Finite Group Databasebeta

← #11778256

Subgroups — #11778256

Order 1152.

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

normal subgroups only

This group has 633 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×#4947C211yesmaximal, characteristic
3#10591186C212yesmaximal, complemented
4C3×#4525C211yesmaximal, characteristic
5#10589154C212yesmaximal, complemented
6#69701—31nomaximal
7#68115—31nomaximal
8C22×C3×Dic6C2211yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3757—21no—
11#64133—21no—
12#64133C2212yes—
13#64087—22no—
14#64087—22no—
15C2×C3×#217—21no—
16C2×#3719—22no—
17C3×C3⋊#95—21no—
18C3×C3⋊#95C2211yescharacteristic
19C3×#830C2212yes—
20#63566—22no—
21#5483—31no—
22#5483—31no—
23#5483—61no—
24C3×#393—31no—
25#5228—32no—
26#4947D311yescharacteristic
27#4739—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—
41C2×C3×Dic6—22no—
42C2×C3×Dic6—42no—
43C32×C22⋊C4—22no—
44#3757—22no—
45#3757—22no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)D412yes—
48#3750—22no—
49#3750—22no—
50C3×#217—42no—
51C2×C3×C3⋊C8—22no—
52#3719—44no—
53#1602—91noSylow
54C22×C3×Q8—31no—
55C22×Dic6C2×D311yescharacteristic
56C2×C3×C22⋊C4—21no—
57C2×C3×C22⋊C4—61no—
58C2×C3×C22⋊C4C2×D311yescharacteristic
59C2×C3×C22⋊C4C2×D311yescharacteristic
60C2×#217—21no—
61C2×#217—62no—
62C2×#217—61no—
63C2×#217—61no—
64C2×#216—62no—
65#924—32no—
66#924—32no—
67#924—62no—
68#924—62no—
69#924—61no—
70#924—61no—
71C2×Dic12—62no—
72#878—62no—
73#878—62no—
74#878—62no—
75#878—62no—
76#878—64no—
77#878—64no—
78C3×C22⋊C8—32no—
79C3×#95—31no—
80C3×#95—61no—
81#835—62no—
82C3⋊#95—21no—
83C3⋊#95C2×D311yescharacteristic
84#830C2×D312yes—
85#816—62no—
86C23×C32—21no—
87C23×C32—21no—
88C23×C32—41no—
89C23×C32—41no—
90C23×C32Q1612yescomplemented
91C23×C32C2×D411yescharacteristic
92C2×C32×C4—21no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
95C2×C32×C4C2×D412yes—
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—81no—
99C2×C3⋊Dic3—81no—
100#634—42no—
101#634—81no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C2×C3×Dic3—41no—
108C3×Dic6—24no—
109C3×Dic6—42no—
110C3×C3⋊C8—42no—
111#543—91no—
112#451—92no—
113#393—31no—
114#328—92no—
115#323—31no—
116C24×C3—21no—
117C24×C3D1211yescharacteristic
118C24×C3#6711yescharacteristic
119C2×C3×Q8—62no—
120C2×C3×Q8—122no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—61no—
124C22×C3×C4—61no—
125C22×C3×C4D1211yescharacteristic
126C22×C3×C4#6711yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×Dic3—21no—
130C22×Dic3—21no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137C2×Dic6—22no—
138C2×Dic6—32no—
139C2×Dic6—32no—
140C2×Dic6—42no—
141C2×Dic6—62no—
142C2×Dic6—62no—
143C2×Dic6—61no—
144C2×Dic6—61no—
145C2×C3×C8—62no—
146C3×C22⋊C4—24no—
147C3×C22⋊C4—22no—
148C3×C22⋊C4—22no—
149C3×C22⋊C4—122no—
150#217—42no—
151#217—64no—
152#217—62no—
153#217—62no—
154#217—64no—
155#217—62no—
156#217—62no—
157#216—124no—
158C4⋊Dic3—32no—
159C4⋊Dic3—32no—
160C4⋊Dic3—62no—
161C4⋊Dic3—62no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164Dic3⋊C4—64no—
165Dic3⋊C4—62no—
166Dic3⋊C4—62no—
167Dic3⋊C4—64no—
168Dic3⋊C4—62no—
169Dic3⋊C4—62no—
170C2×C3⋊C8—22no—
171Dic12—124no—
172C22×C32—22no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32—41no—
176C22×C32—41no—
177C22×C32—42no—
178C22×C32—81no—
179C22×C32#12011yescharacteristic
180C22×C32C2×Q1611yescharacteristic
181C22×C32#13711yescharacteristic
182C32×C4—22no—
183C32×C4—41no—
184C3⋊Dic3—42no—
185C3⋊Dic3—42no—
186C3×Dic3—42no—
187C3×Dic3—81no—
188C22×Q8—31no—
189C2×Q16—182no—
190C22⋊Q8—92no—
191C22⋊Q8—182no—
192C22⋊Q8—182no—
193C22⋊Q8—181no—
194C2×C22⋊C4—61no—
195C2×C22⋊C4—181no—
196C2×C22⋊C4D3211yescharacteristic
197#103—182no—
198C22⋊C8—32no—
199#95—31no—
200#95—61no—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—22no—
208C23×C3—21no—
209C23×C3—41no—
210C23×C3—41no—
211C23×C3—41no—
212C23×C3—41no—
213C23×C3—81no—
214C23×C3—81no—
215C23×C3Dic1212yescomplemented
