Finite Group Databasebeta

← #11868633

Subgroups — #11868633

Order 1152.

654 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3805C211yesmaximal, characteristic
2#10594810C211yesmaximal, characteristic, complemented
3C2×#63779C211yesmaximal, characteristic, complemented
4#10593511C212yesmaximal, complemented
5#10593498C212yesmaximal
6#10593391C211yesmaximal, characteristic, complemented
7#10593385C211yesmaximal, characteristic, complemented
8#10593382C212yesmaximal, complemented
9#10593367C211yesmaximal, characteristic, complemented
10#10593357C211yesmaximal, characteristic, complemented
11#10593350C212yesmaximal, complemented
12C2×#3805C2211yescharacteristic
13C22×#622C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C3×C4×#67—21no—
16C3×#924—21no—
17#63982—21no—
18#67⋊Dic3—21no—
19#63957C2211yescharacteristic
20#63957C2212yes—
21#63919C2211yescharacteristic
22C4×#627C2211yescharacteristic
23#63902C2211yescharacteristic
24C4×#625C2211yescharacteristic
25#63878—21no—
26C4×D3×Dic3—21no—
27#63873C2211yescharacteristic
28#63870C2212yes—
29#63843—21no—
30#63838—21no—
31#63838C2211yescharacteristic
32#63779C2212yes—
33#63779C2211yescharacteristic
34#63779C2211yescharacteristic
35#63743C2212yes—
36#63743C2212yes—
37#63742C2212yes—
38#63742C2212yes—
39#63740C2212yes—
40#63740C2212yes—
41#63739C2212yes—
42#63739C2212yes—
43#5622—61no—
44C4×#237—61no—
45C22×C32×C4D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3⋊Dic3C2311yescharacteristic
48C2×C3×#67—21no—
49C2×C3×C4×D3—21no—
50C2×C3×Dic6—21no—
51C2×#627—21no—
52C2×#627C2311yescharacteristic
53C2×#625C2311yescharacteristic
54#3805—22no—
55#3805Q814yescomplemented
56C2×D3×Dic3—21no—
57C2×D3×Dic3—21no—
58C2×#622—24no—
59C2×#622C2312yes—
60C2×#622C2312yes—
61C4×C3⋊Dic3D411yescharacteristic
62C4×C3⋊Dic3D411yescharacteristic
63C4×C3⋊Dic3C2311yescharacteristic
64C4×C3⋊Dic3C2311yescharacteristic
65C3×#217—22no—
66C3×#217—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×C4⋊Dic3—21no—
69C3×Dic3⋊C4—22no—
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72#3724—21no—
73#3724C2311yescharacteristic
74#3724C2312yes—
75#3724C2312yes—
76#3724C2311yescharacteristic
77Dic3⋊Dic3—22no—
78Dic3⋊Dic3—21no—
79(C2×D3)⋊Dic3—21no—
80Dic32—22no—
81Dic32—21no—
82Dic32—21no—
83#3076—91nomaximal, Sylow
84C2×#237—61no—
85C3×C22⋊Q8—61no—
86C3×C4×D4—61no—
87Q8×Dic3—61no—
88#944—61no—
89D4×Dic3—61no—
90C4×#67—21no—
91C4×#67—61no—
92#924—21no—
93C2×C4×Dic3—61no—
94C2×C4×Dic3—61no—
95C2×C4×Dic3—61no—
96#892—61no—
97#889—62no—
98#888—61no—
99#887—61no—
100#887—62no—
101#887—61no—
102#67⋊C4—61no—
103#67⋊C4—61no—
104#878—62no—
105#877—61no—
106#877—62no—
107#877—61no—
108C42×D3—61no—
109C4×Dic6—61no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—21no—
112C2×C32×C4—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3C2×D411yescharacteristic
117C2×C3⋊Dic3C2×D411yescharacteristic
118C2×C3⋊Dic3C2×D411yescharacteristic
