Finite Group Databasebeta

← #11778111

Subgroups — #11778111

Order 1152.

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

normal subgroups only

This group has 659 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×#5510C211yesmaximal, characteristic, complemented
2C3×#4991C211yesmaximal, characteristic, complemented
3#10591160C212yesmaximal, complemented
4#10589394C211yesmaximal, characteristic, complemented
5#10589149C212yesmaximal, complemented
6#71878—31nomaximal
7#69703—31nomaximal
8C2×C3×#235—21no—
9C22×C3×D12C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C3×#930—21no—
12C3×#930C2212yes—
13C2×C3×(C2×D3)⋊C4—21no—
14C2×C3×(C2×D3)⋊C4—21no—
15C3×#897—22no—
16C3×#895—22no—
17C2×#3713—22no—
18#63657C2212yes—
19C3×C3⋊#95C2211yescharacteristic
20#63562—22no—
21C3×#537—31no—
22#5510D311yescharacteristic, complemented
23C3×#394—31no—
24#5217—32no—
25#5036—32no—
26#4991D311yescharacteristic, complemented
27#4537—32no—
28#4528—31no—
29#4528—31no—
30#4528—61no—
31#4451—32no—
32C23×C3×D3—21no—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C2×C3×#67—22no—
37C22×C3×Dic3—21no—
38C3×#235—42no—
39C3×#235—42no—
40C2×C3×D12—22no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—42no—
44C2×C3×D12D412yes—
45C2×C3×C4×D3—22no—
46C2×C3×Dic6—21no—
47C32×C4⋊C4—22no—
48C2×C3⋊(C3⋊C8)—22no—
49C3×(C2×D3)⋊C4—22no—
50C3×(C2×D3)⋊C4—22no—
51C3×(C2×D3)⋊C4—42no—
52C3×(C2×D3)⋊C4—42no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D412yes—
55#3713—44no—
56#1598—91noSylow
57C2×C3×#41—61no—
58C22×C3×D4—31no—
59C2×#235—21no—
60C22×D12C2×D311yescharacteristic
61C3×C22⋊Q8—62no—
62C3×#121—32no—
63C3×#121—62no—
64C3×#121—61no—
65C2×C3×C4⋊C4—21no—
66C2×C3×C4⋊C4C2×D311yescharacteristic
67C2×C3×C4⋊C4C2×D311yescharacteristic
68C2×C3×C22⋊C4—61no—
69C2×C3×C22⋊C4—61no—
70C2×#213—62no—
71C2×#213—62no—
72#930—21no—
73#930C2×D312yes—
74C2×(C2×D3)⋊C4—21no—
75C2×(C2×D3)⋊C4—21no—
76#897—22no—
77#895—22no—
78C3×#95—31no—
79#832—62no—
80C3⋊#95C2×D311yescharacteristic
81#830—32no—
82#830—32no—
83#830—62no—
84#809—62no—
85C23×C32C2×D411yescharacteristic
86C22×C3×D3—22no—
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×C4D812yescomplemented
100C2×C32×C4C2×D412yes—
101C3×#67—42no—
102C3×#67—42no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C3×D12—24no—
108C3×D12—42no—
109C3×D12—42no—
110C3×D12—42no—
111C3×D12—81no—
112C3×C4×D3—44no—
113C3×Dic6—42no—
114C3⋊(C3⋊C8)—42no—
115#537—31no—
116#447—92no—
117#394—31no—
118#327—92no—
119#324—91no—
120C24×C3—61no—
121C23×D3—21no—
122C3×#41—122no—
123C3×#41—122no—
124C2×C3×Q8—61no—
125C2×C3×D4—32no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—62no—
129C2×C3×D4—62no—
130C2×C3×D4—122no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—62no—
135C22×C3×C4—61no—
136C22×C3×C4#6711yescharacteristic
137C22×C3×C4#6711yescharacteristic
138C22×C3×C4#6711yescharacteristic
