Finite Group Databasebeta

← #11778365

Subgroups — #11778365

Order 1152.

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

normal subgroups only

This group has 550 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×#5623C211yesmaximal, characteristic
2#10592749C211yesmaximal, characteristic
3#10591354C211yesmaximal, characteristic
4#10591190C211yesmaximal, characteristic
5C3×#4538C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic
8#71904—31nomaximal
9#68327—31nomaximal
10C22×#634C2211yescharacteristic
11C32×C22⋊Q8C2211yescharacteristic
12C2×#3756—21no—
13C3×#944—21no—
14C3×#924C2211yescharacteristic
15C2×C3×Dic3⋊C4C2211yescharacteristic
16C3×#889—21no—
17C3×#889—21no—
18C3×#888—21no—
19C3×#878—21no—
20C3×#877—21no—
21C2×Dic3⋊Dic3—21no—
22C2×#3719—21no—
23#63657C2211yescharacteristic
24#63637—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29C3×#544—31no—
30#5623D311yescharacteristic
31#5050—31no—
32#5050—31no—
33#5050—31no—
34#5050—61no—
35#4979—31no—
36#4739—31no—
37#4656—31no—
38C3×#328—31no—
39#4538—31no—
40#4538D311yescharacteristic
41#4528—31no—
42#4469—31no—
43#4452—31no—
44C2×C32×Q8D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—42no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3D411yescharacteristic
52C22×C3×Dic3D411yescharacteristic
53C2×C3×Dic6—21no—
54C2×C3×Dic6D411yescharacteristic
55C32×C4⋊C4—21no—
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58#3756—42no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—42no—
74#3719—42no—
75#1605—91noSylow
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C3×C4⋊Q8—61no—
80C3×C4⋊Q8—61no—
81C3×#125—61no—
82C3×#125—61no—
83C3×C22⋊Q8—21no—
84C3×C22⋊Q8—31no—
85C3×C22⋊Q8—61no—
86C3×C22⋊Q8C2×D311yescharacteristic
87C3×C22⋊Q8C2×D311yescharacteristic
88C3×#117—61no—
89C2×C3×C4⋊C4—31no—
90#944—21no—
91C2×#216—61no—
92C2×#216—62no—
93C2×#216—61no—
94C2×#216—61no—
95C2×C4⋊Dic3—61no—
96#924C2×D311yescharacteristic
97C2×Dic3⋊C4—61no—
98C2×Dic3⋊C4C2×D311yescharacteristic
99C2×Dic12—61no—
100#889—21no—
101#889—21no—
102#888—21no—
103#878—21no—
104#877—21no—
105C3×C22⋊C8—31no—
106C3×#95—31no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95C2×D311yescharacteristic
110#830—31no—
111#830—31no—
112#830—61no—
113#830C2×D311yescharacteristic
114#816—61no—
115#810—61no—
116#810—62no—
117#810—61no—
118#810—61no—
119C23×C32C2×D411yescharacteristic
120C32×Q8—41no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—41no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129#634—22no—
130#634—22no—
131#634—41no—
132#634—41no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3Q1612yescomplemented
143C3×Dic6—41no—
144C3×Dic6—81no—
145C3⋊(C3⋊C8)—41no—
146C3×C3⋊C8—41no—
147#544—31no—
148#451—91no—
149#451—91no—
150#395—91no—
151#328—31no—
152#328—91no—
153#324—91no—
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—31no—
162C22×C3×C4—61no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C22×Dic3—21no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—121no—
169C22×Dic3#6711yescharacteristic
170C22×Dic3#6711yescharacteristic
171C2×Dic6—21no—
172C2×Dic6—62no—
173C2×Dic6—61no—
174C2×Dic6—61no—
175C2×Dic6—61no—
176C2×Dic6—61no—
177C2×Dic6—121no—
178C2×Dic6—122no—
179C2×Dic6—122no—
180C2×Dic6—124no—
181C2×Dic6#6711yescharacteristic
182C2×C3×C8—61no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—31no—
187C3×C4⋊C4—41no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4D1211yescharacteristic
197C3×C4⋊C4#6711yescharacteristic
198C3×C22⋊C4—21no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—41no—
201C3×C22⋊C4—61no—
202C3×C42—61no—
203C3×C42—61no—
204#217—21no—
205#216—122no—
206#216—122no—
207#216—122no—
208#216—124no—
209C4⋊Dic3—21no—
210C4⋊Dic3—122no—
211C4⋊Dic3#6711yescharacteristic
212Dic3⋊C4—21no—
213Dic3⋊C4—21no—
214Dic3⋊C4—21no—
215Dic3⋊C4—21no—
216Dic3⋊C4—21no—
217Dic3⋊C4—21no—
218Dic3⋊C4—21no—
219Dic3⋊C4—122no—
220C4×Dic3—21no—
221C4×Dic3—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226Dic12—122no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32#12011yescharacteristic
230C22×C32C2×Q1611yescharacteristic
231C22×C32#13711yescharacteristic
232C32×C4—21no—
233C32×C4—21no—
