Finite Group Databasebeta

← #11790008

Subgroups — #11790008

Order 1152.

517 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63642C211yesmaximal, characteristic, complemented
2C3×#5110C211yesmaximal, characteristic
3C3×#5102C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5#10591083C211yesmaximal, characteristic
6#10589165C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#70536—31nomaximal
9#69998—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63642—22no—
18C3×(C2×D3)⋊C8—22no—
19C3×Dic3⋊C8—22no—
20#63568—22no—
21#63565C412yescomplemented
22#63562C412yescomplemented
23C3×#424—31no—
24C3×#408—31no—
25C2×#837—31no—
26#5233—31no—
27C2×#825—31no—
28#5110D311yescharacteristic
29#5102D311yescharacteristic, complemented
30C2×#815—31no—
31C2×#815—31no—
32C2×#815—61no—
33#5002—31no—
34#4558—31no—
35#4558—31no—
36#4555—31no—
37#4532—31no—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C2×C3×#67—21no—
41C3×#235—21no—
42C3×#235—21no—
43C3×#235—21no—
44C3×#235—21no—
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×Dic6C2×C411yescharacteristic
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C2×C32×C8D412yes—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3D412yes—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)C2×C412yes—
56C3×#217—21no—
57C3×C4⋊Dic3C2×C412yes—
58C3×C4×Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1938—91noSylow
66C2×C3×#41—31no—
67C2×#235C2×D311yescharacteristic
68C2×C3×M16—31no—
69C2×C3×M16—31no—
70C22×C3×C8—21no—
71C22×C3×C8C2×D311yescharacteristic
72C22×C3×C8C2×D311yescharacteristic
73C3×#117—31no—
74#926C2×D311yescharacteristic
75C2×C4×Dic3—31no—
76C2×C4×Dic3—31no—
77C2×C4×Dic3—61no—
78C2×#208C2×D311yescharacteristic
79C2×#208C2×D311yescharacteristic
80C22×C3⋊C8—31no—
81C22×C3⋊C8—31no—
82C22×C3⋊C8—61no—
83C3×C4⋊C8—62no—
84C3×C22⋊C8—62no—
85#837—62no—
86#835—32no—
87#832—32no—
88#825—62no—
89(C2×D3)⋊C8—22no—
90#815—62no—
91#815—62no—
92#815—64no—
93Dic3⋊C8—22no—
94#810—32no—
95#809—32no—
96C23×C32#4111yescharacteristic
97C22×C3×D3—21no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—42no—
106C3×#67—41no—
107C3×#67—41no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—21no—
110C3×D12—21no—
111C3×D12—21no—
112C3×C4×D3—41no—
113C3×C4×D3—41no—
114C3×Dic6—21no—
115C3×Dic6—21no—
116C32×C8—22no—
117C3⋊(C3⋊C8)—22no—
118C3×C3⋊C8—41no—
119C3×C3⋊C8—41no—
120#424—31no—
121C2×#104—91no—
122#416—91no—
123#408—31no—
124C2×#97—91no—
125#341—91no—
126#339—91no—
127C3×#41—61no—
128C3×#41—61no—
129C3×#41—61no—
130C3×#41—61no—
131C2×C3×Q8—31no—
132C2×C3×D4—31no—
133C2×C3×D4—61no—
134C22×C3×C4—21no—
135C22×C3×C4—61no—
136C22×C3×C4C22×D311yescharacteristic
137C22×C3×C4C22×D311yescharacteristic
138C2×#67—21no—
139C22×Dic3—62no—
140C22×Dic3—61no—
141C22×Dic3—61no—
142#235—21no—
143#235—21no—
144#235—21no—
145#235—21no—
146C2×D12C4×D311yescharacteristic
147C2×C4×D3—21no—
148C2×Dic6C4×D311yescharacteristic
149C3×M16—61no—
150C3×M16—61no—
151C3×M16—61no—
152C3×M16—61no—
153C2×C3×C8—22no—
154C2×C3×C8—22no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—22no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C2×C3×C8#6712yes—
163C2×C3×C8#6712yes—
164C3×C4⋊C4—32no—
165C3×C22⋊C4—61no—
166C3×C42—61no—
167#217—21no—
168C4⋊Dic3C4×D312yes—
169C4×Dic3—21no—
170C4×Dic3—32no—
171C4×Dic3—32no—
172C4×Dic3—62no—
173C4×Dic3—62no—
174C4×Dic3—61no—
175C4×Dic3—61no—
176#208—21no—
177#208—21no—
178#208—21no—
179#208—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—32no—
183C2×C3⋊C8—32no—
184C2×C3⋊C8—62no—
185C2×C3⋊C8—62no—
186C2×C3⋊C8—62no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C22×C32—22no—
192C22×C32C4×D411yescharacteristic
193C22×C32#12311yescharacteristic
194C22×C32#12611yescharacteristic
195C2×C3×D3—41no—
196C2×C3×D3—42no—
197C32×C4#11711yescharacteristic
198C32×C4C4×D411yescharacteristic
199C32×C4#12111yescharacteristic
200C32×C4#12411yescharacteristic
201C3⋊Dic3—42no—
202C3×Dic3—41no—
203C3×Dic3—42no—
204C2×#41—31no—
205C2×M16—31no—
206C2×M16—31no—
207C22×C8—91no—
208C22×C8D3211yescharacteristic
209#117—31no—
210C2×C42—91no—
211C4⋊C8—62no—
212#104—182no—
213#103—92no—
214#102—92no—
