Finite Group Databasebeta

← #11778708

Subgroups — #11778708

Order 1152.

593 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 593 conjugacy classes of subgroups — too many to draw. Only its 88 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#10595954C211yesmaximal, characteristic
2C3×#4949C211yesmaximal, characteristic
3#10591135C212yesmaximal, complemented
4C3×#4525C211yesmaximal, characteristic
5#10589154C212yesmaximal, complemented
6#69716—31nomaximal
7#68117—31nomaximal
8C2×C32×C22⋊C4C2211yescharacteristic
9C2×#3757—21no—
10#64133—21no—
11#64133C2212yes—
12#64087—22no—
13#64087—22no—
14C2×C3×#217—21no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C3×C3⋊#95C2211yescharacteristic
18C3×#830C2212yes—
19#63575—22no—
20#63567—22no—
21#5483—31no—
22#5483—31no—
23#5483—61no—
24C3×#399—31no—
25#4970—32no—
26#4949D311yescharacteristic
27#4722—32no—
28C3×#323—31no—
29#4525D311yescharacteristic
30#4467—32no—
31#4452—32no—
32C24×C32D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C2×#634—21no—
38C2×#634D412yes—
39C22×C3×Dic3—21no—
40C22×C3×Dic3—21no—
41C32×C22⋊C4—22no—
42#3757—22no—
43#3757—22no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)D412yes—
46#3750—22no—
47#3750—22no—
48C3×#217—42no—
49C3×C4⋊Dic3—22no—
50C3×Dic3⋊C4—42no—
51C2×C3×C3⋊C8—22no—
52#1614—91noSylow
53C2×C3×C4⋊C4—31no—
54C2×C3×C4⋊C4—61no—
55C2×C3×C22⋊C4—21no—
56C2×C3×C22⋊C4—61no—
57C2×C3×C22⋊C4C2×D311yescharacteristic
58C2×C3×C22⋊C4C2×D311yescharacteristic
59C2×#217—21no—
60C2×#217—62no—
61C2×#217—61no—
62C2×#217—61no—
63C2×C4⋊Dic3C2×D311yescharacteristic
64#924—32no—
65#924—32no—
66#924—62no—
67#924—62no—
68#924—61no—
69#924—61no—
70C2×Dic3⋊C4—21no—
71#878—62no—
72#878—62no—
73#878—62no—
74#878—62no—
75#878—64no—
76#878—64no—
77C3×C22⋊C8—32no—
78C3×#95—31no—
79C3⋊#95C2×D311yescharacteristic
80#830C2×D312yes—
81#818—62no—
82#816—62no—
83#810—62no—
84#807—62no—
85C23×C32—21no—
86C23×C32—21no—
87C23×C32—41no—
88C23×C32—41no—
89C23×C32Q1612yes—
90C23×C32C2×D411yescharacteristic
91C2×C32×C4—21no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D412yes—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—81no—
98C2×C3⋊Dic3—81no—
99#634—42no—
100#634—81no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C3×C3⋊C8—42no—
108#543—91no—
109#484—92no—
110#399—31no—
111#328—92no—
112#323—31no—
113C24×C3—21no—
114C24×C3D1211yescharacteristic
115C24×C3#6711yescharacteristic
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—61no—
119C22×C3×C4—61no—
120C22×C3×C4D1211yescharacteristic
121C22×C3×C4#6711yescharacteristic
122C22×C3×C4C22×D311yescharacteristic
123C22×C3×C4C22×D311yescharacteristic
124C22×Dic3—21no—
125C22×Dic3—21no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C22×Dic3—61no—
132C2×Dic6—32no—
133C2×Dic6—32no—
134C2×Dic6—62no—
135C2×Dic6—62no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×C3×C8—62no—
139C3×C4⋊C4—62no—
140C3×C4⋊C4—122no—
141C3×C22⋊C4—24no—
142C3×C22⋊C4—22no—
143C3×C22⋊C4—22no—
144C3×C22⋊C4—122no—
145#217—42no—
146#217—64no—
147#217—62no—
148#217—62no—
149#217—64no—
150#217—62no—
151#217—62no—
152C4⋊Dic3—22no—
153C4⋊Dic3—32no—
154C4⋊Dic3—32no—
155C4⋊Dic3—62no—
156C4⋊Dic3—62no—
157C4⋊Dic3—61no—
158C4⋊Dic3—61no—
159Dic3⋊C4—42no—
160Dic3⋊C4—64no—
161Dic3⋊C4—62no—
162Dic3⋊C4—62no—
163Dic3⋊C4—64no—
164Dic3⋊C4—62no—
165Dic3⋊C4—62no—
166C2×C3⋊C8—22no—
167C22×C32—22no—
168C22×C32—21no—
169C22×C32—21no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32—42no—
173C22×C32—81no—
174C22×C32#12011yescharacteristic
175C22×C32C2×Q1611yescharacteristic
176C22×C32#13711yescharacteristic
177C32×C4—22no—
178C32×C4—41no—
179C3⋊Dic3—42no—
180C3⋊Dic3—42no—
181C3×Dic3—42no—
182C3×Dic3—81no—
183C22⋊Q8—92no—
184C22⋊Q8—182no—
185C22⋊Q8—182no—
186C22⋊Q8—181no—
187C2×C4⋊C4—31no—
188C2×C4⋊C4—61no—
189C2×C22⋊C4—61no—
190C2×C22⋊C4—181no—
191C2×C22⋊C4D3211yescharacteristic
192#107—182no—
193#103—182no—
194C22⋊C8—32no—
195#95—31no—
196C23×C3—22no—
