Finite Group Databasebeta

← #11859094

Subgroups — #11859094

Order 1152.

702 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3830C211yesmaximal, characteristic
2#10593822C212yesmaximal
3#10593806C211yesmaximal, characteristic, complemented
4#10593805C211yesmaximal, characteristic, complemented
5#10593795C211yesmaximal, characteristic, complemented
6C2×C4⋊#622C211yesmaximal, characteristic, complemented
7#10593753C212yesmaximal, complemented
8#10593744C212yesmaximal, complemented
9#10593738C212yesmaximal, complemented
10#10593730C211yesmaximal, characteristic, complemented
11#10593727C211yesmaximal, characteristic, complemented
12C2×#3830C2211yescharacteristic
13C2×#3792C2212yes—
14C22×#622C2212yes—
15C32×C4×D4C411yescharacteristic
16D4×C3⋊Dic3C411yescharacteristic
17C4×#638C411yescharacteristic
18C4×#638C411yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21#64101C2211yescharacteristic
22#64096C411yescharacteristic
23#64090C411yescharacteristic
24#64090C411yescharacteristic
25#64086C2211yescharacteristic
26#64086C2211yescharacteristic
27C42×C3⋊D3C2211yescharacteristic
28C4×#634C411yescharacteristic
29C22⋊#622C2212yes—
30C22⋊#622C2212yes—
31#63779C2212yes—
32#63778C2212yes—
33#63778C2212yes—
34#63777C2212yes—
35#63777C2212yes—
36C4⋊#622C2211yescharacteristic
37C4⋊#622C2211yescharacteristic
38C4⋊#622C2212yes—
39C4⋊#622C2211yescharacteristic
40C4⋊#622C2211yescharacteristic
41C4×#622C2212yes—
42C4×#622C2212yes—
43C4×#237—62no—
44C2×C32×D4C2×C411yescharacteristic
45C22×C32×C4C2×C411yescharacteristic
46C22×C32×C4C2×C411yescharacteristic
47C2×#638C2×C411yescharacteristic
48C2×#638C2×C411yescharacteristic
49C22×C3⋊Dic3C2×C411yescharacteristic
50C22×C3⋊Dic3C2×C411yescharacteristic
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2311yescharacteristic
53#3830—22no—
54#3830—22no—
55C2×C4×C3⋊D3C2×C411yescharacteristic
56C2×C4×C3⋊D3C2×C411yescharacteristic
57C2×C4×C3⋊D3C2311yescharacteristic
58C2×#634C2×C411yescharacteristic
59#3792—24no—
60C2×#622—24no—
61C2×#622C2312yes—
62C2×#622C2312yes—
63C2×#622C2312yes—
64C2×#622C2312yes—
65C32×C4⋊C4C2×C411yescharacteristic
66C32×C22⋊C4C2×C411yescharacteristic
67C32×C22⋊C4C2×C411yescharacteristic
68C32×C42C2×C411yescharacteristic
69#3757C2×C411yescharacteristic
70#3757C2×C411yescharacteristic
71#3752C2×C411yescharacteristic
72#3752C2×C411yescharacteristic
73C4⋊(C3⋊Dic3)C2×C411yescharacteristic
74#3750C2×C411yescharacteristic
75#3750C2×C411yescharacteristic
76#3750C2×C411yescharacteristic
77#3750C2×C411yescharacteristic
78C4×C3⋊Dic3C2×C411yescharacteristic
79C4×C3⋊Dic3C2×C411yescharacteristic
80C4×C3⋊Dic3C2×C411yescharacteristic
81C4×C3⋊Dic3C2×C411yescharacteristic
82C4×C3⋊Dic3C2×C411yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C4×C3⋊Dic3C2311yescharacteristic
85C4×C3⋊Dic3C2311yescharacteristic
86C4×C3⋊Dic3C2311yescharacteristic
87#2925—91nomaximal, Sylow
88C2×#237—62no—
89C3×C4×D4—22no—
90D4×Dic3—62no—
91C4×#67—62no—
92C4×#67—62no—
93C2×C4×Dic3—62no—
94C2×C4×Dic3—62no—
95#892—62no—
96#887—62no—
97#67⋊C4—62no—
98#67⋊C4—62no—
99#877—62no—