215C22⋊C8—62no—
216#97—182no—
217C23×C3—21no—
218C23×C3—61no—
219C23×C3#23511yescharacteristic
220C23×C3#23511yescharacteristic
221C22×D3—21no—
222C3×Q8—61no—
223C3×Q8—61no—
224C3×D4—61no—
225C3×D4—61no—
226C3×D4—121no—
227C3×D4—121no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—62no—
235C2×C3×C4—61no—
236C2×C3×C4—121no—
237C2×C3×C4—121no—
238C2×C3×C4C2×C4×D311yescharacteristic
239C2×C3×C4C2×C4×D311yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4#23711yescharacteristic
243C2×C3×C4#23711yescharacteristic
244C2×C3×C4#23711yescharacteristic
245C2×C3×C4#23711yescharacteristic
246C2×C3×C4#23911yescharacteristic
247C2×C3×C4#23911yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250#67—41no—
251#67—41no—
252C2×Dic3—22no—
253C2×Dic3—21no—
254C2×Dic3—64no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—124no—
258C2×Dic3—122no—
259C2×Dic3—122no—
260D12—21no—
261D12—21no—
262C4×D3—41no—
263C4×D3—41no—
264Dic6—21no—
265Dic6—21no—
266C3×C8—24no—
267C3×C8—22no—
268C3×C8—22no—
269C3×C8—121no—
270C3×C8—121no—
271C3⋊C8—41no—
272C3⋊C8—41no—
273C3⋊C8—64no—
274C3⋊C8—62no—
275C3⋊C8—62no—
276C2×C32—21no—
277C2×C32—21no—
278C2×C32#38811yescharacteristic
279C2×C32#44412yes—
280C3×D3—81no—
281#41—61no—
282#41—61no—
283#41—61no—
284#41—61no—
285C2×Q8—31no—
286C2×D4—31no—
287C2×D4—61no—
288C22×C4—61no—
289C22×C4—181no—
290C22×C4C2×D3211yescharacteristic
291M16—61no—
292M16—61no—
293M16—61no—
294M16—61no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—61no—
298C2×C8—61no—
299C2×C8—92no—
300C2×C8—181no—
301C2×C8—181no—
302C2×C8#62512yes—
303C4⋊C4—32no—
304C22⋊C4—61no—
305C42—61no—
306C42—92no—
307C42—181no—
308C22×C3—24no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—122no—
315C22×C3—121no—
316C22×C3#87911yescharacteristic
317C22×C3#88311yescharacteristic
318C22×C3#89411yescharacteristic
319C22×C3#89811yescharacteristic
320C22×C3C4×#6711yescharacteristic
321C22×C3C4×#6711yescharacteristic
322C2×D3—42no—
323C2×D3—41no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—122no—
329C3×C4—121no—
330C3×C4#87711yescharacteristic
331C3×C4#67⋊C411yescharacteristic
332C3×C4#89211yescharacteristic
333C3×C4#89311yescharacteristic
334C3×C4#93611yescharacteristic
335C3×C4#93911yescharacteristic
336C3×C4#93911yescharacteristic
337C3×C4#94711yescharacteristic
338Dic3—42no—
339Dic3—41no—
340Dic3—124no—
341Dic3—122no—
342Dic3—122no—
343C32#193811yescharacteristic, complemented, Sylow
344C23—61no—
345C23#379811yescharacteristic
346Q8—61no—
347Q8—61no—
348D4—61no—
349D4—61no—
350D4—121no—
351D4—121no—
352C2×C4—62no—
353C2×C4—61no—
354C2×C4—121no—
355C2×C4—121no—
356C2×C4—182no—
357C2×C4—362no—
358C2×C4#379611yescharacteristic
359C2×C4#379611yescharacteristic
360C2×C4C4×D3211yescharacteristic
361C2×C4#380511yescharacteristic
362C2×C4C2×#62511yescharacteristic
363C2×C4#381111yescharacteristic
364C8—22no—
365C8—121no—
366C8—121no—
367C8—182no—
368C2×C3—22no—
369C2×C3—22no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—22no—
376C2×C3—241no—
377C2×C3#494511yescharacteristic
378C2×C3#499011yescharacteristic
379C2×C3#514512yes—
380C2×C3#514512yes—
381D3—81no—
382C22—22no—
383C22—121no—
384C22—122no—
385C22#6385311yescharacteristic
386C22#6386211yescharacteristic
387C22C4×#62511yescharacteristic
388C4—121no—
389C4—122no—
390C4—362no—
391C4#6386311yescharacteristic
392C4#6387811yescharacteristic
393C4#6388111yescharacteristic
394C4#6398011yescharacteristic
395C3—21no—
396C3#6999811yescharacteristic, complemented
397C3#7053611yescharacteristic, complemented
398C2—21no—
399C2—21no—
400C2—241no—
401C2#1059092212yes—
402C2#1059128311yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1938
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63642C2semidirect
3. C3×#5102C2semidirect
6. #10589165C2semidirect
7. #10589160C2semidirect
21. #63565C4semidirect
22. #63562C4semidirect
29. #5102D3semidirect
343. C32#1938semidirect
396. C3#69998semidirect
397. C3#70536semidirect

Maximal subgroups

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

subgroupindex
C2×#636422
C3×#51102
C3×#51022
C2×#635682
#105910832
#105891652
#105891602
#705363
#699983