Finite Group Databasebeta

← #11778143

Subgroups — #11778143

Order 1152.

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

normal subgroups only

This group has 571 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
1C3×#5500C211yesmaximal, characteristic, complemented
2C3×#4991C211yesmaximal, characteristic
3#10591169C212yesmaximal
4#10589394C211yesmaximal, characteristic, complemented
5#10589153C212yesmaximal, complemented
6#71902—31nomaximal
7#69704—31nomaximal
8C22×C3×D12C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C3×(C2×D3)⋊C4—21no—
11C2×C3×(C2×D3)⋊C4—21no—
12C3×#926—21no—
13C3×#924—21no—
14C3×#924C2212yes—
15C3×#890—22no—
16C3×#888—22no—
17C2×#3715—22no—
18#63657C2212yes—
19C3×C3⋊#95C2211yescharacteristic
20#63562—22no—
21C3×#544—31no—
22#5500D311yescharacteristic, complemented
23C3×#394—31no—
24#5218—32no—
25#5046—32no—
26#4991D311yescharacteristic
27#4538—32no—
28#4528—31no—
29#4528—31no—
30#4528—61no—
31#4452—32no—
32C23×C3×D3—21no—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3×Dic3—21no—
37C2×C3×D12—22no—
38C2×C3×D12—42no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6D412yes—
41C32×C4⋊C4—22no—
42C2×C3⋊(C3⋊C8)—22no—
43C3×#217—22no—
44C3×(C2×D3)⋊C4—42no—
45C3×(C2×D3)⋊C4—42no—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3D412yes—
50C3×Dic3⋊C4—22no—
51C3×Dic3⋊C4—22no—
52C3×C4×Dic3—22no—
53#3715—44no—
54#1599—91noSylow
55C22×C3×D4—31no—
56C22×D12C2×D311yescharacteristic
57C3×C4⋊Q8—62no—
58C3×#125—62no—
59C3×C22⋊Q8—32no—
60C3×C22⋊Q8—61no—
61C3×#117—61no—
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4C2×D311yescharacteristic
64C2×C3×C4⋊C4C2×D311yescharacteristic
65C2×C3×C22⋊C4—61no—
66C2×C3×C22⋊C4—61no—
67C2×#215—62no—
68C2×#214—62no—
69C2×(C2×D3)⋊C4—21no—
70C2×(C2×D3)⋊C4—21no—
71#926—21no—
72#924—21no—
73#924C2×D312yes—
74#890—22no—
75#888—22no—
76C3×#95—31no—
77#832—62no—
78C3⋊#95C2×D311yescharacteristic
79#830—32no—
80#830—32no—
81#830—62no—
82#809—62no—
83C23×C32C2×D411yescharacteristic
84C22×C3×D3—22no—
85C22×C3×D3—41no—
86C22×C3×D3—41no—
87C22×C3×D3—41no—
88C22×C3×D3—41no—
89C22×C3×D3—41no—
90C22×C3×D3—41no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4SD1612yescomplemented
97C2×C32×C4C2×D412yes—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C2×C3×Dic3—41no—
103C3×D12—24no—
104C3×D12—42no—
105C3×Dic6—42no—
106C3×Dic6—81no—
107C3⋊(C3⋊C8)—42no—
108#544—31no—
109#450—92no—
110#394—31no—
111#328—92no—
112#324—91no—
113C24×C3—61no—
114C23×D3—21no—
115C2×C3×Q8—32no—
116C2×C3×Q8—61no—
117C2×C3×D4—62no—
118C2×C3×D4—122no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—61no—
123C22×C3×C4#6711yescharacteristic
124C22×C3×C4#6711yescharacteristic
125C22×C3×C4#6711yescharacteristic
126C22×C3×C4#6711yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×Dic3—21no—
130C2×D12—22no—
131C2×D12—42no—
132C2×Dic6—21no—
133C2×Dic6#6712yes—
134C3×C4⋊C4—22no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—32no—
137C3×C4⋊C4—42no—
138C3×C4⋊C4—62no—
139C3×C4⋊C4—61no—
140C3×C4⋊C4—61no—
141C3×C4⋊C4—61no—
142C3×C4⋊C4—62no—
143C3×C22⋊C4—62no—
144C3×C22⋊C4—122no—
145C3×C22⋊C4—122no—
146C3×C42—62no—
147#217—22no—
148#215—124no—
149#214—124no—
150(C2×D3)⋊C4—42no—
151(C2×D3)⋊C4—42no—
152C4⋊Dic3—21no—
153C4⋊Dic3—21no—
154C4⋊Dic3—21no—
155C4⋊Dic3#6712yes—
156Dic3⋊C4—22no—
157Dic3⋊C4—22no—
158C4×Dic3—22no—
159C2×C3⋊C8—62no—
160C2×C3⋊C8—62no—
161C2×C3⋊C8—122no—
162C22×C32—21no—
163C22×C32—21no—
164C22×C32#12011yescharacteristic
165C22×C32C2×SD1611yescharacteristic
166C22×C32#13711yescharacteristic
167C2×C3×D3—42no—
168C2×C3×D3—42no—
169C2×C3×D3—42no—
170C2×C3×D3—81no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C32×C4—22no—
175C32×C4—22no—
176C32×C4—41no—
177C3×Dic3—42no—
178C3×Dic3—42no—
179C3×Dic3—81no—
180C22×D4—31no—
181C2×SD16—182no—
182C4⋊Q8—62no—
183#125—62no—
184C22⋊Q8—32no—
185C22⋊Q8—61no—
186#117—61no—
187C2×C4⋊C4D3211yescharacteristic
