Finite Group Databasebeta

← #11775328

Subgroups — #11775328

Order 1152.

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

normal subgroups only

This group has 657 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#10594925C211yesmaximal, characteristic
2#10592363C211yesmaximal, characteristic
3#10591159C211yesmaximal, characteristic
4C3×#4452C212yesmaximal, complemented
5#10589152C212yesmaximal, complemented
6#68336—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3797C411yescharacteristic, complemented
9C2×#3752—21no—
10C3×#924C2212yes—
11#63982—21no—
12#63974—21no—
13#63900C411yescharacteristic, complemented
14#63883—21no—
15#63871C412yescomplemented
16#63865—21no—
17C2×#3712—21no—
18C32×#95C2211yescharacteristic
19#63658—21no—
20#63658C2211yescharacteristic
21C3×#830C2212yes—
22#63557—21no—
23D3×C22⋊Q8—32no—
24#4726—32no—
25#4664—32no—
26#4664—61no—
27C3×#328—32no—
28#4538—32no—
29#4467—32no—
30#4452D312yescomplemented
31C23×C3⋊D3D411yescharacteristic
32C22×C32×C4—21no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3D411yescharacteristic
36C2×C4×C3⋊D3—42no—
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C3×Dic6C2×C412yes—
42C2×#627—21no—
43C2×#624—21no—
44C2×#624—21no—
45#3797—42no—
46#3752—42no—
47C3×#217—22no—
48C3×C4⋊Dic3C2×C412yes—
49C3×Dic3⋊C4—22no—
50C2×C3×C3⋊C8—22no—
51#3724—21no—
52Dic3⋊Dic3—22no—
53#3722—22no—
54#3712—42no—
55#1511—91noSylow
56C2×D3×Q8—32no—
57C22×C4×D3—32no—
58C22×C4×D3—61no—
59C3×C22⋊Q8—32no—
60#946—32no—
61C2×(C2×D3)⋊C4—62no—
62C2×(C2×D3)⋊C4—62no—
63#924C2×D312yes—
64C2×ΓL(1,𝔽25)—62no—
65#897—32no—
66#896—62no—
67D3×C4⋊C4—32no—
68D3×C4⋊C4—62no—
69D3×C22⋊C4—62no—
70#878—62no—
71C3×C22⋊C8—32no—
72C3×#95—21no—
73C3×#95C2×D312yes—
74C3⋊#95—32no—
75C3⋊#95—61no—
76C3⋊#95—62no—
77C3⋊#95—62no—
78#830C2×D312yes—
79(C2×D3)⋊C8—62no—
80C23×C32C2×D411yescharacteristic
81C22×C3⋊D3—22no—
82C22×C3⋊D3—21no—
83C22×C3⋊D3—21no—
84C22×C3⋊D3—41no—
85C22×C3⋊D3C22⋊C411yescharacteristic
86C22×C3⋊D3C22⋊C411yescharacteristic
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3C22⋊C411yescharacteristic
98C2×C3⋊Dic3C22⋊C411yescharacteristic
99C4×C3⋊D3—22no—
100C4×C3⋊D3—22no—
101C4×C3⋊D3—41no—
102C4×C3⋊D3—41no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C3×Dic6—42no—
106#627—42no—
107#624—42no—
108#624—42no—
109C3×C3⋊C8—42no—
110C2×C22⋊Q8—91no—
111#407—91no—
112#381—91no—
113#328—32no—
114#328—92no—
115C23×D3—32no—
116C23×D3—61no—
117C2×C3×Q8—32no—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C22×C3×C4—21no—
121C22×C3×C4C22×D312yes—
122C22×Dic3—32no—
123C22×Dic3—61no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126D3×Q8—124no—
127C2×C4×D3—32no—
128C2×C4×D3—32no—
129C2×C4×D3—32no—
130C2×C4×D3—32no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137C2×C4×D3—124no—
138C2×C4×D3—124no—
139C2×Dic6—62no—
140C2×Dic6C4×D312yes—
141C2×C3×C8—62no—
142C3×C4⋊C4—32no—
143C3×C4⋊C4—62no—
144C3×C22⋊C4—62no—
145#217—22no—
146(C2×D3)⋊C4—62no—
147(C2×D3)⋊C4—62no—
148(C2×D3)⋊C4—124no—
149(C2×D3)⋊C4—124no—
150C4⋊Dic3—62no—
151C4⋊Dic3C4×D312yes—
152Dic3⋊C4—22no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155C2×C3⋊C8—22no—
156ΓL(1,𝔽25)—124no—
157C22×C32—21no—
158C22×C32—21no—
159C22×C32C2×C22⋊C411yescharacteristic
160C22×C32#13711yescharacteristic
161C22×C32#13711yescharacteristic
162C2×C3⋊D3—21no—
163C2×C3⋊D3—21no—
164C2×C3⋊D3—21no—
165C2×C3⋊D3—21no—
166C2×C3⋊D3—21no—
167C2×C3⋊D3—42no—
168C2×C3⋊D3—42no—
169C2×C3⋊D3#9912yes—
170C32×C4—21no—
171C32×C4—21no—
172C32×C4—81no—
173C3⋊Dic3—21no—
174C3⋊Dic3—21no—
175C3⋊Dic3—81no—
176C3×Dic3—42no—
177C3×Dic3—42no—
178C22×Q8—91no—
179C23×C4—91no—
180C2×M16—181no—
181C22⋊Q8—32no—
182C22⋊Q8—92no—
183C22⋊Q8—181no—
184C22⋊Q8—181no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4—181no—
187C2×C22⋊C4—181no—
188C2×C22⋊C4—181no—
189C22⋊C8—32no—
190C22⋊C8—181no—
191#95—91no—
192#95—181no—
193#95D3211yescharacteristic
