Finite Group Databasebeta

← #11780578

Subgroups — #11780578

Order 1152.

491 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 491 conjugacy classes of subgroups — too many to draw. Only its 76 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×#5683C211yesmaximal, characteristic
2C3×#5055C211yesmaximal, characteristic, complemented
3#10590376C211yesmaximal, characteristic, complemented
4#10590280C211yesmaximal, characteristic, complemented
5#10589406C211yesmaximal, characteristic, complemented
6#10589086C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71949—31nomaximal
9#71244—31nomaximal
10C32×#124C2211yescharacteristic
11C3×#947—21no—
12C3×#937—21no—
13C3×#885—21no—
14C3×#885—21no—
15C3×#882—21no—
16C3×#882—21no—
17C3×#875C2211yescharacteristic
18C3×#875C2211yescharacteristic
19C3×#869C2211yescharacteristic, complemented
20C2×#3718—21no—
21C2×#3715—21no—
22#63630C2211yescharacteristic, complemented
23#63630C2211yescharacteristic, complemented
24C3×#835—21no—
25C3×#832—21no—
26C3×#803C2211yescharacteristic, complemented
27#63565—21no—
28#63562—21no—
29C3×H(3,𝔽4)—31no—
30#5683D311yescharacteristic
31C3×#489—31no—
32#5089—31no—
33#5086—31no—
34#5060—31no—
35#5055—31no—
36#5055D311yescharacteristic, complemented
37#4540—31no—
38#4540—31no—
39#4540—31no—
40#4540—31no—
41#4540—61no—
42#4464—31no—
43#4464—31no—
44C23×C3×D3—21no—
45C2×C32×Q8D411yescharacteristic
46C2×C32×D4D411yescharacteristic
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C2×C3×D12—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C22⋊C4—21no—
57C32×C42C2311yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71#3718—42no—
72#3715—42no—
73#1659—91noSylow
74C3×C4⋊Q8—31no—
75C3×#124—21no—
76C3×#124—31no—
77C3×#124—31no—
78C3×#124—61no—
79C3×#124—61no—
80C3×#124—61no—
81C3×#124C2×D311yescharacteristic
82C3×#124C2×D311yescharacteristic
83C3×#120—61no—
84C3×#120—61no—
85C3×#120—61no—
86#947—21no—
87C2×#216—61no—
88C2×#216—61no—
89C2×#215—61no—
90#937—21no—
91C2×#214—61no—
92#885—21no—
93#885—21no—
94#882—21no—
95#882—21no—
96#875C2×D311yescharacteristic
97#875C2×D311yescharacteristic
98#869C2×D311yescharacteristic, complemented
99C3×#103—61no—
100C3×#102—61no—
101C3×#97—31no—
102#835—21no—
103#835—61no—
104#832—21no—
105#832—61no—
106#810—61no—
107#809—61no—
108#803—31no—
109#803—31no—
110#803—31no—
111#803—31no—
112#803—61no—
113#803—61no—
114#803C2×D311yescharacteristic, complemented
115C23×C32—21no—
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3—81no—
119C22×C3×D3—81no—
120C22×C3×D3—81no—
121C32×Q8—41no—
122C32×D4—41no—
123C2×C32×C4—21no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C3×#67—81no—
128C3×#67—81no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C3×D12—41no—
133C3×D12—41no—
134C3×D12—81no—
135C3×Dic6—41no—
136C3×Dic6—41no—
137C3×Dic6—41no—
138C3×Dic6—41no—
139C3⋊(C3⋊C8)—22no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142H(3,𝔽4)—31no—
143#497—91no—
144#489—31no—
145#489—91no—
146#329—91no—
147#329—91no—
148#329—91no—
149C24×C3—61no—
150C23×D3—21no—
151C2×C3×Q8—21no—
152C2×C3×Q8—31no—
153C2×C3×Q8—31no—
154C2×C3×Q8—61no—
155C2×C3×Q8#6711yescharacteristic
156C2×C3×Q8#6711yescharacteristic
157C2×C3×D4—21no—
158C2×C3×D4—31no—
159C2×C3×D4—31no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4#6711yescharacteristic
164C2×C3×D4#6711yescharacteristic
165C2×#67—21no—
166C2×#67—21no—
167C2×D12—21no—
168C2×D12#6711yescharacteristic
169C2×D12#6711yescharacteristic
170C2×Dic6—21no—
171C2×Dic6#6711yescharacteristic
172C2×Dic6#6711yescharacteristic
173C2×C3×C8—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—21no—
178C3×C22⋊C4—21no—
179C3×C22⋊C4—21no—
180C3×C22⋊C4—41no—
181C3×C22⋊C4—41no—
182C3×C22⋊C4—61no—
183C3×C22⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C42—21no—
190C3×C42—61no—
191C3×C42C22×D311yescharacteristic
192C3×C42C22×D311yescharacteristic
193#217—21no—
194#216—122no—
195#216—122no—
196#215—122no—
197#214—122no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—21no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4×Dic3—21no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—121no—
213C2×C3⋊C8—121no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32#12011yescharacteristic
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C2×C3×D3—41no—
224C2×C3×D3—84no—
225C32×C4—21no—
226C32×C4—21no—
227C32×C4—21no—
228C32×C4—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231C3×Dic3—81no—
232C2×Q16—181no—
233C2×SD16—181no—
234C4⋊Q8—31no—
