Finite Group Databasebeta

← #11775578

Subgroups — #11775578

Order 1152.

797 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 797 conjugacy classes of subgroups — too many to draw. Only its 100 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
1#10595081C211yesmaximal, characteristic
2#10592366C211yesmaximal, characteristic, complemented
3#10591152C211yesmaximal, characteristic, complemented
4C3×#4451C212yesmaximal, complemented
5#10589150C212yesmaximal, complemented
6#68307—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3811—21no—
9C2×#3802C411yescharacteristic, complemented
10C2×#3752—21no—
11C2×#3750—21no—
12C3×#930C2212yes—
13#63980—21no—
14#63921—21no—
15#63916C412yescomplemented
16#63912—21no—
17#63900C411yescharacteristic, complemented
18C2×#3710—21no—
19C32×#95C2211yescharacteristic, complemented
20#63658C2211yescharacteristic, complemented
21C3×#830C2212yescomplemented
22#63557—21no—
23D3×#121—32no—
24D3×C22⋊C8—32no—
25#4667—32no—
26#4667—61no—
27C3×#327—32no—
28#4537—32no—
29#4470—32no—
30#4451D312yescomplemented
31C23×C3⋊D3D411yescharacteristic
32C22×D32—21no—
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C2×C4×C3⋊D3—42no—
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C3×#67—22no—
43C2×C3×D12C2×C412yes—
44#3811—42no—
45#3811—42no—
46C2×#626—22no—
47C2×#625—21no—
48C2×#624—21no—
49#3802—42no—
50#3752—42no—
51#3750—42no—
52C3×(C2×D3)⋊C4—22no—
53C3×C4⋊Dic3C2×C412yes—
54C2×C3×C3⋊C8—22no—
55#3724—21no—
56(C2×D3)⋊Dic3—22no—
57#3710—42no—
58#1519—91noSylow
59C2×D3×D4—32no—
60C2×D3×D4—62no—
61C22×C4×D3—32no—
62C22×C4×D3—61no—
63C3×#121—32no—
64#939—62no—
65#938—32no—
66#930C2×D312yes—
67C2×(C2×D3)⋊C4—62no—
68C2×(C2×D3)⋊C4—62no—
69C2×Dic3⋊C4—62no—
70C2×Dic3⋊C4—62no—
71C2×D3×C8—62no—
72#895—32no—
73D3×C4⋊C4—32no—
74#884—62no—
75D3×C22⋊C4—62no—
76C3×C22⋊C8—32no—
77C3×#95—21no—
78C3×#95C2×D312yescomplemented
79C3⋊#95—32no—
80C3⋊#95—61no—
81#830C2×D312yescomplemented
82(C2×D3)⋊C8—62no—
83C23×C32C2×D411yescharacteristic
84C22×C3⋊D3—41no—
85C22×C3⋊D3—41no—
86C22×C3⋊D3C22⋊C411yescharacteristic
87C22×C3⋊D3C22⋊C411yescharacteristic
88C22×C3⋊D3D812yes—
89C22×C3⋊D3SD1612yes—
90C22×C3×D3—22no—
91C2×D32—42no—
92C2×D32—42no—
93C2×D32—42no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C4×C3⋊D3—22no—
107C4×C3⋊D3—22no—
108C4×C3⋊D3—41no—
109C4×C3⋊D3—41no—
110C3×#67—42no—
111C3×#67—42no—
112C2×C3×Dic3—22no—
113C3×D12—42no—
114#626—44no—
115#625—42no—
116#624—42no—
117C3×C3⋊C8—42no—
118C2×#121—91no—
119C2×C22⋊C8—91no—
120#380—91no—
121#327—32no—
122#327—92no—
123C23×D3—32no—
124C23×D3—61no—
125C23×D3—62no—
126C2×C3×D4—32no—
127C2×C3×D4—62no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—21no—
131C22×C3×C4C22×D312yes—
132C2×#67—22no—
133C2×#67—62no—
134C2×#67—62no—
135C22×Dic3—32no—
136C22×Dic3—61no—
137C22×Dic3—62no—
138C22×Dic3—62no—
139D3×D4—124no—
140D3×D4—124no—
141D3×D4—124no—
142C2×D12—62no—
143C2×D12C4×D312yes—
