Finite Group Databasebeta

← #11775607

Subgroups — #11775607

Order 1152.

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

normal subgroups only

This group has 693 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#10594925C211yesmaximal, characteristic
2#10592366C211yesmaximal, characteristic
3#10591152C211yesmaximal, characteristic
4C3×#4452C212yesmaximal, complemented
5#10589152C212yesmaximal, complemented
6#68339—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×#3797C411yescharacteristic, complemented
9C2×#3752—21no—
10C2×#3750—21no—
11C3×#924C2212yes—
12#63982—21no—
13#63974—21no—
14#63900C411yescharacteristic, complemented
15#63883—21no—
16#63871C412yescomplemented
17#63865—21no—
18C2×#3710—21no—
19C32×#95C2211yescharacteristic
20#63658C2211yescharacteristic
21C3×#830C2212yes—
22#63557—21no—
23D3×C22⋊Q8—32no—
24D3×C22⋊C8—32no—
25#4667—32no—
26#4667—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—
47#3750—42no—
48C3×#217—22no—
49C3×C4⋊Dic3C2×C412yes—
50C3×Dic3⋊C4—22no—
51C2×C3×C3⋊C8—22no—
52#3724—21no—
53Dic3⋊Dic3—22no—
54#3722—22no—
55#3710—42no—
56#1520—91noSylow
57C2×D3×Q8—32no—
58C22×C4×D3—32no—
59C22×C4×D3—61no—
60C3×C22⋊Q8—32no—
61#946—32no—
62C2×(C2×D3)⋊C4—62no—
63C2×(C2×D3)⋊C4—62no—
64#924C2×D312yes—
65C2×Dic3⋊C4—62no—
66C2×Dic3⋊C4—62no—
67C2×D3×C8—62no—
68#897—32no—
69#896—62no—
70D3×C4⋊C4—32no—
71D3×C4⋊C4—62no—
72D3×C22⋊C4—62no—
73#878—62no—
74C3×C22⋊C8—32no—
75C3×#95—21no—
76C3×#95C2×D312yes—
77C3⋊#95—32no—
78C3⋊#95—61no—
79#830C2×D312yes—
80(C2×D3)⋊C8—62no—
81C23×C32C2×D411yescharacteristic
82C22×C3⋊D3—41no—
83C22×C3⋊D3—41no—
84C22×C3⋊D3C22⋊C411yescharacteristic
85C22×C3⋊D3C22⋊C411yescharacteristic
86C22×C3⋊D3SD1612yes—
87C22×C3⋊D3Q1612yes—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4C22×C411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3—41no—
98C2×C3⋊Dic3C22⋊C411yescharacteristic
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C4×C3⋊D3—22no—
101C4×C3⋊D3—22no—
102C4×C3⋊D3—41no—
103C4×C3⋊D3—41no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—22no—
106C3×Dic6—42no—
107#627—42no—
108#624—42no—
109#624—42no—
110C3×C3⋊C8—42no—
111C2×C22⋊Q8—91no—
112C2×C22⋊C8—91no—
113#380—91no—
114#328—32no—
115#328—92no—
116C23×D3—32no—
117C23×D3—61no—
118C2×C3×Q8—32no—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—21no—
122C22×C3×C4C22×D312yes—
123C22×Dic3—32no—
124C22×Dic3—61no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127D3×Q8—124no—
128C2×C4×D3—32no—
129C2×C4×D3—32no—
130C2×C4×D3—32no—
131C2×C4×D3—32no—
132C2×C4×D3—61no—
133C2×C4×D3—61no—
134C2×C4×D3—61no—
135C2×C4×D3—61no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—124no—
139C2×C4×D3—124no—
140C2×Dic6—62no—
141C2×Dic6C4×D312yes—
142C2×C3×C8—62no—
143C3×C4⋊C4—32no—
144C3×C4⋊C4—62no—
145C3×C22⋊C4—62no—
146#217—22no—
147(C2×D3)⋊C4—62no—
148(C2×D3)⋊C4—62no—
149(C2×D3)⋊C4—124no—
150(C2×D3)⋊C4—124no—
151C4⋊Dic3—62no—
152C4⋊Dic3C4×D312yes—
153Dic3⋊C4—22no—
154Dic3⋊C4—62no—
155Dic3⋊C4—62no—
156Dic3⋊C4—124no—
157Dic3⋊C4—124no—
158C2×C3⋊C8—22no—
159D3×C8—124no—
160C22×C32—21no—
161C22×C32—21no—
162C22×C32C2×C22⋊C411yescharacteristic
163C22×C32C2×SD1611yescharacteristic
164C22×C32C2×Q1611yescharacteristic
165C2×C3⋊D3—21no—
166C2×C3⋊D3—21no—
167C2×C3⋊D3—21no—
168C2×C3⋊D3—21no—
169C2×C3⋊D3—42no—
170C2×C3⋊D3—42no—
171C2×C3⋊D3#10312yes—
172C2×C3⋊D3#10312yes—
173C32×C4—21no—
174C32×C4—21no—
175C32×C4—81no—
176C3⋊Dic3—21no—
177C3⋊Dic3—81no—
178C3⋊Dic3#9912yes—
179C3×Dic3—42no—
180C3×Dic3—42no—
181C22×Q8—91no—
182C23×C4—91no—
183C22×C8—181no—
184C22⋊Q8—32no—
185C22⋊Q8—92no—
186C22⋊Q8—181no—
187C22⋊Q8—181no—
188C2×C4⋊C4—91no—
189C2×C4⋊C4—181no—
190C2×C4⋊C4—181no—
191C2×C22⋊C4—181no—
192C2×C22⋊C4—181no—
193C22⋊C8—32no—
194C22⋊C8—181no—
195#95—91no—
196#95D3211yescharacteristic
197C23×C3—21no—
198C23×C3D3×D412yes—