119C2×C3⋊Dic3C2×Q812yes—
120C2×C3⋊Dic3#4112yes—
121C2×C3⋊Dic3C2411yescharacteristic
122C3×#67—24no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—22no—
128C3×C4×D3—42no—
129C3×Dic6—42no—
130#627—21no—
131#627—42no—
132#627C2×Q812yes—
133#625—21no—
134#625C2×Q812yes—
135D3×Dic3—24no—
136D3×Dic3—42no—
137#622—22no—
138#622—22no—
139#533—91no—
140C4×#41—91no—
141#479—92no—
142#478—92no—
143#477—91no—
144#476—91no—
145#475—91no—
146#474—91no—
147#427—92no—
148C2×C4⋊C8—91no—
149#416—92no—
150C2×C3×Q8—61no—
151C2×C3×D4—61no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—61no—
155C2×#67—21no—
156C2×#67—61no—
157C22×Dic3—61no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163#237—64no—
164#237—64no—
165C2×C4×D3—21no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×Dic6—21no—
169C2×Dic6—61no—
170C2×Dic6—62no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—62no—
173C3×C4⋊C4—61no—
174C3×C22⋊C4—61no—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—61no—
177C3×C42—61no—
178#217—22no—
179#217—21no—
180#217—61no—
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—61no—
183C4⋊Dic3—21no—
184C4⋊Dic3—61no—
185C4⋊Dic3—62no—
186Dic3⋊C4—21no—
187Dic3⋊C4—22no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192Dic3⋊C4—61no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195C4×Dic3—21no—
196C4×Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—61no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—62no—
207C4×Dic3—62no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32C22⋊Q812yes—
213C22×C32C22×D411yescharacteristic
214C2×C3×D3—22no—
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C32×C4—21no—
218C32×C4—21no—
219C3⋊Dic3—21no—
220C3⋊Dic3C22⋊Q812yes—
221C3⋊Dic3#13512yes—
222C3⋊Dic3C22×Q811yescharacteristic
223C3⋊Dic3C2×#4111yescharacteristic
224C3×Dic3—22no—
225C3×Dic3—41no—
226C3×Dic3—42no—
227C3×Dic3—42no—
228C3×Dic3—41no—
229C2×#41—91no—
230C22×C8—92no—
231C4⋊Q8—91no—
232C4⋊Q8—91no—
233#125—92no—
234C22⋊Q8—61no—
235C22⋊Q8—181no—
236C4×Q8—91no—
237C4×Q8—91no—
238C4×Q8—181no—
239C4×Q8—181no—
240C4×D4—61no—
241C4×D4—91no—
242C4×D4—91no—
243C4×D4—181no—
244#117—91no—
245#117—92no—
246#117—181no—
247C2×C42—91no—
248C2×C42—181no—
249#107—92no—
250#107—92no—
251#106—92no—
252#106—92no—
253C4⋊C8—91no—
254C4⋊C8—91no—
255C4⋊C8—92no—
256#103—92no—
257#103—92no—
258#102—92no—
259#102—92no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—61no—
263C22×D3—21no—
264C3×Q8—122no—
265C3×D4—64no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—62no—
275C2×C3×C4—61no—
276C2×C3×C4—62no—
277C2×C3×C4—122no—
278#67—24no—
279#67—62no—
280#67—62no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—22no—
285C2×Dic3—22no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—64no—
299C2×Dic3—122no—
300C2×Dic3—122no—
301C2×Dic3—122no—
302C4×D3—42no—
303C4×D3—64no—
304C4×D3—122no—
305Dic6—42no—
306Dic6—62no—
307Dic6—62no—
308Dic6—124no—
