Finite Group Databasebeta

← #11793100

Subgroups — #11793100

Order 1152.

535 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5517C211yesmaximal, characteristic, complemented
2C3×#5005C211yesmaximal, characteristic
3#10591231C211yesmaximal, characteristic
4C2×#63569C211yesmaximal, characteristic
5#10589397C211yesmaximal, characteristic, complemented
6#10589169C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#71842—31nomaximal
9#70394—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#890—21no—
18C3×#888—21no—
19C3×#878—22no—
20C3×C4×Dic6—22no—
21C3×#805—22no—
22#63580—22no—
23#63569—21no—
24#63569—21no—
25C3×#533—31no—
26#5517D311yescharacteristic, complemented
27C3×#421—31no—
28#5240—31no—
29C2×#837—31no—
30#5006—31no—
31#5005D311yescharacteristic
32C2×#805—31no—
33#4556—31no—
34#4555—31no—
35#4533—31no—
36#4531—31no—
37#4531—31no—
38#4531—61no—
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×D12Q811yescharacteristic, complemented
48C2×C3×C4×D3—21no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6Q811yescharacteristic, complemented
51C32×C4⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C42D412yes—
54#3757—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4×C3⋊Dic3—21no—
57#3748—21no—
58#3748—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217D412yes—
61C3×C4⋊Dic3—22no—
62C3×C4⋊Dic3—21no—
63C3×Dic3⋊C4—22no—
64C3×Dic3⋊C4—22no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72#2031—91noSylow
73C2×C3×#41—31no—
74C2×#235C2×D311yescharacteristic
75C2×C3×M16—31no—
76C3×C4⋊Q8—61no—
77C3×#125—61no—
78C3×C22⋊Q8—62no—
79C3×C4×Q8—62no—
80C3×#117—21no—
81C3×#117—31no—
82C3×#117C2×D311yescharacteristic
83C3×#117C2×D311yescharacteristic
84C2×C3×C42—31no—
85#926—31no—
86#926—31no—
87#926—61no—
88#926C2×D311yescharacteristic
89C2×C4×Dic3C2×D311yescharacteristic
90C2×#208—31no—
91C2×#208—31no—
92C2×#208—61no—
93C2×#208C2×D311yescharacteristic
94#890—21no—
95#888—21no—
96#878—22no—
97C4×Dic6—22no—
98C3×#104—62no—
99#837—61no—
100#837—61no—
101#834—62no—
102#806—62no—
103#805—22no—
104#805—61no—
105#805—61no—
106C23×C32C2×D411yescharacteristic
107C22×C3×D3—21no—
108C2×C32×C4—22no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×Q811yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3⋊Dic3—41no—
116C3×#67—41no—
117C3×#67—41no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—42no—
123C3×D12—21no—
124C3×D12—21no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—21no—
128C3×Dic6—21no—
129C3×Dic6—44no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—41no—
132#533—31no—
133#421—31no—
134C2×#104—91no—
135#410—91no—
136#344—91no—
137#339—91no—
138H(3,ℤ/4)—91no—
139C3×#41—61no—
140C3×#41—61no—
141C3×#41—61no—
142C3×#41—61no—
143C2×C3×Q8—31no—
144C2×C3×Q8—62no—
145C2×C3×D4—31no—
146C2×C3×D4—61no—
147C22×C3×C4—21no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C2×#67—21no—
153C22×Dic3—21no—
154#235—21no—
155#235—21no—
156#235—21no—
157#235—21no—
158C2×D12Dic611yescharacteristic, complemented
159C2×C4×D3—21no—
160C2×Dic6—22no—
161C2×Dic6Dic611yescharacteristic, complemented
162C3×M16—61no—
163C3×M16—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—41no—
168C3×C4⋊C4—62no—
169C3×C4⋊C4—62no—
170C3×C4⋊C4—62no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—21no—
173C3×C22⋊C4—21no—
174C3×C22⋊C4—32no—
175C3×C22⋊C4—41no—
176C3×C42—22no—
177C3×C42—31no—
178C3×C42—31no—
179C3×C42—61no—
180C3×C42—61no—
181C3×C42#6712yes—
182C3×C42#6712yes—
183#217—61no—
184#217—61no—
185#217—121no—
186#217#6712yes—
187C4⋊Dic3—22no—
188C4⋊Dic3—21no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—121no—
192Dic3⋊C4—22no—
193Dic3⋊C4—22no—
194C4×Dic3—21no—
195C4×Dic3—21no—
196C4×Dic3—62no—
197C4×Dic3—61no—
198C4×Dic3—61no—
199C4×Dic3#6711yescharacteristic
200C4×Dic3#6711yescharacteristic
201#208—21no—
202#208—21no—
203#208—61no—
204#208—61no—
205#208—61no—
206#208—61no—
207#208—121no—
208#208—121no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—62no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C22×C32—41no—
214C22×C32#12011yescharacteristic
215C22×C32C22⋊Q811yescharacteristic
216C22×C32#12411yescharacteristic
217C2×C3×D3—41no—
218C2×C3×D3—81no—
219C32×C4—42no—
220C32×C4C22⋊Q811yescharacteristic
221C32×C4C22⋊Q811yescharacteristic
222C32×C4#12411yescharacteristic
223C32×C4#12411yescharacteristic
224C3⋊Dic3—81no—
225C3×Dic3—22no—
226C3×Dic3—42no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C2×#41—31no—
230C2×M16—31no—
231C2×M16—91no—
232C4⋊Q8—61no—
233#125—61no—
234C22⋊Q8—62no—
235C4×Q8—62no—
236#117—31no—
237#117—91no—
