Finite Group Databasebeta

← #11780689

Subgroups — #11780689

Order 1152.

502 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 72 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#10596155C211yesmaximal, characteristic
2C3×#5055C211yesmaximal, characteristic, complemented
3#10590294C211yesmaximal, characteristic, complemented
4#10590289C211yesmaximal, characteristic, complemented
5C3×#4540C211yesmaximal, characteristic, complemented
6#10589089C211yesmaximal, characteristic, complemented
7#10589087C211yesmaximal, characteristic, complemented
8#71246—31nomaximal
9#68358—31nomaximal
10C32×#124C2211yescharacteristic
11#64155—21no—
12#64148—21no—
13#64095—21no—
14#64093—21no—
15#64092—21no—
16#64087—21no—
17#64084C2211yescharacteristic
18#64079C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×#835—21no—
21C3×#832—21no—
22C3×#803C2211yescharacteristic
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63567—21no—
26#63566—21no—
27#63566—21no—
28#63564—21no—
29#5684—31no—
30#5684—31no—
31#5684—61no—
32C3×#489—31no—
33#5089—31no—
34#5082—31no—
35#5055D311yescharacteristic, complemented
36#4714—31no—
37#4703—31no—
38C3×#329—31no—
39#4540D311yescharacteristic, complemented
40#4465—31no—
41#4465—31no—
42#4464—31no—
43#4464—31no—
44C2×C32×Q8D411yescharacteristic
45C2×C32×D4D411yescharacteristic
46C2×#638—21no—
47C2×#638—21no—
48C22×C3⋊Dic3—21no—
49C2×C4⋊(C3⋊D3)D411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×#634D411yescharacteristic
52C2×C3×Dic6—21no—
53C32×C22⋊C4—21no—
54C32×C22⋊C4—21no—
55C32×C42C2311yescharacteristic
56#3757—21no—
57#3752—21no—
58#3752—21no—
59#3752—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)D411yescharacteristic
62C4⋊(C3⋊Dic3)D411yescharacteristic
63#3750—21no—
64#3750—21no—
65#3750—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1662—91noSylow
72C3×C4⋊Q8—31no—
73C3×#124—21no—
74C3×#124C2×D311yescharacteristic
75C3×#124C2×D311yescharacteristic
76#946—62no—
77#946—61no—
78#946—61no—
79#939—62no—
80#939—61no—
81#939—61no—
82#886—61no—
83#886—61no—
84#886—62no—
85#884—61no—
86#884—61no—
87#884—62no—
88#883—61no—
89#883—61no—
90#883—62no—
91#878—61no—
92#878—61no—
93#878—62no—
94#875—31no—
95#875—31no—
96#875—61no—
97#870—31no—
98#870—31no—
99#870—61no—
100#869C2×D311yescharacteristic
101C3×#103—61no—
102C3×#102—61no—
103C3×#97—31no—
104C3×#97—31no—
105C3×#97—31no—
106#835—21no—
107#835—61no—
108#835—61no—
109#832—21no—
110#821—61no—
111#816—61no—
112#816—61no—
113#816—61no—
114#810—61no—
115#809—61no—
116#803C2×D311yescharacteristic
117#803C2×D311yescharacteristic
118#803C2×D311yescharacteristic
119C23×C32—21no—
120C22×C3⋊D3—21no—
121C32×Q8—41no—
122C32×D4—41no—
123C2×C32×C4—21no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127#638—81no—
128#638—81no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—81no—
133C4⋊(C3⋊D3)—41no—
134C4×C3⋊D3—81no—
135#634—41no—
136C2×C3×Dic3—41no—
137C3×Dic6—42no—
138C3×C3⋊C8—41no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141#562—91no—
142#491—91no—
143#489—31no—
144#489—91no—
145#330—91no—
146#329—31no—
147#329—91no—
148C2×C3×Q8—21no—
149C2×C3×Q8—61no—
150C2×C3×Q8D1211yescharacteristic
151C2×C3×Q8#6711yescharacteristic
152C2×C3×D4—21no—
153C2×C3×D4D1211yescharacteristic
154C2×C3×D4#6711yescharacteristic
155C2×#67—62no—
156C2×#67—61no—
157C2×#67—61no—
158C2×#67—62no—
159C2×#67—61no—
160C2×#67—61no—
161C22×Dic3—62no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C2×D12—31no—
165C2×D12—31no—
166C2×D12—61no—
167C2×C4×D3—62no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×Dic6—21no—
171C2×Dic6—31no—
172C2×Dic6—31no—
173C2×Dic6—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C22⋊C4—22no—
180C3×C22⋊C4—22no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C42—21no—
186C3×C42C22×D311yescharacteristic
187C3×C42C22×D311yescharacteristic
188#217—62no—
189#217—61no—
190#217—61no—
191(C2×D3)⋊C4—62no—
192(C2×D3)⋊C4—62no—
193(C2×D3)⋊C4—62no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—61no—
200C4⋊Dic3—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3—31no—
203C4⋊Dic3—31no—
204C4⋊Dic3—31no—
205C4⋊Dic3—31no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—62no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211Dic3⋊C4—62no—
212Dic3⋊C4—62no—
213Dic3⋊C4—62no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C22×C32—41no—
