Finite Group Databasebeta

← #11778704

Subgroups — #11778704

Order 1152.

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

normal subgroups only

This group has 524 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
1C3×#5634C211yesmaximal, characteristic
2#10592743C211yesmaximal, characteristic, complemented
3#10591317C211yesmaximal, characteristic
4#10591103C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic
8#71891—31nomaximal
9#68322—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C3×#946—21no—
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C3×#924C2211yescharacteristic
15C3×#897—21no—
16C3×#896—21no—
17C3×#896—21no—
18C3×D3×C22⋊C4—21no—
19C3×#878—21no—
20C2×Dic3⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22#63662—21no—
23#63657C2211yescharacteristic
24#63634—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63575—21no—
28#63566—21no—
29C3×#543—31no—
30#5634D311yescharacteristic
31#5044—31no—
32#5044—31no—
33#5044—31no—
34#5044—61no—
35#4949—31no—
36#4722—31no—
37#4677—31no—
38C3×#328—31no—
39#4538—31no—
40#4538D311yescharacteristic, complemented
41#4525—31no—
42#4468—31no—
43#4452—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C22⋊C4—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—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×C4⋊Dic3—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—42no—
72(C2×D3)⋊Dic3—42no—
73#1614—91noSylow
74C3×C22⋊Q8—21no—
75C3×C22⋊Q8—31no—
76C3×C22⋊Q8—61no—
77C3×C22⋊Q8—61no—
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8—61no—
81C3×C22⋊Q8C2×D311yescharacteristic
82C3×C22⋊Q8C2×D311yescharacteristic
83C2×C3×C22⋊C4—31no—
84C2×C3×C22⋊C4—61no—
85C2×#217—61no—
86#946—21no—
87C2×(C2×D3)⋊C4—61no—
88C2×(C2×D3)⋊C4C2×D311yescharacteristic
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3—61no—
93#924C2×D311yescharacteristic
94C2×Dic3⋊C4—61no—
95#897—21no—
96#896—21no—
97#896—21no—
98D3×C22⋊C4—21no—
99#878—21no—
100C3×C22⋊C8—31no—
101C3×#95—31no—
102#835—61no—
103#835—62no—
104#835—61no—
105#835—61no—
106C3⋊#95C2×D311yescharacteristic
107#830—31no—
108#830—31no—
109#830—61no—
110#830C2×D311yescharacteristic
111#818—61no—
112#816—61no—
113#807—61no—
114#807—62no—
115#807—61no—
116#807—61no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3Q1612yes—
123C32×Q8—41no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C3×C4×D3—81no—
140C3×C4×D3—81no—
141C3×Dic6—41no—
142C3×Dic6—81no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—41no—
145#543—31no—
146#484—91no—
147#484—91no—
148#399—91no—
149#328—31no—
150#328—91no—
151#323—91no—
152C24×C3—31no—
153C23×D3#6711yescharacteristic
154C2×C3×Q8—21no—
155C2×C3×Q8—31no—
156C2×C3×Q8—61no—
157C2×C3×Q8D1211yescharacteristic
158C2×C3×Q8#6711yescharacteristic
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—121no—
170C22×Dic3#6711yescharacteristic
171C2×C4×D3—21no—
172C2×C4×D3—21no—
173C2×Dic6—21no—
174C2×Dic6#6711yescharacteristic
175C2×C3×C8—61no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—31no—
180C3×C4⋊C4—41no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4D1211yescharacteristic
186C3×C4⋊C4#6711yescharacteristic
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—41no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195#217—21no—
196#217—122no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—122no—
202C4⋊Dic3—21no—
203C4⋊Dic3—62no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—121no—
209C4⋊Dic3—122no—
210C4⋊Dic3#6711yescharacteristic
211Dic3⋊C4—21no—
212Dic3⋊C4—21no—
213Dic3⋊C4—21no—
214Dic3⋊C4—122no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—61no—
218C2×C3⋊C8—61no—
219C22×C32—21no—
220C22×C32—21no—
221C22×C32#12011yescharacteristic
222C22×C32C2×Q1611yescharacteristic
223C22×C32#13711yescharacteristic
224C2×C3×D3—22no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C2×C3×D3—42no—
228C2×C3×D3—81no—
229C32×C4—21no—
230C32×C4—21no—
231C32×C4—41no—
232C32×C4—41no—
233C3⋊Dic3—81no—
234C3×Dic3—42no—
235C3×Dic3—41no—
236C3×Dic3—41no—
237C3×Dic3—41no—
238C22⋊Q8—31no—
239C22⋊Q8—61no—
240C22⋊Q8—61no—
241C22⋊Q8—61no—
242C22⋊Q8—61no—
243C22⋊Q8—61no—
244C22⋊Q8D3211yescharacteristic
