Finite Group Databasebeta

← #11859328

Subgroups — #11859328

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64289C211yesmaximal, characteristic, complemented
2C22×#3787C211yesmaximal, characteristic, complemented
3#10596098C211yesmaximal, characteristic
4#10593834C211yesmaximal, characteristic, complemented
5#10593803C211yesmaximal, characteristic, complemented
6#10593755C211yesmaximal, characteristic, complemented
7#10593751C212yesmaximal, complemented
8#10593749C212yesmaximal, complemented
9#10593748C211yesmaximal, characteristic, complemented
10#10593740C212yesmaximal, complemented
11#10593739C212yesmaximal, complemented
12C2×#3832C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#622C2211yescharacteristic
15C22×#622C2211yescharacteristic
16#64289—24no—
17C2×#3788C2211yescharacteristic
18C2×#3788C2211yescharacteristic
19C2×#3788C2212yescomplemented
20C2×#3787—24no—
21C2×#3787C2211yescharacteristic
22C2×#3787C2211yescharacteristic
23C2×#3787C2211yescharacteristic
24C2×#3787C2211yescharacteristic
25C2×#3787C2212yescomplemented
26C32×C22⋊Q8C411yescharacteristic
27#64155C411yescharacteristic
28#64139C411yescharacteristic
29#64104C411yescharacteristic
30#64103C412yes—
31#64102C2212yes—
32#64101C2211yescharacteristic
33#64091C412yes—
34#64090C2212yes—
35C22⋊#622C2212yes—
36#63779C2212yescomplemented
37#63778C2212yes—
38#63778C2212yescomplemented
39#63778C2212yescomplemented
40#63777C2212yescomplemented
41C4⋊#622C2212yescomplemented
42C4×#622C2212yescomplemented
43#5627—62no—
44C23×C3⋊D3C2×C411yescharacteristic
45C2×C32×Q8C2×C411yescharacteristic
46C22×C32×C4C2×C411yescharacteristic
47C2×#638C2×C412yes—
48C22×C3⋊Dic3C2311yescharacteristic
49#3832—22no—
50#3832—22no—
51C2×C4⋊(C3⋊D3)C2×C412yes—
52C2×C4⋊(C3⋊D3)C2×C412yes—
53C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3C2×C411yescharacteristic
57C2×C4×C3⋊D3C2×C411yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C4×C3⋊D3C2312yes—
60C2×C4×C3⋊D3C2311yescharacteristic
61C2×#622—22no—
62C2×#622—22no—
63C2×#622C2311yescharacteristic
64C2×#622C2311yescharacteristic
65C2×#622C2312yes—
66C2×#622C2312yes—
67C2×#622C2311yescharacteristic
68C2×#622C2311yescharacteristic
69#3788—22no—
70#3788—22no—
71#3788—24no—
72#3787—22no—
73#3787—22no—
74#3787—22no—
75#3787—24no—
76#3787D414yescomplemented
77C32×C4⋊C4C2×C411yescharacteristic
78C32×C4⋊C4C2×C412yes—
79C32×C22⋊C4C2×C412yes—
80#3752C2×C412yes—
81#3752C2×C412yes—
82#3752C2×C412yes—
83#3752C2×C412yes—
84C4⋊(C3⋊Dic3)C2×C411yescharacteristic
85#3750C2×C412yes—
86C4×C3⋊Dic3C2312yes—
87#2929—91nomaximal, Sylow
88C2×#239—62no—
89C22×C4×D3—62no—
90C3×C22⋊Q8—22no—
91#946—62no—
92#930—62no—
93#895—62no—
94#894—64no—
95#893—64no—
96#892—62no—
97#882—64no—
98#67⋊C4—64no—
99C23×C32C22×C411yescharacteristic
100C22×C3⋊D3—22no—
101C22×C3⋊D3—22no—
102C22×C3⋊D3—22no—
103C22×C3⋊D3C22×C412yes—
104C22×C3⋊D3C22×C411yescharacteristic
105C22×C3⋊D3C22×C411yescharacteristic
106C32×Q8—22no—
107C2×C32×C4—22no—
108C2×C32×C4C22×C412yes—
109C2×C32×C4C22×C412yes—
