Finite Group Databasebeta

← #11778823

Subgroups — #11778823

Order 1152.

456 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 82 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#10594812C211yesmaximal, characteristic
2#10592421C211yesmaximal, characteristic
3#10591226C211yesmaximal, characteristic
4#10591103C211yesmaximal, characteristic
5C3×#4469C211yesmaximal, characteristic
6C3×#4467C211yesmaximal, characteristic
7#10589154C211yesmaximal, characteristic
8#68331—31nomaximal
9#68141—31nomaximal
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11#64133C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14#63964—21no—
15#63955—21no—
16#63846—21no—
17#63845—21no—
18#63840—21no—
19#63839—21no—
20C32×C22⋊C8C2211yescharacteristic
21#63645—21no—
22#63643—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63579—21no—
26#63579—21no—
27#63575—21no—
28#63566—21no—
29#5623—31no—
30#5500—31no—
31#5044—31no—
32#4986—31no—
33#4722—31no—
34#4722—31no—
35#4722—31no—
36#4722—61no—
37#4659—31no—
38C3×#328—31no—
39C3×#324—31no—
40#4469D311yescharacteristic
41#4467—31no—
42#4467D311yescharacteristic
43#4452—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634D411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6D411yescharacteristic
51C2×#627—21no—
52C2×C32×C8—21no—
53#3757—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58C3×#217—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic32—21no—
70Dic32—21no—
71#1617—91noSylow
72C3×C22⋊Q8—31no—
73C2×C3×C4⋊C4—31no—
74#944—61no—
75#926—61no—
76C2×C4⋊Dic3—31no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—61no—
79#924—31no—
80#924—31no—
81#924—61no—
82#924—61no—
83#924C2×D311yescharacteristic
84C2×Dic3⋊C4C2×D311yescharacteristic
85#890—61no—
86#890—61no—
87#889—61no—
88#889—61no—
89#888—61no—
90#888—61no—
91#888—61no—
92#878—61no—
93#877—61no—
94C3×C22⋊C8—21no—
95C3×C22⋊C8—31no—
96C3×C22⋊C8C2×D311yescharacteristic
97C3×C22⋊C8C2×D311yescharacteristic
98C3×#95—31no—
99#835—61no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95C2×D311yescharacteristic
105#830C2×D311yescharacteristic
106#818—61no—
107#818—61no—
108#818—62no—
109#818—61no—
110#816—61no—
111#816—61no—
112#816—62no—
113#816—61no—
114#807—61no—
115C23×C32C2×D411yescharacteristic
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—42no—
123#634—41no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3Q1612yes—
134C3×Dic6—41no—
135#627—81no—
136C32×C8—41no—
137C3×C3⋊C8—41no—
138#544—91no—
139#484—91no—
140#484—91no—
141#400—91no—
142#328—31no—
143#328—91no—
144#324—31no—
145C2×C3×Q8—31no—
146C22×C3×C4—21no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—61no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×Dic3—21no—
153C22×Dic3—61no—
154C22×Dic3—61no—
155C22×Dic3—121no—
156C22×Dic3D1211yescharacteristic
157C22×Dic3D1211yescharacteristic
158C2×Dic6—31no—
159C2×Dic6—31no—
160C2×Dic6—61no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×Dic6D1211yescharacteristic
164C2×C3×C8—22no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—61no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—61no—
173#217—21no—
174#217—61no—
175#217—61no—
176#217—121no—
177C4⋊Dic3—31no—
178C4⋊Dic3—31no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—62no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—121no—
190C4⋊Dic3D1211yescharacteristic
191Dic3⋊C4—21no—
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—121no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C2×C3⋊C8—21no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32#12011yescharacteristic
211C22×C32C2×Q1611yescharacteristic
212C22×C32#13711yescharacteristic
213C32×C4—21no—
214C32×C4—21no—
215C3⋊Dic3—41no—
216C3⋊Dic3—41no—
217C3⋊Dic3—81no—
