Finite Group Databasebeta

← #11793115

Subgroups — #11793115

Order 1152.

533 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595049C211yesmaximal, characteristic, complemented
2C2×C3×#825C211yesmaximal, characteristic
3#10591231C211yesmaximal, characteristic
4#10591111C211yesmaximal, characteristic
5#10589425C211yesmaximal, characteristic, complemented
6C3×#4557C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70368—31nomaximal
9#68714—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17#63964—22no—
18#63918—21no—
19C4×#627—22no—
20#63869—21no—
21C3×#825—21no—
22C3×#825—21no—
23#63580—22no—
24#63569—22no—
25#5517—31no—
26#5470—31no—
27C2×C3×#104—31no—
28#5240—31no—
29#5236—31no—
30C2×#825D311yescharacteristic
31#5006—31no—
32#5005—31no—
33C3×H(3,ℤ/4)—31no—
34#4559—31no—
35#4559—31no—
36#4559—61no—
37#4557D311yescharacteristic, complemented
38#4532—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×D12Q811yescharacteristic, complemented
48C2×C3×C4×D3—21no—
49C2×C3×Dic6Q811yescharacteristic, complemented
50C2×#627—22no—
51C32×M16—21no—
52C32×M16—21no—
53C2×C32×C8—21no—
54#3757D412yes—
55C4⋊(C3⋊Dic3)—21no—
56C4×C3⋊Dic3—21no—
57#3748—21no—
58#3748—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3D412yes—
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69#3724—22no—
70Dic3⋊Dic3—22no—
71Dic3⋊Dic3—22no—
72#2031—91noSylow
73C2×C3×#41—31no—
74C2×#235C2×D311yescharacteristic
75C2×C3×M16—21no—
76C2×C3×M16C2×D311yescharacteristic
77C2×C3×M16C2×D311yescharacteristic
78C3×#117—31no—
79C3×#117—31no—
80C2×C3×C42—31no—
81#926—31no—
82#926—31no—
83#926—61no—
84#926C2×D311yescharacteristic
85#926C2×D311yescharacteristic
86#924—62no—
87C2×C4×Dic3C2×D311yescharacteristic
88C2×#208—31no—
89C2×#208—31no—
90C2×#208—61no—
91#890—61no—
92#888—61no—
93#878—62no—
94#870—61no—
95#869—61no—
96C4×Dic6—62no—
97C4×Dic6—62no—
98C3×#104—61no—
99C3×#104—61no—
100#837—62no—
101#834—62no—
102#825—21no—
103#825—21no—
104#806—62no—
105#805—62no—
106C23×C32C2×D411yescharacteristic
107C22×C3×D3—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×Q811yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C3⋊Dic3—22no—
115C3×#67—41no—
116C3×#67—41no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—41no—
123C3×D12—21no—
124C3×D12—21no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—21no—
128C3×Dic6—21no—
129#627—44no—
130C32×C8—41no—
131C3⋊(C3⋊C8)—41no—
132#533—91no—
133#421—91no—
134C2×#104—31no—
135#410—91no—
136#344—91no—
137#339—91no—
138H(3,ℤ/4)—31no—
139C3×#41—61no—
140C3×#41—61no—
141C3×#41—61no—
142C3×#41—61no—
143C2×C3×Q8—31no—
144C2×C3×D4—31no—
145C2×C3×D4—61no—
146C22×C3×C4—21no—
147C22×C3×C4—61no—
148C22×C3×C4—61no—
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C2×#67—21no—
152C22×Dic3—21no—
153#235—21no—
154#235—21no—
155#235—21no—
156#235—21no—
157C2×D12Dic611yescharacteristic, complemented
158C2×C4×D3—21no—
159C2×Dic6—62no—
160C2×Dic6—62no—
161C2×Dic6Dic611yescharacteristic, complemented
162C3×M16—22no—
163C3×M16—21no—
164C3×M16—21no—
165C3×M16—21no—
166C3×M16—21no—
167C3×M16—41no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—41no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C22⋊C4—61no—
174C3×C22⋊C4—61no—
175C3×C42—32no—
176C3×C42—31no—
177C3×C42—31no—
178C3×C42—61no—
179C3×C42—61no—
180#217—21no—
181#217—21no—
182#217—32no—
183#217—32no—
184#217—62no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—62no—
188C4⋊Dic3—62no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—121no—
192Dic3⋊C4—62no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196C4×Dic3—21no—
197C4×Dic3—21no—
198C4×Dic3—61no—
199C4×Dic3—61no—
200C4×Dic3—121no—
201C4×Dic3D1212yes—
202C4×Dic3#6711yescharacteristic
203C4×Dic3#6711yescharacteristic
204#208—61no—
205#208—61no—
206#208—61no—
207#208—61no—
208#208—121no—
209#208—121no—
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×C4C22⋊Q811yescharacteristic
220C32×C4C22⋊Q811yescharacteristic
221C32×C4#12411yescharacteristic
222C32×C4#12411yescharacteristic
223C3⋊Dic3—42no—
224C3×Dic3—22no—
225C3×Dic3—42no—
226C3×Dic3—41no—
227C3×Dic3—41no—
228C3×Dic3—81no—
229C2×#41—31no—
230C2×M16—91no—
231C2×M16D3211yescharacteristic
232C4⋊Q8—181no—
233#125—181no—
234C22⋊Q8—182no—
235C4×Q8—182no—
236#117—31no—
237#117—31no—
