Finite Group Databasebeta

← #11775586

Subgroups — #11775586

Order 1152.

670 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#10595081C211yesmaximal, characteristic
2#10593800C211yesmaximal, characteristic, complemented
3#10591325C211yesmaximal, characteristic, complemented
4#10590071C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3811—21no—
7C2×#3802C411yescharacteristic, complemented
8C2×#3787—21no—
9C3×#930—21no—
10C2×C3×C4⋊Dic3—21no—
11#63980C2212yes—
12C2×#3722—21no—
13#63921—21no—
14#63916—21no—
15#63912C412yescomplemented
16#63900C411yescharacteristic, complemented
17C22⋊#622C2212yescomplemented
18#63778—21no—
19#63579C2212yescomplemented
20D3×#121—61no—
21#4987—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×D32—21no—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×C4×C3⋊D3—42no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C3×#67—22no—
32C22×C3×Dic3—22no—
33C2×C3×D12—21no—
34#3811—42no—
35#3811—42no—
36C2×#626—22no—
37C2×#625C2×C412yes—
38C2×#624—21no—
39#3802—42no—
40C2×#622—22no—
41#3787—42no—
42C3×(C2×D3)⋊C4—22no—
43C3×C4⋊Dic3—21no—
44C3×C4⋊Dic3—42no—
45#3724C2×C412yes—
46#3722—42no—
47(C2×D3)⋊Dic3—22no—
48#1519—91nomaximal, Sylow
49C2×D3×D4—61no—
50C2×D3×D4—62no—
51C22×C4×D3—61no—
52C22×C4×D3—61no—
53C3×#121—61no—
54C2×C3×C4⋊C4—61no—
55#939—62no—
56#938—61no—
57#930—21no—
58C2×(C2×D3)⋊C4—62no—
59C2×C4⋊Dic3—21no—
60#895—61no—
61D3×C4⋊C4—61no—
62#884—62no—
63D3×C22⋊C4—62no—
64C3⋊#95—62no—
65C23×C32C2×D411yescharacteristic
66C22×C3⋊D3—41no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3C22⋊C411yescharacteristic
69C22×C3⋊D3C22⋊C411yescharacteristic
70C22×C3⋊D3D812yes—
71C22×C3⋊D3SD1612yes—
72C22×C3×D3—22no—
73C2×D32—42no—
74C2×D32—42no—
75C2×D32—42no—
76C2×C32×C4—22no—
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3C22×C411yescharacteristic
81C2×C3⋊Dic3C2×D411yescharacteristic
82C4×C3⋊D3—22no—
83C4×C3⋊D3—22no—
84C4×C3⋊D3—41no—
85C4×C3⋊D3—41no—
86C3×#67—42no—
87C3×#67—42no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91C2×C3×Dic3—42no—
92C3×D12—42no—
93#626—44no—
94#625—42no—
95#624—42no—
96#622—42no—
97C2×#121—91no—
98C2×C22⋊C8—91no—
99#380—91no—
100#327—94no—
101C23×D3—61no—
102C23×D3—61no—
103C23×D3—62no—
104C2×C3×D4—61no—
105C2×C3×D4—62no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—62no—
109C2×#67—22no—
110C2×#67—62no—
111C2×#67—62no—
112C22×Dic3—22no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115D3×D4—124no—
116D3×D4—124no—
117D3×D4—124no—
118C2×D12—21no—
119C2×D12—62no—
120C2×C4×D3—61no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C4×D3—62no—
129C2×C4×D3—124no—
130C2×C4×D3—122no—
131C2×C4×D3—122no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—122no—
134C3×C22⋊C4—62no—
135#217—62no—
136(C2×D3)⋊C4—22no—
137(C2×D3)⋊C4—62no—
138(C2×D3)⋊C4—124no—
139C4⋊Dic3—21no—
140C4⋊Dic3—42no—
141Dic3⋊C4—62no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32C2×C22⋊C411yescharacteristic
145C22×C32C2×D811yescharacteristic
146C22×C32C2×SD1611yescharacteristic
147C2×C3⋊D3—21no—
148C2×C3⋊D3—21no—
149C2×C3⋊D3—21no—
150C2×C3⋊D3—21no—
151C2×C3⋊D3—42no—
152C2×C3⋊D3—42no—
153C2×C3⋊D3#10212yes—
154C2×C3⋊D3#10212yes—
155C2×C3×D3—42no—
156C2×C3×D3—42no—
157C2×C3×D3—42no—
158D32—84no—
159C32×C4—21no—
160C32×C4#9912yes—
161C3⋊Dic3—21no—
162C3⋊Dic3—21no—
163C3×Dic3—42no—
164C3×Dic3—82no—
165C22×D4—91no—
166C22×D4—181no—
167C23×C4—91no—
168C22×C8—181no—
169#121—61no—
170#121—92no—
171#121—92no—
172#121—181no—
173C2×C4⋊C4—61no—
174C2×C4⋊C4—91no—
175C2×C22⋊C4—181no—
176C2×C22⋊C4—181no—
177C22⋊C8—92no—
178C22⋊C8—181no—
179#95—92no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—62no—
183C22×D3—22no—
184C22×D3—61no—
185C22×D3—61no—
186C22×D3—61no—
187C22×D3—61no—
188C22×D3—62no—
189C22×D3—62no—
190C22×D3—62no—
