Finite Group Databasebeta

← #11793103

Subgroups — #11793103

Order 1152.

543 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×#5470C211yesmaximal, characteristic, complemented
2C2×C3×#805C211yesmaximal, characteristic
3#10591231C211yesmaximal, characteristic
4#10591111C211yesmaximal, characteristic
5#10589389C211yesmaximal, characteristic, complemented
6#10589170C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#71842—31nomaximal
9#70368—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C3×#924—22no—
17C2×C3×#208C2211yescharacteristic
18C3×#870—21no—
19C3×#869—21no—
20C3×C4×Dic6—22no—
21C3×#805—21no—
22C3×#805—21no—
23#63580—22no—
24#63569—22no—
25C3×#533—31no—
26#5470D311yescharacteristic, complemented
27C2×C3×#104—31no—
28#5240—31no—
29#5236—31no—
30#5006—31no—
31#5005—31no—
32C2×#805D311yescharacteristic
33#4559—31no—
34#4557—31no—
35#4533—31no—
36#4531—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×D12Q811yescharacteristic, complemented
48C2×C3×C4×D3—21no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6Q811yescharacteristic, complemented
51C32×C42—21no—
52C32×C42D411yescharacteristic
53C32×C42D411yescharacteristic
54#3757—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4×C3⋊Dic3—21no—
57#3748—21no—
58#3748—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×#217D412yes—
62C3×C4⋊Dic3—22no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×Dic3⋊C4—24no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3D412yes—
68C3×#208—21no—
69C3×#208—21no—
70C2×C3×C3⋊C8—21no—
71#2031—91noSylow
72C2×C3×#41—31no—
73C2×#235C2×D311yescharacteristic
74C2×C3×M16—31no—
75C3×C4⋊Q8—61no—
76C3×#125—61no—
77C3×C22⋊Q8—62no—
78C3×C4×Q8—62no—
79C3×#117—31no—
80C3×#117—31no—
81C2×C3×C42—21no—
82C2×C3×C42C2×D311yescharacteristic
83C2×C3×C42C2×D311yescharacteristic
84#926—31no—
85#926—31no—
86#926—61no—
87#926C2×D311yescharacteristic
88#926C2×D311yescharacteristic
89#924—22no—
90C2×#208—31no—
91C2×#208—31no—
92C2×#208—61no—
93C2×#208C2×D311yescharacteristic
94#870—21no—
95#869—21no—
96C4×Dic6—22no—
97C3×#104—61no—
98C3×#104—61no—
99#837—62no—
100#834—62no—
101#806—62no—
102#805—21no—
103#805—21no—
104#805—62no—
105C23×C32C2×D411yescharacteristic
106C22×C3×D3—21no—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4—42no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×Q811yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C3⋊Dic3—41no—
117C3×#67—41no—
118C3×#67—41no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—21no—
122C3×D12—21no—
123C3×D12—21no—
124C3×C4×D3—41no—
125C3×C4×D3—41no—
126C3×Dic6—21no—
127C3×Dic6—21no—
128C3×Dic6—44no—
129C3⋊(C3⋊C8)—41no—
130C3×C3⋊C8—41no—
131#533—31no—
132#421—91no—
133C2×#104—31no—
134#410—91no—
135#344—91no—
136#339—91no—
137H(3,ℤ/4)—91no—
138C3×#41—61no—
139C3×#41—61no—
140C3×#41—61no—
141C3×#41—61no—
142C2×C3×Q8—31no—
143C2×C3×Q8—62no—
144C2×C3×D4—31no—
145C2×C3×D4—61no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—41no—
150C22×C3×C4—61no—
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C2×#67—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—64no—
166C3×C4⋊C4—62no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—32no—
170C3×C22⋊C4—61no—
171C3×C42—21no—
172C3×C42—21no—
173C3×C42—21no—
174C3×C42—21no—
175C3×C42—32no—
176C3×C42—41no—
177C3×C42—61no—
178C3×C42#6711yescharacteristic
179C3×C42#6711yescharacteristic
180C3×C42#6711yescharacteristic
181C3×C42#6711yescharacteristic
182#217—21no—
183#217—61no—
184#217—61no—
185#217—121no—
186#217#6712yes—
187C4⋊Dic3—22no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3—62no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193Dic3⋊C4—24no—
194C4×Dic3—21no—
195C4×Dic3—61no—
196C4×Dic3—61no—
197C4×Dic3—121no—
198C4×Dic3#6712yes—
199#208—21no—
200#208—21no—
201#208—62no—
202#208—61no—
203#208—61no—
204#208—61no—
205#208—61no—
206#208—121no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—121no—
211C22×C32—41no—
212C22×C32#12011yescharacteristic
213C22×C32C22⋊Q811yescharacteristic
214C22×C32#12411yescharacteristic
215C2×C3×D3—41no—
216C2×C3×D3—81no—
217C32×C4—22no—
218C32×C4—41no—
219C32×C4C22⋊Q811yescharacteristic
