Finite Group Databasebeta

← #11780658

Subgroups — #11780658

Order 1152.

451 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 451 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C3×#5684C211yesmaximal, characteristic
2C3×#5055C211yesmaximal, characteristic, complemented
3#10590376C211yesmaximal, characteristic, complemented
4#10590315C211yesmaximal, characteristic, complemented
5#10589406C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71953—31nomaximal
9#71245—31nomaximal
10C32×#124C2211yescharacteristic
11C3×#946—21no—
12C3×#939—21no—
13C3×#886—21no—
14C3×#884—21no—
15C3×#883—21no—
16C3×#878—21no—
17C3×#875C2211yescharacteristic
18C3×#870C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C2×#3718—21no—
21C2×#3715—21no—
22#63630C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×#835—21no—
25C3×#832—21no—
26C3×#803C2211yescharacteristic
27#63576—21no—
28#63574—21no—
29C3×#562—31no—
30#5684D311yescharacteristic
31C3×#489—31no—
32#5086—31no—
33#5081—31no—
34#5064—31no—
35#5060—31no—
36#5055D311yescharacteristic, complemented
37#4543—31no—
38#4540—31no—
39#4540—31no—
40#4540—31no—
41#4540—61no—
42#4465—31no—
43#4464—31no—
44C2×C32×Q8D411yescharacteristic
45C2×C32×D4D411yescharacteristic
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C2×C3×D12D411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—21no—
52C2×C3×Dic6D411yescharacteristic
53C32×C22⋊C4—21no—
54C32×C22⋊C4—21no—
55C32×C42C2311yescharacteristic
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C2×C3×C3⋊C8—21no—
71#3718—42no—
72#3715—42no—
73#1661—91noSylow
74C3×C4⋊Q8—31no—
75C3×#125—31no—
76C3×#124—21no—
77C3×#124—31no—
78C3×#124C2×D311yescharacteristic
79C3×#124C2×D311yescharacteristic
80C3×#123—61no—
81C3×#123—61no—
82C3×C22⋊Q8—61no—
83C3×C22⋊Q8—61no—
84C3×#121—61no—
85C3×#121—61no—
86#946—21no—
87C2×#216—61no—
88C2×#216—61no—
89C2×#215—61no—
90#939—21no—
91C2×#214—61no—
92#886—21no—
93#884—21no—
94#883—21no—
95#878—21no—
96#875C2×D311yescharacteristic
97#870C2×D311yescharacteristic
98#869C2×D311yescharacteristic
99C3×#103—61no—
100C3×#102—61no—
101C3×#97—31no—
102#835—21no—
103#832—21no—
104#808—61no—
105#808—61no—
106#807—61no—
107#807—61no—
108#803—31no—
109#803—31no—
110#803—31no—
111#803—31no—
112#803—61no—
113#803—61no—
114#803C2×D311yescharacteristic
115C23×C32—21no—
116C22×C3×D3—21no—
117C32×Q8—41no—
118C32×D4—41no—
119C2×C32×C4—21no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C3×#67—81no—
124C3×#67—81no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—81no—
130C3×D12—41no—
131C3×C4×D3—81no—
132C3×Dic6—41no—
133C3×Dic6—41no—
134C3×Dic6—41no—
135C3⋊(C3⋊C8)—22no—
136C3⋊(C3⋊C8)—22no—
137C3×C3⋊C8—41no—
138#562—31no—
139#501—91no—
140#497—91no—
141#489—31no—
142#330—91no—
143#329—91no—
144#329—91no—
145C2×C3×Q8—21no—
146C2×C3×Q8—31no—
147C2×C3×Q8—61no—
148C2×C3×Q8#6711yescharacteristic
149C2×C3×Q8#6711yescharacteristic
150C2×C3×D4—21no—
151C2×C3×D4—31no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4#6711yescharacteristic
155C2×C3×D4#6711yescharacteristic
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C2×#67—21no—
159C2×#67—21no—
160C22×Dic3—21no—
161C2×D12#6711yescharacteristic
162C2×C4×D3—21no—
163C2×Dic6—21no—
164C2×Dic6#6711yescharacteristic
165C2×C3×C8—61no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C22⋊C4—21no—
175C3×C22⋊C4—21no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—21no—
178C3×C22⋊C4—41no—
179C3×C22⋊C4—41no—
180C3×C22⋊C4—61no—
181C3×C22⋊C4—61no—
182C3×C22⋊C4—61no—
183C3×C22⋊C4—61no—
184C3×C42—21no—
185C3×C42C22×D311yescharacteristic
186C3×C42C22×D311yescharacteristic
187#217—21no—
188#216—122no—
189#216—122no—
190#215—122no—
191#214—122no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3#6711yescharacteristic
199C4⋊Dic3#6711yescharacteristic
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—121no—
209C2×C3⋊C8—121no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32#12011yescharacteristic