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112#638—24no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3C22×C412yes—
116C2×C3⋊Dic3C22×C411yescharacteristic
117C2×C3⋊Dic3C2411yescharacteristic
118C4⋊(C3⋊D3)—24no—
119C4⋊(C3⋊D3)—24no—
120C4⋊(C3⋊D3)—22no—
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123C4×C3⋊D3—21no—
124C4×C3⋊D3—22no—
125C4×C3⋊D3—21no—
126C4×C3⋊D3—22no—
127C4×C3⋊D3C2×D412yes—
128C4×C3⋊D3#4112yes—
129#622—21no—
130#622—21no—
131#622—22no—
132#622—22no—
133#622C2×D412yes—
134#622C2×D412yes—
135C2×#131—91no—
136C23×C8—91no—
137#525—91no—
138#435—92no—
139#435—92no—
140C8×D4—92no—
141C8×D4—92no—
142#424—91no—
143#408—91no—
144#407—91no—
145#405—91no—
146C23×D3—62no—
147C2×C3×Q8—22no—
148C22×C3×C4—22no—
149C2×#67—64no—
150C22×Dic3—62no—
151#239—124no—
152#239—124no—
153C2×D12—64no—
154C2×D12—64no—
155C2×D12—62no—
156C2×C4×D3—62no—
157C2×C4×D3—64no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×C4×D3—62no—
161C2×C4×D3—124no—
162C2×C4×D3—124no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—24no—
165C3×C22⋊C4—24no—
166(C2×D3)⋊C4—64no—
167(C2×D3)⋊C4—64no—
168(C2×D3)⋊C4—64no—
169(C2×D3)⋊C4—64no—
170C4⋊Dic3—62no—
171Dic3⋊C4—64no—
172C4×Dic3—64no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32#13112yescomplemented
176C22×C32C23×C411yescharacteristic
177C2×C3⋊D3—28no—
178C2×C3⋊D3—21no—
179C2×C3⋊D3—21no—
180C2×C3⋊D3—21no—
181C2×C3⋊D3—21no—
182C2×C3⋊D3—22no—
183C2×C3⋊D3—22no—
184C2×C3⋊D3—22no—
185C2×C3⋊D3C4×D412yes—
186C2×C3⋊D3#13112yescomplemented
187C32×C4—21no—
188C32×C4—22no—
189C32×C4—22no—
190C32×C4C4×D412yes—
191C3⋊Dic3—21no—
192C3⋊Dic3—22no—
193C3⋊Dic3C22×D411yescharacteristic
194C3⋊Dic3C2×#4111yescharacteristic
195C2×#41—91no—
196C23×C4—91no—
197#131—184no—
198C2×M16—91no—
199C2×M16—91no—
200C2×M16—92no—
201C22×C8—91no—
202C22×C8—91no—
203C22×C8—91no—
204C22×C8—91no—
205C22×C8—92no—
206C22×C8—91no—
207C22×C8—91no—
208C22×C8—184no—
209#123—92no—
210C22⋊Q8—91no—
211C22⋊Q8#15711yescharacteristic
212#121—91no—
213#121—91no—
214#120—92no—
215C4×D4—92no—
216C4×D4—92no—
217#117—91no—
218C4⋊C8—92no—
219C4⋊C8—92no—
220C22⋊C8—92no—
221C22⋊C8—92no—
222C22⋊C8—92no—
223C22⋊C8—92no—
224#97—92no—
225C4×C8—92no—
226C23×C3—22no—
227C22×D3—62no—
228C22×D3—62no—
229C22×D3—64no—
230C22×D3—124no—
231C22×D3—124no—
232C22×D3—124no—
233C3×Q8—44no—
234C2×C3×C4—22no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—22no—
238C2×C3×C4—44no—
239#67—128no—
240C2×Dic3—62no—
241C2×Dic3—64no—
242C2×Dic3—62no—
243C2×Dic3—122no—
244C2×Dic3—122no—
245D12—124no—
246D12—128no—
247D12—128no—
248C4×D3—64no—
249C4×D3—64no—
250C4×D3—122no—
251C4×D3—122no—
252C4×D3—124no—
253C4×D3—124no—
254C4×D3—124no—
255C4×D3—124no—
256C2×C32—22no—
257C2×C32C2×C4×D411yescharacteristic
258C2×C32C2×#13111yescharacteristic
259C2×C32C2×#13111yescharacteristic
260C3⋊D3—22no—
261C3⋊D3—22no—
262C3⋊D3—42no—
263C24—91no—
264#41—182no—
265#41—182no—
266C2×Q8C2×#15711yescharacteristic
267C2×D4—92no—
268C2×D4—92no—
269C2×D4—92no—
270C2×D4—91no—
271C22×C4—91no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—92no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—182no—