139C22×C3×C4#6711yescharacteristic
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C2×#67—22no—
143C22×Dic3—21no—
144#235—42no—
145#235—42no—
146C2×D12—22no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—42no—
150C2×D12#6712yes—
151C2×C4×D3—22no—
152C2×Dic6—21no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4—32no—
156C3×C4⋊C4—42no—
157C3×C4⋊C4—61no—
158C3×C22⋊C4—62no—
159C3×C22⋊C4—62no—
160C3×C22⋊C4—122no—
161C3×C22⋊C4—122no—
162#213—124no—
163#213—124no—
164(C2×D3)⋊C4—22no—
165(C2×D3)⋊C4—22no—
166(C2×D3)⋊C4—42no—
167(C2×D3)⋊C4—42no—
168C4⋊Dic3—21no—
169C4⋊Dic3#6712yes—
170C2×C3⋊C8—62no—
171C2×C3⋊C8—62no—
172C2×C3⋊C8—122no—
173C22×C32—21no—
174C22×C32—21no—
175C22×C32#12011yescharacteristic
176C22×C32C2×D811yescharacteristic
177C22×C32AGL(1,ℤ/8)11yescharacteristic
178C2×C3×D3—42no—
179C2×C3×D3—42no—
180C2×C3×D3—42no—
181C2×C3×D3—42no—
182C2×C3×D3—42no—
183C2×C3×D3—42no—
184C2×C3×D3—81no—
185C2×C3×D3—81no—
186C2×C3×D3—81no—
187C2×C3×D3—81no—
188C32×C4—22no—
189C32×C4—22no—
190C32×C4—41no—
191C3×Dic3—42no—
192C3×Dic3—81no—
193C2×#41—61no—
194C22×D4—31no—
195C2×D8—182no—
196C22⋊Q8—62no—
197#121—32no—
198#121—62no—
199#121—61no—
200C2×C4⋊C4D3211yescharacteristic
201C2×C22⋊C4—61no—
202C2×C22⋊C4—61no—
203#102—182no—
204C22⋊C8—92no—
205#95—31no—
206C23×C3—21no—
207C23×C3—62no—
208C23×C3—62no—
209C23×C3—121no—
210C23×C3—121no—
211C23×C3—121no—
212C23×C3—121no—
213C23×C3—121no—
214C23×C3—121no—
215C23×C3C2×#6711yescharacteristic
216C23×C3C2×#6711yescharacteristic
217C22×D3—22no—
218C22×D3—22no—
219C22×D3—41no—
220C22×D3—41no—
221C22×D3—41no—
222C22×D3—41no—
223C22×D3—41no—
224C22×D3—41no—
225C3×Q8—122no—
226C3×D4—64no—
227C3×D4—122no—
228C3×D4—122no—
229C3×D4—122no—
230C3×D4—122no—
231C3×D4—122no—
232C3×D4—241no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—41no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—62no—
249C2×C3×C4—81no—
250C2×C3×C4—81no—
251C2×C3×C4—124no—
252C2×C3×C4—121no—
253C2×C3×C4—121no—
254C2×C3×C4—121no—
255C2×C3×C4#21312yescomplemented
256C2×C3×C4#21312yescomplemented
257C2×C3×C4D3×D412yes—
258C2×C3×C4C2×#6712yes—
259#67—42no—
260#67—42no—
261C2×Dic3—22no—
262C2×Dic3—41no—
263C2×Dic3—41no—
264C2×Dic3—41no—
265D12—24no—
266D12—42no—
267D12—42no—
268D12—42no—
269D12—81no—
270C4×D3—44no—
271Dic6—42no—
272C3⋊C8—122no—
273C3⋊C8—122no—
274C3⋊C8—242no—
275C2×C32—21no—
276C2×C32—21no—
277C2×C32#44711yescharacteristic
278C2×C32#45411yescharacteristic
279C2×C32B(4,𝔽2)11yescharacteristic
280C3×D3—82no—
281C3×D3—82no—
282C24—61no—
283#41—122no—
284#41—122no—
285C2×Q8—61no—
286C2×D4—32no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—62no—
290C2×D4—62no—
291C2×D4—122no—
292C22×C4—62no—
293C22×C4—61no—
294C22×C4#62511yescharacteristic
295C22×C4#62511yescharacteristic
296C22×C4C2×D3211yescharacteristic
297D8—364no—
298C2×C8—182no—
299C4⋊C4—22no—
