no—
250C24GO+(4,𝔽2)11yescharacteristic
251C2×D4—62no—
252C2×D4—62no—
253C2×D4—92no—
254C2×D4—122no—
255C2×D4—122no—
256C2×D4—181no—
257C2×D4—362no—
258C22×C4—61no—
259C22×C4—62no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—362no—
267C2×C8—182no—
268C2×C8—362no—
269C4⋊C4—92no—
270C4⋊C4—181no—
271C4⋊C4—362no—
272C22⋊C4—122no—
273C22⋊C4—182no—
274C22⋊C4—182no—
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—44no—
298C22×C3—44no—
299C22×C3—44no—
300C22×C3—44no—
301C22×C3—122no—
302C22×C3—122no—
303C22×C3—122no—
304C22×C3—244no—
305C2×D3—42no—
306C2×D3—42no—
307C2×D3—42no—
308C2×D3—84no—
309C3×C4—122no—
310C3×C4—242no—
311Dic3—42no—
312Dic3—62no—
313Dic3—62no—
314Dic3—62no—
315Dic3—62no—
316Dic3—82no—
317Dic3—121no—
318Dic3—121no—
319Dic3—121no—
320Dic3—121no—
321C32#151911yescharacteristic, complemented, Sylow
322C23—41no—
323C23—41no—
324C23—62no—
325C23—122no—
326C23—122no—
327C23—122no—
328C23D32⋊C411yescharacteristic
329C23D32⋊C411yescharacteristic
330C23#377412yes—
331C23#377512yes—
332C23C2×GO+(4,𝔽2)11yescharacteristic
333D4—122no—
334D4—122no—
335D4—124no—
336D4—362no—
337D4—362no—
338C2×C4—62no—
339C2×C4—91no—
340C2×C4—91no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—122no—
344C2×C4—122no—
345C2×C4—122no—
346C2×C4—122no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—361no—
351C2×C4—361no—
352C2×C4—361no—
353C8—362no—
354C2×C3—22no—
355C2×C3—24no—
356C2×C3—22no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—41no—
364C2×C3—42no—
365C2×C3—41no—
366C2×C3—42no—
367C2×C3—42no—
368C2×C3—242no—
369D3—82no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—42no—
377C22—42no—
378C22—122no—
379C22—122no—
380C22—122no—
381C22—244no—
382C22#6373912yes—
383C22#6373912yes—
384C22C2×D32⋊C411yescharacteristic
385C22C2×#377411yescharacteristic
386C22C2×#377511yescharacteristic
387C4—92no—
388C4—122no—
389C4—181no—
390C4—181no—
391C4—181no—
392C4—242no—
393C3—21no—
394C3—21no—
395C2—21no—
396C2—22no—
397C2—21no—
398C2—22no—
399C2—242no—
400C2#1059349011yescharacteristic
401C2C2×#6373911yescharacteristic
402C2#1059350611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC24×C32D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#63980C2
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1519
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#622C2semidirect
3. #10591720C2semidirect
4. #10590071C2semidirect
7. C22×#625C4semidirect
12. #63980C4semidirect
15. C2×#3724C4semidirect
18. C22⋊#622C22semidirect
19. #63579C22semidirect
321. C32#1519semidirect

Maximal subgroups

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

subgroupindex
C2×#639802
C2×C22⋊#6222
#105917202
#105900712
#15199