Finite Group Databasebeta

← #11780214

Subgroups — #11780214

Order 1152.

503 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 503 conjugacy classes of subgroups — too many to draw. Only its 92 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#10593904C211yesmaximal, characteristic
2C3×#4846C211yesmaximal, characteristic
3#10590388C211yesmaximal, characteristic, complemented
4#10590312C211yesmaximal, characteristic, complemented
5#10589350C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic
8#71114—31nomaximal
9#68461—31nomaximal
10C2×D3×Dic6—21no—
11C4×#634C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63919—21no—
16#63899—22no—
17#63898—21no—
18#63856—21no—
19C2×#3719—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#821—21no—
23C3×#818—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63576—22no—
26#63566—21no—
27#5727—31no—
28D4×Dic6—31no—
29C3×#474—31no—
30#5090—31no—
31#5078—31no—
32#5078—31no—
33#4849—31no—
34#4846D311yescharacteristic
35C3×#332—31no—
36D4⋊(C3⋊C8)—31no—
37#4486D311yescharacteristic, complemented
38#4484—31no—
39#4484—31no—
40#4484—61no—
41#4483—31no—
42C2×#634D411yescharacteristic
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6—21no—
47C2×#627—22no—
48C2×D3×Dic3—22no—
49D3×Dic6—42no—
50D3×Dic6—42no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)D411yescharacteristic
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D412yes—
62C3×C4⋊Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64#3724—22no—
65(C2×D3)⋊Dic3—22no—
66#3719—42no—
67#1649—91noSylow
68C2×D3×Q8—61no—
69C22×Dic6—61no—
70C3×C4⋊Q8—31no—
71C3×C4⋊Q8—31no—
72C3×C4×D4—31no—
73#946—61no—
74C2×#216—61no—
75D4×Dic3—61no—
76#924—61no—
77C2×Dic12—61no—
78#896—62no—
79#893—61no—
80#888—61no—
81#888—61no—
82#878—62no—
83C4×D12C2×D311yescharacteristic
84#869C2×D311yescharacteristic
85#869C2×D311yescharacteristic
86C4×Dic6—31no—
87C4×Dic6—31no—
88C4×Dic6—61no—
89C3×#107—61no—
90C3×C4⋊C8—21no—
91C3×C4⋊C8—31no—
92C3×C4⋊C8C2×D311yescharacteristic
93C3×C4⋊C8C2×D311yescharacteristic
94C3×#102—61no—
95#835—61no—
96#821—21no—
97#818—21no—
98#816—61no—
99#807—62no—
100#807—62no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C22×C3×D3—21no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—21no—
111#634—21no—
112#634D812yes—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—41no—
116C3×D12—21no—
117C3×D12Q1612yescomplemented
118C3×C4×D3—41no—
119C3×C4×D3—41no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124#627—44no—
125D3×Dic3—44no—
126C32×C8—41no—
127C3⋊(C3⋊C8)—22no—
128C3×C3⋊C8—41no—
129D4×Q8—91no—
130#500—91no—
131#474—31no—
132#462—91no—
133#332—31no—
134Q8⋊C8—91no—
135D4⋊C8—91no—
136C2×C3×Q8—61no—
137C2×C3×Q8—61no—
138C2×C3×D4—31no—
139C22×C3×C4—61no—
140C22×Dic3—62no—
141D3×Q8—122no—
142D3×Q8—122no—
143C2×D12#6711yescharacteristic
144C2×C4×D3—21no—
145C2×C4×D3—62no—
146C2×Dic6—21no—
147C2×Dic6—21no—
148C2×Dic6—31no—
149C2×Dic6—31no—
150C2×Dic6—61no—
151C2×Dic6—62no—
152C2×Dic6—62no—
153C2×Dic6—122no—
154C2×Dic6—122no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—41no—
158C2×C3×C8—61no—
159C3×C4⋊C4—32no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C22⋊C4—61no—
165C3×C42—21no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#217—62no—
169#216—122no—
170(C2×D3)⋊C4—21no—
171(C2×D3)⋊C4—62no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—31no—
176C4⋊Dic3—31no—
177C4⋊Dic3—61no—
178C4⋊Dic3D1212yes—
179C4⋊Dic3#6711yescharacteristic
180Dic3⋊C4—62no—
181Dic3⋊C4—62no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—121no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—121no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—121no—
192Dic12—122no—
193C22×C32#12011yescharacteristic
194C2×C3×D3—22no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C32×C4—21no—
198C32×C4C2×D811yescharacteristic
199C32×C4C2×Q1611yescharacteristic
200C32×C4AGL(1,ℤ/8)11yescharacteristic
201C32×C4#13711yescharacteristic
202C3⋊Dic3—22no—
203C3⋊Dic3—41no—
204C3×Dic3—42no—
205C3×Dic3—41no—
206C3×Dic3—81no—
207C22×Q8—181no—
