Finite Group Databasebeta

← #11789725

Subgroups — #11789725

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
1C3×#5005C211yesmaximal, characteristic
2#10591143C211yesmaximal, characteristic, complemented
3C2×#63568C211yesmaximal, characteristic
4#10591076C211yesmaximal, characteristic
5#10591060C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7C3×#4533C211yesmaximal, characteristic, complemented
8#70401—31nomaximal
9#69012—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#805—22no—
18#63578—22no—
19#63568—21no—
20#63568—21no—
21#63560C412yescomplemented
22#63558C412yescomplemented
23#63555—21no—
24#63553—21no—
25C3×#421—31no—
26#5237—31no—
27C2×#837—31no—
28C2×#825—31no—
29#5132—31no—
30#5124—31no—
31#5124—31no—
32Dic3×M16—31no—
33Dic3×M16—31no—
34#5005D311yescharacteristic
35C3×#344—31no—
36#4533D311yescharacteristic, complemented
37#4532—31no—
38#4532—31no—
39#4532—61no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
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×C4⋊C4—21no—
51C32×C22⋊C4—21no—
52C32×C42—21no—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
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—
74C3×#117—21no—
75C3×#117C2×D311yescharacteristic
76C3×#117C2×D311yescharacteristic
77C2×C4×Dic3—31no—
78C2×C4×Dic3—31no—
79C2×C4×Dic3—61no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C3×#104—62no—
87#837—61no—
88#837—61no—
89#836—32no—
90#833—32no—
91#825—61no—
92#825—61no—
93#824—32no—
94#823—32no—
95#822—62no—
96#822—62no—
97#815—61no—
98#815—61no—
99C8×Dic3—61no—
100C8×Dic3—61no—
101#805—22no—
102C23×C32#4111yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4—41no—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—42no—
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—31no—
129C2×#104—91no—
130#413—91no—
131C4×M16—91no—
132#344—31no—
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×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C2×#67—21no—
146C22×Dic3—61no—
147C22×Dic3—61no—
148C22×Dic3—121no—
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×C4⋊C4—22no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C22⋊C4—21no—
169C3×C22⋊C4—21no—
170C3×C22⋊C4—41no—
171C3×C42—21no—
172C3×C42—21no—
173C3×C42—41no—
174C4×Dic3—31no—
175C4×Dic3—31no—
176C4×Dic3—31no—
177C4×Dic3—31no—
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#208#6712yes—
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—81no—
208C32×C4C4×D411yescharacteristic
209C32×C4C4×D411yescharacteristic
210C32×C4#12111yescharacteristic
211C32×C4#12611yescharacteristic
212C3⋊Dic3—22no—
213C3⋊Dic3—41no—
214C3×Dic3—41no—
215C2×#41—31no—
216C2×M16—31no—
217C2×M16—31no—
218C2×M16—31no—
219C2×M16—91no—
220#117D3211yescharacteristic
221C2×C42—91no—
222#108—182no—
223#104—62no—
224#104—181no—
225#104—181no—
226#101—92no—
227#100—92no—
228#97—181no—
229C4×C8—181no—
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—42no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—61no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4C2×C4×D311yescharacteristic
254C2×C3×C4C2×C4×D311yescharacteristic
255C2×C3×C4#23511yescharacteristic
256C2×C3×C4#23511yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4#23711yescharacteristic
261C2×C3×C4#23711yescharacteristic
262C2×C3×C4#23711yescharacteristic
263C2×C3×C4#23911yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265#67—41no—
266#67—41no—
267C2×Dic3—21no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—121no—
273C2×Dic3—121no—
274C2×Dic3—122no—
275C2×Dic3—122no—
276C2×Dic3—124no—
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—61no—
305C22×C4—181no—
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—21no—
320C22⋊C4—21no—
321C42—21no—
322C42—91no—
323C42—91no—
324C42—181no—
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#87711yescharacteristic
335C22×C3#88311yescharacteristic
336C22×C3#88511yescharacteristic
337C22×C3#89411yescharacteristic
338C22×C3#93611yescharacteristic
339C2×D3—41no—
340C2×D3—81no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—82no—
346C3×C4—81no—
347C3×C4—81no—
348C3×C4—121no—
349C3×C4#87911yescharacteristic
350C3×C4#67⋊C411yescharacteristic
351C3×C4#67⋊C411yescharacteristic
352C3×C4#88411yescharacteristic
353C3×C4#89311yescharacteristic
354C3×C4#89811yescharacteristic
355C3×C4C4×#6711yescharacteristic
356C3×C4#93911yescharacteristic
357Dic3—41no—
358Dic3—62no—
359Dic3—62no—
360Dic3—122no—
361Dic3—121no—
362Dic3—121no—
363Dic3—122no—
364C32#193211yescharacteristic, complemented, Sylow
365C23—61no—
366C23#380411yescharacteristic
367Q8—61no—
368Q8—61no—
369D4—61no—
370D4—61no—
371D4—121no—
372D4—121no—
373C2×C4—41no—
374C2×C4—61no—
375C2×C4—121no—
376C2×C4—121no—
377C2×C4—181no—
378C2×C4—181no—
379C2×C4—362no—
380C2×C4#379511yescharacteristic
381C2×C4#379911yescharacteristic
382C2×C4C4×D3211yescharacteristic
383C2×C4#380211yescharacteristic
384C2×C4#380511yescharacteristic
385C2×C4D3×#6711yescharacteristic
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#466911yescharacteristic
402C2×C3#494511yescharacteristic
403D3—81no—
404C22—41no—
405C22—121no—
406C22—241no—
407C22#6385411yescharacteristic
408C22#6387711yescharacteristic
409C22#6395911yescharacteristic
410C4—81no—
411C4—121no—
412C4—182no—
413C4—361no—
414C4#6386111yescharacteristic
415C4#6388511yescharacteristic
416C4#6390211yescharacteristic
417C4#6390411yescharacteristic
418C3—21no—
419C3#6901211yescharacteristic, complemented
420C3#7040111yescharacteristic, complemented
421C2—21no—
422C2—21no—
423C2—21no—
424C2—241no—
425C2#1059128211yescharacteristic
subgroupG/H
centerC4#63885
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#388
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10591143C2semidirect
5. #10591060C2semidirect
6. #10589398C2semidirect
7. C3×#4533C2semidirect
21. #63560C4semidirect
22. #63558C4semidirect
36. #4533D3semidirect
364. C32#1932semidirect
419. C3#69012semidirect
420. C3#70401semidirect

Maximal subgroups

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

subgroupindex
C3×#50052
#105911432
C2×#635682
#105910762
#105910602
#105893982
C3×#45332
#704013
#690123