Finite Group Databasebeta

← #11789718

Subgroups — #11789718

Order 1152.

487 conjugacy classes of subgroups.

The subgroup lattice has 427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#805C211yesmaximal, characteristic
2C3×C4×#208C211yesmaximal, characteristic, complemented
3#10591143C211yesmaximal, characteristic, complemented
4#10591110C211yesmaximal, characteristic
5#10591076C211yesmaximal, characteristic
6#10589389C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#70378—31nomaximal
9#69874—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#805—21no—
18C3×#805—21no—
19C3×#803—21no—
20C3×C4×C3⋊C8—21no—
21#63578—22no—
22#63568—22no—
23#63560C412yescomplemented
24#63558C412yescomplemented
25C2×C3×#104—31no—
26C3×C4×M16—31no—
27#5237—31no—
28#5236—31no—
29#5139—31no—
30#5132—31no—
31#5124—31no—
32#5124—31no—
33C2×#805D311yescharacteristic
34C4×#208D311yescharacteristic, complemented
35#4559—31no—
36#4556—31no—
37#4523—31no—
38#4523—31no—
39#4523—61no—
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C2×C3×#67—21no—
43C3×#235—21no—
44C3×#235—21no—
45C3×#235—21no—
46C3×#235—21no—
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C32×C42—21no—
51C32×C42D411yescharacteristic
52C32×C42D411yescharacteristic
53#3757—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4×C3⋊Dic3—21no—
56#3748—21no—
57#3748C2×C412yes—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208C2×C412yes—
64C3×#208D412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—91noSylow
69C2×C3×#41—31no—
70C2×#235C2×D311yescharacteristic
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C2×C3×C42—21no—
75C2×C3×C42C2×D311yescharacteristic
76C2×C3×C42C2×D311yescharacteristic
77#926—31no—
78#926—31no—
79#926—61no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#104—61no—
87C3×#104—61no—
88C3×#97—61no—
89C3×C4×C8—61no—
90#837—62no—
91#836—32no—
92#833—32no—
93#825—62no—
94#824—32no—
95#823—32no—
96#822—62no—
97#822—62no—
98#805—21no—
99#805—21no—
100#803—21no—
101C4×C3⋊C8—21no—
102C23×C32#4111yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4—42no—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C3⋊Dic3—41no—
114C3×#67—41no—
115C3×#67—41no—
116C2×C3×Dic3—21no—
117C3×D12—21no—
118C3×D12—21no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—21no—
122C3×Dic6—21no—
123C3⋊(C3⋊C8)—22no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127#430—91no—
128#421—91no—
129C2×#104—31no—
130#413—91no—
131C4×M16—31no—
132#344—91no—
133#339—91no—
134C3×#41—61no—
135C3×#41—61no—
136C3×#41—61no—
137C3×#41—61no—
138C2×C3×Q8—31no—
139C2×C3×D4—31no—
140C2×C3×D4—61no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—41no—
145C22×C3×C4—61no—
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C22×D311yescharacteristic
148C2×#67—21no—
149#235—21no—
150#235—21no—
151#235—21no—
152#235—21no—
153C2×D12C4×D311yescharacteristic
154C2×C4×D3—21no—
155C2×Dic6C4×D311yescharacteristic
156C3×M16—32no—
157C3×M16—32no—
158C3×M16—61no—
159C3×M16—61no—
160C3×M16—61no—
161C3×M16—61no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—41no—
170C3×C42#6711yescharacteristic
171C3×C42#6711yescharacteristic
172C3×C42#6711yescharacteristic
173C3×C42#6711yescharacteristic
174#217—61no—
175#217—61no—
176#217—121no—
177C4⋊Dic3—62no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182C4×Dic3—121no—
183#208—21no—
184#208—21no—
185#208—21no—
186#208—21no—
187#208—32no—
188#208—32no—
189#208—62no—
190#208—61no—
191#208—61no—
192#208—121no—
193#208C4×D312yes—
194#208D1212yes—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—121no—
201C22×C32—41no—
202C22×C32#11711yescharacteristic
203C22×C32#12311yescharacteristic
204C22×C32#12411yescharacteristic
205C2×C3×D3—41no—
206C2×C3×D3—81no—
207C32×C4—22no—
208C32×C4—41no—
209C32×C4C4×D411yescharacteristic
210C32×C4C4×D411yescharacteristic
211C32×C4#12111yescharacteristic
212C32×C4#12611yescharacteristic
213C3⋊Dic3—81no—
214C3×Dic3—41no—
215C2×#41—31no—
216C2×M16—31no—
217C2×M16—31no—
218C2×M16—31no—
219C2×M16—91no—
220#117—91no—
