Finite Group Databasebeta

← #11793106

Subgroups — #11793106

Order 1152.

567 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595049C211yesmaximal, characteristic, complemented
2#10592939C211yesmaximal, characteristic
3C3×#5236C211yesmaximal, characteristic
4C2×C3×#837C211yesmaximal, characteristic
5#10589171C211yesmaximal, characteristic, complemented
6#10589162C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70394—31nomaximal
9#70368—31nomaximal
10C2×C32×#41C2211yescharacteristic
11#64135C2211yescharacteristic
12#64135C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63964—22no—
18#63918—21no—
19C4×#627—22no—
20#63869—21no—
21#63661—22no—
22C3×#837—21no—
23C3×#837—21no—
24C3×#837—22no—
25#5517—31no—
26#5470—31no—
27C3×#421—31no—
28C2×C3×#104—31no—
29#5240—31no—
30#5240—31no—
31#5240—61no—
32#5236D311yescharacteristic
33C2×#837D311yescharacteristic
34#4559—31no—
35#4557—31no—
36#4556—31no—
37#4555—31no—
38#4531—31no—
39#4523—31no—
40C32×#41—21no—
41C32×#41—21no—
42C32×#41—21no—
43C32×#41—21no—
44C2×C32×Q8Q811yescharacteristic, complemented
45C2×C32×D4—21no—
46C2×C32×D4Q811yescharacteristic, complemented
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3—21no—
50C2×#627—22no—
51#3757—21no—
52#3757D412yes—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C3×#217—21no—
58C3×C4⋊Dic3—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D412yes—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#3724—22no—
70Dic3⋊Dic3—22no—
71Dic3⋊Dic3—22no—
72#2031—91noSylow
73C2×C3×#41—21no—
74C2×C3×#41C2×D311yescharacteristic
75C2×C3×#41C2×D311yescharacteristic
76C2×C3×M16—31no—
77C2×C3×M16—31no—
78C3×#117—31no—
79C2×C3×C42—31no—
80#926—31no—
81#926—31no—
82#926—31no—
83#926—31no—
84#926—61no—
85#926—61no—
86#926C2×D311yescharacteristic
87#924—62no—
88C2×C4×Dic3C2×D311yescharacteristic
89C2×#208C2×D311yescharacteristic
90C2×#208C2×D311yescharacteristic
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—
100C3×#104—62no—
101#837—21no—
102#837—21no—
103#837—22no—
104#834—62no—
105#834—62no—
106#834—64no—
107C23×C32—21no—
108C23×C32C2×D411yescharacteristic
109C32×Q8—21no—
110C32×Q8—21no—
111C32×D4—21no—
112C32×D4—21no—
113C32×D4—41no—
114C32×D4—41no—
115C2×C32×C4—21no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×Q811yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—42no—
130#627—44no—
131C3×C3⋊C8—41no—
132C3×C3⋊C8—41no—
133#533—91no—
134#421—31no—
135C2×#104—31no—
136#410—91no—
137#344—91no—
138#339—91no—
139H(3,ℤ/4)—91no—
140C3×#41—21no—
141C3×#41—21no—
142C3×#41—21no—
143C3×#41—21no—
144C3×#41—21no—
145C3×#41—21no—
146C3×#41—21no—
147C3×#41—21no—
148C3×#41—41no—
149C3×#41—41no—
150C3×#41—41no—
151C3×#41—41no—
152C2×C3×Q8—21no—
153C2×C3×Q8Dic611yescharacteristic, complemented
154C2×C3×Q8Dic611yescharacteristic, complemented
155C2×C3×D4—22no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4Dic611yescharacteristic, complemented
160C2×C3×D4Dic611yescharacteristic, complemented
161C22×C3×C4—22no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×Dic3—21no—
169C2×Dic6—62no—
170C2×Dic6—62no—
171C3×M16—61no—
172C3×M16—61no—
173C3×M16—61no—
174C3×M16—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C3×C4⋊C4—61no—
178C3×C22⋊C4—61no—
179C3×C42—32no—
180C3×C42—31no—
181C3×C42—31no—
182C3×C42—61no—
183#217—21no—
184#217—32no—
185#217—32no—
186#217—62no—
187#217—62no—
188#217—61no—
189#217—61no—
190C4⋊Dic3—21no—
191C4⋊Dic3—62no—
192C4⋊Dic3—62no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—121no—
198C4⋊Dic3—121no—
199Dic3⋊C4—62no—
200Dic3⋊C4—62no—
201Dic3⋊C4—62no—
202Dic3⋊C4—62no—
203C4×Dic3—21no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—121no—
209C4×Dic3—121no—
210C4×Dic3#6712yes—
211C4×Dic3#6711yescharacteristic
212C4×Dic3#6711yescharacteristic
213#208—21no—
214#208—21no—
215#208—21no—
216#208—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—81no—
222C22×C32#12011yescharacteristic
223C22×C32C22⋊Q811yescharacteristic
224C22×C32#12411yescharacteristic
225C32×C4—41no—
226C32×C4C22⋊Q811yescharacteristic
227C32×C4C22⋊Q811yescharacteristic
228C32×C4#12411yescharacteristic
229C32×C4#12411yescharacteristic
230C3⋊Dic3—42no—
231C3⋊Dic3—81no—
232C3×Dic3—22no—
233C3×Dic3—42no—
234C3×Dic3—41no—
235C2×#41D3211yescharacteristic
236C2×M16—31no—
237C2×M16—31no—
238C4⋊Q8—181no—
239#125—181no—
240C22⋊Q8—182no—
241C4×Q8—182no—
242#117—31no—
243#117—91no—
244#117—91no—
245C2×C42—31no—
246#104—61no—