194C23×C3—21no—
195C23×C3D3×D412yes—
196C22×D3—32no—
197C22×D3—32no—
198C22×D3—61no—
199C22×D3—61no—
200C22×D3—64no—
201C22×D3—64no—
202C22×D3—62no—
203C22×D3—62no—
204C22×D3—121no—
205C22×D3—121no—
206C22×D3—122no—
207C22×D3—122no—
208C3×Q8—122no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—42no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—42no—
215C2×C3×C4—42no—
216C2×C3×C4—42no—
217C2×C3×C4—42no—
218C2×C3×C4—42no—
219C2×C3×C4—62no—
220C2×C3×C4—62no—
221C2×C3×C4C2×C4×D312yes—
222C2×C3×C4D3×D412yes—
223C2×Dic3—22no—
224C2×Dic3—22no—
225C2×Dic3—32no—
226C2×Dic3—32no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—122no—
230C2×Dic3—122no—
231C2×Dic3—122no—
232C2×Dic3—122no—
233C2×Dic3—122no—
234C2×Dic3—122no—
235C2×Dic3—122no—
236C2×Dic3—122no—
237C4×D3—64no—
238C4×D3—64no—
239C4×D3—122no—
240C4×D3—122no—
241C4×D3—124no—
242C4×D3—124no—
243C4×D3—122no—
244C4×D3—122no—
245C4×D3—122no—
246C4×D3—122no—
247Dic6—42no—
248Dic6—124no—
249C3×C8—122no—
250C3⋊C8—42no—
251C2×C32—21no—
252C2×C32—21no—
253C2×C32C2×#9911yescharacteristic
254C2×C32#41911yescharacteristic
255C2×C32#42111yescharacteristic
256C3⋊D3—22no—
257C3⋊D3—41no—
258C24—91no—
259C2×Q8—32no—
260C2×Q8—181no—
261C2×Q8—362no—
262C22×C4—21no—
263C22×C4—91no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4—181no—
269C22×C4—181no—
270C22×C4—181no—
271C22×C4—362no—
272C22×C4C2×D3211yescharacteristic
273M16—362no—
274C2×C8—62no—
275C4⋊C4—32no—
276C4⋊C4—62no—
277C4⋊C4—181no—
278C4⋊C4—182no—
279C22⋊C4—62no—
280C22⋊C4—182no—
281C22⋊C4—362no—
282C22×C3—22no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3D3×C22⋊C412yes—
290C22×C3#91512yes—
291C22×C3#91812yes—
292C2×D3—34no—
293C2×D3—62no—
294C2×D3—62no—
295C2×D3—62no—
296C2×D3—62no—
297C2×D3—62no—
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—121no—
301C2×D3—121no—
302C2×D3—121no—
303C2×D3—121no—
304C2×D3—124no—
305C2×D3—124no—
306C2×D3—124no—
307C2×D3—124no—
308C3×C4—22no—
309C3×C4—22no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4—82no—
313C3×C4—82no—
314C3×C4—122no—
315C3×C4—122no—
316Dic3—42no—
317Dic3—42no—
318Dic3—62no—
319Dic3—62no—
320Dic3—121no—
321Dic3—121no—
322Dic3—242no—
323Dic3—242no—
324C32#151111yescharacteristic, complemented, Sylow
325C23—91no—
326C23—91no—
327C23—182no—
328C23—181no—
329C23—181no—
330C23—361no—
331C23#381111yescharacteristic
332Q8—122no—
333Q8—362no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—91no—
341C2×C4—91no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—361no—
345C2×C4—361no—
346C2×C4—362no—
347C2×C4—362no—
348C2×C4—361no—
349C2×C4—361no—
350C2×C4—361no—
351C2×C4—361no—
352C2×C4C4×D3211yescharacteristic
353C2×C4#380211yescharacteristic
354C8—122no—
355C2×C3—22no—
356C2×C3—22no—
357C2×C3—22no—
358C2×C3—22no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3D3×#9912yes—
363C2×C3#480212yes—
364C2×C3#482112yes—
365D3—64no—
366D3—122no—
367D3—122no—
368D3—122no—
369C22—21no—
370C22—21no—
371C22—92no—
372C22—181no—
373C22—181no—
374C22—181no—
375C22—181no—
376C22—181no—
377C22—362no—
378C22—362no—
379C22#6392111yescharacteristic
380C22#6393111yescharacteristic
381C22#6394511yescharacteristic
382C4—21no—
383C4—21no—
384C4—81no—
385C4—122no—
386C4—122no—
387C4—181no—
388C4—181no—
389C4—721no—
390C3—21no—
391C3#6833612yescomplemented
392C2—21no—
393C2—21no—
394C2—182no—
395C2—361no—
396C2#1059039411yescharacteristic
397C2#1059040411yescharacteristic
398C2#1059060211yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1511
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
4. C3×#4452C2semidirect
5. #10589152C2semidirect
8. C2×#3797C4semidirect
13. #63900C4semidirect
15. #63871C4semidirect
30. #4452D3semidirect
324. C32#1511semidirect
391. C3#68336semidirect

Maximal subgroups

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

subgroupindex
#105949252
#105923632
#105911592
C3×#44522
#105891522
#683363