220C32×C4C22⋊Q811yescharacteristic
221C32×C4#12411yescharacteristic
222C32×C4#12411yescharacteristic
223C3⋊Dic3—81no—
224C3×Dic3—42no—
225C3×Dic3—42no—
226C3×Dic3—41no—
227C2×#41—31no—
228C2×M16—31no—
229C2×M16—91no—
230C4⋊Q8—61no—
231#125—61no—
232C22⋊Q8—62no—
233C4×Q8—62no—
234#117—31no—
235#117—31no—
236#117—91no—
237C2×C42D3211yescharacteristic
238#104—61no—
239#104—61no—
240#104—182no—
241#99—182no—
242C23×C3—21no—
243C23×C3—61no—
244C23×C3D3×D411yescharacteristic
245C23×C3C2×#6711yescharacteristic
246C22×D3—21no—
247C3×Q8—61no—
248C3×Q8—61no—
249C3×Q8—124no—
250C3×D4—61no—
251C3×D4—61no—
252C3×D4—121no—
253C3×D4—121no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
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—41no—
265C2×C3×C4—41no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—44no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—61no—
272C2×C3×C4—121no—
273C2×C3×C4—121no—
274C2×C3×C4C2×Dic611yescharacteristic
275C2×C3×C4#23511yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4#23711yescharacteristic
279C2×C3×C4D3×Q811yescharacteristic
280C2×C3×C4#23911yescharacteristic
281C2×C3×C4#23911yescharacteristic
282C2×C3×C4#23911yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286#67—41no—
287#67—41no—
288C2×Dic3—21no—
289C2×Dic3—22no—
290C2×Dic3—22no—
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—21no—
320C22×C4—61no—
321C22×C4C2×D3211yescharacteristic
322M16—61no—
323M16—61no—
324M16—181no—
325M16—181no—
326C2×C8—61no—
327C2×C8—181no—
328C4⋊C4—64no—
329C4⋊C4—62no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—181no—
333C22⋊C4—32no—
334C22⋊C4—61no—
335C22⋊C4—181no—
336C42—21no—
337C42—32no—
338C42—61no—
339C42—181no—
340C42#62511yescharacteristic
341C42#62511yescharacteristic
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—42no—
348C22×C3—121no—
349C22×C3—241no—
350C22×C3#87811yescharacteristic
351C22×C3#88511yescharacteristic
352C22×C3#93711yescharacteristic
353C22×C3#94611yescharacteristic
354C22×C3#94711yescharacteristic
355C22×C3#95311yescharacteristic
356C2×D3—41no—
357C2×D3—81no—
358C3×C4—22no—
359C3×C4—22no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—42no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—42no—
368C3×C4—122no—
369C3×C4—122no—
370C3×C4—121no—
371C3×C4#87811yescharacteristic
372C3×C4#88511yescharacteristic
373C3×C4#92411yescharacteristic
374C3×C4#93611yescharacteristic
375C3×C4#94611yescharacteristic
376C3×C4#94611yescharacteristic
377C3×C4#94711yescharacteristic
378C3×C4#94711yescharacteristic
379Dic3—42no—
380Dic3—42no—
381Dic3—41no—
382Dic3—242no—
383Dic3—241no—
384Dic3—241no—
385C32#203111yescharacteristic, complemented, Sylow
386C23—61no—
387C23D3×#6711yescharacteristic
388Q8—61no—
389Q8—61no—
390Q8—124no—
391D4—61no—
392D4—61no—
393D4—121no—
394D4—121no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—42no—
398C2×C4—61no—
399C2×C4—62no—
400C2×C4—62no—
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—22no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
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—22no—
433C4—41no—
434C4—122no—
435C4—122no—
436C4—121no—
437C4—721no—
438C4#6385611yescharacteristic
439C4#6386311yescharacteristic
440C4#6388711yescharacteristic
441C4#6390711yescharacteristic
442C3—21no—
443C3#7036811yescharacteristic, complemented
444C3#7184211yescharacteristic, complemented
445C2—21no—
446C2—21no—
447C2—21no—
448C2—241no—
449C2#1059130411yescharacteristic
subgroupG/H
centerC4#63907
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC2×C32#393
prime radicalC2×C3×#235C22
hypercenterC2×C42D32
hypocenterC32#2031
LCSG ▷ C22×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
1. C3×#5470C2semidirect
5. #10589389C2semidirect
6. #10589170C2semidirect
7. #10589158C2semidirect
26. #5470D3semidirect
47. C2×C3×D12Q8semidirect
50. C2×C3×Dic6Q8semidirect
158. C2×D12Dic6semidirect
161. C2×Dic6Dic6semidirect
385. C32#2031semidirect
443. C3#70368semidirect
444. C3#71842semidirect

Maximal subgroups

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

subgroupindex
C3×#54702
C2×C3×#8052
#105912312
#105911112
#105893892
#105891702
#105891582
#718423
#703683