Finite Group Databasebeta

← #11780298

Subgroups — #11780298

Order 1152.

517 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 517 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic6×D12C211yesmaximal, characteristic
2#10592379C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic
4#10590301C211yesmaximal, characteristic, complemented
5C3×#4459C211yesmaximal, characteristic
6C3×#4456C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#68251—31nomaximal
9#68210—31nomaximal
10C2×D3×Dic6—21no—
11#64078C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63918—21no—
16#63893—22no—
17Dic3×D12—21no—
18#63857—21no—
19C2×#3716—21no—
20C32×C4×C8C2211yescharacteristic
21#63644—22no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63573—21no—
25#63567—21no—
26#63566—21no—
27Q8×D12—31no—
28D4×Dic6—31no—
29#5020—31no—
30#5019—31no—
31#4851—31no—
32#4841—31no—
33#4680—31no—
34#4680—31no—
35#4680—61no—
36C3×Q8⋊C8—31no—
37C3×D4⋊C8—31no—
38#4486—31no—
39#4482—31no—
40#4459D311yescharacteristic
41#4456D311yescharacteristic, complemented
42C2×#634—21no—
43C2×#634—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×#627—22no—
48C2×D3×Dic3—22no—
49D3×Dic6—42no—
50D3×Dic6—42no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D412yes—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64Dic3⋊Dic3—22no—
65(C2×D3)⋊Dic3—22no—
66#3716—42no—
67#1651—91noSylow
68C2×D3×Q8—61no—
69C22×Dic6—61no—
70C3×C4×Q8—31no—
71C3×C4×D4—31no—
72D4×Dic3—61no—
73C2×#214—61no—
74#924—61no—
75C2×#204—61no—
76#897—62no—
77#897—61no—
78#888—61no—
79#878—62no—
80C4×D12—61no—
81C4×D12C2×D311yescharacteristic
82#869—31no—
83#869—31no—
84#869—31no—
85#869—31no—
86#869—61no—
87#869—61no—
88#869—61no—
89C4×Dic6C2×D311yescharacteristic
90C3×C4⋊C8—31no—
91C3×C4⋊C8—31no—
92C3×C4×C8—21no—
93C3×C4×C8C2×D311yescharacteristic
94C3×C4×C8C2×D311yescharacteristic
95#835—61no—
96#817—62no—
97#817—62no—
98#817—64no—
99#817—61no—
100#816—61no—
101#816—61no—
102#810—61no—
103#808—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C22×C3×D3—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—41no—
112#634—41no—
113#634—41no—
114#634—41no—
115#634—41no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C3×D12—21no—
120C3×D12SD1612yes—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×Dic6—21no—
124C3×Dic6SD1612yescomplemented
125#627—44no—
126D3×Dic3—44no—
127C32×C8—22no—
128C3×C3⋊C8—41no—
129C3×C3⋊C8—41no—
130D4×Q8—91no—
131#498—91no—
132#475—91no—
133#461—91no—
134#332—91no—
135Q8⋊C8—31no—
136D4⋊C8—31no—
137C2×C3×Q8—31no—
138C2×C3×D4—31no—
139C22×C3×C4—61no—
140C22×Dic3—62no—
141D3×Q8—122no—
142D3×Q8—122no—
143C2×D12D1211yescharacteristic
144C2×C4×D3—21no—
145C2×C4×D3—62no—
146C2×Dic6—62no—
147C2×Dic6—62no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C2×Dic6—121no—
153C2×Dic6—121no—
154C2×Dic6—122no—
155C2×Dic6—122no—
156C2×Dic6D1211yescharacteristic
157C2×C3×C8—22no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C3×C4⋊C4—31no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—61no—
165C3×C22⋊C4—61no—
166C3×C42—21no—
167C3×C42—61no—
168C3×C42C22×D311yescharacteristic
169C3×C42C22×D311yescharacteristic
170#217—62no—
171#214—122no—
172(C2×D3)⋊C4—21no—
173(C2×D3)⋊C4—62no—
174C4⋊Dic3—32no—
175C4⋊Dic3—32no—
176C4⋊Dic3—62no—
177C4⋊Dic3—62no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—62no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—121no—
186C4⋊Dic3—121no—
187C4⋊Dic3D1211yescharacteristic
188C4⋊Dic3D1211yescharacteristic
189Dic3⋊C4—21no—
190Dic3⋊C4—62no—
191C4×Dic3—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194#204—122no—
195C22×C32#12011yescharacteristic
196C2×C3×D3—22no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C32×C4—21no—
200C32×C4C2×SD1611yescharacteristic
201C32×C4C2×SD1611yescharacteristic
202C32×C4AGL(1,ℤ/8)11yescharacteristic
203C32×C4#13711yescharacteristic
204C3⋊Dic3—42no—
205C3⋊Dic3—81no—
206C3×Dic3—22no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C22×Q8—181no—
210C2×SD16—181no—
211C4⋊Q8—91no—
212C4⋊Q8—91no—
213C4⋊Q8—181no—
