Finite Group Databasebeta

← #11788354

Subgroups — #11788354

Order 1152.

837 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 837 conjugacy classes of subgroups — too many to draw. Only its 134 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
1C2×#64106C211yesmaximal, characteristic
2C2×#63818C211yesmaximal, characteristic
3C2×#63561C212yesmaximal, complemented
4#10591074C211yesmaximal, characteristic
5C3×#4530C212yesmaximal, complemented
6#68993—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#634C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3752C412yes—
11C2×C4⋊(C3⋊Dic3)C412yes—
12#64106—21no—
13#64106—21no—
14#64106—21no—
15#64106—21no—
16C2×C3×#208C2212yes—
17C2×C3×#208C2212yes—
18C2×#3712—21no—
19#63818—24no—
20C2×#3710—21no—
21#63561—24no—
22#63557—21no—
23#63557—21no—
24C2×D3×M16—32no—
25C2×#897—32no—
26C2×#897—61no—
27C2×#824—32no—
28C2×#824—32no—
29#5126—32no—
30C3×#343—32no—
31#4530D312yescomplemented
32C23×C3⋊D3C2×C411yescharacteristic
33C22×C32×C4C2×C412yes—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3C2×C412yes—
36C22×C3⋊Dic3C2×C411yescharacteristic
37C2×C4×C3⋊D3—22no—
38C2×C4×C3⋊D3—22no—
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×#634—21no—
44C2×#634—21no—
45C2×#634—22no—
46C2×#634—22no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49#3752—22no—
50#3752—22no—
51C4⋊(C3⋊Dic3)—22no—
52C4⋊(C3⋊Dic3)—22no—
53C3×#208—22no—
54C3×#208—22no—
55C3×#208—22no—
56C3×#208D414yes—
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8—22no—
59#3712—24no—
60#3710—24no—
61#1901—91noSylow
62C22×C4×D3—32no—
63C22×C4×D3—61no—
64C22×Dic6—32no—
65C22×Dic6—61no—
66C2×C3×M16—32no—
67C2×C3×M16—32no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4C2×D312yes—
70C2×(C2×D3)⋊C4—34no—
71C2×(C2×D3)⋊C4—62no—
72C2×C4⋊Dic3—34no—
73C2×C4⋊Dic3—62no—
74C2×#208C2×D312yes—
75C2×#208C2×D312yes—
76D3×M16—64no—
77D3×M16—64no—
78C2×ΓL(1,𝔽25)—62no—
79C2×D3×C8—62no—
80#897—62no—
81#897—62no—
82#897—62no—
83#897—62no—
84#897—62no—
85#897—62no—
86#897—62no—
87#897—62no—
88#824—64no—
89#824—64no—
90(C2×D3)⋊C8—62no—
91(C2×D3)⋊C8—62no—
92C23×C32C22×C411yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—22no—
95C22×C3⋊D3—41no—
96C22×C3⋊D3C22⋊C411yescharacteristic
97C22×C3⋊D3C22⋊C411yescharacteristic
98C2×C32×C4—22no—
99C2×C32×C4—42no—
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4112yes—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C4×C3⋊D3—21no—
110C4×C3⋊D3—21no—
111C4×C3⋊D3—22no—
112C4×C3⋊D3—22no—
113C4×C3⋊D3—21no—
114C4×C3⋊D3—21no—
115#634—41no—
116#634—42no—
117#634—41no—
118C3×C3⋊C8—24no—
119C3×C3⋊C8—42no—
120C22×M16—91no—
121C2×C22⋊Q8—91no—
122C2×#101—92no—
123#407—91no—
124#343—32no—
125C23×D3—32no—
126C23×D3—61no—
127C22×C3×C4—22no—