235#124—31no—
236#124—31no—
237#124—61no—
238#124—61no—
239#124—61no—
240#124D3211yescharacteristic
241#120—61no—
242#120—61no—
243#120—61no—
244#103—61no—
245#103—181no—
246#102—61no—
247#102—181no—
248#97—31no—
249#97—91no—
250#97—91no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—41no—
254C23×C3—61no—
255C23×C3—61no—
256C23×C3—241no—
257C23×C3—241no—
258C23×C3—241no—
259C22×D3—21no—
260C22×D3—21no—
261C22×D3—81no—
262C22×D3—81no—
263C22×D3—81no—
264C3×Q8—41no—
265C3×Q8—41no—
266C3×Q8—81no—
267C3×Q8—121no—
268C3×Q8—121no—
269C3×Q8—121no—
270C3×Q8—121no—
271C3×D4—41no—
272C3×D4—41no—
273C3×D4—81no—
274C3×D4—121no—
275C3×D4—121no—
276C3×D4—241no—
277C3×D4—241no—
278C3×D4—241no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—41no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—121no—
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4C2×#6711yescharacteristic
291C2×C3×C4C2×#6711yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294#67—81no—
295#67—81no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299D12—41no—
300D12—41no—
301D12—81no—
302Dic6—41no—
303Dic6—41no—
304Dic6—41no—
305Dic6—41no—
306C3×C8—121no—
307C3⋊C8—41no—
308C3⋊C8—62no—
309C3⋊C8—62no—
310C3⋊C8—122no—
311C3⋊C8—121no—
312C3⋊C8—121no—
313C3⋊C8—122no—
314C2×C32—81no—
315C2×C32#45311yescharacteristic
316C2×C32#45511yescharacteristic
317C2×C32#45511yescharacteristic
318C3×D3—81no—
319C3×D3—81no—
320C24—61no—
321C2×Q8—31no—
322C2×Q8—31no—
323C2×Q8—61no—
324C2×Q8#62511yescharacteristic
325C2×D4—31no—
326C2×D4—31no—
327C2×D4—61no—
328C2×D4—61no—
329C2×D4—61no—
330C2×D4#62511yescharacteristic
331Q16—362no—
332SD16—362no—
333C2×C8—61no—
334C2×C8—181no—
335C2×C8—181no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—61no—
341C22⋊C4—61no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C42—61no—
348C42C2×D3211yescharacteristic
349C22×C3—21no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—81no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3—121no—
360C22×C3—121no—
361C22×C3—121no—
362C22×C3—121no—
363C22×C3—121no—
364C22×C3—121no—
365C22×C3—244no—
366C22×C3#93711yescharacteristic
367C22×C3#95311yescharacteristic
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—41no—
371C2×D3—41no—
372C2×D3—41no—
373C2×D3—41no—
374C2×D3—84no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—81no—
387C3×C4—121no—
388C3×C4—121no—
389C3×C4—241no—
390Dic3—41no—
391Dic3—41no—
392Dic3—81no—
393C32#165911yescharacteristic, complemented, Sylow
394C23—21no—
395C23—61no—
396C23—61no—
397C23—241no—
398C23—241no—
399C23—241no—
400Q8—41no—
401Q8—121no—
402Q8—121no—
403Q8—121no—
404Q8—121no—
405D4—41no—
406D4—121no—
407D4—121no—
408D4—241no—
409D4—241no—
410D4—241no—
411C2×C4—21no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—121no—
415C2×C4C2×#62511yescharacteristic
416C2×C4D3×#6711yescharacteristic
417C2×C4D3×#6711yescharacteristic
418C8—121no—
419C8—182no—
420C8—361no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—81no—
425C2×C3—81no—
426C2×C3—161no—
427C2×C3—241no—
428C2×C3—241no—
429C2×C3#506111yescharacteristic
430C2×C3#519811yescharacteristic
431C2×C3#520211yescharacteristic
432C2×C3#524111yescharacteristic
433C2×C3#524211yescharacteristic
434C2×C3#524211yescharacteristic
435D3—81no—
436D3—81no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—121no—
441C22—121no—
442C22—121no—
443C22—121no—
444C22—121no—
445C22—121no—
446C22—244no—
447C22#6397611yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—41no—
452C4—121no—
453C4—121no—
454C4—241no—
455C3—21no—
456C3#7124411yescharacteristic, complemented
457C3#7194911yescharacteristic, complemented
458C2—81no—
459C2—241no—
460C2—241no—
461C2#1059151211yescharacteristic
462C2#1059166411yescharacteristic
463C2#1059166511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32#120
prime radicalC3×#5683C2
hypercenter#124D32
hypocenterC32#1659
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C3×#5055C2semidirect
3. #10590376C2semidirect
4. #10590280C2semidirect
5. #10589406C2semidirect
6. #10589086C2semidirect
7. #10589086C2semidirect
19. C3×#869C22semidirect
22. #63630C22semidirect
23. #63630C22semidirect
26. C3×#803C22semidirect
36. #5055D3semidirect
98. #869C2×D3semidirect
114. #803C2×D3semidirect
393. C32#1659semidirect
456. C3#71244semidirect
457. C3#71949semidirect

Maximal subgroups

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

subgroupindex
C3×#56832
C3×#50552
#105903762
#105902802
#105894062
#105890862
#719493
#712443