Finite Group Databasebeta

← #11793116

Subgroups — #11793116

Order 1152.

543 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595050C211yesmaximal, characteristic, complemented
2C3×#5006C211yesmaximal, characteristic
3#10591111C211yesmaximal, characteristic
4C2×#63568C211yesmaximal, characteristic
5#10589398C211yesmaximal, characteristic, complemented
6C3×#4531C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#70038—31nomaximal
9#68714—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63982—22no—
18#63919—21no—
19C4×#627—22no—
20#63872—21no—
21C3×#806—22no—
22#63569—22no—
23#63568—21no—
24#63568—21no—
25#5517—31no—
26#5517—31no—
27C3×#410—31no—
28#5236—31no—
29C2×#837—31no—
30C2×#825—31no—
31#5006D311yescharacteristic
32#5005—31no—
33C3×H(3,ℤ/4)—31no—
34#4559—31no—
35#4533—31no—
36#4532—31no—
37#4532—31no—
38#4532—61no—
39#4531D311yescharacteristic, complemented
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×D12Q811yescharacteristic, complemented
48C2×C3×C4×D3—21no—
49C2×C3×Dic6Q811yescharacteristic, complemented
50C2×#627—22no—
51C32×C4⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C42—21no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57#3748—21no—
58#3748—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×#217D412yes—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3D412yes—
66C3×#208—21no—
67C3×#208—21no—
68C2×C3×C3⋊C8—21no—
69#3724—22no—
70Dic3⋊Dic3—22no—
71Dic3⋊Dic3—22no—
72#2031—91noSylow
73C2×C3×#41—31no—
74C2×#235C2×D311yescharacteristic
75C2×C3×M16—31no—
76C3×#117—21no—
77C3×#117—31no—
78C3×#117—31no—
79C3×#117C2×D311yescharacteristic
80C3×#117C2×D311yescharacteristic
81#926C2×D311yescharacteristic
82#926C2×D311yescharacteristic
83C2×C4×Dic3—31no—
84C2×C4×Dic3—31no—
85C2×C4×Dic3—61no—
86C2×#208—31no—
87C2×#208—31no—
88C2×#208—61no—
89C2×#208C2×D311yescharacteristic
90#890—61no—
91#890—61no—
92#888—61no—
93#888—61no—
94#878—62no—
95#878—62no—
96C4×Dic6—62no—
97C4×Dic6—62no—
98C3×#99—62no—
99#837—61no—
100#837—61no—
101#837—62no—
102#825—61no—
103#825—61no—
104#806—22no—
105#805—62no—
106C23×C32C2×D411yescharacteristic
107C22×C3×D3—21no—
108C2×C32×C4—41no—
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—21no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—42no—
118C3×#67—41no—
119C3×#67—41no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—21no—
123C3×D12—21no—
124C3×D12—21no—
125C3×C4×D3—41no—
126C3×C4×D3—41no—
127C3×Dic6—21no—
128C3×Dic6—21no—
129#627—44no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—41no—
132#533—91no—
133#421—91no—
134C2×#104—91no—
135#410—31no—
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×C4C22×D311yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C2×#67—21no—
151C22×Dic3—61no—
152C22×Dic3—61no—
153C22×Dic3—121no—
154#235—21no—
155#235—21no—
156#235—21no—
157#235—21no—
158C2×D12Dic611yescharacteristic, complemented
159C2×C4×D3—21no—
160C2×Dic6—62no—
161C2×Dic6—62no—
162C2×Dic6Dic611yescharacteristic, complemented
163C3×M16—61no—
164C3×M16—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C22⋊C4—21no—
172C3×C22⋊C4—21no—
173C3×C22⋊C4—32no—
174C3×C22⋊C4—41no—
175C3×C22⋊C4—61no—
176C3×C42—21no—
177C3×C42—21no—
178C3×C42—32no—
179C3×C42—41no—
180C3×C42—61no—
181#217—21no—
182#217#6712yes—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—62no—
186C4⋊Dic3—62no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191C4×Dic3—21no—
192C4×Dic3—31no—
193C4×Dic3—31no—
194C4×Dic3—31no—
195C4×Dic3—31no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—61no—
199C4×Dic3—61no—
200C4×Dic3—121no—
201C4×Dic3D1212yes—
202#208—21no—
203#208—21no—
204#208—62no—
205#208—61no—
206#208—61no—
207#208—61no—
208#208—61no—
209#208—121no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—121no—
214C22×C32—41no—
215C22×C32#12011yescharacteristic
216C22×C32C22⋊Q811yescharacteristic
217C22×C32#12411yescharacteristic
218C2×C3×D3—41no—
219C2×C3×D3—81no—
220C32×C4—81no—
221C32×C4C22⋊Q811yescharacteristic
222C32×C4C22⋊Q811yescharacteristic
223C32×C4#12411yescharacteristic
224C32×C4#12411yescharacteristic
225C3⋊Dic3—22no—
226C3⋊Dic3—41no—
227C3×Dic3—42no—
228C3×Dic3—42no—
229C3×Dic3—41no—
230C2×#41—31no—
231C2×M16—31no—
232C2×M16—91no—
233C4⋊Q8—181no—
234#125—181no—
235C22⋊Q8—182no—
236C4×Q8—182no—
237#117—31no—
238#117—31no—
239#117D3211yescharacteristic
240C2×C42—91no—
241#104—182no—
242#104—181no—
