Finite Group Databasebeta

← #11778819

Subgroups — #11778819

Order 1152.

444 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×#5623C211yesmaximal, characteristic
2C3×#5044C211yesmaximal, characteristic
3#10591225C211yesmaximal, characteristic
4#10591132C211yesmaximal, characteristic
5#10589404C211yesmaximal, characteristic
6#10589152C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#71899—31nomaximal
9#71179—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C3×#944—21no—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C3×#924C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15C3×#889—21no—
16C3×#889—21no—
17C3×#888—21no—
18C3×#878—21no—
19C3×#877—21no—
20#63658C2211yescharacteristic
21#63657C2211yescharacteristic
22C3×#835—21no—
23C3×#830C2211yescharacteristic
24C3×#807—21no—
25#63579—21no—
26#63579—21no—
27#63576—21no—
28#63565—21no—
29C3×#544—31no—
30#5623D311yescharacteristic
31C3×#484—31no—
32#5044—31no—
33#5044D311yescharacteristic
34#4986—31no—
35#4985—31no—
36#4970—31no—
37#4538—31no—
38#4538—31no—
39#4538—31no—
40#4538—61no—
41#4528—31no—
42#4469—31no—
43#4467—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×Dic6—21no—
51C2×C3×Dic6D411yescharacteristic
52C32×C4⋊C4—21no—
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71#1617—91noSylow
72C3×C4⋊Q8—61no—
73C3×C4⋊Q8—61no—
74C3×#125—61no—
75C3×#125—61no—
76C3×C22⋊Q8—21no—
77C3×C22⋊Q8—31no—
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8C2×D311yescharacteristic
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×#117—61no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84#944—21no—
85C2×C4⋊Dic3C2×D311yescharacteristic
86#924C2×D311yescharacteristic
87C2×Dic3⋊C4C2×D311yescharacteristic
88#889—21no—
89#889—21no—
90#888—21no—
91#878—21no—
92#877—21no—
93C3×#107—61no—
94C3×#103—61no—
95C3×C22⋊C8—31no—
96#835—21no—
97#835—61no—
98C3⋊#95—31no—
99C3⋊#95—31no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105#830—31no—
106#830—31no—
107#830—61no—
108#830C2×D311yescharacteristic
109#810—61no—
110#807—21no—
111#807—61no—
112#807—61no—
113C23×C32C2×D411yescharacteristic
114C32×Q8—41no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—42no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3Q1612yes—
132C3×Dic6—41no—
133C3×Dic6—81no—
134C3⋊(C3⋊C8)—41no—
135C3×C3⋊C8—41no—
136#544—31no—
137#484—31no—
138#484—91no—
139#400—91no—
140#328—91no—
141#328—91no—
142#324—91no—
143C2×C3×Q8—21no—
144C2×C3×Q8—31no—
145C2×C3×Q8—61no—
146C2×C3×Q8#6711yescharacteristic
147C2×C3×Q8#6711yescharacteristic
148C22×C3×C4—21no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—61no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×Dic3—21no—
155C22×Dic3—61no—
156C22×Dic3—61no—
157C22×Dic3—121no—
158C22×Dic3#6711yescharacteristic
159C22×Dic3#6711yescharacteristic
160C2×Dic6—21no—
161C2×Dic6#6711yescharacteristic
162C2×C3×C8—61no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—41no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4#6711yescharacteristic
179C3×C4⋊C4#6711yescharacteristic
180C3×C22⋊C4—21no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—41no—
183C3×C22⋊C4—61no—
184C3×C42—61no—
185C3×C42—61no—
186#217—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3#6711yescharacteristic
191Dic3⋊C4—21no—
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198C4×Dic3—21no—
199C4×Dic3—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—121no—
204C22×C32—21no—
205C22×C32—21no—
206C22×C32#12011yescharacteristic
207C22×C32C2×Q1611yescharacteristic
208C22×C32#13711yescharacteristic
209C32×C4—21no—
210C32×C4—21no—
211C32×C4—41no—
212C32×C4—41no—
213C3⋊Dic3—81no—
