Finite Group Databasebeta

← #11780655

Subgroups — #11780655

Order 1152.

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

normal subgroups only

This group has 451 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#10593953C211yesmaximal, characteristic
2C3×#4702C211yesmaximal, characteristic, complemented
3#10590376C211yesmaximal, characteristic, complemented
4#10590294C211yesmaximal, characteristic, complemented
5#10589330C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#71392—31nomaximal
9#68356—31nomaximal
10#64084C2211yescharacteristic
11C3×#875C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63910—21no—
15#63896—21no—
16#63890—21no—
17#63888—21no—
18#63886—21no—
19#63854—21no—
20C2×#3718—21no—
21C2×#3715—21no—
22C32×#97C2211yescharacteristic
23#63630C2211yescharacteristic
24C3×#818—21no—
25C3×#817—21no—
26C3×#803C2211yescharacteristic
27#63567—21no—
28#63564—21no—
29#5700—31no—
30#5684—31no—
31C3×#501—31no—
32#5089—31no—
33#5086—31no—
34#5060—31no—
35#4714—31no—
36#4702D311yescharacteristic, complemented
37C3×#329—31no—
38#4543—31no—
39#4465—31no—
40#4464—31no—
41#4464—31no—
42#4464—61no—
43#4464D311yescharacteristic, complemented
44C2×C4⋊(C3⋊D3)D411yescharacteristic
45C2×#634D411yescharacteristic
46C2×C3×D12D411yescharacteristic
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×#626—21no—
50C2×#626—21no—
51C2×#624—21no—
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55#3752—21no—
56#3752—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C2×C3×C3⋊C8—21no—
67#3724—21no—
68Dic3⋊Dic3—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71#3718—42no—
72#3715—42no—
73#1661—91noSylow
74C3×C4⋊Q8—31no—
75C3×#125—31no—
76C3×#124—31no—
77#946—61no—
78C2×#216—61no—
79C2×#216—61no—
80C2×#215—61no—
81#939—61no—
82C2×#214—61no—
83#896—61no—
84#896—61no—
85#895—61no—
86#895—61no—
87#894—61no—
88#894—61no—
89#886—61no—
90#884—61no—
91#883—61no—
92#878—61no—
93#875—31no—
94#875—31no—
95#875—61no—
96#875C2×D311yescharacteristic
97#870C2×D311yescharacteristic
98#869C2×D311yescharacteristic
99C3×#107—61no—
100C3×#106—61no—
101C3×#97—21no—
102C3×#97—31no—
103C3×#97C2×D311yescharacteristic
104C3×#97C2×D311yescharacteristic
105#821—61no—
106#818—21no—
107#817—21no—
108#816—61no—
109#810—61no—
110#809—61no—
111#803—31no—
112#803—31no—
113#803—61no—
114#803C2×D311yescharacteristic
115C22×C3⋊D3—21no—
116C22×C3×D3—21no—
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—41no—
127C3×D12—41no—
128C3×Dic6—41no—
129C3×Dic6—41no—
130C3×Dic6—41no—
131#626—81no—
132#626—81no—
133#624—81no—
134D3×Dic3—81no—
135C32×C8—22no—
136C3⋊(C3⋊C8)—22no—
137C3×C3⋊C8—41no—
138#562—91no—
139#501—31no—
140#497—91no—
141#489—91no—
142#330—91no—
143#329—31no—
144#329—91no—
145C2×C3×Q8—31no—
146C2×C3×Q8—61no—
147C2×C3×D4—31no—
148C2×#67—61no—
149C2×#67—61no—
150C22×Dic3—61no—
151C2×D12—31no—
152C2×D12—31no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12D1211yescharacteristic
157C2×C4×D3—61no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×Dic6—21no—
161C2×Dic6—31no—
162C2×Dic6—31no—
163C2×Dic6—61no—
164C2×Dic6D1211yescharacteristic
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—41no—
168C2×C3×C8—61no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C22⋊C4—61no—
176C3×C22⋊C4—61no—
177C3×C42—21no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#217—61no—
181#216—122no—
182#216—122no—
183#215—122no—
184#214—122no—
185(C2×D3)⋊C4—21no—
186(C2×D3)⋊C4—21no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—121no—
195(C2×D3)⋊C4—121no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—61no—
199C4⋊Dic3#6711yescharacteristic
200C4⋊Dic3#6711yescharacteristic
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210C22×C32#12011yescharacteristic
211C2×C3⋊D3—41no—
212C2×C3⋊D3—41no—
213C2×C3⋊D3—41no—
214C2×C3×D3—41no—
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—21no—
220C3⋊Dic3—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#124—91no—
