Finite Group Databasebeta

← #11780533

Subgroups — #11780533

Order 1152.

447 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 447 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593857C211yesmaximal, characteristic, complemented
2C3×#4713C211yesmaximal, characteristic, complemented
3#10590371C211yesmaximal, characteristic
4#10590279C211yesmaximal, characteristic, complemented
5#10589330C211yesmaximal, characteristic, complemented
6C3×#4465C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#71249—31nomaximal
9#68371—31nomaximal
10#64084C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63897—21no—
15#63895—21no—
16#63895—21no—
17#63848—21no—
18#63848—21no—
19#63840—21no—
20C2×#3716—21no—
21C2×#3714—21no—
22C32×#97C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×#821—21no—
25C3×#821—21no—
26C3×#803C2211yescharacteristic
27#63562—21no—
28#63562—21no—
29#5699—31no—
30#5699—31no—
31C3×#490—31no—
32#5074—31no—
33#5071—31no—
34#5067—31no—
35#4713D311yescharacteristic, complemented
36#4712—31no—
37C3×#330—31no—
38#4543—31no—
39#4465—31no—
40#4465D311yescharacteristic, complemented
41#4464—31no—
42#4464—31no—
43#4464—61no—
44C2×C4⋊(C3⋊D3)D411yescharacteristic
45C2×#634D411yescharacteristic
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×#627—21no—
50C2×#624—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53#3752—21no—
54#3752—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C2×C3×C3⋊C8—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67#3722—21no—
68#3722—21no—
69#3722—21no—
70Dic32—21no—
71#3716—42no—
72#3714—42no—
73#1657—91noSylow
74C3×#127—31no—
75C3×#125—31no—
76C3×#125—31no—
77C2×#214—61no—
78C2×#213—61no—
79C2×D24—61no—
80C2×#204—61no—
81#898—61no—
82#898—61no—
83#898—61no—
84#898—61no—
85#897—61no—
86#897—61no—
87#896—61no—
88#896—61no—
89#894—61no—
90#894—61no—
91#888—61no—
92#888—61no—
93#875—31no—
94#875—31no—
95#875—61no—
96#874C2×D311yescharacteristic
97#870C2×D311yescharacteristic
98#870C2×D311yescharacteristic
99C3×#102—61no—
100C3×#102—61no—
101C3×#97—21no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105#832—61no—
106#832—61no—
107#821—21no—
108#821—21no—
109#809—61no—
110#809—61no—
111#803—31no—
112#803—31no—
113#803—61no—
114#803C2×D311yescharacteristic
115C22×C3⋊D3—21no—
116C22×C3×D3—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C4⋊(C3⋊D3)—41no—
122#634—41no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C3×D12—41no—
128C3×D12—41no—
129C3×D12—42no—
130C3×D12—42no—
131#627—81no—
132#624—81no—
133C32×C8—41no—
134C3⋊(C3⋊C8)—41no—
135C3×C3⋊C8—22no—
136#563—91no—
137#496—91no—
138#490—31no—
139#490—91no—
140#330—31no—
141#330—91no—
142#329—91no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×D12—21no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—31no—
150C2×D12—31no—
151C2×D12—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×Dic6—31no—
155C2×Dic6—31no—
156C2×Dic6—61no—
157C2×Dic6—61no—
158C2×Dic6—61no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—41no—
162C2×C3×C8—61no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C42—21no—
172C3×C42C22×D311yescharacteristic
173C3×C42C22×D311yescharacteristic
174#214—122no—
175#213—122no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—61no—
178(C2×D3)⋊C4—61no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—121no—
187(C2×D3)⋊C4—121no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3D1211yescharacteristic
191C4⋊Dic3D1211yescharacteristic
192C4⋊Dic3#6711yescharacteristic
193C4⋊Dic3#6711yescharacteristic
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206D24—122no—
207#204—122no—
208C22×C32#12011yescharacteristic
209C2×C3⋊D3—41no—
210C2×C3⋊D3—41no—
211C2×C3⋊D3—41no—
212C2×C3×D3—81no—
213C2×C3×D3—81no—
214C2×C3×D3—81no—
215C32×C4—21no—
216C32×C4—21no—
217C32×C4—21no—
