Finite Group Databasebeta

← #11775300

Subgroups — #11775300

Order 1152.

761 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 761 conjugacy classes of subgroups — too many to draw. Only its 92 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#10592363C211yesmaximal, characteristic, complemented
3#10591159C211yesmaximal, characteristic, complemented
4C3×#4451C212yesmaximal, complemented
5#10589150C212yesmaximal, complemented
6#68304—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3811—21no—
9C2×#3802C411yescharacteristic, complemented
10C2×#3752—21no—
11C3×#930C2212yes—
12#63980—21no—
13#63921—21no—
14#63916C412yescomplemented
15#63912—21no—
16#63900C411yescharacteristic, complemented
17C2×#3712—21no—
18C32×#95C2211yescharacteristic, complemented
19#63658—21no—
20#63658C2211yescharacteristic, complemented
21C3×#830C2212yescomplemented
22#63557—21no—
23D3×#121—32no—
24#4726—32no—
25#4664—32no—
26#4664—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—
51C3×(C2×D3)⋊C4—22no—
52C3×C4⋊Dic3C2×C412yes—
53C2×C3×C3⋊C8—22no—
54#3724—21no—
55(C2×D3)⋊Dic3—22no—
56#3712—42no—
57#1510—91noSylow
58C2×D3×D4—32no—
59C2×D3×D4—62no—
60C22×C4×D3—32no—
61C22×C4×D3—61no—
62C3×#121—32no—
63#939—62no—
64#938—32no—
65#930C2×D312yes—
66C2×(C2×D3)⋊C4—62no—
67C2×(C2×D3)⋊C4—62no—
68C2×ΓL(1,𝔽25)—62no—
69#895—32no—
70D3×C4⋊C4—32no—
71#884—62no—
72D3×C22⋊C4—62no—
73C3×C22⋊C8—32no—
74C3×#95—21no—
75C3×#95C2×D312yescomplemented
76C3⋊#95—32no—
77C3⋊#95—61no—
78C3⋊#95—62no—
79C3⋊#95—62no—
80#830C2×D312yescomplemented
81(C2×D3)⋊C8—62no—
82C23×C32C2×D411yescharacteristic
83C22×C3⋊D3—22no—
84C22×C3⋊D3—21no—
85C22×C3⋊D3—21no—
86C22×C3⋊D3—41no—
87C22×C3⋊D3C22⋊C411yescharacteristic
88C22×C3⋊D3C22⋊C411yescharacteristic
89C22×C3×D3—22no—
90C2×D32—42no—
91C2×D32—42no—
92C2×D32—42no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C4×C3⋊D3—22no—
106C4×C3⋊D3—22no—
107C4×C3⋊D3—41no—
108C4×C3⋊D3—41no—
109C3×#67—42no—
110C3×#67—42no—
111C2×C3×Dic3—22no—
112C3×D12—42no—
113#626—44no—
114#625—42no—
115#624—42no—
116C3×C3⋊C8—42no—
117C2×#121—91no—
118#407—91no—
119#381—91no—
120#327—32no—
121#327—92no—
122C23×D3—32no—
123C23×D3—61no—
124C23×D3—62no—
125C2×C3×D4—32no—
126C2×C3×D4—62no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4C22×D312yes—
131C2×#67—22no—
132C2×#67—62no—
133C2×#67—62no—
134C22×Dic3—32no—
135C22×Dic3—61no—
136C22×Dic3—62no—
137C22×Dic3—62no—
138D3×D4—124no—
139D3×D4—124no—
140D3×D4—124no—
141C2×D12—62no—
142C2×D12C4×D312yes—
143C2×C4×D3—32no—
144C2×C4×D3—32no—
145C2×C4×D3—32no—
146C2×C4×D3—32no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—61no—
151C2×C4×D3—62no—
152C2×C4×D3—124no—
153C2×C4×D3—124no—
154C2×C3×C8—62no—
155C3×C4⋊C4—32no—
156C3×C22⋊C4—62no—