221C2×C42D3211yescharacteristic
222#108—182no—
223#104—61no—
224#104—61no—
225#104—182no—
226#101—92no—
227#100—92no—
228#97—61no—
229C4×C8—61no—
230C23×C3—21no—
231C23×C3—61no—
232C23×C3#23511yescharacteristic
233C23×C3#23711yescharacteristic
234C22×D3—21no—
235C3×Q8—61no—
236C3×Q8—61no—
237C3×D4—61no—
238C3×D4—61no—
239C3×D4—121no—
240C3×D4—121no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—44no—
256C2×C3×C4—61no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4C2×C4×D311yescharacteristic
260C2×C3×C4C2×C4×D311yescharacteristic
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4#23711yescharacteristic
268C2×C3×C4#23711yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271#67—41no—
272#67—41no—
273C2×Dic3—21no—
274C2×Dic3—122no—
275C2×Dic3—121no—
276C2×Dic3—121no—
277D12—21no—
278D12—21no—
279C4×D3—41no—
280C4×D3—41no—
281Dic6—21no—
282Dic6—21no—
283C3×C8—62no—
284C3×C8—62no—
285C3×C8—121no—
286C3⋊C8—22no—
287C3⋊C8—22no—
288C3⋊C8—41no—
289C3⋊C8—62no—
290C3⋊C8—62no—
291C3⋊C8—122no—
292C2×C32—21no—
293C2×C32—21no—
294C2×C32—21no—
295C2×C32#38811yescharacteristic
296C3×D3—81no—
297#41—61no—
298#41—61no—
299#41—61no—
300#41—61no—
301C2×Q8—31no—
302C2×D4—31no—
303C2×D4—61no—
304C22×C4—21no—
305C22×C4—61no—
306C22×C4C2×D3211yescharacteristic
307M16—32no—
308M16—32no—
309M16—61no—
310M16—61no—
311M16—61no—
312M16—61no—
313M16—92no—
314M16—181no—
315C2×C8—61no—
316C2×C8—61no—
317C2×C8—61no—
318C2×C8—181no—
319C4⋊C4—181no—
320C22⋊C4—181no—
321C42—21no—
322C42—181no—
323C42#62511yescharacteristic
324C42#62511yescharacteristic
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—42no—
331C22×C3—121no—
332C22×C3—241no—
333C22×C3#87211yescharacteristic
334C22×C3#87511yescharacteristic
335C22×C3#87711yescharacteristic
336C22×C3#88511yescharacteristic
337C22×C3#92911yescharacteristic
338C22×C3#93511yescharacteristic
339C2×D3—41no—
340C2×D3—81no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—42no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—42no—
351C3×C4—121no—
352C3×C4C4×D1211yescharacteristic
353C3×C4#87611yescharacteristic
354C3×C4#87911yescharacteristic
355C3×C4#67⋊C411yescharacteristic
356C3×C4C4×#6711yescharacteristic
357C3×C4C4×#6711yescharacteristic
358C3×C4#93011yescharacteristic
359C3×C4#93811yescharacteristic
360Dic3—41no—
361Dic3—242no—
362Dic3—241no—
363Dic3—241no—
364C32#193211yescharacteristic, complemented, Sylow
365C23—61no—
366C23#380411yescharacteristic
367Q8—61no—
368Q8—61no—
369D4—61no—
370D4—61no—
371D4—121no—
372D4—121no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—61no—
377C2×C4—121no—
378C2×C4—121no—
379C2×C4—361no—
380C2×C4#379511yescharacteristic
381C2×C4#379811yescharacteristic
382C2×C4C4×D3211yescharacteristic
383C2×C4D3×D1211yescharacteristic
384C2×C4#380411yescharacteristic
385C2×C4C2×#62511yescharacteristic
386C8—62no—
387C8—62no—
388C8—121no—
389C8—182no—
390C2×C3—22no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3—241no—
401C2×C3#494011yescharacteristic
402C2×C3#494411yescharacteristic
403D3—81no—
404C22—41no—
405C22—121no—
406C22—241no—
407C22#6385211yescharacteristic
408C22#6387711yescharacteristic
409C22#6396111yescharacteristic
410C4—22no—
411C4—41no—
412C4—121no—
413C4—721no—
414C4#6385911yescharacteristic
415C4#6388011yescharacteristic
416C4C4×#62511yescharacteristic
417C4#6390811yescharacteristic
418C3—21no—
419C3#6987411yescharacteristic, complemented
420C3#7037811yescharacteristic, complemented
421C2—21no—
422C2—21no—
423C2—21no—
424C2—241no—
425C2#1059127911yescharacteristic
subgroupG/H
centerC4#63908
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC2×C32#388
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#208C2semidirect
3. #10591143C2semidirect
6. #10589389C2semidirect
7. #10589171C2semidirect
23. #63560C4semidirect
24. #63558C4semidirect
34. C4×#208D3semidirect
364. C32#1932semidirect
419. C3#69874semidirect
420. C3#70378semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8052
C3×C4×#2082
#105911432
#105911102
#105910762
#105893892
#105891712
#703783
#698743