197C23×C3—22no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—21no—
201C23×C3—21no—
202C23×C3—22no—
203C23×C3—21no—
204C23×C3—41no—
205C23×C3—41no—
206C23×C3—41no—
207C23×C3—41no—
208C23×C3—81no—
209C23×C3—81no—
210C23×C3Dic1212yes—
211C23×C3#21612yes—
212C23×C3C2×D1211yescharacteristic
213C23×C3C2×#6711yescharacteristic
214C2×C3×C4—22no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—22no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—62no—
223C2×C3×C4—81no—
224C2×C3×C4—81no—
225C2×C3×C4—121no—
226C2×C3×C4—121no—
227C2×C3×C4—121no—
228C2×C3×C4—121no—
229C2×C3×C4—121no—
230C2×C3×C4D3×D412yes—
231C2×C3×C4D3×D412yes—
232C2×Dic3—22no—
233C2×Dic3—41no—
234C2×Dic3—41no—
235C2×Dic3—41no—
236C2×Dic3—41no—
237C2×Dic3—41no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—242no—
245C2×Dic3—242no—
246C2×Dic3—241no—
247C2×Dic3—241no—
248C2×Dic3—241no—
249C2×Dic3—241no—
250Dic6—122no—
251Dic6—122no—
252Dic6—242no—
253Dic6—242no—
254Dic6—241no—
255Dic6—241no—
256C3×C8—122no—
257C3⋊C8—42no—
258C2×C32—21no—
259C2×C32—21no—
260C2×C32—42no—
261C2×C32#45111yescharacteristic
262C2×C32#45311yescharacteristic
263C2×C32#45811yescharacteristic
264C24#62611yescharacteristic
265C2×Q8—92no—
266C2×Q8—181no—
267C22×C4—61no—
268C22×C4—61no—
269C22×C4—181no—
270C22×C4—181no—
271C22×C4#62611yescharacteristic
272C22×C4C2×D3211yescharacteristic
273C2×C8—62no—
274C4⋊C4—62no—
275C4⋊C4—92no—
276C4⋊C4—122no—
277C4⋊C4—182no—
278C4⋊C4—181no—
279C4⋊C4—182no—
280C22⋊C4—22no—
281C22⋊C4—122no—
282C22⋊C4—182no—
283C22⋊C4—182no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—24no—
289C22×C3—22no—
290C22×C3—22no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—42no—
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—42no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—82no—
305C22×C3—81no—
306C22×C3—81no—
307C22×C3—82no—
308C22×C3#88211yescharacteristic
309C22×C3C2×Dic1211yescharacteristic
310C22×C3#90911yescharacteristic
311C22×C3#93711yescharacteristic
312C22×C3C2×#21611yescharacteristic
313C22×C3#95111yescharacteristic
314C3×C4—22no—
315C3×C4—22no—
316C3×C4—42no—
317C3×C4—42no—
318C3×C4—41no—
319C3×C4—41no—
320C3×C4—122no—
321C3×C4—241no—
322Dic3—42no—
323Dic3—81no—
324Dic3—124no—
325Dic3—124no—
326Dic3—122no—
327Dic3—122no—
328Dic3—122no—
329Dic3—122no—
330C32#161411yescharacteristic, complemented, Sylow
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23#371912yes—
336C23C2×#62611yescharacteristic
337Q8—362no—
338Q8—721no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—62no—
343C2×C4—121no—
344C2×C4—121no—
345C2×C4—121no—
346C2×C4—121no—
347C2×C4—121no—
348C2×C4—182no—
349C2×C4—182no—
350C2×C4—721no—
351C2×C4—721no—
352C2×C4#381112yes—
353C8—122no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—41no—
362C2×C3—41no—
363C2×C3—44no—
364C2×C3—42no—
365C2×C3—42no—
366C2×C3#473911yescharacteristic
367C2×C3#474211yescharacteristic
368C2×C3#474711yescharacteristic
369C2×C3#505011yescharacteristic
370C2×C3#505311yescharacteristic
371C2×C3#507711yescharacteristic
372C22—21no—
373C22—21no—
374C22—22no—
375C22—42no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22#6383111yescharacteristic
380C22C2×#371911yescharacteristic
381C22#6398111yescharacteristic
382C4—22no—
383C4—41no—
384C4—122no—
385C4—241no—
386C4—362no—
387C4—362no—
388C3—21no—
389C3#6811711yescharacteristic, complemented
390C3#6971611yescharacteristic, complemented
391C2—21no—
392C2—21no—
393C2—42no—
394C2#1059119011yescharacteristic
395C2#1059151111yescharacteristic
396C2#1059153511yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC24×C32D4
hypercenterC2×C22⋊C4D32
hypocenterC32#1614
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #10591135C2semidirect
5. #10589154C2semidirect
330. C32#1614semidirect
389. C3#68117semidirect
390. C3#69716semidirect

Maximal subgroups

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

subgroupindex
#105959542
C3×#49492
#105911352
C3×#45252
#105891542
#697163
#681173