214C2×C3×D3—41no—
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—41no—
221C3×Dic3—41no—
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—81no—
225C2×Q16—181no—
226C2×SD16—181no—
227C4⋊Q8—31no—
228#125—31no—
229#124—31no—
230#124D3211yescharacteristic
231#123—61no—
232#123—61no—
233C22⋊Q8—61no—
234C22⋊Q8—61no—
235#121—61no—
236#121—61no—
237#107—181no—
238#106—181no—
239#103—61no—
240#102—61no—
241#97—31no—
242#97—91no—
243#97—91no—
244C23×C3—21no—
245C23×C3—21no—
246C23×C3—41no—
247C23×C3—61no—
248C22×D3—21no—
249C3×Q8—41no—
250C3×Q8—41no—
251C3×Q8—81no—
252C3×Q8—121no—
253C3×Q8—121no—
254C3×Q8—121no—
255C3×D4—41no—
256C3×D4—41no—
257C3×D4—81no—
258C3×D4—121no—
259C3×D4—241no—
260C3×D4—241no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—41no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—121no—
271C2×C3×C4—241no—
272C2×C3×C4—241no—
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279#67—81no—
280#67—81no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—41no—
285C2×Dic3—81no—
286D12—41no—
287C4×D3—81no—
288Dic6—41no—
289Dic6—41no—
290Dic6—41no—
291C3×C8—121no—
292C3⋊C8—41no—
293C3⋊C8—62no—
294C3⋊C8—62no—
295C3⋊C8—62no—
296C3⋊C8—62no—
297C3⋊C8—122no—
298C3⋊C8—122no—
299C2×C32—81no—
300C2×C32#45311yescharacteristic
301C2×C32#45511yescharacteristic
302C2×C32#45611yescharacteristic
303C3×D3—81no—
304C2×Q8—31no—
305C2×Q8—61no—
306C2×Q8#62511yescharacteristic
307C2×D4—31no—
308C2×D4—61no—
309C2×D4—61no—
310C2×D4#62511yescharacteristic
311C22×C4—61no—
312C22×C4—61no—
313Q16—362no—
314SD16—362no—
315C2×C8—61no—
316C2×C8—181no—
317C2×C8—181no—
318C4⋊C4—31no—
319C4⋊C4—31no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—61no—
329C22⋊C4—61no—
330C22⋊C4—61no—
331C22⋊C4—61no—
332C42C2×D3211yescharacteristic
333C22×C3—21no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—81no—
341C22×C3—81no—
342C22×C3—81no—
343C22×C3—121no—
344C22×C3—121no—
345C22×C3—121no—
346C22×C3#93711yescharacteristic
347C22×C3#95311yescharacteristic
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—81no—
363C3×C4—121no—
364C3×C4—121no—
365C3×C4—121no—
366C3×C4—241no—
367Dic3—41no—
368Dic3—41no—
369Dic3—41no—
370Dic3—81no—
371C32#166111yescharacteristic, complemented, Sylow
372C23—21no—
373C23—61no—
374Q8—41no—
375Q8—121no—
376Q8—121no—
377Q8—121no—
378D4—41no—
379D4—121no—
380D4—241no—
381D4—241no—
382C2×C4—21no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—121no—
387C2×C4—241no—
388C2×C4—241no—
389C2×C4C2×#62511yescharacteristic
390C2×C4D3×#6711yescharacteristic
391C2×C4D3×#6711yescharacteristic
392C8—121no—
393C8—182no—
394C8—182no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—81no—
399C2×C3—81no—
400C2×C3—161no—
401C2×C3—241no—
402C2×C3#506111yescharacteristic
403C2×C3#519811yescharacteristic
404C2×C3#520511yescharacteristic
405C2×C3#524111yescharacteristic
406C2×C3#524211yescharacteristic
407C2×C3#524611yescharacteristic
408D3—81no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—121no—
413C22—121no—
414C22—121no—
415C22#6397611yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—41no—
420C4—121no—
421C4—121no—
422C4—121no—
423C4—241no—
424C3—21no—
425C3#7124511yescharacteristic, complemented
426C3#7195311yescharacteristic, complemented
427C2—81no—
428C2—241no—
429C2#1059151211yescharacteristic
430C2#1059166511yescharacteristic
431C2#1059168711yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32#120
prime radicalC3×#5684C2
hypercenter#124D32
hypocenterC32#1661
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. #10590376C2semidirect
4. #10590315C2semidirect
5. #10589406C2semidirect
6. #10589088C2semidirect
7. #10589086C2semidirect
36. #5055D3semidirect
371. C32#1661semidirect
425. C3#71245semidirect
426. C3#71953semidirect

Maximal subgroups

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

subgroupindex
C3×#56842
C3×#50552
#105903762
#105903152
#105894062
#105890882
#105890862
#719533
#712453