128C22×C3×C4—21no—
129C22×C3×C4C4×D314yes—
130C22×C3×C4C22×D312yes—
131C22×Dic3—32no—
132C22×Dic3—34no—
133C22×Dic3—61no—
134C22×Dic3—62no—
135C2×C4×D3—32no—
136C2×C4×D3—32no—
137C2×C4×D3—32no—
138C2×C4×D3—32no—
139C2×C4×D3—61no—
140C2×C4×D3—61no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×C4×D3—62no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—122no—
148C2×C4×D3—122no—
149C2×Dic6—62no—
150C2×Dic6—62no—
151C2×Dic6—62no—
152C2×Dic6—62no—
153C2×Dic6—62no—
154C2×Dic6—62no—
155C2×Dic6—62no—
156C2×Dic6—62no—
157C2×Dic6—122no—
158C2×Dic6—122no—
159C3×M16—34no—
160C3×M16—62no—
161C3×M16—62no—
162C3×M16—62no—
163C2×C3×C8—62no—
164C2×C3×C8—62no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—22no—
169(C2×D3)⋊C4—64no—
170(C2×D3)⋊C4—64no—
171(C2×D3)⋊C4—64no—
172(C2×D3)⋊C4—64no—
173C4⋊Dic3—64no—
174C4⋊Dic3—64no—
175C4⋊Dic3—64no—
176C4⋊Dic3—64no—
177#208—22no—
178#208—22no—
179#208—22no—
180#208D1214yes—
181C2×C3⋊C8—22no—
182C2×C3⋊C8—22no—
183ΓL(1,𝔽25)—68no—
184D3×C8—68no—
185C22×C32—21no—
186C22×C32—21no—
187C22×C32C2×C22⋊C411yescharacteristic
188C22×C32C4×D412yes—
189C2×C3⋊D3—21no—
190C2×C3⋊D3—21no—
191C2×C3⋊D3—21no—
192C2×C3⋊D3—21no—
193C2×C3⋊D3—21no—
194C2×C3⋊D3—44no—
195C2×C3⋊D3#10112yescomplemented
196C32×C4—42no—
197C32×C4#12011yescharacteristic
198C32×C4#12112yes—
199C32×C4#12311yescharacteristic
200C3⋊Dic3—21no—
201C3⋊Dic3—21no—
202C3⋊Dic3—42no—
203C22×Q8—91no—
204C23×C4—91no—
205C2×M16—32no—
206C2×M16—32no—
207C2×M16—181no—
208C2×M16—184no—
209C22×C8—181no—
210C22⋊Q8—181no—
211C22⋊Q8—181no—
212C22⋊Q8—181no—
213C22⋊Q8—181no—
214C2×C4⋊C4—92no—
215C2×C4⋊C4D3211yescharacteristic
216C2×C22⋊C4—92no—
217#101—184no—
218C22⋊C8—181no—
219C22⋊C8—181no—
220C23×C3—21no—
221C23×C3C2×C4×D312yes—
222C22×D3—32no—
223C22×D3—32no—
224C22×D3—61no—
225C22×D3—61no—
226C22×D3—64no—
227C22×D3—64no—
228C22×D3—62no—
229C22×D3—62no—
230C22×D3—122no—
231C22×D3—122no—
232C22×D3—122no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—44no—
240C2×C3×C4—44no—
241C2×C3×C4C2×D1212yes—
242C2×C3×C4#23512yes—
243C2×C3×C4D3×D412yes—
244C2×C3×C4D3×D412yes—
245C2×C3×C4D3×D412yes—
246C2×C3×C4#23912yes—
247C2×Dic3—32no—
248C2×Dic3—32no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—64no—
254C2×Dic3—64no—
255C2×Dic3—64no—
256C2×Dic3—64no—
257C2×Dic3—124no—
258C2×Dic3—122no—
259C4×D3—62no—
260C4×D3—62no—
261C4×D3—62no—
262C4×D3—62no—
263C4×D3—62no—
264C4×D3—62no—
265C4×D3—62no—
266C4×D3—62no—
267C4×D3—121no—
268C4×D3—121no—
269C4×D3—122no—
270C4×D3—122no—
271C4×D3—121no—
272C4×D3—121no—
273Dic6—122no—
274Dic6—124no—
275Dic6—122no—
276Dic6—122no—
277Dic6—122no—
278Dic6—122no—
279Dic6—122no—
280C3×C8—64no—
281C3×C8—122no—
282C3⋊C8—24no—
283C3⋊C8—42no—
284C2×C32—22no—
285C2×C32#38611yescharacteristic