199C22×D3—32no—
200C22×D3—32no—
201C22×D3—34no—
202C22×D3—34no—
203C22×D3—61no—
204C22×D3—61no—
205C22×D3—62no—
206C22×D3—62no—
207C22×D3—122no—
208C22×D3—122no—
209C22×D3—122no—
210C22×D3—122no—
211C3×Q8—122no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—42no—
215C2×C3×C4—42no—
216C2×C3×C4—42no—
217C2×C3×C4—42no—
218C2×C3×C4—42no—
219C2×C3×C4—42no—
220C2×C3×C4—42no—
221C2×C3×C4—42no—
222C2×C3×C4—62no—
223C2×C3×C4—62no—
224C2×C3×C4C2×C4×D312yes—
225C2×C3×C4D3×D412yes—
226C2×Dic3—22no—
227C2×Dic3—22no—
228C2×Dic3—32no—
229C2×Dic3—32no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C2×Dic3—122no—
235C2×Dic3—122no—
236C2×Dic3—122no—
237C2×Dic3—122no—
238C2×Dic3—122no—
239C2×Dic3—122no—
240C4×D3—64no—
241C4×D3—64no—
242C4×D3—122no—
243C4×D3—122no—
244C4×D3—124no—
245C4×D3—124no—
246C4×D3—122no—
247C4×D3—122no—
248C4×D3—122no—
249C4×D3—122no—
250Dic6—42no—
251Dic6—124no—
252C3×C8—122no—
253C3⋊C8—42no—
254C2×C32—21no—
255C2×C32—21no—
256C2×C32C2×#9911yescharacteristic
257C2×C32C2×#10311yescharacteristic
258C2×C32#42111yescharacteristic
259C3⋊D3—22no—
260C3⋊D3—22no—
261C24—91no—
262C2×Q8—32no—
263C2×Q8—181no—
264C2×Q8—362no—
265C22×C4—21no—
266C22×C4—91no—
267C22×C4—91no—
268C22×C4—91no—
269C22×C4—91no—
270C22×C4—91no—
271C22×C4—181no—
272C22×C4—181no—
273C22×C4—181no—
274C22×C4—362no—
275C22×C4C2×D3211yescharacteristic
276C2×C8—62no—
277C2×C8—362no—
278C4⋊C4—32no—
279C4⋊C4—62no—
280C4⋊C4—181no—
281C4⋊C4—182no—
282C4⋊C4—362no—
283C22⋊C4—62no—
284C22⋊C4—182no—
285C22⋊C4—362no—
286C22×C3—22no—
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3D3×C22⋊C412yes—
294C22×C3D3×SD1612yes—
295C22×C3D3×Q1612yes—
296C2×D3—34no—
297C2×D3—34no—
298C2×D3—62no—
299C2×D3—62no—
300C2×D3—62no—
301C2×D3—62no—
302C2×D3—62no—
303C2×D3—62no—
304C2×D3—121no—
305C2×D3—121no—
306C2×D3—121no—
307C2×D3—121no—
308C2×D3—124no—
309C2×D3—124no—
310C2×D3—124no—
311C2×D3—124no—
312C3×C4—22no—
313C3×C4—22no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4—82no—
317C3×C4—82no—
318C3×C4—122no—
319C3×C4—122no—
320Dic3—34no—
321Dic3—42no—
322Dic3—42no—
323Dic3—62no—
324Dic3—62no—
325Dic3—62no—
326Dic3—242no—
327Dic3—242no—
328C32#152011yescharacteristic, complemented, Sylow
329C23—91no—
330C23—91no—
331C23—92no—
332C23—92no—
333C23—361no—
334C23—361no—
335C23#381111yescharacteristic
336Q8—122no—
337Q8—362no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—62no—
343C2×C4—62no—
344C2×C4—91no—
345C2×C4—91no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4—361no—
350C2×C4—361no—
351C2×C4—362no—
352C2×C4—362no—
353C2×C4—361no—
354C2×C4—361no—
355C2×C4—361no—
356C2×C4C4×D3211yescharacteristic
357C2×C4#380211yescharacteristic
358C8—122no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—22no—
362C2×C3—22no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3D3×#9912yes—
367C2×C3D3×#10312yes—
368C2×C3#482112yes—
369D3—64no—
370D3—64no—
371D3—122no—
372D3—122no—
373C22—21no—
374C22—21no—
375C22—92no—
376C22—92no—
377C22—181no—
378C22—181no—
379C22—181no—
380C22—181no—
381C22—362no—
382C22—362no—
383C22#6392111yescharacteristic
384C22#6393011yescharacteristic
385C22#6394411yescharacteristic
386C4—21no—
387C4—21no—
388C4—81no—
389C4—92no—
390C4—122no—
391C4—122no—
392C4—181no—
393C4—721no—
394C3—21no—
395C3#6833912yescomplemented
396C2—21no—
397C2—21no—
398C2—182no—
399C2—182no—
400C2#1059039411yescharacteristic
401C2#1059040411yescharacteristic
402C2#1059060111yescharacteristic
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#1520
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
14. #63900C4semidirect
16. #63871C4semidirect
30. #4452D3semidirect
328. C32#1520semidirect
395. C3#68339semidirect

Maximal subgroups

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

subgroupindex
#105949252
#105923662
#105911522
C3×#44522
#105891522
#683393