247#104—61no—
248#104—62no—
249#99—182no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3D3×D411yescharacteristic
255C23×C3D3×D411yescharacteristic
256C3×Q8—21no—
257C3×Q8—21no—
258C3×Q8—21no—
259C3×Q8—21no—
260C3×Q8—41no—
261C3×Q8—41no—
262C3×D4—21no—
263C3×D4—21no—
264C3×D4—21no—
265C3×D4—21no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—42no—
269C3×D4—42no—
270C3×D4—41no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—41no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—62no—
292C2×C3×C4—122no—
293C2×C3×C4C2×Dic611yescharacteristic
294C2×C3×C4C2×Dic611yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4#23711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—22no—
308C2×Dic3—42no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315Dic6—124no—
316Dic6—124no—
317C3×C8—121no—
318C3×C8—121no—
319C3⋊C8—41no—
320C3⋊C8—41no—
321C2×C32—21no—
322C2×C32—21no—
323C2×C32—21no—
324C2×C32—81no—
325C2×C32#39311yescharacteristic
326#41—21no—
327#41—21no—
328#41—21no—
329#41—21no—
330C2×Q8—182no—
331C2×Q8#62711yescharacteristic, complemented
332C2×D4—21no—
333C2×D4#62711yescharacteristic, complemented
334C22×C4—21no—
335C22×C4—61no—
336C22×C4C2×D3211yescharacteristic
337M16—61no—
338M16—61no—
339M16—61no—
340M16—61no—
341C2×C8—61no—
342C2×C8—61no—
343C4⋊C4—61no—
344C4⋊C4—182no—
345C4⋊C4—182no—
346C4⋊C4—182no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C22⋊C4—61no—
350C22⋊C4—92no—
351C22⋊C4—181no—
352C42—31no—
353C42—31no—
354C42—32no—
355C42—61no—
356C42—181no—
357C42—181no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—42no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—81no—
367C22×C3—81no—
368C22×C3—81no—
369C22×C3—82no—
370C22×C3#87811yescharacteristic
371C22×C3#87811yescharacteristic
372C22×C3#88511yescharacteristic
373C22×C3#88511yescharacteristic
374C22×C3#93711yescharacteristic
375C22×C3#93711yescharacteristic
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—42no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—62no—
384C3×C4—122no—
385C3×C4—121no—
386C3×C4#87811yescharacteristic
387C3×C4#87811yescharacteristic
388C3×C4#88511yescharacteristic
389C3×C4#88511yescharacteristic
390C3×C4#92411yescharacteristic
391C3×C4#92411yescharacteristic
392C3×C4#93611yescharacteristic
393C3×C4#93611yescharacteristic
394Dic3—22no—
395Dic3—42no—
396Dic3—41no—
397Dic3—122no—
398Dic3—122no—
399Dic3—242no—
400Dic3—241no—
401Dic3—241no—
402Dic3—242no—
403C32#203111yescharacteristic, complemented, Sylow
404C23—21no—
405C23#381111yescharacteristic
406Q8—21no—
407Q8—21no—
408Q8—364no—
409D4—21no—
410D4—21no—
411D4—41no—
412D4—41no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—62no—
419C2×C4—122no—
420C2×C4—182no—
421C2×C4—361no—
422C2×C4#380411yescharacteristic
423C2×C4#380411yescharacteristic
424C2×C4#380511yescharacteristic
425C2×C4C2×#62711yescharacteristic
426C2×C4D3×#6711yescharacteristic
427C2×C4D3×#6711yescharacteristic
428C8—121no—
429C8—121no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—41no—
438C2×C3—41no—
439C2×C3—41no—
440C2×C3—82no—
441C2×C3—81no—
442C2×C3—81no—
443C2×C3#494711yescharacteristic
444C2×C3#494711yescharacteristic
445C22—41no—
446C22—41no—
447C22—81no—
448C22#6395311yescharacteristic
449C22#6398211yescharacteristic
450C22#6398311yescharacteristic
451C4—41no—
452C4—62no—
453C4—121no—
454C4—122no—
455C4—362no—
456C4—721no—
457C4#6395911yescharacteristic
458C4#6395911yescharacteristic
459C4#6396411yescharacteristic
460C4#6396411yescharacteristic
461C3—21no—
462C3#7036811yescharacteristic, complemented
463C3#7039411yescharacteristic, complemented
464C2—21no—
465C2—21no—
466C2—21no—
467C2—81no—
468C2#1059169211yescharacteristic
subgroupG/H
centerC4#63959
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#393
hypercenterC2×#41D32
hypocenterC32#2031
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10595049C2semidirect
5. #10589171C2semidirect
6. #10589162C2semidirect
7. #10589158C2semidirect
44. C2×C32×Q8Q8semidirect
46. C2×C32×D4Q8semidirect
153. C2×C3×Q8Dic6semidirect
154. C2×C3×Q8Dic6semidirect
159. C2×C3×D4Dic6semidirect
160. C2×C3×D4Dic6semidirect
331. C2×Q8#627semidirect
333. C2×D4#627semidirect
403. C32#2031semidirect
462. C3#70368semidirect
463. C3#70394semidirect

Maximal subgroups

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

subgroupindex
#105950492
#105929392
C3×#52362
C2×C3×#8372
#105891712
#105891622
#105891582
#703943
#703683