278C22×C4—182no—
279C22×C4C2×#15711yescharacteristic
280M16—184no—
281M16—182no—
282M16—182no—
283C2×C8—91no—
284C2×C8—91no—
285C2×C8—94no—
286C2×C8—92no—
287C2×C8—91no—
288C2×C8—91no—
289C2×C8—92no—
290C2×C8—182no—
291C2×C8—182no—
292C2×C8—182no—
293C2×C8—182no—
294C2×C8—184no—
295C2×C8—182no—
296C4⋊C4—91no—
297C4⋊C4—92no—
298C4⋊C4C2×#15711yescharacteristic
299C4⋊C4C2×#15712yes—
300C22⋊C4—92no—
301C22⋊C4—92no—
302C22⋊C4—92no—
303C22⋊C4—92no—
304C22⋊C4C2×#15712yes—
305C42—92no—
306C22×C3—24no—
307C22×C3—22no—
308C22×C3—42no—
309C22×C3—42no—
310C2×D3—64no—
311C2×D3—64no—
312C2×D3—122no—
313C2×D3—122no—
314C2×D3—122no—
315C2×D3—122no—
316C2×D3—1216no—
317C2×D3—124no—
318C2×D3—124no—
319C2×D3—124no—
320C3×C4—24no—
321C3×C4—42no—
322C3×C4—44no—
323C3×C4—44no—
324Dic3—62no—
325Dic3—62no—
326Dic3—122no—
327Dic3—124no—
328C32#292911yescharacteristic, complemented, Sylow
329C23—91no—
330C23—91no—
331C23—92no—
332C23—182no—
333C23—182no—
334C23—182no—
335C23C22×#15711yescharacteristic
336Q8—22no—
337D4—184no—
338D4—184no—
339D4—184no—
340D4—182no—
341C2×C4—22no—
342C2×C4—91no—
343C2×C4—92no—
344C2×C4—92no—
345C2×C4—92no—
346C2×C4—91no—
347C2×C4—181no—
348C2×C4—182no—
349C2×C4—181no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4—181no—
353C2×C4—181no—
354C2×C4—182no—
355C2×C4C22×#15712yes—
356C2×C4C22×#15711yescharacteristic
357C2×C4C22×#15712yes—
358C2×C4C22×#15711yescharacteristic
359C8—92no—
360C8—92no—
361C8—181no—
362C8—181no—
363C8—182no—
364C8—182no—
365C2×C3—22no—
366C2×C3—22no—
367C2×C3—22no—
368C2×C3—44no—
369D3—124no—
370D3—124no—
371D3—244no—
372C22—21no—
373C22—21no—
374C22—92no—
375C22—92no—
376C22—188no—
377C22—181no—
378C22—181no—
379C22—181no—
380C22—181no—
381C22—182no—
382C22—182no—
383C22—182no—
384C22#6428912yescomplemented
385C22C23×#15711yescharacteristic
386C4—21no—
387C4—22no—
388C4—22no—
389C4—91no—
390C4—91no—
391C4—181no—
392C4—182no—
393C4D4×#15712yes—
394C3—22no—
395C2—22no—
396C2—182no—
397C2—182no—
398C2—362no—
399C2C2×D4×#15711yescharacteristic
400C2C2×#6428911yescharacteristic
401C2#1059664711yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C22⋊Q8C4
prime radical#10596098C2
cosocleC2×C3⋊Dic3C24
hypercenterC22⋊Q8#157
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64289C2semidirect
2. C22×#3787C2semidirect
4. #10593834C2semidirect
5. #10593803C2semidirect
6. #10593755C2semidirect
7. #10593751C2semidirect
8. #10593749C2semidirect
9. #10593748C2semidirect
10. #10593740C2semidirect
11. #10593739C2semidirect
19. C2×#3788C22semidirect
25. C2×#3787C22semidirect
36. #63779C22semidirect
38. #63778C22semidirect
39. #63778C22semidirect
40. #63777C22semidirect
41. C4⋊#622C22semidirect
42. C4×#622C22semidirect
76. #3787D4semidirect
175. C22×C32#131semidirect
186. C2×C3⋊D3#131semidirect
328. C32#2929semidirect
384. C22#64289semidirect

Maximal subgroups

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

subgroupindex
C2×#642892
C22×#37872
#105960982
#105938342
#105938032
#105937552
#105937512
#105937492
#105937482
#105937402
#105937392
#29299