208C2×Q16—181no—
209C4⋊Q8—31no—
210C4⋊Q8—31no—
211C4⋊Q8—181no—
212C22⋊Q8—182no—
213C22⋊Q8—181no—
214C4×Q8—91no—
215C4×D4—31no—
216C4×D4—181no—
217#107—61no—
218#107—182no—
219C4⋊C8—31no—
220C4⋊C8D3211yescharacteristic
221#103—181no—
222#102—61no—
223C4×C8—91no—
224C23×C3—61no—
225C22×D3—21no—
226C3×Q8—121no—
227C3×Q8—121no—
228C3×Q8—121no—
229C3×Q8—121no—
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—62no—
237C2×C3×C4—121no—
238C2×C3×C4—121no—
239C2×C3×C4—121no—
240C2×C3×C4C2×D1211yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4C2×#6711yescharacteristic
246C2×Dic3—22no—
247C2×Dic3—21no—
248C2×Dic3—41no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—121no—
254C2×Dic3—121no—
255C2×Dic3—124no—
256D12—21no—
257D12#21612yescomplemented
258C4×D3—41no—
259C4×D3—41no—
260C4×D3—124no—
261Dic6—32no—
262Dic6—32no—
263Dic6—41no—
264Dic6—41no—
265Dic6—41no—
266Dic6—41no—
267Dic6—62no—
268Dic6—61no—
269Dic6—61no—
270Dic6—121no—
271Dic6—124no—
272Dic6—124no—
273C3×C8—41no—
274C3×C8—41no—
275C3×C8—81no—
276C3×C8—121no—
277C3⋊C8—41no—
278C3⋊C8—62no—
279C3⋊C8—62no—
280C3⋊C8—122no—
281C2×C32#44711yescharacteristic
282C2×C32#45111yescharacteristic
283C2×C32#45611yescharacteristic
284C3×D3—42no—
285C2×Q8—61no—
286C2×Q8—61no—
287C2×Q8—91no—
288C2×Q8—182no—
289C2×Q8—362no—
290C2×Q8—362no—
291C2×D4—31no—
292C22×C4—61no—
293C22×C4—182no—
294Q16—362no—
295C2×C8—21no—
296C2×C8—61no—
297C2×C8—181no—
298C4⋊C4—32no—
299C4⋊C4—31no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—61no—
303C4⋊C4—91no—
304C4⋊C4—182no—
305C4⋊C4—181no—
306C22⋊C4—61no—
307C22⋊C4—182no—
308C42—181no—
309C42C2×D3211yescharacteristic
310C22×C3—21no—
311C22×C3—62no—
312C22×C3—121no—
313C22×C3—121no—
314C22×C3#88211yescharacteristic
315C22×C3#93711yescharacteristic
316C2×D3—22no—
317C2×D3—41no—
318C2×D3—41no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—41no—
326C3×C4—122no—
327C3×C4—121no—
328C3×C4—241no—
329C3×C4D3×D811yescharacteristic
330C3×C4D3×D811yescharacteristic
331C3×C4#91111yescharacteristic
332C3×C4#91411yescharacteristic
333C3×C4#91511yescharacteristic
334C3×C4D3×Q1611yescharacteristic
335C3×C4C2×#21611yescharacteristic
336C3×C4#95111yescharacteristic
337Dic3—41no—
338Dic3—42no—
339Dic3—62no—
340Dic3—62no—
341Dic3—81no—
342Dic3—122no—
343Dic3—121no—
344Dic3—121no—
345Dic3—241no—
346C32#164911yescharacteristic, complemented, Sylow
347C23—61no—
348Q8—92no—
349Q8—121no—
350Q8—121no—
351Q8—121no—
352Q8—121no—
353Q8—181no—
354Q8—364no—
355D4—32no—
356D4—61no—
357C2×C4—61no—
358C2×C4—62no—
359C2×C4—121no—
360C2×C4—121no—
361C2×C4—121no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4—364no—
365C2×C4D3×D1211yescharacteristic
366C2×C4#380211yescharacteristic
367C2×C4D3×#6711yescharacteristic
368C8—41no—
369C8—121no—
370C8—182no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—122no—
375C2×C3#475211yescharacteristic
376C2×C3#477311yescharacteristic
377C2×C3#480911yescharacteristic
378C2×C3#505011yescharacteristic
379C2×C3#515611yescharacteristic
380C2×C3#520511yescharacteristic
381D3—42no—
382C22—62no—
383C22—121no—
384C22—121no—
385C22#6392211yescharacteristic
386C4—21no—
387C4—121no—
388C4—122no—
389C4—182no—
390C4—241no—
391C4—361no—
392C4#6379711yescharacteristic
393C4#6379811yescharacteristic
394C4#6392911yescharacteristic
395C4D3×#21611yescharacteristic
396C3—21no—
397C3#6846111yescharacteristic, complemented
398C3#7111411yescharacteristic, complemented
399C2—122no—
400C2#1059060411yescharacteristic
401C2#1059094511yescharacteristic
402C2#1059101811yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1649
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
3. #10590388C2semidirect
4. #10590312C2semidirect
5. #10589350C2semidirect
6. C3×#4486C2semidirect
37. #4486D3semidirect
117. C3×D12Q16semidirect
257. D12#216semidirect
346. C32#1649semidirect
397. C3#68461semidirect
398. C3#71114semidirect

Maximal subgroups

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

subgroupindex
#105939042
C3×#48462
#105903882
#105903122
#105893502
C3×#44862
#105890802
#711143
#684613