Finite Group Databasebeta

← #11779023

Subgroups — #11779023

Order 1152.

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

normal subgroups only

This group has 542 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
1#10593958C211yesmaximal, characteristic, complemented
2#10592542C211yesmaximal, characteristic
3#10590373C211yesmaximal, characteristic, complemented
4#10590367C211yesmaximal, characteristic, complemented
5C3×#4484C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#68490—31nomaximal
9#68244—31nomaximal
10C2×#3745—21no—
11#64083C2211yescharacteristic
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63900—21no—
16#63894—21no—
17#63888—22no—
18#63871—21no—
19#63869—21no—
20C2×#3717—21no—
21C2×#3717—22no—
22C32×C4⋊C8C2211yescharacteristic
23#63648—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26#63564—21no—
27#5730—31no—
28#5579—31no—
29#5085—31no—
30#5027—31no—
31#4848—31no—
32#4843—31no—
33#4843—31no—
34#4843—61no—
35#4693—31no—
36C3×#333—31no—
37C3×Q8⋊C8—31no—
38#4484D311yescharacteristic, complemented
39#4483—31no—
40#4481D311yescharacteristic, complemented
41#4459—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)D411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×C3×Dic6D411yescharacteristic
48C2×C3×Dic6D412yes—
49C2×#624—22no—
50C2×C32×C8—21no—
51C32×C42C2311yescharacteristic
52#3752—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54#3745—42no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62#3724—22no—
63Dic3⋊Dic3—22no—
64#3722—22no—
65#3717—44no—
66#3717—42no—
67#1622—91noSylow
68C3×C4⋊Q8—31no—
69C3×C4×Q8—31no—
70#946—62no—
71#946—61no—
72C2×#215—61no—
73C2×#215—62no—
74C2×D24—61no—
75C2×D24—61no—
76C2×D24—62no—
77C2×#204—62no—
78C2×#204—61no—
79#897—61no—
80#896—62no—
81#893—61no—
82D3×C4⋊C4—61no—
83D3×C4⋊C4—61no—
84#890—61no—
85#874—31no—
86#874—31no—
87#874—61no—
88C4×D12—31no—
89C4×D12—31no—
90C4×D12—61no—
91C4×D12—61no—
92#870—61no—
93#869C2×D311yescharacteristic
94C4×Dic6C2×D311yescharacteristic
95C3×C4⋊C8—21no—
96C3×C4⋊C8—31no—
97C3×C4⋊C8C2×D311yescharacteristic
98C3×C4⋊C8C2×D311yescharacteristic
99C3×C4×C8—31no—
100#821—61no—
101#821—61no—
102#821—62no—
103#821—61no—
104#809—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊D3—21no—
108C22×C3⋊D3—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C4⋊(C3⋊D3)—21no—
114C4⋊(C3⋊D3)—41no—
115C4⋊(C3⋊D3)—41no—
116C4⋊(C3⋊D3)—42no—
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—41no—
119C4⋊(C3⋊D3)SD1612yescomplemented
120C4×C3⋊D3—41no—
121C4×C3⋊D3—41no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—21no—
125C3×Dic6—21no—
126C3×Dic6—21no—
127C3×Dic6—42no—
128#624—82no—
129C32×C8—41no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—41no—
132#554—91no—
133#492—91no—
134#460—91no—
135#459—91no—
136#333—31no—
137Q8⋊C8—31no—
138D4⋊C8—91no—
139C2×C3×Q8—31no—
140C2×C3×Q8—32no—
141C2×D12—31no—
142C2×D12—31no—
143C2×D12—61no—
144C2×D12—62no—
145C2×D12—61no—
146C2×D12—61no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—121no—
152C2×D12—121no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×C4×D3—62no—
156C2×C4×D3—62no—
157C2×C4×D3—121no—
158C2×Dic6D1211yescharacteristic
159C2×Dic6D1212yes—
160C2×C3×C8—22no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C42—21no—
170C3×C42—61no—
171C3×C42C22×D311yescharacteristic
172C3×C42C22×D311yescharacteristic
173#215—124no—
174#215—122no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—121no—
180C4⋊Dic3—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3—31no—
183C4⋊Dic3—31no—
184C4⋊Dic3—61no—
185C4⋊Dic3—62no—
186C4⋊Dic3D1211yescharacteristic
187Dic3⋊C4—21no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191C4×Dic3—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194D24—122no—
195D24—122no—
196D24—124no—
197#204—124no—
198#204—122no—
199C22×C32#12011yescharacteristic
200C2×C3⋊D3—22no—
201C2×C3⋊D3—41no—
202C2×C3⋊D3—41no—
203C2×C3⋊D3—81no—
204C2×C3⋊D3—81no—
205C2×C3⋊D3—81no—
206C32×C4—21no—
207C32×C4C2×SD1611yescharacteristic
208C32×C4#13511yescharacteristic
209C32×C4AGL(1,ℤ/8)11yescharacteristic
210C32×C4#13711yescharacteristic
211C3⋊Dic3—41no—
212C3×Dic3—41no—
213C3×Dic3—41no—
214C3×Dic3—42no—
215C2×SD16—181no—
216C2×SD16—182no—
217C2×D8—181no—
218C4⋊Q8—31no—
219#127—91no—
220#125—181no—
221C22⋊Q8—182no—
222C22⋊Q8—181no—
223C4×Q8—31no—
224C4×D4—91no—
225C4×D4—181no—
226C2×C4⋊C4—181no—