238#117D3211yescharacteristic
239C2×C42—31no—
240#104—62no—
241#104—181no—
242#104—181no—
243#99—182no—
244C23×C3—21no—
245C23×C3—61no—
246C23×C3D3×D411yescharacteristic
247C23×C3C2×#6711yescharacteristic
248C22×D3—21no—
249C3×Q8—61no—
250C3×Q8—61no—
251C3×Q8—124no—
252C3×D4—61no—
253C3×D4—61no—
254C3×D4—121no—
255C3×D4—121no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—42no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—62no—
268C2×C3×C4—61no—
269C2×C3×C4—122no—
270C2×C3×C4—121no—
271C2×C3×C4—121no—
272C2×C3×C4C2×Dic611yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4#23711yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4D3×Q811yescharacteristic
278C2×C3×C4#23911yescharacteristic
279C2×C3×C4#23911yescharacteristic
280C2×C3×C4#23911yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284#67—41no—
285#67—41no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—22no—
290C2×Dic3—42no—
291C2×Dic3—122no—
292C2×Dic3—121no—
293C2×Dic3—121no—
294D12—21no—
295D12—21no—
296C4×D3—41no—
297C4×D3—41no—
298Dic6—21no—
299Dic6—21no—
300Dic6—44no—
301C3×C8—121no—
302C3⋊C8—41no—
303C3⋊C8—122no—
304C3⋊C8—121no—
305C3⋊C8—121no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32—21no—
309C2×C32#39311yescharacteristic
310C3×D3—81no—
311#41—61no—
312#41—61no—
313#41—61no—
314#41—61no—
315C2×Q8—31no—
316C2×Q8—62no—
317C2×D4—31no—
318C2×D4—61no—
319C22×C4—61no—
320C22×C4—61no—
321C22×C4C2×D3211yescharacteristic
322M16—61no—
323M16—61no—
324M16—181no—
325M16—181no—
326C2×C8—61no—
327C2×C8—181no—
328C4⋊C4—21no—
329C4⋊C4—62no—
330C4⋊C4—62no—
331C4⋊C4—62no—
332C4⋊C4—61no—
333C4⋊C4—181no—
334C22⋊C4—21no—
335C22⋊C4—32no—
336C22⋊C4—181no—
337C42—31no—
338C42—31no—
339C42—61no—
340C42—61no—
341C42—181no—
342C42#62512yes—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—81no—
349C22×C3—121no—
350C22×C3—241no—
351C22×C3#87811yescharacteristic
352C22×C3#88511yescharacteristic
353C22×C3#93711yescharacteristic
354C22×C3#94611yescharacteristic
355C22×C3#94711yescharacteristic
356C22×C3#95311yescharacteristic
357C2×D3—41no—
358C2×D3—81no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—42no—
364C3×C4—42no—
365C3×C4—62no—
366C3×C4—82no—
367C3×C4—121no—
368C3×C4—122no—
369C3×C4—121no—
370C3×C4#87811yescharacteristic
371C3×C4#88511yescharacteristic
372C3×C4#92411yescharacteristic
373C3×C4#93611yescharacteristic
374C3×C4#94611yescharacteristic
375C3×C4#94611yescharacteristic
376C3×C4#94711yescharacteristic
377C3×C4#94711yescharacteristic
378Dic3—22no—
379Dic3—42no—
380Dic3—41no—
381Dic3—41no—
382Dic3—241no—
383Dic3—241no—
384Dic3—242no—
385C32#203111yescharacteristic, complemented, Sylow
386C23—61no—
387C23D3×#6711yescharacteristic
388Q8—61no—
389Q8—61no—
390Q8—124no—
391D4—61no—
392D4—61no—
393D4—121no—
394D4—121no—
395C2×C4—22no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—62no—
400C2×C4—122no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—361no—
404C2×C4D3×Dic611yescharacteristic
405C2×C4#379611yescharacteristic
406C2×C4#379611yescharacteristic
407C2×C4#379911yescharacteristic
408C2×C4C2×#62511yescharacteristic
409C2×C4D3×#6711yescharacteristic
410C8—121no—
411C8—361no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—41no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3—241no—
423C2×C3#494711yescharacteristic
424C2×C3#523111yescharacteristic
425D3—81no—
426C22—41no—
427C22—121no—
428C22—241no—
429C22#6388711yescharacteristic
430C22#6390711yescharacteristic
431C22#6397611yescharacteristic
432C4—42no—
433C4—62no—
434C4—121no—
435C4—122no—
436C4—121no—
437C4—721no—
438C4#6385611yescharacteristic
439C4#6386311yescharacteristic
440C4#6388711yescharacteristic
441C4#6390711yescharacteristic
442C3—21no—
443C3#7039411yescharacteristic, complemented
444C3#7184211yescharacteristic, complemented
445C2—21no—
446C2—21no—
447C2—21no—
448C2—241no—
449C2#1059130411yescharacteristic
subgroupG/H
centerC4#63863
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#393
prime radicalC2×C3×#235C22
hypercenter#117D32
hypocenterC32#2031
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5517C2semidirect
5. #10589397C2semidirect
6. #10589169C2semidirect
7. #10589162C2semidirect
26. #5517D3semidirect
47. C2×C3×D12Q8semidirect
50. C2×C3×Dic6Q8semidirect
158. C2×D12Dic6semidirect
161. C2×Dic6Dic6semidirect
385. C32#2031semidirect
443. C3#70394semidirect
444. C3#71842semidirect

Maximal subgroups

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

subgroupindex
C3×#55172
C3×#50052
#105912312
C2×#635692
#105893972
#105891692
#105891622
#718423
#703943