Finite Group Databasebeta

← #11868630

Subgroups — #11868630

Order 1152.

654 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 115 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×#3798C211yesmaximal, characteristic
2#10593882C211yesmaximal, characteristic, complemented
3#10593726C211yesmaximal, characteristic, complemented
4#10593393C211yesmaximal, characteristic, complemented
5#10593389C212yesmaximal, complemented
6#10593382C212yesmaximal, complemented
7#10593376C211yesmaximal, characteristic, complemented
8#10593359C211yesmaximal, characteristic, complemented
9#10593350C212yesmaximal, complemented
10#10593349C212yesmaximal
11#10593347C211yesmaximal, characteristic, complemented
12C2×#3798C2211yescharacteristic
13C2×#3787C2212yes—
14C42×C3⋊D3C2211yescharacteristic
15C3×C42×D3—21no—
16C3×C4×Dic6—21no—
17#63919C2211yescharacteristic
18C4×#627—21no—
19C4×#627C2211yescharacteristic
20C4×#627C2211yescharacteristic
21C4×#626—21no—
22C4×#626—21no—
23C4×#625C2211yescharacteristic
24C4×#625C2211yescharacteristic
25#63874C2212yes—
26#63874C2211yescharacteristic
27#63873C2211yescharacteristic
28#63871—21no—
29#63870C2212yes—
30#63865—21no—
31#63855—21no—
32#63779C2212yes—
33C4⋊#622C2211yescharacteristic
34C4⋊#622C2211yescharacteristic
35#63743C2212yes—
36#63743C2212yes—
37#63742C2212yes—
38#63742C2212yes—
39#63740C2212yes—
40#63740C2212yes—
41#63739C2212yes—
42#63739C2212yes—
43#5578—61no—
44C4×#235—61no—
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C4×C3⋊D3C2311yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—21no—
52C2×#627—21no—
53C2×#627C2311yescharacteristic
54C2×#626—21no—
55C2×#625C2311yescharacteristic
56#3798—22no—
57#3798Q814yescomplemented
58C2×#622C2312yes—
59C2×#622C2312yes—
60#3787—24no—
61C32×C42D411yescharacteristic
62C4×C3⋊Dic3D411yescharacteristic
63C4×C3⋊Dic3C2311yescharacteristic
64C4×C3⋊Dic3C2311yescharacteristic
65C3×C4⋊Dic3—21no—
66C3×Dic3⋊C4—22no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—22no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71#3724—21no—
72#3724C2312yes—
73#3724C2312yes—
74#3724C2311yescharacteristic
75#3724C2311yescharacteristic
76Dic3⋊Dic3—21no—
77Dic3⋊Dic3—21no—
78Dic3⋊Dic3—22no—
79#3722—22no—
80#3722—21no—
81(C2×D3)⋊Dic3—21no—
82(C2×D3)⋊Dic3—21no—
83#3076—91nomaximal, Sylow
84C2×#235—61no—
85C3×C4×Q8—61no—
86C2×C3×C42—61no—
87#946—61no—
88#944—61no—
89C4×#67—61no—
90C4×#67—61no—
91C4×#67—61no—
92C4×#67—61no—
93#926—61no—
94#897—61no—
95#896—62no—
96#889—62no—
97#888—61no—
98C4×D12—61no—
99C4×D12—61no—
100#872—61no—
101#872—62no—
102#872—61no—
103C42×D3—21no—
104C42×D3—61no—
105C42×D3—61no—
106C4×Dic6—21no—
107C4×Dic6—61no—
108C4×Dic6—61no—
109C4×Dic6—62no—
110C22×C3⋊D3C2×D411yescharacteristic
111C22×C3×D3—21no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C3⋊Dic3C2×D411yescharacteristic
116C2×C3⋊Dic3C2×D411yescharacteristic
117C2×C3⋊Dic3C2411yescharacteristic
118C4×C3⋊D3—22no—
119C4×C3⋊D3—41no—
120C4×C3⋊D3C2×Q812yes—
121C4×C3⋊D3#4112yes—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C3×C4×D3—24no—
128C3×C4×D3—42no—
129C3×C4×D3—42no—
130C3×Dic6—42no—
131#627—21no—
132#627—42no—
133#627C2×Q812yes—
134#626—24no—
135#625—21no—
136#625C2×Q812yes—
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—
151C22×C3×C4—61no—
152C22×C3×C4—61no—
153C22×C3×C4—61no—
154C2×#67—61no—
155C2×#67—61no—
156#235—64no—
157#235—64no—
158C2×D12—61no—
159C2×C4×D3—21no—
160C2×C4×D3—21no—
161C2×C4×D3—21no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—61no—
165C2×C4×D3—61no—
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×C42—21no—
174C3×C42—21no—
175C3×C42—62no—
176C3×C42—61no—
177C3×C42—61no—
178C3×C42—61no—
179#217—61no—
180#217—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—62no—
184(C2×D3)⋊C4—62no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187C4⋊Dic3—21no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—62no—
191Dic3⋊C4—22no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—62no—
199Dic3⋊C4—62no—
200C4×Dic3—22no—
201C4×Dic3—21no—
202C4×Dic3—21no—
203C4×Dic3—21no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C22×C32C22×D411yescharacteristic
211C2×C3⋊D3—21no—
212C2×C3⋊D3—21no—
213C2×C3⋊D3C22⋊Q812yes—
214C2×C3×D3—22no—
