Finite Group Databasebeta

← #11868530

Subgroups — #11868530

Order 1152.

646 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 119 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#10593948C211yesmaximal, characteristic
2C4×#3797C211yesmaximal, characteristic
3#10593726C211yesmaximal, characteristic
4#10593396C211yesmaximal, characteristic
5#10593387C211yesmaximal, characteristic
6#10593382C214yesmaximal, complemented
7#10593375C211yesmaximal, characteristic
8#10593375C211yesmaximal, characteristic
9#10593373C214yesmaximal, complemented
10C2×#3797C2211yescharacteristic
11C2×#3787C2211yescharacteristic
12C2×#3787C2211yescharacteristic
13C42×C3⋊D3C2211yescharacteristic
14C3×#870—21no—
15C3×C4×Dic6—21no—
16C4×#627C2212yes—
17#63900C2211yescharacteristic
18#63900C2211yescharacteristic
19#63900C2211yescharacteristic
20#63883—21no—
21#63883—21no—
22#63883—21no—
23C4×#624—21no—
24#63872—21no—
25#63870C2212yes—
26#63870C2212yes—
27#63843—21no—
28#63838C2212yes—
29#63779C2212yes—
30C4⋊#622C2212yes—
31#63743C2214yes—
32#63742C2214yes—
33#63740C2214yes—
34#63740C2214yes—
35D3×#125—61no—
36C4×D3×Q8—61no—
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3C2311yescharacteristic
40C2×C3×Dic6—21no—
41C2×#627C2312yes—
42C2×#624—21no—
43C2×#624—21no—
44C2×#624—21no—
45C2×#624—21no—
46#3797—22no—
47#3797Q814yes—
48C2×#622C2312yes—
49C2×#622C2312yes—
50#3787—22no—
51#3787—22no—
52C32×C42D411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3C2311yescharacteristic
55C4×C3⋊Dic3C2311yescharacteristic
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×Dic3⋊C4—22no—
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—22no—
62C3×C4×Dic3—22no—
63#3724C2312yes—
64#3724C2312yes—
65#3724C2312yes—
66Dic3⋊Dic3—22no—
67Dic3⋊Dic3—22no—
68Dic3⋊Dic3—22no—
69Dic32—22no—
70C2×#479—91nomaximal, Sylow
71C2×D3×Q8—61no—
72C3×#125—61no—
73C3×C4×Q8—61no—
74Q8×Dic3—61no—
75D3×C4⋊C4—61no—
76D3×C4⋊C4—61no—
77D3×C4⋊C4—61no—
78D3×C4⋊C4—62no—
79D3×C4⋊C4—62no—
80D3×C4⋊C4—62no—
81#890—61no—
82#890—61no—
83#889—62no—
84#889—62no—
85#887—62no—
86#887—61no—
87C42×D3—61no—
88C42×D3—61no—
89C42×D3—62no—
90#870—21no—
91C4×Dic6—21no—
92C4×Dic6—62no—
93C22×C3⋊D3C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C3⋊Dic3C2×D411yescharacteristic
98C2×C3⋊Dic3C2×D411yescharacteristic
99C2×C3⋊Dic3C2411yescharacteristic
100C4×C3⋊D3—22no—
101C4×C3⋊D3—22no—
102C4×C3⋊D3C2×Q812yes—
103C4×C3⋊D3#4112yes—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—22no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—22no—
108C3×Dic6—24no—
109#627—22no—
110#627C2×Q814yes—
111#624—24no—
112#624—42no—
113#624—42no—
114#624—42no—
115#622—22no—
116#622—22no—
117C2×#125—91no—
118C2×C4×Q8—91no—
119#479—94no—
120#479—94no—
121C2×#107—91no—
122C2×#106—91no—
123C2×C4⋊C8—91no—
124C2×#103—91no—
125C2×#103—91no—
126C2×C3×Q8—61no—
127D3×Q8—64no—
128D3×Q8—64no—
129C2×C4×D3—61no—
130C2×C4×D3—61no—
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—62no—
138C2×C4×D3—62no—
139C2×Dic6—21no—
140C2×Dic6—62no—
141C3×C4⋊C4—62no—
142C3×C4⋊C4—61no—
143C3×C4⋊C4—62no—
144C3×C4⋊C4—62no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C42—21no—
148C3×C42—21no—
149C3×C42—62no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3—62no—
154C4⋊Dic3—62no—
155C4⋊Dic3—62no—
156Dic3⋊C4—22no—
157Dic3⋊C4—22no—
158Dic3⋊C4—22no—
159Dic3⋊C4—62no—
160Dic3⋊C4—62no—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163Dic3⋊C4—62no—
164Dic3⋊C4—62no—
165C4×Dic3—22no—
166C4×Dic3—61no—
167C4×Dic3—61no—
168C4×Dic3—61no—
169C4×Dic3—61no—
170C4×Dic3—61no—
171C4×Dic3—61no—
172C4×Dic3—62no—
173C4×Dic3—62no—