157#217—62no—
158(C2×D3)⋊C4—22no—
159(C2×D3)⋊C4—62no—
160(C2×D3)⋊C4—124no—
161(C2×D3)⋊C4—124no—
162C4⋊Dic3C4×D312yes—
163Dic3⋊C4—62no—
164C2×C3⋊C8—22no—
165ΓL(1,𝔽25)—124no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32C2×C22⋊C411yescharacteristic
169C22×C32AGL(1,ℤ/8)11yescharacteristic
170C22×C32AGL(1,ℤ/8)11yescharacteristic
171C2×C3⋊D3—21no—
172C2×C3⋊D3—21no—
173C2×C3⋊D3—21no—
174C2×C3⋊D3—21no—
175C2×C3⋊D3—21no—
176C2×C3⋊D3—42no—
177C2×C3⋊D3—42no—
178C2×C3⋊D3#9912yes—
179C2×C3×D3—42no—
180C2×C3×D3—42no—
181C2×C3×D3—42no—
182D32—84no—
183C32×C4—21no—
184C32×C4—21no—
185C32×C4—81no—
186C3⋊Dic3—21no—
187C3⋊Dic3—21no—
188C3⋊Dic3—81no—
189C3×Dic3—42no—
190C22×D4—91no—
191C22×D4—181no—
192C23×C4—91no—
193C2×M16—181no—
194#121—32no—
195#121—92no—
196#121—181no—
197#121—181no—
198C2×C4⋊C4—91no—
199C2×C22⋊C4—181no—
200C2×C22⋊C4—181no—
201C22⋊C8—32no—
202C22⋊C8—181no—
203#95—91no—
204#95—181no—
205#95D3211yescharacteristic, complemented
206C23×C3—21no—
207C23×C3—62no—
208C23×C3D3×D412yes—
209C22×D3—22no—
210C22×D3—32no—
211C22×D3—32no—
212C22×D3—61no—
213C22×D3—61no—
214C22×D3—64no—
215C22×D3—64no—
216C22×D3—62no—
217C22×D3—62no—
218C22×D3—121no—
219C22×D3—121no—
220C22×D3—124no—
221C22×D3—124no—
222C22×D3—124no—
223C22×D3—122no—
224C22×D3—122no—
225C3×D4—122no—
226C3×D4—122no—
227C3×D4—122no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—42no—
231C2×C3×C4—42no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—42no—
236C2×C3×C4—42no—
237C2×C3×C4—42no—
238C2×C3×C4—62no—
239C2×C3×C4C2×C4×D312yes—
240C2×C3×C4D3×D412yes—
241#67—42no—
242#67—42no—
243#67—124no—
244#67—124no—
245C2×Dic3—22no—
246C2×Dic3—32no—
247C2×Dic3—32no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—122no—
251C2×Dic3—122no—
252C2×Dic3—122no—
253C2×Dic3—122no—
254C2×Dic3—122no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C2×Dic3—122no—
258D12—42no—
259D12—124no—
260C4×D3—64no—
261C4×D3—64no—
262C4×D3—122no—
263C4×D3—122no—
264C4×D3—124no—
265C4×D3—122no—
266C4×D3—122no—
267C4×D3—122no—
268C4×D3—122no—
269C3×C8—122no—
270C3⋊C8—42no—
271C2×C32—21no—
272C2×C32—21no—
273C2×C32C2×#9911yescharacteristic
274C2×C32#41811yescharacteristic
275C2×C32#42111yescharacteristic
276C3⋊D3—22no—
277C3⋊D3—41no—
278C3×D3—82no—
279C24—91no—
280C24—181no—
281C2×D4—32no—
282C2×D4—62no—
283C2×D4—182no—
284C2×D4—181no—
285C2×D4—362no—
286C2×D4—362no—
287C2×D4—362no—
288C22×C4—21no—
289C22×C4—91no—
290C22×C4—91no—
291C22×C4—91no—
292C22×C4—91no—
293C22×C4—91no—
294C22×C4—181no—
295C22×C4—181no—
296C22×C4—362no—
297C22×C4C2×D3211yescharacteristic
298M16—362no—
299C2×C8—62no—
300C4⋊C4—32no—
301C4⋊C4—181no—
302C22⋊C4—62no—
303C22⋊C4—182no—
304C22⋊C4—362no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—122no—