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C32×C4—21no—
218C32×C4C22⋊Q812yes—
219C32×C4#13512yes—
220C3⋊Dic3—21no—
221C3⋊Dic3—21no—
222C3⋊Dic3C22×Q811yescharacteristic
223C3⋊Dic3C2×#4111yescharacteristic
224C3×Dic3—22no—
225C3×Dic3—42no—
226C3×Dic3—41no—
227C3×Dic3—42no—
228C3×Dic3—41no—
229C2×#41—91no—
230C22×C8—92no—
231C4⋊Q8—91no—
232C4⋊Q8—91no—
233#125—92no—
234C22⋊Q8—181no—
235C22⋊Q8—181no—
236C4×Q8—61no—
237C4×Q8—91no—
238C4×Q8—91no—
239C4×Q8—181no—
240C4×D4—91no—
241C4×D4—91no—
242C4×D4—181no—
243C4×D4—181no—
244#117—91no—
245#117—92no—
246#117—181no—
247C2×C42—61no—
248C2×C42—91no—
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—61no—
261C22×D3—21no—
262C22×D3—61no—
263C22×D3—61no—
264C3×Q8—122no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—64no—
272C2×C3×C4—61no—
273C2×C3×C4—62no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—62no—
277C2×C3×C4—122no—
278C2×C3×C4—122no—
279#67—62no—
280#67—64no—
281#67—62no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—22no—
286C2×Dic3—22no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293D12—64no—
294C4×D3—24no—
295C4×D3—42no—
296C4×D3—42no—
297C4×D3—62no—
298C4×D3—62no—
299C4×D3—62no—
300C4×D3—62no—
301C4×D3—122no—
302C4×D3—122no—
303C4×D3—122no—
304C4×D3—122no—
305Dic6—42no—
306Dic6—62no—
307Dic6—62no—
308Dic6—124no—
309C2×C32C2×C22⋊Q811yescharacteristic
310C2×C32C2×#13511yescharacteristic
311C2×C32#57511yescharacteristic
312C3⋊D3—22no—
313C3×D3—42no—
314#41—94no—
315#41—182no—
316C2×Q8—61no—
317C2×Q8—91no—
318C2×Q8—181no—
319C2×D4—91no—
320C2×D4—181no—
321C22×C4—61no—
322C22×C4—61no—
323C22×C4—61no—
324C22×C4—91no—
325C22×C4—91no—
326C22×C4—91no—
327C2×C8—92no—
328C2×C8—92no—
329C2×C8—184no—
330C4⋊C4—62no—
331C4⋊C4—61no—
332C4⋊C4—92no—
333C4⋊C4—92no—
334C4⋊C4—91no—
335C4⋊C4—91no—
336C4⋊C4—181no—
337C4⋊C4—181no—
338C4⋊C4—182no—
339C4⋊C4—181no—
340C22⋊C4—181no—
341C22⋊C4—182no—
342C22⋊C4—181no—
343C22⋊C4—181no—
344C42—61no—
345C42—61no—
346C42—61no—
347C42—62no—
348C42—91no—
349C42—91no—
350C42—91no—
351C42GO+(4,𝔽2)11yescharacteristic
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—62no—
355C22×C3—121no—
356C22×C3—121no—
357C2×D3—22no—
358C2×D3—41no—
359C2×D3—41no—
360C2×D3—62no—
361C2×D3—62no—
362C2×D3—121no—
363C2×D3—121no—
364C2×D3—121no—
365C2×D3—121no—
366C3×C4—22no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—22no—
371C3×C4—41no—
372C3×C4—62no—
373C3×C4—122no—
374C3×C4—121no—
375C3×C4—121no—
376C3×C4—122no—
377Dic3—22no—
378Dic3—42no—
379Dic3—42no—
380Dic3—41no—
381Dic3—41no—
382Dic3—61no—
383Dic3—61no—
384Dic3—61no—
385Dic3—61no—
386Dic3—62no—
387Dic3—121no—
388Dic3—121no—
389Dic3—121no—
390C32#307611yescharacteristic, complemented, Sylow
391C23—61no—
392C23—91no—
393Q8—92no—
394Q8—122no—
395Q8—181no—
396Q8—362no—
397D4—92no—
398D4—184no—
399D4—181no—
400C2×C4—61no—
401C2×C4—64no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—91no—
407C2×C4—92no—
408C2×C4—92no—
409C2×C4—91no—
410C2×C4—91no—
411C2×C4—122no—
412C2×C4—122no—
413C2×C4—182no—
414C2×C4—361no—
415C2×C4C2×GO+(4,𝔽2)11yescharacteristic
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—122no—
427D3—42no—
428D3—122no—
429D3—122no—
430C22—62no—
431C22—92no—
432C22—121no—
433C22—121no—
434C22—181no—
435C22—181no—
436C22C22×GO+(4,𝔽2)11yescharacteristic
437C4—21no—
438C4—62no—
439C4—91no—
440C4—91no—
441C4—121no—
442C4—122no—
443C4—121no—
444C4—122no—
445C4—181no—
446C4—181no—
447C4D32⋊Q812yes—
448C4#6422312yes—
449C3—21no—
450C3—21no—
451C2—122no—
452C2—182no—
453C2C2×D32⋊Q811yescharacteristic
454C2C2×#6422311yescharacteristic
455C2#1059649911yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC2×#3798C22
hypercenterC42GO+(4,𝔽2)
hypocenterC32#3076
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593882C2semidirect
3. #10593726C2semidirect
4. #10593393C2semidirect
5. #10593389C2semidirect
6. #10593382C2semidirect
7. #10593376C2semidirect
8. #10593359C2semidirect
9. #10593350C2semidirect
11. #10593347C2semidirect
57. #3798Q8semidirect
390. C32#3076semidirect

Maximal subgroups

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

subgroupindex
C4×#37982
#105938822
#105937262
#105933932
#105933892
#105933822
#105933762
#105933592
#105933502
#105933492
#105933472
#30769