144C2×C4×D3—32no—
145C2×C4×D3—32no—
146C2×C4×D3—32no—
147C2×C4×D3—32no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—61no—
151C2×C4×D3—61no—
152C2×C4×D3—62no—
153C2×C4×D3—124no—
154C2×C4×D3—124no—
155C2×C3×C8—62no—
156C3×C4⋊C4—32no—
157C3×C22⋊C4—62no—
158#217—62no—
159(C2×D3)⋊C4—22no—
160(C2×D3)⋊C4—62no—
161(C2×D3)⋊C4—124no—
162(C2×D3)⋊C4—124no—
163C4⋊Dic3C4×D312yes—
164Dic3⋊C4—62no—
165Dic3⋊C4—124no—
166Dic3⋊C4—124no—
167C2×C3⋊C8—22no—
168D3×C8—124no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32C2×C22⋊C411yescharacteristic
172C22×C32C2×D811yescharacteristic
173C22×C32C2×SD1611yescharacteristic
174C2×C3⋊D3—21no—
175C2×C3⋊D3—21no—
176C2×C3⋊D3—21no—
177C2×C3⋊D3—21no—
178C2×C3⋊D3—42no—
179C2×C3⋊D3—42no—
180C2×C3⋊D3#10212yes—
181C2×C3⋊D3#10212yes—
182C2×C3×D3—42no—
183C2×C3×D3—42no—
184C2×C3×D3—42no—
185D32—84no—
186C32×C4—21no—
187C32×C4—21no—
188C32×C4—81no—
189C3⋊Dic3—21no—
190C3⋊Dic3—81no—
191C3⋊Dic3#9912yes—
192C3×Dic3—42no—
193C22×D4—91no—
194C22×D4—181no—
195C23×C4—91no—
196C22×C8—181no—
197#121—32no—
198#121—92no—
199#121—181no—
200#121—181no—
201C2×C4⋊C4—91no—
202C2×C4⋊C4—181no—
203C2×C22⋊C4—181no—
204C2×C22⋊C4—181no—
205C22⋊C8—32no—
206C22⋊C8—181no—
207#95—91no—
208#95D3211yescharacteristic, complemented
209C23×C3—21no—
210C23×C3—62no—
211C23×C3D3×D412yes—
212C22×D3—22no—
213C22×D3—32no—
214C22×D3—32no—
215C22×D3—34no—
216C22×D3—34no—
217C22×D3—61no—
218C22×D3—61no—
219C22×D3—62no—
220C22×D3—62no—
221C22×D3—124no—
222C22×D3—124no—
223C22×D3—124no—
224C22×D3—122no—
225C22×D3—122no—
226C22×D3—122no—
227C22×D3—122no—
228C3×D4—122no—
229C3×D4—122no—
230C3×D4—122no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—42no—
236C2×C3×C4—42no—
237C2×C3×C4—42no—
238C2×C3×C4—42no—
239C2×C3×C4—42no—
240C2×C3×C4—42no—
241C2×C3×C4—62no—
242C2×C3×C4C2×C4×D312yes—
243C2×C3×C4D3×D412yes—
244#67—42no—
245#67—42no—
246#67—124no—
247#67—124no—
248C2×Dic3—22no—
249C2×Dic3—32no—
250C2×Dic3—32no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—64no—
254C2×Dic3—64no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C2×Dic3—122no—
258C2×Dic3—122no—
259C2×Dic3—122no—
260C2×Dic3—122no—
261D12—42no—
262D12—124no—
263C4×D3—64no—
264C4×D3—64no—
265C4×D3—122no—
266C4×D3—122no—
267C4×D3—124no—
268C4×D3—122no—
269C4×D3—122no—
270C4×D3—122no—
271C4×D3—122no—
272C3×C8—122no—
273C3⋊C8—42no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32C2×#9911yescharacteristic
277C2×C32C2×#10211yescharacteristic
278C2×C32#42111yescharacteristic
279C3⋊D3—22no—
280C3⋊D3—22no—
281C3×D3—82no—
282C24—91no—
283C24—181no—
284C2×D4—32no—
285C2×D4—62no—
286C2×D4—182no—
287C2×D4—181no—
288C2×D4—362no—
289C2×D4—362no—
290C2×D4—362no—
291C22×C4—21no—
292C22×C4—91no—
293C22×C4—91no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—91no—
297C22×C4—181no—
298C22×C4—181no—
299C22×C4—362no—
300C22×C4C2×D3211yescharacteristic
301C2×C8—62no—
302C2×C8—362no—
303C4⋊C4—32no—
304C4⋊C4—181no—