100#877—62no—
101C42×D3—62no—
102C4×Dic6—62no—
103C23×C32C22×C411yescharacteristic
104C23×C32C22×C411yescharacteristic
105C22×C3⋊D3C22×C411yescharacteristic
106C32×D4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C22×C411yescharacteristic
114#638—22no—
115#638—22no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3C22×C411yescharacteristic
121C2×C3⋊Dic3C22×C411yescharacteristic
122C2×C3⋊Dic3C22×C411yescharacteristic
123C2×C3⋊Dic3C22×C411yescharacteristic
124C2×C3⋊Dic3C22×C411yescharacteristic
125C2×C3⋊Dic3C22×C411yescharacteristic
126C2×C3⋊Dic3#4112yes—
127C2×C3⋊Dic3#4112yes—
128C2×C3⋊Dic3C2411yescharacteristic
129C4×C3⋊D3—21no—
130C4×C3⋊D3—21no—
131C4×C3⋊D3—22no—
132C4×C3⋊D3—41no—
133#634—22no—
134#622—22no—
135#622—22no—
136#622—22no—
137#622—22no—
138C4×#41—91no—
139#433—92no—
140#433—92no—
141#432—91no—
142#432—91no—
143#431—91no—
144#431—91no—
145#423—91no—
146C2×C4⋊C8—91no—
147#408—92no—
148#405—92no—
149C2×C3×D4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C2×#67—62no—
153C2×#67—62no—
154C22×Dic3—62no—
155C22×Dic3—62no—
156C22×Dic3—62no—
157C22×Dic3—62no—
158#237—68no—
159#237—68no—
160C2×C4×D3—62no—
161C2×C4×D3—62no—
162C2×C4×D3—62no—
163C2×Dic6—62no—
164C3×C4⋊C4—22no—
165C3×C22⋊C4—22no—
166C3×C22⋊C4—22no—
167C3×C42—22no—
168#217—62no—
169#217—62no—
170(C2×D3)⋊C4—62no—
171(C2×D3)⋊C4—62no—
172C4⋊Dic3—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—62no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177C4×Dic3—62no—
178C4×Dic3—62no—
179C4×Dic3—62no—
180C4×Dic3—62no—
181C4×Dic3—62no—
182C4×Dic3—62no—
183C4×Dic3—62no—
184C4×Dic3—62no—
185C4×Dic3—62no—
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32#11712yes—
192C22×C32C23×C411yescharacteristic
193C2×C3⋊D3—21no—
194C2×C3⋊D3—21no—
195C2×C3⋊D3—21no—
196C32×C4—21no—
197C32×C4—21no—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4#13112yes—
201C3⋊Dic3—21no—
202C3⋊Dic3—21no—
203C3⋊Dic3—21no—
204C3⋊Dic3—21no—
205C3⋊Dic3—21no—
206C3⋊Dic3#11712yes—
207C3⋊Dic3C2×#4111yescharacteristic
208C3⋊Dic3C2×#4111yescharacteristic
209C2×#41—91no—
210C2×M16—92no—
211C22×C8—92no—
212C4×Q8—91no—
213C4×Q8—91no—
214C4×D4—91no—
215C4×D4—91no—
216C4×D4—91no—
217C4×D4—91no—
218C4×D4—91no—
219C4×D4#15711yescharacteristic
220#117—91no—
221#117—91no—
222#117—91no—
223C2×C42—91no—
224C2×C42—91no—
225C2×C42—91no—
226C4⋊C8—91no—
227C4⋊C8—91no—
228C4⋊C8—92no—
229C4⋊C8—91no—
230C4⋊C8—91no—
231C4⋊C8—92no—
232C22⋊C8—92no—
233C22⋊C8—92no—
234C22⋊C8—92no—
235C22⋊C8—92no—
236#97—92no—
237#97—92no—
238C4×C8—92no—
239C4×C8—92no—
240C23×C3—22no—
241C23×C3—22no—
242C22×D3—62no—
243C3×D4—28no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—44no—
250C2×C3×C4—44no—
251#67—68no—
252#67—68no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—64no—
257C2×Dic3—64no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—62no—
262C2×Dic3—64no—
263C2×Dic3—64no—
264C2×Dic3—124no—
265C2×Dic3—124no—
266C4×D3—64no—
267C4×D3—64no—
268C4×D3—124no—
269C4×D3—124no—
270Dic6—68no—
271C2×C32—22no—
272C2×C32—41no—
273C2×C32C2×#11711yescharacteristic