214C3×Dic3—22no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3—41no—
218C3×Dic3—81no—
219C4⋊Q8—61no—
220C4⋊Q8—61no—
221#125—61no—
222#125—61no—
223C22⋊Q8—31no—
224C22⋊Q8—61no—
225C22⋊Q8D3211yescharacteristic
226#117—61no—
227C2×C4⋊C4—31no—
228C2×C4⋊C4—31no—
229#107—61no—
230#107—181no—
231#103—61no—
232#103—181no—
233C22⋊C8—31no—
234C22⋊C8—91no—
235#95—91no—
236#95—181no—
237#95—181no—
238C23×C3—21no—
239C23×C3D3×D411yescharacteristic
240C23×C3C2×#6711yescharacteristic
241C3×Q8—41no—
242C3×Q8—41no—
243C3×Q8—81no—
244C3×Q8—121no—
245C3×Q8—241no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—32no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
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—81no—
263C2×C3×C4—121no—
264C2×C3×C4—122no—
265C2×C3×C4—121no—
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—41no—
276C2×Dic3—42no—
277C2×Dic3—41no—
278C2×Dic3—121no—
279C2×Dic3—121no—
280C2×Dic3—121no—
281C2×Dic3—121no—
282C2×Dic3—122no—
283C2×Dic3—121no—
284C2×Dic3—121no—
285C2×Dic3—241no—
286C2×Dic3—241no—
287C2×Dic3#21612yes—
288Dic6—41no—
289Dic6—81no—
290C3×C8—121no—
291C3⋊C8—41no—
292C3⋊C8—121no—
293C3⋊C8—121no—
294C3⋊C8—241no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32#45111yescharacteristic
298C2×C32#45411yescharacteristic
299C2×C32#45811yescharacteristic
300C2×Q8—31no—
301C2×Q8—61no—
302C2×Q8#62511yescharacteristic
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—61no—
306C22×C4—181no—
307C22×C4C2×D3211yescharacteristic
308C2×C8—61no—
309C2×C8—181no—
310C4⋊C4—21no—
311C4⋊C4—31no—
312C4⋊C4—61no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4#62511yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—61no—
325C42—61no—
326C42—61no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3D3×Q1611yescharacteristic
337C22×C3#91811yescharacteristic
338C22×C3#93711yescharacteristic
339C22×C3#94211yescharacteristic
340C22×C3C2×#21611yescharacteristic
341C22×C3#95311yescharacteristic
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—62no—
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—241no—
365Dic3—241no—
366Dic3—242no—
367C32#161711yescharacteristic, complemented, Sylow
368C23D3×#6711yescharacteristic
369Q8—41no—
370Q8—121no—
371Q8—241no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—32no—
375C2×C4—41no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—121no—
382C2×C4—122no—
383C2×C4—121no—
384C2×C4—361no—
385C2×C4—361no—
386C2×C4—361no—
387C2×C4C2×#62511yescharacteristic
388C2×C4D3×#6711yescharacteristic
389C8—121no—
390C8—361no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3#505311yescharacteristic
401C2×C3#518611yescharacteristic
402C2×C3#520111yescharacteristic
403C2×C3#522811yescharacteristic
404C2×C3#524311yescharacteristic
405C2×C3#524511yescharacteristic
406C22—21no—
407C22—21no—
408C22D3×#21611yescharacteristic
409C22#6394811yescharacteristic
410C22#6397611yescharacteristic
411C4—21no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—62no—
416C4—121no—
417C4—121no—
418C4—121no—
419C4—241no—
420C4—721no—
421C3—21no—
422C3#7117911yescharacteristic, complemented
423C3#7189911yescharacteristic, complemented
424C2—21no—
425C2—21no—
426C2#1059153311yescharacteristic
427C2#1059159411yescharacteristic
428C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊Q8D32
hypocenterC32#1617
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
367. C32#1617semidirect
422. C3#71179semidirect
423. C3#71899semidirect

Maximal subgroups

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

subgroupindex
C3×#56232
C3×#50442
#105912252
#105911322
#105894042
#105891522
#105891472
#718993
#711793