238#117—91no—
239C2×C42—31no—
240#104—61no—
241#104—61no—
242#104—182no—
243#99—182no—
244C23×C3—21no—
245C23×C3—61no—
246C23×C3D3×D411yescharacteristic
247C23×C3D3×D411yescharacteristic
248C22×D3—21no—
249C3×Q8—61no—
250C3×Q8—61no—
251C3×D4—61no—
252C3×D4—61no—
253C3×D4—121no—
254C3×D4—121no—
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—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—62no—
265C2×C3×C4—122no—
266C2×C3×C4—121no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4C2×Dic611yescharacteristic
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4#23511yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4#23711yescharacteristic
279C2×C3×C4D3×Q811yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281#67—41no—
282#67—41no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—22no—
286C2×Dic3—21no—
287C2×Dic3—42no—
288C2×Dic3—41no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—122no—
292D12—21no—
293D12—21no—
294C4×D3—41no—
295C4×D3—41no—
296Dic6—21no—
297Dic6—21no—
298Dic6—124no—
299Dic6—124no—
300C3×C8—42no—
301C3×C8—41no—
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—182no—
317C2×D4—31no—
318C2×D4—61no—
319C22×C4—61no—
320C22×C4—61no—
321C22×C4C2×D3211yescharacteristic
322M16—21no—
323M16—21no—
324M16—181no—
325M16—181no—
326C2×C8—21no—
327C2×C8—181no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—182no—
331C4⋊C4—182no—
332C4⋊C4—182no—
333C4⋊C4—181no—
334C22⋊C4—61no—
335C22⋊C4—61no—
336C22⋊C4—92no—
337C42—32no—
338C42—31no—
339C42—31no—
340C42—61no—
341C42—61no—
342C42—181no—
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#88211yescharacteristic
353C22×C3#88511yescharacteristic
354C22×C3#88511yescharacteristic
355C22×C3#89611yescharacteristic
356C22×C3#93711yescharacteristic
357C2×D3—41no—
358C2×D3—81no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—62no—
364C3×C4—122no—
365C3×C4—121no—
366C3×C4—121no—
367C3×C4—241no—
368C3×C4#87511yescharacteristic
369C3×C4#87811yescharacteristic
370C3×C4#88511yescharacteristic
371C3×C4#88511yescharacteristic
372C3×C4#89611yescharacteristic
373C3×C4#89711yescharacteristic
374C3×C4#92411yescharacteristic
375C3×C4#93611yescharacteristic
376Dic3—22no—
377Dic3—42no—
378Dic3—41no—
379Dic3—41no—
380Dic3—81no—
381Dic3—122no—
382Dic3—122no—
383Dic3—242no—
384C32#203111yescharacteristic, complemented, Sylow
385C23—61no—
386C23#380211yescharacteristic
387Q8—61no—
388Q8—61no—
389Q8—364no—
390D4—61no—
391D4—61no—
392D4—121no—
393D4—121no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—62no—
398C2×C4—122no—
399C2×C4—121no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—182no—
403C2×C4D3×Dic611yescharacteristic
404C2×C4#379811yescharacteristic
405C2×C4D3×D1211yescharacteristic
406C2×C4#380411yescharacteristic
407C2×C4#380511yescharacteristic
408C2×C4D3×#6711yescharacteristic
409C8—41no—
410C8—361no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—41no—
419C2×C3—41no—
420C2×C3—41no—
421C2×C3—241no—
422C2×C3#467311yescharacteristic
423C2×C3#494711yescharacteristic
424D3—81no—
425C22—41no—
426C22—121no—
427C22—241no—
428C22#6389911yescharacteristic
429C22#6391511yescharacteristic
430C22#6392211yescharacteristic
431C4—62no—
432C4—121no—
433C4—122no—
434C4—121no—
435C4—241no—
436C4—362no—
437C4#6385111yescharacteristic
438C4#6385211yescharacteristic
439C4#6389311yescharacteristic
440C4#6395911yescharacteristic
441C3—21no—
442C3#6871411yescharacteristic, complemented
443C3#7036811yescharacteristic, complemented
444C2—21no—
445C2—21no—
446C2—21no—
447C2—241no—
448C2#1059129311yescharacteristic
subgroupG/H
centerC4#63852
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#393
prime radicalC2×C3×#235C22
hypercenterC2×M16D32
hypocenterC32#2031
LCSG ▷ C22×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
1. #10595049C2semidirect
5. #10589425C2semidirect
6. C3×#4557C2semidirect
7. #10589161C2semidirect
37. #4557D3semidirect
47. C2×C3×D12Q8semidirect
49. C2×C3×Dic6Q8semidirect
157. C2×D12Dic6semidirect
161. C2×Dic6Dic6semidirect
384. C32#2031semidirect
442. C3#68714semidirect
443. C3#70368semidirect

Maximal subgroups

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

subgroupindex
#105950492
C2×C3×#8252
#105912312
#105911112
#105894252
C3×#45572
#105891612
#703683
#687143