Finite Group Databasebeta

← #11778826

Subgroups — #11778826

Order 1152.

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

normal subgroups only

This group has 444 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
2C3×#4659C211yesmaximal, characteristic
3#10591135C211yesmaximal, characteristic
4#10591132C211yesmaximal, characteristic
5#10589318C211yesmaximal, characteristic
6C3×#4452C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#69719—31nomaximal
9#68331—31nomaximal
10#64133C2211yescharacteristic
11C2×C3×C4⋊Dic3C2211yescharacteristic
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×#95C2211yescharacteristic
21#63657C2211yescharacteristic
22C3×C3⋊#95—21no—
23C3×C3⋊#95—21no—
24C3×#830C2211yescharacteristic
25#63576—21no—
26#63575—21no—
27#63567—21no—
28#63565—21no—
29#5623—31no—
30#5500—31no—
31C3×#400—31no—
32#5044—31no—
33#4970—31no—
34#4970—31no—
35#4722—31no—
36#4659D311yescharacteristic
37C3×#328—31no—
38#4528—31no—
39#4469—31no—
40#4452—31no—
41#4452—31no—
42#4452—61no—
43#4452D311yescharacteristic
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—
52#3757—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54#3750—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—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—
74C2×C3×C4⋊C4—31no—
75#944—61no—
76#926—61no—
77C2×C4⋊Dic3C2×D311yescharacteristic
78#924—31no—
79#924—31no—
80#924—61no—
81#924—61no—
82#924C2×D311yescharacteristic
83C2×Dic3⋊C4C2×D311yescharacteristic
84#890—61no—
85#890—61no—
86#889—61no—
87#889—61no—
88#888—61no—
89#888—61no—
90#888—61no—
91#878—61no—
92#877—61no—
93C3×C22⋊C8—31no—
94C3×#95—21no—
95C3×#95—61no—
96C3×#95—61no—
97C3×#95C2×D311yescharacteristic
98C3×#95C2×D311yescharacteristic
99#835—61no—
100C3⋊#95—21no—
101C3⋊#95—21no—
102#830—31no—
103#830—31no—
104#830—61no—
105#830C2×D311yescharacteristic
106#818—61no—
107#816—61no—
108#810—61no—
109#810—61no—
110#807—61no—
111#807—61no—
112#807—61no—
113C23×C32C2×D411yescharacteristic
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122#634—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—
133#627—81no—
134C3⋊(C3⋊C8)—41no—
135C3×C3⋊C8—41no—
136#544—91no—
137#484—91no—
138#484—91no—
139#400—31no—
140#328—31no—
141#328—91no—
142#324—91no—
143C2×C3×Q8—31no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—41no—
150C22×C3×C4—61no—
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C22×Dic3—21no—
154C22×Dic3#6711yescharacteristic
155C22×Dic3#6711yescharacteristic
156C2×Dic6—31no—
157C2×Dic6—31no—
158C2×Dic6—61no—
159C2×Dic6—61no—
160C2×Dic6—61no—
161C2×Dic6D1211yescharacteristic
162C2×C3×C8—61no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—61no—
170#217—21no—
171#217—61no—
172#217—61no—
173#217—121no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3D1211yescharacteristic
184Dic3⋊C4—21no—
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—121no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—61no—
199C4×Dic3—61no—
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—81no—
212C3⋊Dic3—41no—
213C3⋊Dic3—41no—
214C3×Dic3—22no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3—41no—
218C3×Dic3—81no—
219C4⋊Q8—181no—
220C4⋊Q8—181no—
221#125—181no—
222#125—181no—
223C22⋊Q8—31no—
224C22⋊Q8—91no—
225C22⋊Q8—181no—
226#117—181no—
227C2×C4⋊C4—31no—
228C2×C4⋊C4—31no—
229#107—181no—
230#107—181no—
231#103—181no—
232#103—181no—
233C22⋊C8—31no—
234C22⋊C8—91no—
235#95—61no—
236#95—61no—
237#95D3211yescharacteristic
238C23×C3—21no—
239C23×C3D3×D411yescharacteristic
240C23×C3C2×#6711yescharacteristic
241C3×Q8—121no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—32no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—42no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—81no—
260C2×C3×C4—81no—
261C2×C3×C4—81no—
262C2×C3×C4—121no—
263C2×C3×C4—122no—
264C2×C3×C4—121no—
265C2×C3×C4C2×D1211yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—41no—
275C2×Dic3—42no—
276C2×Dic3—41no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—121no—
282C2×Dic3—121no—
283C2×Dic3#21612yes—
284Dic6—41no—
285Dic6—121no—
286Dic6—121no—
287Dic6—241no—
288Dic6—241no—
289Dic6—241no—
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—91no—
302C2×Q8—181no—
303C22×C4—21no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—61no—
307C22×C4C2×D3211yescharacteristic
308C2×C8—61no—
309C2×C8—181no—
310C4⋊C4—31no—
311C4⋊C4—61no—
312C4⋊C4—61no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—91no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C22⋊C4—61no—
324C22⋊C4—181no—
325C42—181no—
326C42—181no—
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×C3#88211yescharacteristic
337C22×C3#91511yescharacteristic
338C22×C3D3×Q1611yescharacteristic
339C22×C3#93711yescharacteristic
340C22×C3C2×#21611yescharacteristic
341C22×C3#95111yescharacteristic
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—62no—
349C3×C4—81no—
350C3×C4—81no—
351C3×C4—82no—
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—
367C32#161711yescharacteristic, complemented, Sylow
368C23D3×#6711yescharacteristic
369Q8—121no—
370Q8—361no—
371Q8—721no—
372C2×C4—32no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—121no—
383C2×C4—122no—
384C2×C4—121no—
385C2×C4—181no—
386C2×C4—181no—
387C2×C4D3×D1211yescharacteristic
388C2×C4#380211yescharacteristic
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#474211yescharacteristic
401C2×C3#480911yescharacteristic
402C2×C3#482711yescharacteristic
403C2×C3#505011yescharacteristic
404C2×C3#505311yescharacteristic
405C2×C3#506211yescharacteristic
406C22—21no—
407C22—21no—
408C22#6392211yescharacteristic
409C22#6392911yescharacteristic
410C22D3×#21611yescharacteristic
411C4—21no—
412C4—21no—
413C4—62no—
414C4—81no—
415C4—121no—
416C4—121no—
417C4—121no—
418C4—241no—
419C4—361no—
420C4—361no—
421C3—21no—
422C3#6833111yescharacteristic, complemented
423C3#6971911yescharacteristic, complemented
424C2—21no—
425C2—21no—
426C2#1059040011yescharacteristic
427C2#1059040811yescharacteristic
428C2#1059060411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenter#95D32
hypocenterC32#1617
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
367. C32#1617semidirect
422. C3#68331semidirect
423. C3#69719semidirect

Maximal subgroups

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

subgroupindex
#105948122
C3×#46592
#105911352
#105911322
#105893182
C3×#44522
#105891472
#697193
#683313