218C3×Dic3—22no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223C4⋊Q8—181no—
224C4⋊Q8—181no—
225#125—181no—
226#125—181no—
227C22⋊Q8—31no—
228C22⋊Q8—91no—
229C22⋊Q8—181no—
230#117—181no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—91no—
233#107—181no—
234#107—181no—
235#103—181no—
236#103—181no—
237C22⋊C8—31no—
238C22⋊C8D3211yescharacteristic
239#95—31no—
240#95—181no—
241#95—181no—
242C23×C3—21no—
243C23×C3C2×D1211yescharacteristic
244C23×C3D3×D411yescharacteristic
245C3×Q8—121no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—32no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—42no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4—121no—
260C2×C3×C4—121no—
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—41no—
271C2×Dic3—41no—
272C2×Dic3—41no—
273C2×Dic3—41no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—121no—
279C2×Dic3—121no—
280C2×Dic3—122no—
281C2×Dic3—122no—
282C2×Dic3—122no—
283C2×Dic3—121no—
284C2×Dic3—121no—
285C2×Dic3—242no—
286C2×Dic3Dic1212yes—
287Dic6—41no—
288Dic6—121no—
289Dic6—121no—
290Dic6—122no—
291Dic6—241no—
292Dic6—241no—
293C3×C8—42no—
294C3×C8—41no—
295C3×C8—41no—
296C3×C8—121no—
297C3⋊C8—41no—
298C2×C32—21no—
299C2×C32—21no—
300C2×C32#45111yescharacteristic
301C2×C32#45411yescharacteristic
302C2×C32#45811yescharacteristic
303C2×Q8—31no—
304C2×Q8—91no—
305C2×Q8—181no—
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—61no—
309C22×C4—181no—
310C22×C4C2×D3211yescharacteristic
311C2×C8—21no—
312C2×C8—61no—
313C4⋊C4—31no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—91no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C22⋊C4—61no—
327C22⋊C4—181no—
328C42—181no—
329C42—181no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3#88211yescharacteristic
340C22×C3#88211yescharacteristic
341C22×C3C2×Dic1211yescharacteristic
342C22×C3#90911yescharacteristic
343C22×C3#91511yescharacteristic
344C22×C3D3×Q1611yescharacteristic
345C3×C4—22no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—62no—
352C3×C4—121no—
353C3×C4—121no—
354C3×C4—121no—
355C3×C4—241no—
356Dic3—22no—
357Dic3—41no—
358Dic3—41no—
359Dic3—41no—
360Dic3—81no—
361Dic3—121no—
362Dic3—121no—
363Dic3—121no—
364Dic3—121no—
365Dic3—241no—
366Dic3—241no—
367Dic3—242no—
368Dic3—241no—
369Dic3—241no—
370C32#161711yescharacteristic, complemented, Sylow
371C23D3×D1211yescharacteristic
372Q8—121no—
373Q8—361no—
374Q8—721no—
375C2×C4—32no—
376C2×C4—41no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4—181no—
387C2×C4—181no—
388C2×C4—362no—
389C2×C4—361no—
390C2×C4D3×D1211yescharacteristic
391C2×C4#381111yescharacteristic
392C8—41no—
393C8—121no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—41no—
402C2×C3—41no—
403C2×C3#473911yescharacteristic
404C2×C3#474211yescharacteristic
405C2×C3#474211yescharacteristic
406C2×C3#475311yescharacteristic
407C2×C3#480911yescharacteristic
408C2×C3#482711yescharacteristic
409C22—21no—
410C22—21no—
411C22D3×Dic1211yescharacteristic
412C22#6380011yescharacteristic
413C22#6392311yescharacteristic
414C4—21no—
415C4—21no—
416C4—62no—
417C4—121no—
418C4—121no—
419C4—121no—
420C4—241no—
421C4—361no—
422C4—361no—
423C4—721no—
424C3—21no—
425C3#6814111yescharacteristic, complemented
426C3#6833111yescharacteristic, complemented
427C2—21no—
428C2—21no—
429C2#1059040911yescharacteristic
430C2#1059095211yescharacteristic
431C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊C8D32
hypocenterC32#1617
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
370. C32#1617semidirect
425. C3#68141semidirect
426. C3#68331semidirect

Maximal subgroups

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

subgroupindex
#105948122
#105924212
#105912262
#105911032
C3×#44692
C3×#44672
#105891542
#683313
#681413