191C22×D3—62no—
192C22×D3—124no—
193C22×D3—124no—
194C22×D3—124no—
195C22×D3—122no—
196C22×D3—122no—
197C22×D3—121no—
198C22×D3—121no—
199C22×D3—121no—
200C22×D3—121no—
201C3×D4—122no—
202C3×D4—122no—
203C3×D4—122no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—42no—
211C2×C3×C4—62no—
212C2×C3×C4—122no—
213C2×C3×C4—122no—
214C2×C3×C4—122no—
215#67—42no—
216#67—42no—
217#67—124no—
218#67—124no—
219C2×Dic3—22no—
220C2×Dic3—42no—
221C2×Dic3—42no—
222C2×Dic3—42no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—122no—
228C2×Dic3—121no—
229C2×Dic3—121no—
230D12—42no—
231D12—124no—
232C4×D3—64no—
233C4×D3—122no—
234C4×D3—122no—
235C4×D3—122no—
236C4×D3—124no—
237C4×D3—122no—
238C4×D3—122no—
239C4×D3—122no—
240C4×D3—122no—
241C2×C32—21no—
242C2×C32—21no—
243C2×C32C2×#9911yescharacteristic
244C2×C32C2×#10211yescharacteristic
245C2×C32#42111yescharacteristic
246C3⋊D3—22no—
247C3⋊D3—22no—
248C3×D3—82no—
249C24—91no—
250C24—181no—
251C2×D4—62no—
252C2×D4—61no—
253C2×D4—92no—
254C2×D4—182no—
255C2×D4—362no—
256C2×D4—362no—
257C2×D4—362no—
258C22×C4—62no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—181no—
265C22×C4—362no—
266C22×C4GO+(4,𝔽2)11yescharacteristic
267C2×C8—182no—
268C2×C8—362no—
269C4⋊C4—61no—
270C4⋊C4—92no—
271C4⋊C4—122no—
272C22⋊C4—62no—
273C22⋊C4—182no—
274C22⋊C4—362no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—122no—
288C22×C3—122no—
289C22×C3—122no—
290C2×D3—42no—
291C2×D3—42no—
292C2×D3—42no—
293C2×D3—62no—
294C2×D3—62no—
295C2×D3—62no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—62no—
299C2×D3—121no—
300C2×D3—121no—
301C2×D3—121no—
302C2×D3—121no—
303C2×D3—121no—
304C2×D3—121no—
305C2×D3—124no—
306C2×D3—124no—
307C2×D3—122no—
308C2×D3—122no—
309C2×D3—122no—
310C2×D3—122no—
311C2×D3—248no—
312C3×C4—22no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—41no—
316C3×C4—122no—
317C3×C4—242no—
318Dic3—42no—
319Dic3—62no—
320Dic3—82no—
321Dic3—121no—
322Dic3—121no—
323Dic3—121no—
324C32#151911yescharacteristic, complemented, Sylow
325C23—62no—
326C23—91no—
327C23—91no—
328C23—92no—
329C23—92no—
330C23—361no—
331C23—361no—
332C23—362no—
333C23—362no—
334C23—362no—
335C23C2×GO+(4,𝔽2)11yescharacteristic
336D4—122no—
337D4—122no—
338D4—122no—
339D4—364no—
340D4—362no—
341C2×C4—22no—
342C2×C4—62no—
343C2×C4—91no—
344C2×C4—91no—
345C2×C4—122no—
346C2×C4—122no—
347C2×C4—122no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—361no—
351C2×C4—361no—
352C2×C4—362no—
353C2×C4—361no—
354C2×C4D32⋊C411yescharacteristic
355C2×C4D32⋊C411yescharacteristic
356C8—362no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—41no—
368C2×C3—41no—
369C2×C3—242no—
370D3—64no—
371D3—82no—
372D3—122no—
373D3—122no—
374D3—122no—
375C22—21no—
376C22—21no—
377C22—92no—
378C22—92no—
379C22—122no—
380C22—122no—
381C22—122no—
382C22—181no—
383C22—181no—
384C22—181no—
385C22—181no—
386C22—362no—
387C22—362no—
388C22—724no—
389C22#6422511yescharacteristic
390C22#6422711yescharacteristic
391C22C2×D32⋊C411yescharacteristic
392C4—21no—
393C4—122no—
394C4—181no—
395C4—181no—
396C4—242no—
397C4#6373812yes—
398C3—21no—
399C3—21no—
400C2—21no—
401C2—21no—
402C2—182no—
403C2—182no—
404C2—242no—
405C2#1059336511yescharacteristic
406C2#1059338111yescharacteristic
407C2C2×#6373811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595081C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1519
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593800C2semidirect
3. #10591325C2semidirect
4. #10590071C2semidirect
7. C2×#3802C4semidirect
15. #63912C4semidirect
16. #63900C4semidirect
17. C22⋊#622C22semidirect
19. #63579C22semidirect
324. C32#1519semidirect

Maximal subgroups

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

subgroupindex
#105950812
#105938002
#105913252
#105900712
#15199