174C22×C32C22×D411yescharacteristic
175C2×C3⋊D3C22⋊Q812yes—
176C2×C3⋊D3#13512yes—
177C2×C3⋊D3#13712yes—
178C32×C4—21no—
179C32×C4—21no—
180C32×C4C22⋊Q812yes—
181C3⋊Dic3—21no—
182C3⋊Dic3—21no—
183C3⋊Dic3C22×Q811yescharacteristic
184C3⋊Dic3C2×#4111yescharacteristic
185C3×Dic3—24no—
186C3×Dic3—42no—
187C3×Dic3—42no—
188C3×Dic3—42no—
189C22×Q8—91no—
190C22×C8—91no—
191C22×C8—91no—
192#125—61no—
193#125—92no—
194#125—92no—
195#125—181no—
196C4×Q8—61no—
197C4×Q8—92no—
198C4×Q8—92no—
199C4×Q8—181no—
200C2×C4⋊C4—91no—
201C2×C4⋊C4—91no—
202C2×C4⋊C4—91no—
203C2×C4⋊C4—181no—
204C2×C4⋊C4—181no—
205C2×C4⋊C4—181no—
206C2×C42—91no—
207C2×C42—181no—
208#107—94no—
209#106—94no—
210C4⋊C8—92no—
211C4⋊C8—92no—
212#103—94no—
213#103—94no—
214C22×D3—61no—
215C22×D3—61no—
216C3×Q8—64no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—62no—
224C2×C3×C4—62no—
225C2×C3×C4—62no—
226C2×C3×C4—62no—
227C2×Dic3—22no—
228C2×Dic3—22no—
229C2×Dic3—22no—
230C2×Dic3—22no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C4×D3—62no—
238C4×D3—62no—
239C4×D3—62no—
240C4×D3—62no—
241C4×D3—68no—
242C4×D3—64no—
243C4×D3—122no—
244C4×D3—122no—
245C4×D3—122no—
246C4×D3—124no—
247C4×D3—124no—
248C4×D3—124no—
249Dic6—24no—
250Dic6—64no—
251Dic6—64no—
252C2×C32C2×C22⋊Q811yescharacteristic
253C2×C32C2×#13511yescharacteristic
254C2×C32C2×#13711yescharacteristic
255C3⋊D3#47914yescomplemented
256C2×Q8—61no—
257C2×Q8—92no—
258C2×Q8—94no—
259C2×Q8—182no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—181no—
264C22×C4—181no—
265C22×C4—181no—
266C22×C4—181no—
267C2×C8—92no—
268C2×C8—92no—
269C2×C8—182no—
270C2×C8—182no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C4⋊C4—62no—
277C4⋊C4—92no—
278C4⋊C4—92no—
279C4⋊C4—92no—
280C4⋊C4—182no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C42—62no—
284C42—91no—
285C42—91no—
286C42—91no—
287C42—182no—
288C42GO+(4,𝔽2)11yescharacteristic
289C22×C3—21no—
290C22×C3—21no—
291C2×D3—62no—
292C2×D3—62no—
293C2×D3—62no—
294C2×D3—62no—
295C2×D3—62no—
296C2×D3—62no—
297C3×C4—22no—
298C3×C4—22no—
299C3×C4—22no—
300C3×C4—41no—
301C3×C4—41no—
302C3×C4—41no—
303C3×C4—64no—
304C3×C4—122no—
305C3×C4—122no—
306C3×C4—122no—
307Dic3—24no—
308Dic3—42no—
309Dic3—42no—
310Dic3—42no—
311Dic3—61no—
312Dic3—61no—
313Dic3—61no—
314Dic3—61no—
315Dic3—62no—
316Dic3—121no—
317Dic3—121no—
318Dic3—121no—
319C32C2×#47911yescharacteristic, complemented, Sylow
320C23—91no—
321Q8—64no—
322Q8—94no—
323Q8—182no—
324C2×C4—62no—
325C2×C4—62no—
326C2×C4—62no—
327C2×C4—62no—
328C2×C4—91no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—184no—
336C2×C4—362no—
337C2×C4—362no—
338C2×C4—362no—
339C2×C4C2×GO+(4,𝔽2)11yescharacteristic
340C2×C4C2×GO+(4,𝔽2)11yescharacteristic
341C2×C4C2×GO+(4,𝔽2)11yescharacteristic
342C8—182no—
343C8—182no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350D3—64no—
351D3—64no—
352C22—92no—
353C22—92no—
354C22—92no—
355C22C22×GO+(4,𝔽2)11yescharacteristic
356C4—21no—
357C4—21no—
358C4—64no—
359C4—91no—
360C4—91no—
361C4—122no—
362C4—122no—
363C4—122no—
364C4—181no—
365C4—181no—
366C4D32⋊Q812yes—
367C3—21no—
368C3—21no—
369C2—94no—
370C2C2×D32⋊Q811yescharacteristic
371C2#1059650011yescharacteristic
372C2#1059650511yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#479
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
6. #10593382C2semidirect
9. #10593373C2semidirect
255. C3⋊D3#479semidirect
319. C32C2×#479semidirect

Maximal subgroups

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

subgroupindex
#105939482
C4×#37972
#105937262
#105933962
#105933872
#105933822
#105933752
#105933732
C2×#4799