245C2×C4⋊C4—91no—
246C2×C4⋊C4—181no—
247C2×C22⋊C4—31no—
248C2×C22⋊C4—61no—
249C2×C22⋊C4—181no—
250#107—181no—
251#107—181no—
252#103—181no—
253#103—181no—
254C22⋊C8—31no—
255C22⋊C8—91no—
256#95—31no—
257C23×C3—21no—
258C23×C3—32no—
259C23×C3—61no—
260C23×C3—61no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3D3×D411yescharacteristic
264C23×C3C2×#6711yescharacteristic
265C22×D3—21no—
266C22×D3—21no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3#21612yes—
270C3×Q8—41no—
271C3×Q8—41no—
272C3×Q8—42no—
273C3×Q8—121no—
274C3×Q8—241no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—42no—
286C2×C3×C4—62no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4—241no—
294C2×C3×C4—241no—
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—121no—
307C2×Dic3—122no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3—121no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—241no—
314C2×Dic3—241no—
315C4×D3—81no—
316C4×D3—81no—
317Dic6—41no—
318Dic6—81no—
319C3×C8—121no—
320C3⋊C8—41no—
321C3⋊C8—122no—
322C3⋊C8—121no—
323C3⋊C8—121no—
324C2×C32—21no—
325C2×C32—21no—
326C2×C32#45111yescharacteristic
327C2×C32#45311yescharacteristic
328C2×C32#45811yescharacteristic
329C3×D3—42no—
330C24—31no—
331C2×Q8—31no—
332C2×Q8—61no—
333C2×Q8#62611yescharacteristic
334C22×C4—31no—
335C22×C4—61no—
336C22×C4—61no—
337C22×C4—61no—
338C22×C4—181no—
339C22×C4C2×D3211yescharacteristic
340C2×C8—61no—
341C2×C8—181no—
342C4⋊C4—21no—
343C4⋊C4—31no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4—362no—
351C4⋊C4#62611yescharacteristic
352C22⋊C4—21no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C22⋊C4—61no—
357C22⋊C4—61no—
358C22⋊C4—362no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—62no—
369C22×C3—122no—
370C22×C3—121no—
371C22×C3—121no—
372C22×C3—241no—
373C22×C3#88211yescharacteristic
374C22×C3#91511yescharacteristic
375C22×C3D3×Q1611yescharacteristic
376C22×C3#94211yescharacteristic
377C22×C3C2×#21611yescharacteristic
378C22×C3#95311yescharacteristic
379C2×D3—22no—
380C2×D3—41no—
381C2×D3—41no—
382C2×D3—42no—
383C2×D3—81no—
384C3×C4—22no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4—41no—
394C3×C4—81no—
395C3×C4—81no—
396C3×C4—122no—
397C3×C4—121no—
398C3×C4—121no—
399C3×C4—121no—
400Dic3—42no—
401Dic3—41no—
402Dic3—41no—
403Dic3—41no—
404Dic3—242no—
405Dic3—241no—
406Dic3—241no—
407C32#161411yescharacteristic, complemented, Sylow
408C23—32no—
409C23—61no—
410C23—61no—
411C23—121no—
412C23—121no—
413C23D3×#6711yescharacteristic
414Q8—41no—
415Q8—121no—
416Q8—241no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—62no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—241no—
428C2×C4—241no—
429C2×C4—361no—
430C2×C4—361no—
431C2×C4—361no—
432C2×C4C2×#62611yescharacteristic
433C2×C4D3×#6711yescharacteristic
434C8—121no—
435C8—361no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—122no—
446C2×C3#474211yescharacteristic
447C2×C3#480911yescharacteristic
448C2×C3#482211yescharacteristic
449C2×C3#522811yescharacteristic
450C2×C3#524111yescharacteristic
451C2×C3#524311yescharacteristic
452D3—42no—
453C22—21no—
454C22—21no—
455C22—62no—
456C22—122no—
457C22—121no—
458C22—121no—
459C22—241no—
460C22D3×#21611yescharacteristic
461C22#6394611yescharacteristic
462C22#6397711yescharacteristic
463C4—21no—
464C4—21no—
465C4—41no—
466C4—41no—
467C4—122no—
468C4—121no—
469C4—121no—
470C4—121no—
471C4—721no—
472C3—21no—
473C3#6832211yescharacteristic, complemented
474C3#7189111yescharacteristic, complemented
475C2—21no—
476C2—21no—
477C2—122no—
478C2#1059153411yescharacteristic
479C2#1059159511yescharacteristic
480C2#1059166611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C3×D3D4
hypercenterC22⋊Q8D32
hypocenterC32#1614
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10592743C2semidirect
4. #10591103C2semidirect
5. C3×#4538C2semidirect
6. #10589153C2semidirect
40. #4538D3semidirect
407. C32#1614semidirect
473. C3#68322semidirect
474. C3#71891semidirect

Maximal subgroups

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

subgroupindex
C3×#56342
#105927432
#105913172
#105911032
C3×#45382
#105891532
#105891452
#718913
#683223