Finite Group Databasebeta

← #11779030

Subgroups — #11779030

Order 1152.

536 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593956C211yesmaximal, characteristic, complemented
2#10592547C211yesmaximal, characteristic, complemented
3#10590373C211yesmaximal, characteristic, complemented
4#10590349C211yesmaximal, characteristic
5C3×#4483C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68490—31nomaximal
9#68198—31nomaximal
10C2×#3744—21no—
11#64083C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63898—21no—
16D3×C4⋊Dic3—21no—
17#63887—22no—
18#63872—21no—
19#63857—21no—
20C2×#3717—22no—
21C2×#3714—21no—
22C32×C4⋊C8C2211yescharacteristic
23#63648—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26#63564—21no—
27#5730—31no—
28#5543—31no—
29#5085—31no—
30#5015—31no—
31#4848—31no—
32#4848—31no—
33#4848—61no—
34#4843—31no—
35#4693—31no—
36C3×#333—31no—
37C3×D4⋊C8—31no—
38#4484—31no—
39#4483D311yescharacteristic, complemented
40#4481D311yescharacteristic, complemented
41#4456—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×#634D411yescharacteristic
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6D412yes—
49C2×D3×Dic3—22no—
50C2×C32×C8—21no—
51C32×C42C2311yescharacteristic
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—21no—
54C4×C3⋊Dic3—21no—
55#3744—42no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62Dic3⋊Dic3—22no—
63Dic3⋊Dic3—22no—
64(C2×D3)⋊Dic3—22no—
65#3717—44no—
66#3714—42no—
67#1622—91noSylow
68C3×C4⋊Q8—31no—
69C3×C4×D4—31no—
70#946—62no—
71C2×#215—62no—
72D4×Dic3—61no—
73C2×#213—61no—
74C2×C4⋊Dic3—61no—
75#924—61no—
76C2×D24—61no—
77C2×#204—61no—
78C2×#204—61no—
79C2×#204—62no—
80C2×#204—62no—
81#897—61no—
82#893—61no—
83D3×C4⋊C4—61no—
84#890—61no—
85#890—61no—
86#878—62no—
87#874—31no—
88#874—31no—
89#874—61no—
90C4×D12C2×D311yescharacteristic
91#869C2×D311yescharacteristic
92C4×Dic6—31no—
93C4×Dic6—31no—
94C4×Dic6—61no—
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—41no—
108C22×C3×D3—21no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—21no—
114C4⋊(C3⋊D3)—41no—
115C4⋊(C3⋊D3)—41no—
116C4⋊(C3⋊D3)—42no—
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—41no—
119#634—21no—
120#634—21no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—21no—
123C3×D12—21no—
124C3×D12SD1612yescomplemented
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—42no—
128D3×Dic3—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—91no—
138D4⋊C8—31no—
139C2×C3×Q8—32no—
140C2×C3×D4—31no—
141C22×C3×C4—61no—
142C22×Dic3—62no—
143C2×D12—62no—
144C2×D12—61no—
145C2×D12—61no—
146C2×D12—61no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—121no—
151C2×D12—121no—
152C2×D12D1211yescharacteristic
153C2×C4×D3—21no—
154C2×C4×D3—62no—
155C2×Dic6—31no—
156C2×Dic6—31no—
157C2×Dic6—61no—
158C2×Dic6D1212yes—
159C2×C3×C8—22no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C22⋊C4—61no—
168C3×C42—21no—
169C3×C42C22×D311yescharacteristic
170C3×C42C22×D311yescharacteristic
171#217—62no—
172#215—124no—
173#213—122no—
174(C2×D3)⋊C4—21no—
175(C2×D3)⋊C4—62no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—31no—
179C4⋊Dic3—31no—
180C4⋊Dic3—61no—
181C4⋊Dic3—62no—
182C4⋊Dic3—62no—
183C4⋊Dic3D1211yescharacteristic
184Dic3⋊C4—62no—
185Dic3⋊C4—62no—
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—121no—
189C4×Dic3—61no—
190C4×Dic3—61no—
191C4×Dic3—121no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194D24—122no—
195#204—124no—
196#204—122no—
197#204—122no—
198#204—124no—
199C22×C32#12011yescharacteristic
200C2×C3⋊D3—81no—
201C2×C3⋊D3—81no—
202C2×C3⋊D3—81no—
203C2×C3×D3—22no—
204C2×C3×D3—41no—
205C2×C3×D3—41no—
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—91no—
224C4×D4—31no—
225C4×D4—181no—
226C2×C4⋊C4—181no—
227C4⋊C8—31no—
228C4⋊C8D3211yescharacteristic
229#102—181no—
230#102—181no—
231C4×C8—31no—
232C23×C3—61no—
233C22×D3—21no—
234C22×D3—122no—
235C22×D3—121no—
236C22×D3—121no—
237C3×Q8—122no—
238C3×D4—32no—
239C3×D4—61no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—61no—