286C2×C32C2×#10111yescharacteristic
287C2×C32#41311yescharacteristic
288C3⋊D3—22no—
289C3⋊D3—41no—
290C24—91no—
291C2×Q8—182no—
292C2×Q8—182no—
293C2×Q8—181no—
294C2×Q8—181no—
295C22×C4—91no—
296C22×C4—91no—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—92no—
301C22×C4—182no—
302C22×C4—182no—
303C22×C4#62412yes—
304C22×C4C2×D3211yescharacteristic
305M16—34no—
306M16—62no—
307M16—62no—
308M16—62no—
309M16—184no—
310C2×C8—62no—
311C2×C8—62no—
312C2×C8—184no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—182no—
316C4⋊C4—182no—
317C22⋊C4—182no—
318C22⋊C4—182no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3C4×D1212yes—
326C22×C3D3×C22⋊C412yes—
327C22×C3#89312yes—
328C2×D3—34no—
329C2×D3—62no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—62no—
336C2×D3—121no—
337C2×D3—121no—
338C2×D3—121no—
339C2×D3—121no—
340C2×D3—124no—
341C2×D3—124no—
342C2×D3—128no—
343C3×C4—21no—
344C3×C4—22no—
345C3×C4—21no—
346C3×C4—44no—
347C3×C4—44no—
348C3×C4#88212yes—
349C3×C4#88412yes—
350C3×C4#89412yes—
351C3×C4#89512yes—
352Dic3—62no—
353Dic3—62no—
354Dic3—121no—
355Dic3—121no—
356Dic3—124no—
357Dic3—124no—
358C32#190111yescharacteristic, complemented, Sylow
359C23—91no—
360C23—91no—
361C23—182no—
362C23—182no—
363C23—361no—
364C23C2×#62411yescharacteristic
365Q8—361no—
366Q8—362no—
367Q8—361no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—91no—
371C2×C4—91no—
372C2×C4—182no—
373C2×C4—181no—
374C2×C4—181no—
375C2×C4—182no—
376C2×C4—182no—
377C2×C4—181no—
378C2×C4—181no—
379C2×C4—184no—
380C2×C4—182no—
381C2×C4#379912yes—
382C2×C4D3×D1212yes—
383C2×C4#381111yescharacteristic
384C2×C4#381111yescharacteristic
385C8—64no—
386C8—122no—
387C2×C3—24no—
388C2×C3—22no—
389C2×C3—22no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3#466512yes—
394C2×C3#474512yes—
395C2×C3D3×#10112yes—
396D3—64no—
397D3—122no—
398D3—122no—
399D3—122no—
400C22—21no—
401C22—21no—
402C22—92no—
403C22—181no—
404C22—181no—
405C22—181no—
406C22—181no—
407C22—181no—
408C22—364no—
409C22#6389412yes—
410C22#6397411yescharacteristic
411C4—42no—
412C4—181no—
413C4—181no—
414C4—362no—
415C4#6389711yescharacteristic
416C4#6391012yes—
417C4#6392311yescharacteristic
418C3—21no—
419C3#6899312yescomplemented
420C2—22no—
421C2—182no—
422C2—361no—
423C2#1059138011yescharacteristic
424C2#1059150411yescharacteristic
425C2#1059163911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1901
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63561C2semidirect
5. C3×#4530C2semidirect
31. #4530D3semidirect
195. C2×C3⋊D3#101semidirect
358. C32#1901semidirect
419. C3#68993semidirect

Maximal subgroups

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

subgroupindex
C2×#641062
C2×#638182
C2×#635612
#105910742
C3×#45302
#689933