Finite Group Databasebeta

← #11789714

Subgroups — #11789714

Order 1152.

477 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#825C211yesmaximal, characteristic
2C3×#5124C211yesmaximal, characteristic, complemented
3#10591110C211yesmaximal, characteristic
4#10591076C211yesmaximal, characteristic
5Dic3×#208C211yesmaximal, characteristic, complemented
6#10589422C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70727—31nomaximal
9#70378—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#825—21no—
18C3×#825—21no—
19C3×#822—22no—
20#63568—22no—
21#63560C412yescomplemented
22#63558C412yescomplemented
23#63554—21no—
24Dic3×C3⋊C8—21no—
25C3×#430—31no—
26C2×C3×#104—31no—
27#5237—31no—
28#5236—31no—
29#5139—31no—
30C2×#825D311yescharacteristic
31#5132—31no—
32#5124D311yescharacteristic, complemented
33Dic3×M16—31no—
34C4×#208—31no—
35#4556—31no—
36#4556—31no—
37#4556—61no—
38#4555—31no—
39#4523—31no—
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—21no—
42C22×C3×Dic3—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×M16—21no—
51C32×M16—21no—
52C2×C32×C8—21no—
53#3757—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4×C3⋊Dic3—21no—
56#3748—21no—
57#3748C2×C412yes—
58C2×C3⋊(C3⋊C8)—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×#208—21no—
63C3×#208—21no—
64C3×#208C2×C412yes—
65C3×#208D412yes—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—91noSylow
69C2×C3×#41—31no—
70C2×#235C2×D311yescharacteristic
71C2×C3×M16—21no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×C42—31no—
77#926—31no—
78#926—31no—
79#926—61no—
80C2×C4×Dic3C2×D311yescharacteristic
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#108—62no—
87C3×#104—61no—
88C3×#104—61no—
89#837—62no—
90#836—32no—
91#833—32no—
92#825—21no—
93#825—21no—
94#825—62no—
95#824—32no—
96#823—32no—
97#822—22no—
98#815—61no—
99C8×Dic3—61no—
100#803—61no—
101C4×C3⋊C8—61no—
102C23×C32#4111yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C3⋊Dic3—41no—
111C3×#67—41no—
112C3×#67—41no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—42no—
117C3×D12—21no—
118C3×D12—21no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—21no—
122C3×Dic6—21no—
123C32×C8—41no—
124C3⋊(C3⋊C8)—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—22no—
127#430—31no—
128#421—91no—
129C2×#104—31no—
130#413—91no—
131C4×M16—91no—
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—61no—
143C22×C3×C4—61no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C2×#67—21no—
147C22×Dic3—21no—
148#235—21no—
149#235—21no—
150#235—21no—
151#235—21no—
152C2×D12C4×D311yescharacteristic
153C2×C4×D3—21no—
154C2×Dic6C4×D311yescharacteristic
155C3×M16—21no—
156C3×M16—21no—
157C3×M16—21no—
158C3×M16—21no—
159C3×M16—32no—
160C3×M16—32no—
161C3×M16—41no—
162C3×M16—41no—
163C3×M16—61no—
164C3×M16—61no—
165C2×C3×C8—22no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C42—31no—
171C3×C42—31no—
172C3×C42—61no—
173#217—62no—
174#217—61no—
175#217—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—121no—
179C4×Dic3—21no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182C4×Dic3—121no—
183C4×Dic3#6711yescharacteristic
184C4×Dic3#6711yescharacteristic
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#208#6712yes—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—121no—
200C22×C32—41no—
201C22×C32#11711yescharacteristic
202C22×C32#12311yescharacteristic
203C22×C32#12411yescharacteristic
204C2×C3×D3—41no—
205C2×C3×D3—81no—
206C32×C4C4×D411yescharacteristic
207C32×C4C4×D411yescharacteristic
208C32×C4#12111yescharacteristic
209C32×C4#12611yescharacteristic
210C3⋊Dic3—81no—
211C3×Dic3—22no—
212C3×Dic3—41no—
213C3×Dic3—41no—
214C2×#41—31no—
215C2×M16—31no—
216C2×M16—31no—
217C2×M16—91no—
218C2×M16D3211yescharacteristic
219#117—91no—
220C2×C42—31no—
221#108—62no—
222#104—61no—
223#104—61no—
224#104—182no—
225#101—92no—
226#100—92no—
227#97—181no—
228C4×C8—181no—
229C23×C3—21no—
230C23×C3—61no—
231C23×C3#23711yescharacteristic
232C23×C3#23911yescharacteristic