243#104—181no—
244#99—62no—
245C23×C3—21no—
246C23×C3—61no—
247C23×C3D3×D411yescharacteristic
248C23×C3C2×#6711yescharacteristic
249C22×D3—21no—
250C3×Q8—61no—
251C3×Q8—61no—
252C3×D4—61no—
253C3×D4—61no—
254C3×D4—121no—
255C3×D4—121no—
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—42no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—62no—
266C2×C3×C4—61no—
267C2×C3×C4—62no—
268C2×C3×C4—121no—
269C2×C3×C4—121no—
270C2×C3×C4C2×Dic611yescharacteristic
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4#23511yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4#23711yescharacteristic
279C2×C3×C4#23711yescharacteristic
280C2×C3×C4#23711yescharacteristic
281C2×C3×C4D3×Q811yescharacteristic
282#67—41no—
283#67—41no—
284C2×Dic3—22no—
285C2×Dic3—21no—
286C2×Dic3—22no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—121no—
292C2×Dic3—121no—
293C2×Dic3—122no—
294C2×Dic3—122no—
295C2×Dic3—124no—
296D12—21no—
297D12—21no—
298C4×D3—41no—
299C4×D3—41no—
300Dic6—21no—
301Dic6—21no—
302Dic6—124no—
303Dic6—124no—
304C3×C8—121no—
305C3⋊C8—41no—
306C3⋊C8—122no—
307C3⋊C8—121no—
308C3⋊C8—121no—
309C2×C32—21no—
310C2×C32—21no—
311C2×C32—21no—
312C2×C32#39311yescharacteristic
313C3×D3—81no—
314#41—61no—
315#41—61no—
316#41—61no—
317#41—61no—
318C2×Q8—31no—
319C2×Q8—182no—
320C2×D4—31no—
321C2×D4—61no—
322C22×C4—61no—
323C22×C4—181no—
324C22×C4C2×D3211yescharacteristic
325M16—61no—
326M16—61no—
327M16—181no—
328M16—181no—
329C2×C8—61no—
330C2×C8—181no—
331C4⋊C4—21no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—182no—
335C4⋊C4—182no—
336C4⋊C4—182no—
337C22⋊C4—21no—
338C22⋊C4—32no—
339C22⋊C4—61no—
340C42—21no—
341C42—32no—
342C42—61no—
343C42—91no—
344C42—91no—
345C42—181no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—42no—
352C22×C3—121no—
353C22×C3—241no—
354C22×C3#88211yescharacteristic
355C22×C3#88511yescharacteristic
356C22×C3#89611yescharacteristic
357C22×C3#92411yescharacteristic
358C22×C3#93611yescharacteristic
359C22×C3#93711yescharacteristic
360C2×D3—41no—
361C2×D3—81no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—82no—
367C3×C4—81no—
368C3×C4—81no—
369C3×C4—122no—
370C3×C4—122no—
371C3×C4—121no—
372C3×C4#87511yescharacteristic
373C3×C4#87811yescharacteristic
374C3×C4#87811yescharacteristic
375C3×C4#88511yescharacteristic
376C3×C4#88511yescharacteristic
377C3×C4#88511yescharacteristic
378C3×C4#89611yescharacteristic
379C3×C4#89711yescharacteristic
380Dic3—42no—
381Dic3—42no—
382Dic3—41no—
383Dic3—62no—
384Dic3—62no—
385Dic3—122no—
386Dic3—121no—
387Dic3—121no—
388Dic3—122no—
389C32#203111yescharacteristic, complemented, Sylow
390C23—61no—
391C23D3×#6711yescharacteristic
392Q8—61no—
393Q8—61no—
394Q8—364no—
395D4—61no—
396D4—61no—
397D4—121no—
398D4—121no—
399C2×C4—41no—
400C2×C4—61no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—181no—
406C2×C4—181no—
407C2×C4—362no—
408C2×C4D3×Dic611yescharacteristic
409C2×C4#379811yescharacteristic
410C2×C4D3×D1211yescharacteristic
411C2×C4#380211yescharacteristic
412C2×C4#380411yescharacteristic
413C2×C4#380511yescharacteristic
414C8—121no—
415C8—361no—
416C2×C3—22no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—41no—
425C2×C3—41no—
426C2×C3—241no—
427C2×C3#467311yescharacteristic
428C2×C3#494711yescharacteristic
429D3—81no—
430C22—41no—
431C22—121no—
432C22—241no—
433C22#6385111yescharacteristic
434C22#6392211yescharacteristic
435C22#6395911yescharacteristic
436C4—81no—
437C4—122no—
438C4—122no—
439C4—121no—
440C4—182no—
441C4—361no—
442C4#6385211yescharacteristic
443C4#6389311yescharacteristic
444C4#6389911yescharacteristic
445C4#6391511yescharacteristic
446C3—21no—
447C3#6871411yescharacteristic, complemented
448C3#7003811yescharacteristic, complemented
449C2—21no—
450C2—21no—
451C2—21no—
452C2—241no—
453C2#1059129311yescharacteristic
subgroupG/H
centerC4#63852
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. #10595050C2semidirect
5. #10589398C2semidirect
6. C3×#4531C2semidirect
7. #10589170C2semidirect
39. #4531D3semidirect
47. C2×C3×D12Q8semidirect
49. C2×C3×Dic6Q8semidirect
158. C2×D12Dic6semidirect
162. C2×Dic6Dic6semidirect
389. C32#2031semidirect
447. C3#68714semidirect
448. C3#70038semidirect

Maximal subgroups

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

subgroupindex
#105950502
C3×#50062
#105911112
C2×#635682
#105893982
C3×#45312
#105891702
#700383
#687143