Finite Group Databasebeta

← #11778141

Subgroups — #11778141

Order 1152.

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

normal subgroups only

This group has 651 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
2#10592690C211yesmaximal, characteristic
3#10591183C212yesmaximal
4C3×#4528C211yesmaximal, characteristic, complemented
5#10589152C212yesmaximal, complemented
6#71902—31nomaximal
7#68138—31nomaximal
8C22×C4⋊(C3⋊D3)C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3752—21no—
11C2×#3752—21no—
12C3×#926—21no—
13C3×#924—21no—
14C3×#924C2212yes—
15C3×#890—22no—
16C3×#888—22no—
17C2×#3717—22no—
18#63658C2211yescharacteristic
19C3×#830C2212yes—
20#63564—22no—
21C3×#544—31no—
22#5500D311yescharacteristic, complemented
23#5046—32no—
24#4991—31no—
25#4991—31no—
26#4991—61no—
27#4731—32no—
28C3×#324—31no—
29#4538—32no—
30#4528D311yescharacteristic, complemented
31#4467—32no—
32C23×C3⋊D3—21no—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C2×C4⋊(C3⋊D3)—22no—
38C2×C4⋊(C3⋊D3)—42no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6D412yes—
41C32×C4⋊C4—22no—
42#3752—42no—
43#3752—42no—
44C3×#217—22no—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3D412yes—
49C3×Dic3⋊C4—22no—
50C3×Dic3⋊C4—22no—
51C3×C4×Dic3—22no—
52C2×C3×C3⋊C8—22no—
53#3717—44no—
54#1599—91noSylow
55C22×D12—31no—
56C22×D12—31no—
57C22×D12—61no—
58C3×C4⋊Q8—62no—
59C3×#125—62no—
60C3×C22⋊Q8—32no—
61C3×C22⋊Q8—61no—
62C3×#117—61no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4C2×D311yescharacteristic
65C2×C3×C4⋊C4C2×D311yescharacteristic
66C2×#215—62no—
67C2×(C2×D3)⋊C4—62no—
68C2×(C2×D3)⋊C4—62no—
69C2×(C2×D3)⋊C4—61no—
70C2×(C2×D3)⋊C4—61no—
71C2×(C2×D3)⋊C4—61no—
72C2×(C2×D3)⋊C4—61no—
73#926—21no—
74#924—21no—
75#924C2×D312yes—
76C2×#204—62no—
77#890—22no—
78#888—22no—
79C3×C22⋊C8—32no—
80C3⋊#95—31no—
81C3⋊#95—31no—
82C3⋊#95—61no—
83#830C2×D312yes—
84#821—62no—
85#809—62no—
86C23×C32C2×D411yescharacteristic
87C22×C3⋊D3—22no—
88C22×C3⋊D3—41no—
89C22×C3⋊D3—41no—
90C22×C3⋊D3—41no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3—41no—
93C22×C3⋊D3—41no—
94C2×C32×C4—21no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4SD1612yescomplemented
100C2×C32×C4C2×D412yes—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C4⋊(C3⋊D3)—24no—
105C4⋊(C3⋊D3)—42no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—22no—
108C3×Dic6—42no—
109C3×Dic6—81no—
110C3×C3⋊C8—42no—
111#544—31no—
112#450—92no—
113#394—91no—
114#328—92no—
115#324—31no—
116C23×D3—62no—
117C23×D3—61no—
118C23×D3—61no—
119C2×C3×Q8—32no—
120C2×C3×Q8—61no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4D1211yescharacteristic
125C22×C3×C4D1211yescharacteristic
126C22×C3×C4#6711yescharacteristic
127C22×C3×C4#6711yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C22×Dic3—62no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C2×D12—62no—
134C2×D12—62no—
135C2×D12—122no—
136C2×D12—122no—
137C2×D12—122no—
138C2×D12—124no—
139C2×Dic6—21no—
140C2×Dic6#6712yes—
141C2×C3×C8—62no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—32no—
145C3×C4⋊C4—42no—
146C3×C4⋊C4—62no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—62no—
151C3×C22⋊C4—62no—
152C3×C42—62no—
153#217—22no—
154#215—124no—
155(C2×D3)⋊C4—124no—
156(C2×D3)⋊C4—122no—
157(C2×D3)⋊C4—122no—
158(C2×D3)⋊C4—124no—
159(C2×D3)⋊C4—122no—
160(C2×D3)⋊C4—122no—
161C4⋊Dic3—21no—
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164C4⋊Dic3#6712yes—
165Dic3⋊C4—22no—
166Dic3⋊C4—22no—
167C4×Dic3—22no—
168C2×C3⋊C8—22no—
169#204—124no—
170C22×C32—21no—
171C22×C32—21no—
172C22×C32#12011yescharacteristic
173C22×C32C2×SD1611yescharacteristic
174C22×C32#13711yescharacteristic
175C2×C3⋊D3—42no—
176C2×C3⋊D3—42no—
177C2×C3⋊D3—42no—
178C2×C3⋊D3—81no—
179C2×C3⋊D3—81no—
180C2×C3⋊D3—81no—
181C2×C3⋊D3—81no—
182C32×C4—22no—
183C32×C4—22no—
184C32×C4—41no—
185C3⋊Dic3—81no—
186C3×Dic3—42no—
187C3×Dic3—42no—
188C22×D4—91no—
189C2×SD16—182no—
190C4⋊Q8—62no—
191#125—62no—
192C22⋊Q8—32no—
193C22⋊Q8—61no—
194#117—61no—
195C2×C4⋊C4D3211yescharacteristic
196C2×C22⋊C4—181no—
197C2×C22⋊C4—181no—
198#102—182no—
199C22⋊C8—32no—
200#95—91no—
201C23×C3—21no—
202C23×C3C2×D1211yescharacteristic
203C23×C3C2×#6711yescharacteristic