216C23×C3#21612yescomplemented
217C23×C3C2×D1211yescharacteristic
218C23×C3C2×#6711yescharacteristic
219C3×Q8—64no—
220C3×Q8—122no—
221C2×C3×C4—22no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—22no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—62no—
230C2×C3×C4—81no—
231C2×C3×C4—81no—
232C2×C3×C4—121no—
233C2×C3×C4—121no—
234C2×C3×C4—121no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×C3×C4D3×D412yes—
238C2×C3×C4D3×D412yes—
239C2×Dic3—22no—
240C2×Dic3—41no—
241C2×Dic3—41no—
242C2×Dic3—41no—
243C2×Dic3—41no—
244C2×Dic3—41no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C2×Dic3—242no—
252C2×Dic3—242no—
253C2×Dic3—241no—
254C2×Dic3—241no—
255C2×Dic3—241no—
256C2×Dic3—241no—
257Dic6—24no—
258Dic6—42no—
259Dic6—122no—
260Dic6—122no—
261Dic6—242no—
262Dic6—242no—
263Dic6—241no—
264Dic6—241no—
265C3×C8—122no—
266C3⋊C8—42no—
267C2×C32—21no—
268C2×C32—21no—
269C2×C32—42no—
270C2×C32#45111yescharacteristic
271C2×C32#45511yescharacteristic
272C2×C32B(4,𝔽2)11yescharacteristic
273C24#62611yescharacteristic
274C2×Q8—62no—
275C2×Q8—92no—
276C2×Q8—122no—
277C2×Q8—181no—
278C22×C4—61no—
279C22×C4—61no—
280C22×C4—181no—
281C22×C4—181no—
282C22×C4#62611yescharacteristic
283C22×C4C2×D3211yescharacteristic
284Q16—364no—
285C2×C8—62no—
286C4⋊C4—92no—
287C4⋊C4—182no—
288C4⋊C4—181no—
289C4⋊C4—182no—
290C22⋊C4—22no—
291C22⋊C4—122no—
292C22⋊C4—182no—
293C22⋊C4—182no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—24no—
299C22×C3—22no—
300C22×C3—22no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—42no—
307C22×C3—42no—
308C22×C3—42no—
309C22×C3—42no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—82no—
315C22×C3—81no—
316C22×C3—81no—
317C22×C3—82no—
318C22×C3#88211yescharacteristic
319C22×C3C2×Dic1211yescharacteristic
320C22×C3#90911yescharacteristic
321C22×C3#93711yescharacteristic
322C22×C3C2×#21611yescharacteristic
323C22×C3#95111yescharacteristic
324C3×C4—22no—
325C3×C4—22no—
326C3×C4—42no—
327C3×C4—42no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4—122no—
331C3×C4—241no—
332Dic3—42no—
333Dic3—81no—
334Dic3—124no—
335Dic3—124no—
336Dic3—122no—
337Dic3—122no—
338Dic3—122no—
339Dic3—122no—
340C32#160211yescharacteristic, complemented, Sylow
341C23—21no—
342C23—21no—
343C23—41no—
344C23—41no—
345C23#371912yescomplemented
346C23C2×#62611yescharacteristic
347Q8—64no—
348Q8—122no—
349Q8—362no—
350Q8—721no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—62no—
355C2×C4—121no—
356C2×C4—121no—
357C2×C4—121no—
358C2×C4—121no—
359C2×C4—121no—
360C2×C4—182no—
361C2×C4—182no—
362C2×C4—721no—
363C2×C4—721no—
364C2×C4#381112yes—
365C8—122no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—41no—
374C2×C3—41no—
375C2×C3—44no—
376C2×C3—42no—
377C2×C3—42no—
378C2×C3#473911yescharacteristic
379C2×C3#474111yescharacteristic
380C2×C3#474611yescharacteristic
381C2×C3#503211yescharacteristic
382C2×C3#505011yescharacteristic
383C2×C3#506111yescharacteristic
384C22—21no—
385C22—21no—
386C22—22no—
387C22—42no—
388C22—41no—
389C22—41no—
390C22—81no—
391C22#6383111yescharacteristic
392C22C2×#371911yescharacteristic
393C22#6398111yescharacteristic
394C4—22no—
395C4—41no—
396C4—122no—
397C4—241no—
398C4—362no—
399C4—362no—
400C3—21no—
401C3#6811511yescharacteristic, complemented
402C3#6970111yescharacteristic, complemented
403C2—21no—
404C2—21no—
405C2—42no—
406C2#1059119011yescharacteristic
407C2#1059151411yescharacteristic
408C2#1059153211yescharacteristic
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#1602
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. #10591186C2semidirect
5. #10589154C2semidirect
90. C23×C32Q16semidirect
215. C23×C3Dic12semidirect
216. C23×C3#216semidirect
340. C32#1602semidirect
345. C23#3719semidirect
401. C3#68115semidirect
402. C3#69701semidirect

Maximal subgroups

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

subgroupindex
#105959542
C3×#49472
#105911862
C3×#45252
#105891542
#697013
#681153