244C2×C3×C4—62no—
245C2×C3×C4—121no—
246C2×C3×C4—121no—
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—22no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—121no—
260C2×Dic3—121no—
261C2×Dic3—242no—
262D12—21no—
263D12—122no—
264D12—122no—
265D12—122no—
266D12—122no—
267D12—121no—
268D12—121no—
269D12—121no—
270D12—121no—
271D12—121no—
272D12—121no—
273D12—121no—
274D12—121no—
275D12—241no—
276D12—241no—
277D12—242no—
278D12#20412yescomplemented
279C4×D3—41no—
280C4×D3—41no—
281C4×D3—242no—
282Dic6—42no—
283Dic6—62no—
284Dic6—61no—
285Dic6—61no—
286Dic6—61no—
287Dic6—61no—
288Dic6—121no—
289C3×C8—42no—
290C3×C8—41no—
291C3×C8—41no—
292C3×C8—62no—
293C3×C8—121no—
294C3⋊C8—22no—
295C3⋊C8—41no—
296C2×C32#44811yescharacteristic
297C2×C32#44911yescharacteristic
298C2×C32#45311yescharacteristic
299C3⋊D3—161no—
300C3×D3—42no—
301C2×Q8—32no—
302C2×Q8—91no—
303C2×D4—31no—
304C2×D4—181no—
305C2×D4—181no—
306C2×D4—181no—
307C22×C4—61no—
308C22×C4—182no—
309SD16—362no—
310SD16—364no—
311D8—362no—
312C2×C8—21no—
313C2×C8—61no—
314C2×C8—61no—
315C4⋊C4—31no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—91no—
319C4⋊C4—182no—
320C4⋊C4—182no—
321C4⋊C4—181no—
322C22⋊C4—61no—
323C22⋊C4—182no—
324C42—181no—
325C42C2×D3211yescharacteristic
326C22×C3—21no—
327C22×C3—62no—
328C22×C3—121no—
329C22×C3—121no—
330C22×C3#88211yescharacteristic
331C22×C3#88211yescharacteristic
332C2×D3—22no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—242no—
336C2×D3—242no—
337C2×D3—242no—
338C2×D3—241no—
339C2×D3—241no—
340C2×D3—241no—
341C2×D3—241no—
342C2×D3—241no—
343C2×D3—241no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—121no—
352C3×C4—122no—
353C3×C4C2×#20411yescharacteristic
354C3×C4#90911yescharacteristic
355C3×C4#91111yescharacteristic
356C3×C4D3×SD1611yescharacteristic
357C3×C4#91411yescharacteristic
358C3×C4#91611yescharacteristic
359C3×C4#91811yescharacteristic
360C3×C4#91911yescharacteristic
361Dic3—42no—
362Dic3—41no—
363Dic3—122no—
364Dic3—121no—
365Dic3—121no—
366Dic3—121no—
367Dic3—121no—
368Dic3—241no—
369C32#162211yescharacteristic, complemented, Sylow
370C23—61no—
371C23—361no—
372Q8—122no—
373Q8—181no—
374Q8—181no—
375D4—32no—
376D4—61no—
377D4—362no—
378D4—361no—
379D4—361no—
380D4—361no—
381D4—361no—
382C2×C4—61no—
383C2×C4—62no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4—181no—
387C2×C4—181no—
388C2×C4—722no—
389C2×C4D3×D1211yescharacteristic
390C2×C4D3×D1211yescharacteristic
391C2×C4#381111yescharacteristic
392C8—41no—
393C8—62no—
394C8—121no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—122no—
399C2×C3#473811yescharacteristic
400C2×C3#474711yescharacteristic
401C2×C3#478111yescharacteristic
402C2×C3#480611yescharacteristic
403C2×C3#481011yescharacteristic
404C2×C3#482211yescharacteristic
405D3—42no—
406D3—482no—
407D3—481no—
408D3—481no—
409C22—62no—
410C22—121no—
411C22—121no—
412C22—721no—
413C22—721no—
414C22—721no—
415C22#6392311yescharacteristic
416C4—21no—
417C4—122no—
418C4—121no—
419C4—361no—
420C4—361no—
421C4D3×#20411yescharacteristic
422C4#6380111yescharacteristic
423C4#6393711yescharacteristic
424C4#6395011yescharacteristic
425C3—21no—
426C3#6819811yescharacteristic, complemented
427C3#6849011yescharacteristic, complemented
428C2—122no—
429C2—1441no—
430C2#1059061711yescharacteristic
431C2#1059095111yescharacteristic
432C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#10590349C2
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. #10593956C2semidirect
2. #10592547C2semidirect
3. #10590373C2semidirect
5. C3×#4483C2semidirect
6. C3×#4481C2semidirect
7. #10589085C2semidirect
39. #4483D3semidirect
40. #4481D3semidirect
124. C3×D12SD16semidirect
278. D12#204semidirect
369. C32#1622semidirect
426. C3#68198semidirect
427. C3#68490semidirect

Maximal subgroups

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

subgroupindex
#105939562
#105925472
#105903732
#105903492
C3×#44832
C3×#44812
#105890852
#684903
#681983