214C22⋊Q8—182no—
215C22⋊Q8—181no—
216C4×Q8—31no—
217C4×D4—31no—
218C4×D4—181no—
219#106—181no—
220#106—182no—
221C4⋊C8—31no—
222C4⋊C8—31no—
223#103—181no—
224#103—181no—
225C4×C8D3211yescharacteristic
226C23×C3—61no—
227C22×D3—21no—
228C3×Q8—32no—
229C3×Q8—61no—
230C3×D4—32no—
231C3×D4—61no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—61no—
236C2×C3×C4—61no—
237C2×C3×C4—61no—
238C2×C3×C4—121no—
239C2×C3×C4—121no—
240C2×C3×C4C2×D1211yescharacteristic
241C2×C3×C4C2×D1211yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—122no—
252C2×Dic3—124no—
253C2×Dic3—122no—
254C2×Dic3—121no—
255C2×Dic3—121no—
256D12—21no—
257D12#20412yes—
258C4×D3—41no—
259C4×D3—41no—
260C4×D3—124no—
261Dic6—21no—
262Dic6—124no—
263Dic6—124no—
264Dic6—121no—
265Dic6—121no—
266Dic6—121no—
267Dic6—121no—
268Dic6—121no—
269Dic6—121no—
270Dic6—121no—
271Dic6—121no—
272Dic6—241no—
273Dic6—241no—
274Dic6—241no—
275Dic6—241no—
276Dic6#20412yescomplemented
277C3×C8—24no—
278C3×C8—22no—
279C3×C8—22no—
280C3×C8—121no—
281C3×C8—121no—
282C3⋊C8—41no—
283C3⋊C8—41no—
284C2×C32#44811yescharacteristic
285C2×C32#45011yescharacteristic
286C2×C32#45611yescharacteristic
287C3×D3—42no—
288C2×Q8—31no—
289C2×Q8—182no—
290C2×Q8—181no—
291C2×Q8—181no—
292C2×Q8—362no—
293C2×Q8—362no—
294C2×D4—31no—
295C22×C4—61no—
296C22×C4—182no—
297SD16—362no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—61no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—61no—
304C4⋊C4—92no—
305C4⋊C4—182no—
306C4⋊C4—181no—
307C4⋊C4—181no—
308C4⋊C4—181no—
309C22⋊C4—61no—
310C22⋊C4—182no—
311C42—61no—
312C42C2×D3211yescharacteristic
313C22×C3—21no—
314C22×C3—62no—
315C22×C3—121no—
316C22×C3—121no—
317C22×C3#88211yescharacteristic
318C22×C3#88211yescharacteristic
319C2×D3—22no—
320C2×D3—41no—
321C2×D3—41no—
322C3×C4—22no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—62no—
330C3×C4—121no—
331C3×C4—121no—
332C3×C4C2×#20411yescharacteristic
333C3×C4C2×#20411yescharacteristic
334C3×C4#90811yescharacteristic
335C3×C4#90911yescharacteristic
336C3×C4#91111yescharacteristic
337C3×C4D3×SD1611yescharacteristic
338C3×C4D3×SD1611yescharacteristic
339C3×C4#91811yescharacteristic
340Dic3—22no—
341Dic3—41no—
342Dic3—41no—
343Dic3—122no—
344Dic3—122no—
345Dic3—242no—
346Dic3—242no—
347Dic3—241no—
348Dic3—241no—
349C32#165111yescharacteristic, complemented, Sylow
350C23—61no—
351Q8—32no—
352Q8—61no—
353Q8—364no—
354Q8—361no—
355Q8—361no—
356Q8—361no—
357Q8—361no—
358D4—32no—
359D4—61no—
360C2×C4—61no—
361C2×C4—61no—
362C2×C4—61no—
363C2×C4—121no—
364C2×C4—121no—
365C2×C4—182no—
366C2×C4—364no—
367C2×C4—361no—
368C2×C4D3×D1211yescharacteristic
369C2×C4D3×D1211yescharacteristic
370C2×C4#381111yescharacteristic
371C8—22no—
372C8—121no—
373C8—121no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—122no—
378C2×C3#473111yescharacteristic
379C2×C3#473811yescharacteristic
380C2×C3#477611yescharacteristic
381C2×C3#480611yescharacteristic
382C2×C3#482611yescharacteristic
383C2×C3#482611yescharacteristic
384D3—42no—
385C22—62no—
386C22—121no—
387C22—121no—
388C22#6392311yescharacteristic
389C4—21no—
390C4—62no—
391C4—121no—
392C4—121no—
393C4—362no—
394C4—721no—
395C4D3×#20411yescharacteristic
396C4D3×#20411yescharacteristic
397C4#6379511yescharacteristic
398C4#6380111yescharacteristic
399C3—21no—
400C3#6821011yescharacteristic, complemented
401C3#6825111yescharacteristic, complemented
402C2—122no—
403C2#1059040111yescharacteristic
404C2#1059094611yescharacteristic
405C2#1059095111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4×C8D32
hypocenterC32#1651
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10592379C2semidirect
4. #10590301C2semidirect
6. C3×#4456C2semidirect
7. #10589094C2semidirect
41. #4456D3semidirect
124. C3×Dic6SD16semidirect
276. Dic6#204semidirect
349. C32#1651semidirect
400. C3#68210semidirect
401. C3#68251semidirect

Maximal subgroups

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

subgroupindex
Dic6×D122
#105923792
#105903652
#105903012
C3×#44592
C3×#44562
#105890942
#682513
#682103