Finite Group Databasebeta

← #11778815

Subgroups — #11778815

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#10592669C211yesmaximal, characteristic
3C3×#4985C211yesmaximal, characteristic
4C3×#4970C211yesmaximal, characteristic
5#10589154C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#71179—31nomaximal
9#69719—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
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—
20#63657C2211yescharacteristic
21#63637—21no—
22#63634—21no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#810—21no—
28C3×#807—21no—
29#5623—31no—
30#5500—31no—
31C3×#484—31no—
32C3×#400—31no—
33#4985D311yescharacteristic
34#4970—31no—
35#4970—31no—
36#4970—61no—
37#4970D311yescharacteristic
38#4538—31no—
39#4528—31no—
40#4469—31no—
41#4467—31no—
42#4452—31no—
43#4452—31no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#634D411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6D411yescharacteristic
51C2×#627—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54#3757—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
56#3750—21no—
57C2×C3⋊(C3⋊C8)—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—21no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C3×C4⋊C4C2×D311yescharacteristic
77#944—61no—
78#926—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×#107—61no—
95C3×#103—61no—
96C3×C22⋊C8—31no—
97C3×#95—31no—
98C3×#95—61no—
99C3×#95—61no—
100C3⋊#95—21no—
101C3⋊#95—21no—
102C3⋊#95C2×D311yescharacteristic
103#830—31no—
104#830—31no—
105#830—61no—
106#830C2×D311yescharacteristic
107#810—21no—
108#810—61no—
109#810—61no—
110#810—62no—
111#807—21no—
112#807—61no—
113#807—61no—
114#807—62no—
115C23×C32C2×D411yescharacteristic
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4—42no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
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—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—41no—
138#544—91no—
139#484—31no—
140#484—91no—
141#400—31no—
142#328—91no—
143#328—91no—
144#324—91no—
145C2×C3×Q8—31no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—41no—
152C22×C3×C4—61no—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×Dic3—21no—
156C22×Dic3#6711yescharacteristic
157C22×Dic3#6711yescharacteristic
158C2×Dic6—31no—
159C2×Dic6—31no—
160C2×Dic6—61no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×Dic6#6711yescharacteristic
164C2×C3×C8—61no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—41no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C22⋊C4—61no—
176#217—21no—
177#217—61no—
178#217—61no—
179#217—121no—
180C4⋊Dic3—31no—
181C4⋊Dic3—31no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—61no—
187C4⋊Dic3#6711yescharacteristic
188Dic3⋊C4—21no—
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—121no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32#12011yescharacteristic
211C22×C32C2×Q1611yescharacteristic
212C22×C32#13711yescharacteristic
213C32×C4—21no—
214C32×C4—21no—
215C32×C4—81no—
216C3⋊Dic3—41no—
217C3⋊Dic3—41no—
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⋊C4D3211yescharacteristic
233#107—61no—
234#107—181no—
235#103—61no—
236#103—181no—
237C22⋊C8—31no—
238C22⋊C8—91no—
239#95—31no—
240#95—61no—
241#95—61no—
242C23×C3—21no—
243C23×C3D3×D411yescharacteristic
244C23×C3C2×#6711yescharacteristic
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—42no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—82no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—41no—
277C2×Dic3—41no—
278C2×Dic3—41no—
279C2×Dic3—41no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286C2×Dic3#21612yes—
287Dic6—41no—
288Dic6—121no—
289Dic6—121no—
290Dic6—122no—
291Dic6—241no—
292Dic6—241no—
293C3×C8—121no—
294C3⋊C8—41no—
295C3⋊C8—122no—
296C3⋊C8—121no—
297C3⋊C8—121no—
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—21no—
307C22×C4—31no—
308C22×C4—31no—
309C22×C4—61no—
310C22×C4C2×D3211yescharacteristic
311C2×C8—61no—
312C2×C8—181no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—31no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—91no—
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×C3D3×Q1611yescharacteristic
340C22×C3#91811yescharacteristic
341C22×C3#93711yescharacteristic
342C22×C3#93711yescharacteristic
343C22×C3C2×#21611yescharacteristic
344C22×C3#95111yescharacteristic
345C3×C4—22no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—62no—
352C3×C4—82no—
353C3×C4—81no—
354C3×C4—81no—
355C3×C4—121no—
356C3×C4—121no—
357C3×C4—121no—
358C3×C4—241no—
359Dic3—22no—
360Dic3—41no—
361Dic3—41no—
362Dic3—41no—
363Dic3—81no—
364Dic3—121no—
365Dic3—121no—
366Dic3—121no—
367Dic3—121no—
368Dic3—241no—
369Dic3—241no—
370C32#161711yescharacteristic, complemented, Sylow
371C23D3×#6711yescharacteristic
372Q8—121no—
373Q8—361no—
374Q8—721no—
375C2×C4—32no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4—181no—
389C2×C4—181no—
390C2×C4D3×#6711yescharacteristic
391C2×C4#381111yescharacteristic
392C8—121no—
393C8—361no—
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#505011yescharacteristic
404C2×C3#505311yescharacteristic
405C2×C3#505311yescharacteristic
406C2×C3#506211yescharacteristic
407C2×C3#518611yescharacteristic
408C2×C3#520111yescharacteristic
409C22—21no—
410C22—21no—
411C22D3×#21611yescharacteristic
412C22#6394311yescharacteristic
413C22#6398311yescharacteristic
414C4—21no—
415C4—21no—
416C4—62no—
417C4—81no—
418C4—121no—
419C4—121no—
420C4—121no—
421C4—241no—
422C4—361no—
423C4—361no—
424C3—21no—
425C3#6971911yescharacteristic, complemented
426C3#7117911yescharacteristic, complemented
427C2—21no—
428C2—21no—
429C2#1059139811yescharacteristic
430C2#1059152511yescharacteristic
431C2#1059165311yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#1617
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
370. C32#1617semidirect
425. C3#69719semidirect
426. C3#71179semidirect

Maximal subgroups

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

subgroupindex
#105948122
#105926692
C3×#49852
C3×#49702
#105891542
#105891532
#105891472
#711793
#697193