313C22×C3—122no—
314C22×C3—122no—
315C22×C3D3×C22⋊C412yes—
316C22×C3#91112yes—
317C22×C3#91412yes—
318C2×D3—34no—
319C2×D3—42no—
320C2×D3—42no—
321C2×D3—42no—
322C2×D3—62no—
323C2×D3—62no—
324C2×D3—62no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—121no—
330C2×D3—121no—
331C2×D3—121no—
332C2×D3—121no—
333C2×D3—124no—
334C2×D3—124no—
335C2×D3—124no—
336C2×D3—124no—
337C2×D3—248no—
338C3×C4—22no—
339C3×C4—22no—
340C3×C4—41no—
341C3×C4—41no—
342C3×C4—82no—
343C3×C4—82no—
344C3×C4—122no—
345Dic3—42no—
346Dic3—62no—
347Dic3—62no—
348Dic3—121no—
349Dic3—121no—
350Dic3—242no—
351Dic3—242no—
352C32#151011yescharacteristic, complemented, Sylow
353C23—62no—
354C23—91no—
355C23—91no—
356C23—182no—
357C23—181no—
358C23—181no—
359C23—361no—
360C23—362no—
361C23—362no—
362C23—362no—
363C23#381111yescharacteristic
364D4—122no—
365D4—122no—
366D4—122no—
367D4—364no—
368D4—362no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—62no—
374C2×C4—91no—
375C2×C4—91no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4—361no—
379C2×C4—361no—
380C2×C4—362no—
381C2×C4—361no—
382C2×C4—361no—
383C2×C4—361no—
384C2×C4—361no—
385C2×C4C4×D3211yescharacteristic
386C2×C4#380211yescharacteristic
387C8—122no—
388C2×C3—22no—
389C2×C3—22no—
390C2×C3—22no—
391C2×C3—22no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—242no—
396C2×C3D3×#9912yes—
397C2×C3#477012yes—
398C2×C3#482112yes—
399D3—64no—
400D3—82no—
401D3—122no—
402D3—122no—
403D3—122no—
404C22—21no—
405C22—21no—
406C22—92no—
407C22—122no—
408C22—122no—
409C22—122no—
410C22—181no—
411C22—181no—
412C22—181no—
413C22—181no—
414C22—181no—
415C22—362no—
416C22—362no—
417C22—724no—
418C22#6392111yescharacteristic
419C22#6392711yescharacteristic
420C22#6394111yescharacteristic
421C4—21no—
422C4—21no—
423C4—81no—
424C4—122no—
425C4—181no—
426C4—181no—
427C4—721no—
428C3—21no—
429C3#6830412yescomplemented
430C2—21no—
431C2—21no—
432C2—182no—
433C2—242no—
434C2—361no—
435C2#1059039411yescharacteristic
436C2#1059040411yescharacteristic
437C2#1059059411yescharacteristic
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#1510
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. #10592363C2semidirect
3. #10591159C2semidirect
4. C3×#4451C2semidirect
5. #10589150C2semidirect
9. C2×#3802C4semidirect
14. #63916C4semidirect
16. #63900C4semidirect
18. C32×#95C22semidirect
20. #63658C22semidirect
21. C3×#830C22semidirect
30. #4451D3semidirect
75. C3×#95C2×D3semidirect
80. #830C2×D3semidirect
205. #95D32semidirect
352. C32#1510semidirect
429. C3#68304semidirect

Maximal subgroups

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

subgroupindex
#105950812
#105923632
#105911592
C3×#44512
#105891502
#683043