305C4⋊C4—362no—
306C22⋊C4—62no—
307C22⋊C4—182no—
308C22⋊C4—362no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—22no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—122no—
317C22×C3—122no—
318C22×C3—122no—
319C22×C3D3×C22⋊C412yes—
320C22×C3D3×D812yes—
321C22×C3D3×SD1612yes—
322C2×D3—34no—
323C2×D3—34no—
324C2×D3—42no—
325C2×D3—42no—
326C2×D3—42no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—62no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—121no—
334C2×D3—121no—
335C2×D3—121no—
336C2×D3—121no—
337C2×D3—124no—
338C2×D3—124no—
339C2×D3—124no—
340C2×D3—124no—
341C2×D3—248no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4—82no—
347C3×C4—82no—
348C3×C4—122no—
349Dic3—34no—
350Dic3—42no—
351Dic3—62no—
352Dic3—62no—
353Dic3—62no—
354Dic3—242no—
355Dic3—242no—
356C32#151911yescharacteristic, complemented, Sylow
357C23—62no—
358C23—91no—
359C23—91no—
360C23—92no—
361C23—92no—
362C23—361no—
363C23—361no—
364C23—362no—
365C23—362no—
366C23—362no—
367C23#381111yescharacteristic
368D4—122no—
369D4—122no—
370D4—122no—
371D4—362no—
372D4—364no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—62no—
378C2×C4—91no—
379C2×C4—91no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—361no—
384C2×C4—361no—
385C2×C4—362no—
386C2×C4—361no—
387C2×C4—361no—
388C2×C4—361no—
389C2×C4C4×D3211yescharacteristic
390C2×C4#380211yescharacteristic
391C8—122no—
392C2×C3—22no—
393C2×C3—22no—
394C2×C3—22no—
395C2×C3—22no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—242no—
400C2×C3D3×#9912yes—
401C2×C3D3×#10212yes—
402C2×C3#482112yes—
403D3—64no—
404D3—64no—
405D3—82no—
406D3—122no—
407D3—122no—
408C22—21no—
409C22—21no—
410C22—92no—
411C22—92no—
412C22—122no—
413C22—122no—
414C22—122no—
415C22—181no—
416C22—181no—
417C22—181no—
418C22—181no—
419C22—362no—
420C22—362no—
421C22—724no—
422C22#6392111yescharacteristic
423C22#6392611yescharacteristic
424C22#6394011yescharacteristic
425C4—21no—
426C4—21no—
427C4—81no—
428C4—92no—
429C4—122no—
430C4—181no—
431C4—721no—
432C3—21no—
433C3#6830712yescomplemented
434C2—21no—
435C2—21no—
436C2—182no—
437C2—182no—
438C2—242no—
439C2#1059039411yescharacteristic
440C2#1059040411yescharacteristic
441C2#1059059311yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radical#10595081C2
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1519
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592366C2semidirect
3. #10591152C2semidirect
4. C3×#4451C2semidirect
5. #10589150C2semidirect
9. C2×#3802C4semidirect
15. #63916C4semidirect
17. #63900C4semidirect
19. C32×#95C22semidirect
20. #63658C22semidirect
21. C3×#830C22semidirect
30. #4451D3semidirect
78. C3×#95C2×D3semidirect
81. #830C2×D3semidirect
208. #95D32semidirect
356. C32#1519semidirect
433. C3#68307semidirect

Maximal subgroups

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

subgroupindex
#105950812
#105923662
#105911522
C3×#44512
#105891502
#683073