218C3⋊Dic3—41no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—41no—
223C2×SD16—181no—
224C2×D8—181no—
225C4⋊Q8—181no—
226#127—31no—
227#126—181no—
228#126—181no—
229#125—31no—
230#125—31no—
231#124—91no—
232#123—181no—
233C22⋊Q8—181no—
234C22⋊Q8—181no—
235#102—61no—
236#102—61no—
237#102—181no—
238#102—181no—
239#97—31no—
240#97—91no—
241#97D3211yescharacteristic
242C23×C3—121no—
243C22×D3—41no—
244C22×D3—61no—
245C22×D3—61no—
246C22×D3—121no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—122no—
250C3×D4—122no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4C2×D1211yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—121no—
271D12—41no—
272D12—41no—
273D12—42no—
274D12—42no—
275D12—121no—
276D12—121no—
277D12—241no—
278C4×D3—241no—
279C4×D3—241no—
280Dic6—121no—
281Dic6—121no—
282Dic6—241no—
283Dic6—241no—
284Dic6—241no—
285C3×C8—41no—
286C3×C8—41no—
287C3×C8—42no—
288C3×C8—62no—
289C3⋊C8—22no—
290C3⋊C8—121no—
291C3⋊C8—121no—
292C3⋊C8—122no—
293C2×C32#45311yescharacteristic
294C2×C32#45411yescharacteristic
295C2×C32#45411yescharacteristic
296C3⋊D3—81no—
297C3×D3—161no—
298C2×Q8—91no—
299C2×Q8—181no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—91no—
304C22×C4—181no—
305SD16—362no—
306D8—362no—
307C2×C8—21no—
308C2×C8—61no—
309C2×C8—181no—
310C4⋊C4—31no—
311C4⋊C4—31no—
312C4⋊C4—31no—
313C4⋊C4—31no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C22⋊C4—181no—
321C22⋊C4—181no—
322C22⋊C4—181no—
323C22⋊C4—181no—
324C22⋊C4—181no—
325C42—181no—
326C42C2×D3211yescharacteristic
327C22×C3—21no—
328C22×C3—241no—
329C22×C3—241no—
330C22×C3—241no—
331C22×C3#88211yescharacteristic
332C22×C3#93711yescharacteristic
333C2×D3—81no—
334C2×D3—81no—
335C2×D3—81no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—121no—
339C2×D3—121no—
340C2×D3—121no—
341C2×D3—121no—
342C2×D3—241no—
343C2×D3—241no—
344C2×D3—241no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—121no—
355C3×C4—121no—
356C3×C4—121no—
357C3×C4—121no—
358Dic3—41no—
359Dic3—41no—
360Dic3—41no—
361Dic3—41no—
362Dic3—121no—
363Dic3—121no—
364Dic3—241no—
365C32#165711yescharacteristic, complemented, Sylow
366C23—121no—
367C23—181no—
368Q8—361no—
369Q8—721no—
370D4—121no—
371D4—121no—
372D4—122no—
373D4—122no—
374D4—361no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—181no—
380C2×C4—721no—
381C2×C4D3×D1211yescharacteristic
382C2×C4#380211yescharacteristic
383C2×C4D3×#6711yescharacteristic
384C8—41no—
385C8—62no—
386C8—361no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—481no—
391C2×C3#475311yescharacteristic
392C2×C3#482211yescharacteristic
393C2×C3#482711yescharacteristic
394C2×C3#506211yescharacteristic
395C2×C3#519811yescharacteristic
396C2×C3#520111yescharacteristic
397D3—161no—
398D3—241no—
399D3—241no—
400D3—481no—
401C22—241no—
402C22—241no—
403C22—241no—
404C22—361no—
405C22—361no—
406C22—361no—
407C22#6392211yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—121no—
412C4—121no—
413C4—121no—
414C4—121no—
415C4—361no—
416C3—21no—
417C3#6837111yescharacteristic, complemented
418C3#7124911yescharacteristic, complemented
419C2—481no—
420C2—721no—
421C2#1059040011yescharacteristic
422C2#1059101311yescharacteristic
423C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radical#10590371C2
hypercenter#97D32
hypocenterC32#1657
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593857C2semidirect
2. C3×#4713C2semidirect
4. #10590279C2semidirect
5. #10589330C2semidirect
6. C3×#4465C2semidirect
7. #10589088C2semidirect
35. #4713D3semidirect
40. #4465D3semidirect
365. C32#1657semidirect
417. C3#68371semidirect
418. C3#71249semidirect

Maximal subgroups

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

subgroupindex
#105938572
C3×#47132
#105903712
#105902792
#105893302
C3×#44652
#105890882
#712493
#683713