300C4⋊C4—32no—
301C4⋊C4—61no—
302C22⋊C4—62no—
303C22⋊C4—62no—
304C22⋊C4—122no—
305C22⋊C4—122no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—122no—
316C22×C3—122no—
317C22×C3—122no—
318C22×C3—122no—
319C22×C3—122no—
320C22×C3—122no—
321C22×C3—241no—
322C22×C3—241no—
323C22×C3—241no—
324C22×C3—241no—
325C22×C3C2×#21311yescharacteristic
326C22×C3C2×#21311yescharacteristic
327C22×C3#93211yescharacteristic
328C22×C3#93711yescharacteristic
329C22×C3#94911yescharacteristic
330C22×C3#95311yescharacteristic
331C2×D3—42no—
332C2×D3—42no—
333C2×D3—42no—
334C2×D3—42no—
335C2×D3—42no—
336C2×D3—42no—
337C2×D3—81no—
338C2×D3—81no—
339C2×D3—81no—
340C2×D3—81no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—42no—
346C3×C4—42no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—81no—
350C3×C4—122no—
351C3×C4—241no—
352Dic3—42no—
353Dic3—81no—
354C32#159811yescharacteristic, complemented, Sylow
355C23—62no—
356C23—62no—
357C23—121no—
358C23—121no—
359C23—121no—
360C23—121no—
361C23—121no—
362C23—121no—
363C23C2×#62511yescharacteristic
364Q8—122no—
365D4—64no—
366D4—122no—
367D4—122no—
368D4—122no—
369D4—122no—
370D4—122no—
371D4—241no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—62no—
378C2×C4—124no—
379C2×C4—121no—
380C2×C4—121no—
381C2×C4—121no—
382C2×C4#371312yescomplemented
383C2×C4D3×#6712yes—
384C8—362no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—242no—
395C2×C3—242no—
396C2×C3#503211yescharacteristic
397C2×C3#503611yescharacteristic
398C2×C3#506211yescharacteristic
399C2×C3#521711yescharacteristic
400C2×C3#524411yescharacteristic
401C2×C3#524511yescharacteristic
402D3—82no—
403D3—82no—
404C22—21no—
405C22—21no—
406C22—122no—
407C22—122no—
408C22—122no—
409C22—122no—
410C22—122no—
411C22—122no—
412C22—241no—
413C22—241no—
414C22—241no—
415C22—241no—
416C22C2×#371311yescharacteristic
417C22#6382311yescharacteristic
418C22#6397611yescharacteristic
419C4—22no—
420C4—22no—
421C4—41no—
422C4—122no—
423C4—241no—
424C3—21no—
425C3#6970311yescharacteristic, complemented
426C3#7187811yescharacteristic, complemented
427C2—21no—
428C2—21no—
429C2—242no—
430C2—242no—
431C2#1059116011yescharacteristic
432C2#1059153011yescharacteristic
433C2#1059164511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
hypercenterC2×C4⋊C4D32
hypocenterC32#1598
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×#5510C2semidirect
2. C3×#4991C2semidirect
3. #10591160C2semidirect
4. #10589394C2semidirect
5. #10589149C2semidirect
22. #5510D3semidirect
26. #4991D3semidirect
99. C2×C32×C4D8semidirect
255. C2×C3×C4#213semidirect
256. C2×C3×C4#213semidirect
354. C32#1598semidirect
382. C2×C4#3713semidirect
425. C3#69703semidirect
426. C3#71878semidirect

Maximal subgroups

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

subgroupindex
C3×#55102
C3×#49912
#105911602
#105893942
#105891492
#718783
#697033