224C22×C32—41no—
225C22×C32—41no—
226C22×C32#12011yescharacteristic
227C2×C3⋊D3—41no—
228C2×C3⋊D3—41no—
229C2×C3⋊D3—41no—
230C32×C4—21no—
231C32×C4—21no—
232C32×C4—21no—
233C32×C4—41no—
234C3⋊Dic3—41no—
235C3⋊Dic3—41no—
236C3⋊Dic3—41no—
237C3×Dic3—81no—
238C4⋊Q8—31no—
239#125—91no—
240#124—91no—
241#124D3211yescharacteristic
242#123—181no—
243#123—181no—
244C22⋊Q8—181no—
245C22⋊Q8—181no—
246#121—181no—
247#121—181no—
248#103—61no—
249#103—181no—
250#103—181no—
251#103—181no—
252#102—61no—
253#102—181no—
254#97—31no—
255#97—31no—
256#97—31no—
257C23×C3—22no—
258C23×C3—21no—
259C23×C3—21no—
260C22×D3—62no—
261C22×D3—61no—
262C22×D3—61no—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×Q8—81no—
266C3×Q8—122no—
267C3×D4—41no—
268C3×D4—41no—
269C3×D4—81no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—121no—
277C2×C3×C4C2×D1211yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283#67—242no—
284#67—242no—
285#67—241no—
286#67—241no—
287#67—241no—
288#67—241no—
289C2×Dic3—41no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—242no—
300C2×Dic3—241no—
301C2×Dic3—241no—
302D12—121no—
303D12—121no—
304D12—241no—
305C4×D3—242no—
306C4×D3—241no—
307C4×D3—241no—
308Dic6—42no—
309Dic6—121no—
310Dic6—121no—
311Dic6—241no—
312C3×C8—121no—
313C3×C8—121no—
314C3×C8—121no—
315C3⋊C8—41no—
316C3⋊C8—41no—
317C3⋊C8—41no—
318C2×C32—81no—
319C2×C32#45411yescharacteristic
320C2×C32#45511yescharacteristic
321C2×C32#45511yescharacteristic
322C3⋊D3—81no—
323C2×Q8—61no—
324C2×Q8—91no—
325C2×Q8#62611yescharacteristic
326C2×D4—91no—
327C2×D4—181no—
328C2×D4—181no—
329C2×D4#62611yescharacteristic
330C22×C4—181no—
331C22×C4—181no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—61no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4—91no—
338C4⋊C4—91no—
339C4⋊C4—181no—
340C4⋊C4—181no—
341C4⋊C4—181no—
342C4⋊C4—181no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—181no—
346C22⋊C4—181no—
347C22⋊C4—181no—
348C22⋊C4—181no—
349C42C2×D3211yescharacteristic
350C22×C3—21no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3#88211yescharacteristic
361C22×C3#93711yescharacteristic
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—121no—
366C2×D3—121no—
367C2×D3—121no—
368C2×D3—121no—
369C2×D3—121no—
370C2×D3—121no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—41no—
380C3×C4—42no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—241no—
384Dic3—81no—
385Dic3—122no—
386Dic3—122no—
387Dic3—122no—
388Dic3—121no—
389Dic3—121no—
390Dic3—121no—
391Dic3—121no—
392Dic3—121no—
393Dic3—121no—
394C32#166211yescharacteristic, complemented, Sylow
395C23—21no—
396C23—181no—
397Q8—41no—
398Q8—122no—
399Q8—361no—
400D4—41no—
401D4—361no—
402D4—721no—
403D4—721no—
404C2×C4—21no—
405C2×C4—121no—
406C2×C4—181no—
407C2×C4—181no—
408C2×C4—181no—
409C2×C4—721no—
410C2×C4—721no—
411C2×C4C2×#62611yescharacteristic
412C2×C4#381111yescharacteristic
413C2×C4#381111yescharacteristic
414C8—121no—
415C8—121no—
416C8—121no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—82no—
421C2×C3—81no—
422C2×C3—81no—
423C2×C3#474611yescharacteristic
424C2×C3#482511yescharacteristic
425C2×C3#482711yescharacteristic
426C2×C3#506111yescharacteristic
427C2×C3#520111yescharacteristic
428C2×C3#520211yescharacteristic
429D3—242no—
430D3—241no—
431D3—241no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—361no—
436C22—361no—
437C22—361no—
438C22#6398111yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—241no—
444C4—361no—
445C4—361no—
446C4—361no—
447C3—21no—
448C3#6835811yescharacteristic, complemented
449C3#7124611yescharacteristic, complemented
450C2—81no—
451C2—721no—
452C2#1059151411yescharacteristic
453C2#1059168611yescharacteristic
454C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32#120
prime radical#10596155C2
hypercenter#124D32
hypocenterC32#1662
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C3×#5055C2semidirect
3. #10590294C2semidirect
4. #10590289C2semidirect
5. C3×#4540C2semidirect
6. #10589089C2semidirect
7. #10589087C2semidirect
35. #5055D3semidirect
39. #4540D3semidirect
394. C32#1662semidirect
448. C3#68358semidirect
449. C3#71246semidirect

Maximal subgroups

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

subgroupindex
#105961552
C3×#50552
#105902942
#105902892
C3×#45402
#105890892
#105890872
#712463
#683583