233C22×D3—21no—
234C3×Q8—61no—
235C3×Q8—61no—
236C3×D4—61no—
237C3×D4—61no—
238C3×D4—121no—
239C3×D4—121no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—61no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—122no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4C2×C4×D311yescharacteristic
253C2×C3×C4C2×C4×D311yescharacteristic
254C2×C3×C4#23511yescharacteristic
255C2×C3×C4#23511yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4#23711yescharacteristic
259C2×C3×C4#23711yescharacteristic
260C2×C3×C4#23711yescharacteristic
261C2×C3×C4#23911yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264#67—41no—
265#67—41no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—42no—
270C2×Dic3—122no—
271C2×Dic3—121no—
272C2×Dic3—121no—
273D12—21no—
274D12—21no—
275C4×D3—41no—
276C4×D3—41no—
277Dic6—21no—
278Dic6—21no—
279C3×C8—42no—
280C3×C8—41no—
281C3×C8—41no—
282C3×C8—62no—
283C3×C8—62no—
284C3⋊C8—22no—
285C3⋊C8—22no—
286C3⋊C8—62no—
287C3⋊C8—62no—
288C3⋊C8—122no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32#38811yescharacteristic
293C3×D3—81no—
294#41—61no—
295#41—61no—
296#41—61no—
297#41—61no—
298C2×Q8—31no—
299C2×D4—31no—
300C2×D4—61no—
301C22×C4—61no—
302C22×C4—61no—
303C22×C4C2×D3211yescharacteristic
304M16—21no—
305M16—21no—
306M16—32no—
307M16—32no—
308M16—61no—
309M16—61no—
310M16—92no—
311M16—181no—
312C2×C8—21no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—181no—
316C4⋊C4—181no—
317C22⋊C4—181no—
318C42—31no—
319C42—31no—
320C42—61no—
321C42—181no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—81no—
328C22×C3—121no—
329C22×C3—241no—
330C22×C3#87711yescharacteristic
331C22×C3#88511yescharacteristic
332C22×C3#89211yescharacteristic
333C22×C3#89411yescharacteristic
334C22×C3#93511yescharacteristic
335C22×C3#94711yescharacteristic
336C2×D3—41no—
337C2×D3—81no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—62no—
343C3×C4—121no—
344C3×C4—121no—
345C3×C4#87911yescharacteristic
346C3×C4#67⋊C411yescharacteristic
347C3×C4#89311yescharacteristic
348C3×C4#89811yescharacteristic
349C3×C4C4×#6711yescharacteristic
350C3×C4C4×#6711yescharacteristic
351C3×C4#93811yescharacteristic
352C3×C4#93911yescharacteristic
353Dic3—22no—
354Dic3—41no—
355Dic3—41no—
356Dic3—241no—
357Dic3—241no—
358Dic3—242no—
359C32#193211yescharacteristic, complemented, Sylow
360C23—61no—
361C23#379611yescharacteristic
362Q8—61no—
363Q8—61no—
364D4—61no—
365D4—61no—
366D4—121no—
367D4—121no—
368C2×C4—61no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—122no—
372C2×C4—121no—
373C2×C4—121no—
374C2×C4—361no—
375C2×C4#379511yescharacteristic
376C2×C4#379911yescharacteristic
377C2×C4C4×D3211yescharacteristic
378C2×C4#380511yescharacteristic
379C2×C4D3×#6711yescharacteristic
380C2×C4D3×#6711yescharacteristic
381C8—41no—
382C8—62no—
383C8—62no—
384C8—182no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—41no—
395C2×C3—241no—
396C2×C3#494411yescharacteristic
397C2×C3#499011yescharacteristic
398D3—81no—
399C22—41no—
400C22—121no—
401C22—241no—
402C22#6387811yescharacteristic
403C22#6388411yescharacteristic
404C22#6390711yescharacteristic
405C4—62no—
406C4—121no—
407C4—121no—
408C4—721no—
409C4#6386111yescharacteristic
410C4#6387911yescharacteristic
411C4#6390411yescharacteristic
412C4#6397011yescharacteristic
413C3—21no—
414C3#7037811yescharacteristic, complemented
415C3#7072711yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—21no—
419C2—241no—
420C2#1059128511yescharacteristic
subgroupG/H
centerC4#63970
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#388
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#5124C2semidirect
5. Dic3×#208C2semidirect
6. #10589422C2semidirect
7. #10589162C2semidirect
21. #63560C4semidirect
22. #63558C4semidirect
32. #5124D3semidirect
359. C32#1932semidirect
414. C3#70378semidirect
415. C3#70727semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8252
C3×#51242
#105911102
#105910762
Dic3×#2082
#105894222
#105891622
#707273
#703783