274C2×C32C2×#13111yescharacteristic
275C2×C32#56811yescharacteristic
276C3⋊D3—41no—
277#41—182no—
278#41—182no—
279C2×Q8—91no—
280C2×D4—91no—
281C2×D4—91no—
282C2×D4C2×#15711yescharacteristic
283C22×C4—91no—
284C22×C4—91no—
285C22×C4—91no—
286C22×C4—91no—
287C22×C4—91no—
288C22×C4—91no—
289C22×C4—91no—
290C22×C4C2×#15711yescharacteristic
291C22×C4C2×#15711yescharacteristic
292M16—184no—
293C2×C8—92no—
294C2×C8—92no—
295C2×C8—92no—
296C2×C8—92no—
297C2×C8—184no—
298C4⋊C4—91no—
299C4⋊C4—91no—
300C4⋊C4—91no—
301C4⋊C4—91no—
302C4⋊C4—91no—
303C4⋊C4C2×#15711yescharacteristic
304C22⋊C4—91no—
305C22⋊C4—91no—
306C22⋊C4—91no—
307C22⋊C4—91no—
308C22⋊C4C2×#15711yescharacteristic
309C22⋊C4C2×#15711yescharacteristic
310C42—91no—
311C42—91no—
312C42—91no—
313C42—91no—
314C42—91no—
315C42—91no—
316C42—91no—
317C42—91no—
318C42—91no—
319C42C2×#15711yescharacteristic
320C22×C3—24no—
321C22×C3—24no—
322C22×C3—22no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—42no—
326C22×C3—42no—
327C2×D3—64no—
328C2×D3—122no—
329C2×D3—122no—
330C3×C4—24no—
331C3×C4—24no—
332C3×C4—42no—
333C3×C4—42no—
334C3×C4—42no—
335Dic3—64no—
336Dic3—62no—
337Dic3—62no—
338Dic3—64no—
339Dic3—64no—
340Dic3—122no—
341Dic3—122no—
342Dic3—122no—
343C32#292511yescharacteristic, complemented, Sylow
344C23—91no—
345C23C22×#15711yescharacteristic
346C23C22×#15711yescharacteristic
347Q8—182no—
348D4—22no—
349D4—182no—
350D4—182no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—92no—
354C2×C4—92no—
355C2×C4—91no—
356C2×C4—91no—
357C2×C4—91no—
358C2×C4—91no—
359C2×C4—91no—
360C2×C4—91no—
361C2×C4—91no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4—181no—
365C2×C4—181no—
366C2×C4—182no—
367C2×C4—361no—
368C2×C4—361no—
369C2×C4—361no—
370C2×C4C22×#15711yescharacteristic
371C2×C4C22×#15711yescharacteristic
372C2×C4C22×#15711yescharacteristic
373C2×C4C22×#15711yescharacteristic
374C2×C4C22×#15711yescharacteristic
375C8—182no—
376C8—182no—
377C8—182no—
378C8—182no—
379C2×C3—22no—
380C2×C3—22no—
381C2×C3—22no—
382C2×C3—44no—
383C2×C3—44no—
384D3—124no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—181no—
391C22—181no—
392C22—181no—
393C22#6428612yes—
394C22C23×#15711yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—91no—
400C4—91no—
401C4—92no—
402C4—181no—
403C4—181no—
404C4—181no—
405C4—181no—
406C4—181no—
407C4#6428712yes—
408C3—22no—
409C2—22no—
410C2—41no—
411C2—361no—
412C2C2×#6428611yescharacteristic
413C2C2×#6428711yescharacteristic
414C2#1059664811yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C4
prime radicalC2×#3830C22
cosocleC2×C3⋊Dic3C24
hypercenterC4×D4#157
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593806C2semidirect
4. #10593805C2semidirect
5. #10593795C2semidirect
6. C2×C4⋊#622C2semidirect
7. #10593753C2semidirect
8. #10593744C2semidirect
9. #10593738C2semidirect
10. #10593730C2semidirect
11. #10593727C2semidirect
343. C32#2925semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
#105938222
#105938062
#105938052
#105937952
C2×C4⋊#6222
#105937532
#105937442
#105937382
#105937302
#105937272
#29259