188C2×C22⋊C4—61no—
189C2×C22⋊C4—61no—
190#102—182no—
191C22⋊C8—92no—
192#95—31no—
193C23×C3—21no—
194C23×C3—62no—
195C23×C3—121no—
196C23×C3—121no—
197C23×C3—121no—
198C23×C3—121no—
199C23×C3—121no—
200C23×C3—121no—
201C23×C3C2×#6711yescharacteristic
202C23×C3C2×#6711yescharacteristic
203C22×D3—22no—
204C22×D3—41no—
205C22×D3—41no—
206C22×D3—41no—
207C22×D3—41no—
208C22×D3—41no—
209C22×D3—41no—
210C3×Q8—122no—
211C3×Q8—241no—
212C3×D4—64no—
213C3×D4—122no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—62no—
230C2×C3×C4—62no—
231C2×C3×C4—81no—
232C2×C3×C4—81no—
233C2×C3×C4—121no—
234C2×C3×C4—121no—
235C2×C3×C4—121no—
236C2×C3×C4#21412yescomplemented
237C2×C3×C4#21512yescomplemented
238C2×C3×C4D3×D412yes—
239C2×C3×C4C2×#6712yes—
240C2×Dic3—22no—
241C2×Dic3—22no—
242C2×Dic3—41no—
243C2×Dic3—41no—
244C2×Dic3—41no—
245D12—24no—
246D12—42no—
247Dic6—42no—
248Dic6—81no—
249C3⋊C8—122no—
250C3⋊C8—122no—
251C3⋊C8—242no—
252C2×C32—21no—
253C2×C32—21no—
254C2×C32#44811yescharacteristic
255C2×C32#45411yescharacteristic
256C2×C32B(4,𝔽2)11yescharacteristic
257C3×D3—82no—
258C24—61no—
259C2×Q8—32no—
260C2×Q8—61no—
261C2×D4—62no—
262C2×D4—122no—
263C22×C4—61no—
264C22×C4#62511yescharacteristic
265C22×C4#62511yescharacteristic
266C22×C4C2×D3211yescharacteristic
267SD16—364no—
268C2×C8—182no—
269C4⋊C4—22no—
270C4⋊C4—32no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C22⋊C4—62no—
277C22⋊C4—122no—
278C22⋊C4—122no—
279C42—62no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—122no—
290C22×C3—122no—
291C22×C3—122no—
292C22×C3—241no—
293C22×C3—241no—
294C22×C3—241no—
295C22×C3—241no—
296C22×C3C2×#21411yescharacteristic
297C22×C3#93711yescharacteristic
298C22×C3C2×#21511yescharacteristic
299C22×C3#94211yescharacteristic
300C22×C3#95111yescharacteristic
301C22×C3#95311yescharacteristic
302C2×D3—42no—
303C2×D3—42no—
304C2×D3—42no—
305C2×D3—81no—
306C2×D3—81no—
307C2×D3—81no—
308C2×D3—81no—
309C3×C4—22no—
310C3×C4—22no—
311C3×C4—22no—
312C3×C4—22no—
313C3×C4—42no—
314C3×C4—42no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—81no—
318C3×C4—122no—
319C3×C4—122no—
320C3×C4—241no—
321Dic3—42no—
322Dic3—42no—
323Dic3—81no—
324C32#159911yescharacteristic, complemented, Sylow
325C23—62no—
326C23—121no—
327C23—121no—
328C23—121no—
329C23—121no—
330C23—121no—
331C23—121no—
332C23C2×#62511yescharacteristic
333Q8—122no—
334Q8—241no—
335D4—64no—
336D4—122no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—62no—
343C2×C4—62no—
344C2×C4—121no—
345C2×C4—121no—
346C2×C4—121no—
347C2×C4#371512yescomplemented
348C2×C4D3×#6712yes—
349C8—362no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—41no—
358C2×C3—41no—
359C2×C3—242no—
360C2×C3#503211yescharacteristic
361C2×C3#504011yescharacteristic
362C2×C3#506211yescharacteristic
363C2×C3#522711yescharacteristic
364C2×C3#524411yescharacteristic
365C2×C3#524511yescharacteristic
366D3—82no—
367C22—21no—
368C22—21no—
369C22—122no—
370C22—122no—
371C22—122no—
372C22—241no—
373C22—241no—
374C22—241no—
375C22—241no—
376C22C2×#371511yescharacteristic
377C22#6382711yescharacteristic
378C22#6397611yescharacteristic
379C4—22no—
380C4—22no—
381C4—41no—
382C4—122no—
383C4—122no—
384C4—241no—
385C3—21no—
386C3#6970411yescharacteristic, complemented
387C3#7190211yescharacteristic, complemented
388C2—21no—
389C2—21no—
390C2—242no—
391C2#1059117111yescharacteristic
392C2#1059153011yescharacteristic
393C2#1059164511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#1599
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5500C2semidirect
4. #10589394C2semidirect
5. #10589153C2semidirect
22. #5500D3semidirect
96. C2×C32×C4SD16semidirect
236. C2×C3×C4#214semidirect
237. C2×C3×C4#215semidirect
324. C32#1599semidirect
347. C2×C4#3715semidirect
386. C3#69704semidirect
387. C3#71902semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
C3×#49912
#105911692
#105893942
#105891532
#719023
#697043