227C4⋊C8—31no—
228C4⋊C8D3211yescharacteristic
229#102—181no—
230#102—181no—
231C4×C8—31no—
232C22×D3—61no—
233C22×D3—61no—
234C22×D3—121no—
235C22×D3—122no—
236C22×D3—121no—
237C22×D3—121no—
238C3×Q8—61no—
239C3×Q8—61no—
240C3×Q8—122no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—61no—
245C2×C3×C4—61no—
246C2×C3×C4—62no—
247C2×C3×C4C2×D1211yescharacteristic
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—22no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—121no—
259D12—32no—
260D12—32no—
261D12—62no—
262D12—61no—
263D12—61no—
264D12—121no—
265D12—122no—
266D12—122no—
267D12—122no—
268D12—122no—
269D12—121no—
270D12—121no—
271D12—121no—
272D12—121no—
273D12—121no—
274D12—121no—
275D12—121no—
276D12—121no—
277D12—241no—
278D12—241no—
279D12—242no—
280C4×D3—121no—
281C4×D3—121no—
282C4×D3—121no—
283C4×D3—121no—
284C4×D3—241no—
285C4×D3—241no—
286C4×D3—242no—
287C4×D3—242no—
288Dic6—21no—
289Dic6—21no—
290Dic6—42no—
291C3×C8—42no—
292C3×C8—41no—
293C3×C8—41no—
294C3×C8—62no—
295C3×C8—121no—
296C3⋊C8—22no—
297C3⋊C8—41no—
298C2×C32#44811yescharacteristic
299C2×C32#44911yescharacteristic
300C2×C32#45311yescharacteristic
301C3⋊D3—42no—
302C3⋊D3—161no—
303C2×Q8—31no—
304C2×Q8—32no—
305C2×D4—91no—
306C2×D4—181no—
307C2×D4—181no—
308C2×D4—181no—
309C22×C4—182no—
310C22×C4—181no—
311SD16—364no—
312SD16—362no—
313D8—362no—
314C2×C8—21no—
315C2×C8—61no—
316C2×C8—61no—
317C4⋊C4—31no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—91no—
322C4⋊C4—182no—
323C4⋊C4—182no—
324C22⋊C4—182no—
325C22⋊C4—181no—
326C42—61no—
327C42C2×D3211yescharacteristic
328C22×C3—21no—
329C22×C3#88211yescharacteristic
330C22×C3#88211yescharacteristic
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—122no—
334C2×D3—121no—
335C2×D3—121no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—241no—
339C2×D3—241no—
340C2×D3—242no—
341C2×D3—242no—
342C2×D3—242no—
343C2×D3—241no—
344C2×D3—241no—
345C2×D3—241no—
346C2×D3—241no—
347C2×D3—241no—
348C2×D3—241no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—41no—
356C3×C4—121no—
357C3×C4—121no—
358C3×C4—122no—
359C3×C4#90411yescharacteristic
360C3×C4#90811yescharacteristic
361C3×C4D3×SD1611yescharacteristic
362C3×C4D3×SD1611yescharacteristic
363C3×C4#91411yescharacteristic
364C3×C4#91811yescharacteristic
365C3×C4#91811yescharacteristic
366C3×C4#91911yescharacteristic
367Dic3—41no—
368Dic3—42no—
369Dic3—41no—
370Dic3—121no—
371Dic3—121no—
372Dic3—241no—
373C32#162211yescharacteristic, complemented, Sylow
374C23—181no—
375C23—361no—
376Q8—61no—
377Q8—61no—
378Q8—122no—
379D4—92no—
380D4—181no—
381D4—362no—
382D4—361no—
383D4—361no—
384D4—361no—
385D4—361no—
386C2×C4—61no—
387C2×C4—61no—
388C2×C4—62no—
389C2×C4—181no—
390C2×C4—361no—
391C2×C4—361no—
392C2×C4—722no—
393C2×C4D3×D1211yescharacteristic
394C2×C4D3×D1211yescharacteristic
395C2×C4#381111yescharacteristic
396C8—41no—
397C8—62no—
398C8—121no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3#473411yescharacteristic
403C2×C3#474711yescharacteristic
404C2×C3#480611yescharacteristic
405C2×C3#480611yescharacteristic
406C2×C3#481011yescharacteristic
407C2×C3#482211yescharacteristic
408D3—122no—
409D3—122no—
410D3—242no—
411D3—482no—
412D3—481no—
413D3—481no—
414C22—182no—
415C22—361no—
416C22—361no—
417C22—721no—
418C22—721no—
419C22—721no—
420C22#6392311yescharacteristic
421C4—21no—
422C4—121no—
423C4—122no—
424C4—121no—
425C4—361no—
426C4#6379411yescharacteristic
427C4#6380811yescharacteristic
428C4#6393011yescharacteristic
429C4#6394511yescharacteristic
430C3—21no—
431C3#6824411yescharacteristic, complemented
432C3#6849011yescharacteristic, complemented
433C2—362no—
434C2—1441no—
435C2#1059060611yescharacteristic
436C2#1059096711yescharacteristic
437C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10592542C2
hypercenterC4⋊C8D32
hypocenterC32#1622
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
1. #10593958C2semidirect
3. #10590373C2semidirect
4. #10590367C2semidirect
5. C3×#4484C2semidirect
6. C3×#4481C2semidirect
7. #10589082C2semidirect
38. #4484D3semidirect
40. #4481D3semidirect
119. C4⋊(C3⋊D3)SD16semidirect
373. C32#1622semidirect
431. C3#68244semidirect
432. C3#68490semidirect

Maximal subgroups

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

subgroupindex
#105939582
#105925422
#105903732
#105903672
C3×#44842
C3×#44812
#105890822
#684903
#682443