231#123—181no—
232#123—181no—
233C22⋊Q8—181no—
234C22⋊Q8—181no—
235#121—181no—
236#121—181no—
237#107—61no—
238#106—61no—
239#103—181no—
240#102—181no—
241#97—31no—
242#97—91no—
243#97D3211yescharacteristic
244C23×C3—61no—
245C22×D3—21no—
246C22×D3—61no—
247C22×D3—61no—
248C22×D3—121no—
249C3×Q8—121no—
250C3×Q8—121no—
251C3×Q8—121no—
252C3×D4—121no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—121no—
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4C2×#6711yescharacteristic
266#67—241no—
267#67—241no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—41no—
272C2×Dic3—61no—
273C2×Dic3—61no—
274C2×Dic3—121no—
275C2×Dic3—241no—
276D12—41no—
277D12—121no—
278D12—121no—
279D12—241no—
280D12—241no—
281D12—241no—
282C4×D3—241no—
283C4×D3—241no—
284C4×D3—241no—
285Dic6—41no—
286Dic6—41no—
287Dic6—41no—
288Dic6—121no—
289Dic6—121no—
290Dic6—241no—
291C3×C8—22no—
292C3×C8—22no—
293C3×C8—42no—
294C3×C8—121no—
295C3⋊C8—41no—
296C3⋊C8—62no—
297C3⋊C8—62no—
298C3⋊C8—122no—
299C2×C32#45311yescharacteristic
300C2×C32#45511yescharacteristic
301C2×C32#45611yescharacteristic
302C3⋊D3—81no—
303C3×D3—81no—
304C2×Q8—31no—
305C2×Q8—61no—
306C2×Q8—91no—
307C2×D4—31no—
308C2×D4—91no—
309C2×D4—181no—
310C2×D4—181no—
311C22×C4—181no—
312C22×C4—181no—
313Q16—362no—
314SD16—362no—
315C2×C8—21no—
316C2×C8—61no—
317C2×C8—181no—
318C4⋊C4—31no—
319C4⋊C4—31no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—181no—
325C4⋊C4—181no—
326C22⋊C4—61no—
327C22⋊C4—61no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C22⋊C4—181no—
331C22⋊C4—181no—
332C42C2×D3211yescharacteristic
333C22×C3—21no—
334C22×C3—121no—
335C22×C3—121no—
336C22×C3—121no—
337C22×C3#88211yescharacteristic
338C22×C3#93711yescharacteristic
339C2×D3—41no—
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—121no—
343C2×D3—121no—
344C2×D3—121no—
345C2×D3—121no—
346C2×D3—121no—
347C2×D3—121no—
348C2×D3—241no—
349C2×D3—241no—
350C2×D3—241no—
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—121no—
361C3×C4—121no—
362C3×C4—121no—
363C3×C4—241no—
364Dic3—41no—
365Dic3—41no—
366Dic3—41no—
367Dic3—81no—
368Dic3—121no—
369Dic3—121no—
370Dic3—241no—
371C32#166111yescharacteristic, complemented, Sylow
372C23—61no—
373C23—181no—
374Q8—121no—
375Q8—121no—
376Q8—121no—
377Q8—361no—
378D4—121no—
379D4—361no—
380D4—721no—
381D4—721no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—121no—
386C2×C4—181no—
387C2×C4—721no—
388C2×C4—721no—
389C2×C4D3×D1211yescharacteristic
390C2×C4#380211yescharacteristic
391C2×C4D3×#6711yescharacteristic
392C8—22no—
393C8—121no—
394C8—182no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—241no—
399C2×C3#474711yescharacteristic
400C2×C3#482511yescharacteristic
401C2×C3#482611yescharacteristic
402C2×C3#509511yescharacteristic
403C2×C3#519811yescharacteristic
404C2×C3#520211yescharacteristic
405D3—81no—
406D3—241no—
407D3—241no—
408D3—481no—
409C22—121no—
410C22—121no—
411C22—121no—
412C22—361no—
413C22—361no—
414C22—361no—
415C22#6392211yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—121no—
420C4—121no—
421C4—121no—
422C4—241no—
423C4—361no—
424C3—21no—
425C3#6835611yescharacteristic, complemented
426C3#7139211yescharacteristic, complemented
427C2—241no—
428C2—721no—
429C2#1059039911yescharacteristic
430C2#1059101111yescharacteristic
431C2#1059101411yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radical#10593953C2
hypercenter#97D32
hypocenterC32#1661
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C3×#4702C2semidirect
3. #10590376C2semidirect
4. #10590294C2semidirect
5. #10589330C2semidirect
6. C3×#4464C2semidirect
7. #10589088C2semidirect
36. #4702D3semidirect
43. #4464D3semidirect
371. C32#1661semidirect
425. C3#68356semidirect
426. C3#71392semidirect

Maximal subgroups

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

subgroupindex
#105939532
C3×#47022
#105903762
#105902942
#105893302
C3×#44642
#105890882
#713923
#683563