309C2×C32—22no—
310C2×C32C2×C22⋊Q811yescharacteristic
311C2×C32C2×#13511yescharacteristic
312C2×C32#57511yescharacteristic
313C3×D3—42no—
314#41—94no—
315#41—182no—
316C2×Q8—61no—
317C2×Q8—91no—
318C2×Q8—181no—
319C2×D4—61no—
320C2×D4—91no—
321C22×C4—61no—
322C22×C4—91no—
323C22×C4—91no—
324C22×C4—181no—
325C22×C4—181no—
326C22×C4GO+(4,𝔽2)11yescharacteristic
327C2×C8—92no—
328C2×C8—92no—
329C2×C8—184no—
330C4⋊C4—61no—
331C4⋊C4—62no—
332C4⋊C4—61no—
333C4⋊C4—92no—
334C4⋊C4—92no—
335C4⋊C4—91no—
336C4⋊C4—91no—
337C4⋊C4—181no—
338C4⋊C4—182no—
339C4⋊C4—181no—
340C22⋊C4—61no—
341C22⋊C4—62no—
342C22⋊C4—61no—
343C22⋊C4—181no—
344C42—61no—
345C42—91no—
346C42—91no—
347C42—91no—
348C42—91no—
349C42—181no—
350C42—181no—
351C42—182no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—62no—
361C22×C3—121no—
362C22×C3—121no—
363C2×D3—22no—
364C2×D3—41no—
365C2×D3—41no—
366C3×C4—22no—
367C3×C4—22no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—62no—
371C3×C4—122no—
372C3×C4—121no—
373C3×C4—121no—
374C3×C4—122no—
375Dic3—22no—
376Dic3—42no—
377Dic3—42no—
378Dic3—41no—
379Dic3—41no—
380Dic3—61no—
381Dic3—61no—
382Dic3—62no—
383Dic3—62no—
384Dic3—62no—
385Dic3—62no—
386Dic3—61no—
387Dic3—61no—
388Dic3—121no—
389Dic3—121no—
390C32#307611yescharacteristic, complemented, Sylow
391C23—61no—
392C23C2×GO+(4,𝔽2)11yescharacteristic
393Q8—92no—
394Q8—122no—
395Q8—181no—
396Q8—362no—
397D4—64no—
398D4—92no—
399D4—181no—
400C2×C4—41no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—91no—
407C2×C4—91no—
408C2×C4—91no—
409C2×C4—92no—
410C2×C4—92no—
411C2×C4—91no—
412C2×C4—122no—
413C2×C4—184no—
414C2×C4—182no—
415C2×C4—362no—
416C2×C4C2×GO+(4,𝔽2)11yescharacteristic
417C2×C4C2×GO+(4,𝔽2)11yescharacteristic
418C8—182no—
419C8—182no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—42no—
427C2×C3—42no—
428C2×C3—122no—
429D3—42no—
430C22—21no—
431C22—21no—
432C22—62no—
433C22—121no—
434C22—121no—
435C22D32⋊Q812yes—
436C22C22×GO+(4,𝔽2)11yescharacteristic
437C4—21no—
438C4—21no—
439C4—62no—
440C4—91no—
441C4—92no—
442C4—91no—
443C4—92no—
444C4—121no—
445C4—122no—
446C4—121no—
447C4—122no—
448C4—181no—
449C3—21no—
450C3—21no—
451C2—22no—
452C2—122no—
453C2C2×D32⋊Q811yescharacteristic
454C2#1059650011yescharacteristic
455C2#1059653211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#3805C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#3076
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10594810C2semidirect
3. C2×#63779C2semidirect
4. #10593511C2semidirect
6. #10593391C2semidirect
7. #10593385C2semidirect
8. #10593382C2semidirect
9. #10593367C2semidirect
10. #10593357C2semidirect
11. #10593350C2semidirect
55. #3805Q8semidirect
390. C32#3076semidirect

Maximal subgroups

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

subgroupindex
C4×#38052
#105948102
C2×#637792
#105935112
#105934982
#105933912
#105933852
#105933822
#105933672
#105933572
#105933502
#30769