204C22×D3—64no—
205C22×D3—62no—
206C22×D3—62no—
207C22×D3—122no—
208C22×D3—122no—
209C22×D3—121no—
210C22×D3—121no—
211C22×D3—122no—
212C22×D3—122no—
213C22×D3—122no—
214C22×D3—121no—
215C22×D3—121no—
216C22×D3—121no—
217C22×D3—121no—
218C22×D3—122no—
219C22×D3—121no—
220C22×D3—121no—
221C22×D3—121no—
222C22×D3—121no—
223C22×D3—121no—
224C22×D3—121no—
225C3×Q8—122no—
226C3×Q8—241no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—42no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—42no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4#20412yescomplemented
247C2×C3×C4#21512yescomplemented
248C2×C3×C4D3×D412yes—
249C2×C3×C4C2×#6712yes—
250C2×Dic3—22no—
251C2×Dic3—22no—
252C2×Dic3—122no—
253C2×Dic3—121no—
254C2×Dic3—121no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C2×Dic3—121no—
258C2×Dic3—121no—
259C2×Dic3—121no—
260C2×Dic3—121no—
261D12—64no—
262D12—64no—
263D12—124no—
264D12—122no—
265D12—122no—
266D12—124no—
267Dic6—42no—
268Dic6—81no—
269C3×C8—122no—
270C3⋊C8—42no—
271C2×C32—21no—
272C2×C32—21no—
273C2×C32#44811yescharacteristic
274C2×C32#45411yescharacteristic
275C2×C32B(4,𝔽2)11yescharacteristic
276C3⋊D3—82no—
277C24—181no—
278C2×Q8—32no—
279C2×Q8—61no—
280C2×D4—182no—
281C2×D4—362no—
282C22×C4—181no—
283C22×C4#62611yescharacteristic
284C22×C4#62611yescharacteristic
285C22×C4C2×D3211yescharacteristic
286SD16—364no—
287C2×C8—62no—
288C4⋊C4—22no—
289C4⋊C4—32no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4—62no—
294C4⋊C4—62no—
295C22⋊C4—62no—
296C22⋊C4—362no—
297C22⋊C4—362no—
298C42—62no—
299C22×C3—22no—
300C22×C3—22no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3#88211yescharacteristic
309C22×C3C2×#20411yescharacteristic
310C22×C3#90911yescharacteristic
311C22×C3C2×#21511yescharacteristic
312C22×C3#94211yescharacteristic
313C22×C3#95311yescharacteristic
314C2×D3—124no—
315C2×D3—124no—
316C2×D3—124no—
317C2×D3—122no—
318C2×D3—122no—
319C2×D3—122no—
320C2×D3—122no—
321C2×D3—122no—
322C2×D3—122no—
323C2×D3—242no—
324C2×D3—242no—
325C2×D3—241no—
326C2×D3—241no—
327C2×D3—241no—
328C2×D3—241no—
329C2×D3—242no—
330C2×D3—242no—
331C2×D3—241no—
332C2×D3—241no—
333C2×D3—241no—
334C2×D3—241no—
335C3×C4—22no—
336C3×C4—22no—
337C3×C4—22no—
338C3×C4—22no—
339C3×C4—42no—
340C3×C4—42no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—81no—
344C3×C4—122no—
345C3×C4—122no—
346Dic3—42no—
347Dic3—42no—
348Dic3—242no—
349Dic3—241no—
350Dic3—241no—
351C32#159911yescharacteristic, complemented, Sylow
352C23—182no—
353C23—361no—
354C23—361no—
355C23—361no—
356C23—361no—
357C23—361no—
358C23—361no—
359C23C2×#62611yescharacteristic
360Q8—122no—
361Q8—241no—
362D4—184no—
363D4—362no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—62no—
370C2×C4—62no—
371C2×C4—361no—
372C2×C4—361no—
373C2×C4—361no—
374C2×C4#371712yescomplemented
375C2×C4D3×#6712yes—
376C8—122no—
377C2×C3—22no—
378C2×C3—22no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3#473811yescharacteristic
387C2×C3#474111yescharacteristic
388C2×C3#475311yescharacteristic
389C2×C3#522711yescharacteristic
390C2×C3#524411yescharacteristic
391C2×C3#524511yescharacteristic
392D3—244no—
393D3—242no—
394D3—242no—
395C22—21no—
396C22—21no—
397C22—362no—
398C22—362no—
399C22—362no—
400C22—721no—
401C22—721no—
402C22—721no—
403C22—721no—
404C22C2×#371711yescharacteristic
405C22#6383311yescharacteristic
406C22#6397711yescharacteristic
407C4—22no—
408C4—22no—
409C4—41no—
410C4—122no—
411C4—122no—
412C4—721no—
413C3—21no—
414C3#6813811yescharacteristic, complemented
415C3#7190211yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—722no—
419C2#1059117411yescharacteristic
420C2#1059153111yescharacteristic
421C2#1059164611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC22×C4⋊(C3⋊D3)C22
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. C3×#4528C2semidirect
5. #10589152C2semidirect
22. #5500D3semidirect
30. #4528D3semidirect
99. C2×C32×C4SD16semidirect
246. C2×C3×C4#204semidirect
247. C2×C3×C4#215semidirect
351. C32#1599semidirect
374. C2×C4#3717semidirect
414. C3#68138semidirect
415. C3#71902semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
#105926902
#105911832
C3×#45282
#105891522
#719023
#681383