234C32×C4—41no—
235C32×C4—41no—
236C3⋊Dic3—42no—
237C3×Dic3—22no—
238C3×Dic3—42no—
239C3×Dic3—41no—
240C3×Dic3—41no—
241C3×Dic3—41no—
242C22×Q8—91no—
243C2×Q16—181no—
244C2×Q16—181no—
245C4⋊Q8—61no—
246C4⋊Q8—61no—
247#125—61no—
248#125—61no—
249C22⋊Q8—31no—
250C22⋊Q8—61no—
251C22⋊Q8D3211yescharacteristic
252#117—61no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—181no—
255#103—181no—
256#103—181no—
257C22⋊C8—31no—
258C22⋊C8—91no—
259#95—31no—
260#95—181no—
261C23×C3—21no—
262C23×C3D3×D411yescharacteristic
263C23×C3C2×#6711yescharacteristic
264C3×Q8—41no—
265C3×Q8—41no—
266C3×Q8—42no—
267C3×Q8—121no—
268C3×Q8—241no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—32no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—42no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—62no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4C2×D1211yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3—22no—
297C2×Dic3—21no—
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—122no—
310C2×Dic3—121no—
311C2×Dic3—121no—
312C2×Dic3#21612yescomplemented
313Dic6—41no—
314Dic6—62no—
315Dic6—64no—
316Dic6—62no—
317Dic6—62no—
318Dic6—62no—
319Dic6—81no—
320Dic6—122no—
321Dic6—122no—
322Dic6—121no—
323Dic6—121no—
324Dic6—121no—
325Dic6—121no—
326Dic6—122no—
327C3×C8—121no—
328C3⋊C8—41no—
329C3⋊C8—122no—
330C3⋊C8—121no—
331C3⋊C8—121no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32#45111yescharacteristic
335C2×C32#45611yescharacteristic
336C2×C32B(4,𝔽2)11yescharacteristic
337C2×Q8—31no—
338C2×Q8—61no—
339C2×Q8—181no—
340C2×Q8—181no—
341C2×Q8—362no—
342C2×Q8#62611yescharacteristic
343C22×C4—31no—
344C22×C4—31no—
345C22×C4—61no—
346C22×C4—181no—
347C22×C4C2×D3211yescharacteristic
348Q16—362no—
349Q16—362no—
350C2×C8—61no—
351C2×C8—181no—
352C4⋊C4—21no—
353C4⋊C4—31no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—362no—
363C4⋊C4#62611yescharacteristic
364C22⋊C4—21no—
365C22⋊C4—61no—
366C42—61no—
367C42—61no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3#88211yescharacteristic
378C22×C3#91511yescharacteristic
379C22×C3D3×Q1611yescharacteristic
380C22×C3#94211yescharacteristic
381C22×C3C2×#21611yescharacteristic
382C22×C3#95311yescharacteristic
383C3×C4—22no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—41no—
393C3×C4—62no—
394C3×C4—81no—
395C3×C4—81no—
396C3×C4—122no—
397C3×C4—121no—
398C3×C4—121no—
399C3×C4—121no—
400Dic3—22no—
401Dic3—42no—
402Dic3—41no—
403Dic3—41no—
404Dic3—41no—
405Dic3—124no—
406Dic3—122no—
407Dic3—122no—
408C32#160511yescharacteristic, complemented, Sylow
409C23D3×#6711yescharacteristic
410Q8—41no—
411Q8—121no—
412Q8—182no—
413Q8—182no—
414Q8—241no—
415Q8—361no—
416Q8—361no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—32no—
420C2×C4—41no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—62no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4—121no—
430C2×C4—182no—
431C2×C4—361no—
432C2×C4—361no—
433C2×C4C2×#62611yescharacteristic
434C2×C4D3×#6711yescharacteristic
435C8—121no—
436C8—361no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—41no—
445C2×C3—41no—
446C2×C3#474111yescharacteristic
447C2×C3#480911yescharacteristic
448C2×C3#482611yescharacteristic
449C2×C3#522811yescharacteristic
450C2×C3#524411yescharacteristic
451C2×C3#524611yescharacteristic
452C22—21no—
453C22—21no—
454C22D3×#21611yescharacteristic
455C22#6394611yescharacteristic
456C22#6397711yescharacteristic
457C4—21no—
458C4—21no—
459C4—41no—
460C4—41no—
461C4—62no—
462C4—122no—
463C4—121no—
464C4—121no—
465C4—121no—
466C4—362no—
467C3—21no—
468C3#6832711yescharacteristic, complemented
469C3#7190411yescharacteristic, complemented
470C2—21no—
471C2—21no—
472C2#1059153111yescharacteristic
473C2#1059159511yescharacteristic
474C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC22⋊Q8D32
hypocenterC32#1605
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
142. C2×C3×Dic3Q16semidirect
312. C2×Dic3#216semidirect
408. C32#1605semidirect
468. C3#68327semidirect
469. C3#71904semidirect

Maximal subgroups

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

subgroupindex
C3×#56232
#105927492
#105913542
#105911902
C3×#45382
#105891532
#105891472
#719043
#683273