Finite Group Databasebeta

← #11775609

Subgroups — #11775609

Order 1152.

737 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 737 conjugacy classes of subgroups — too many to draw. Only its 102 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⋊D3×C22⋊Q8C211yesmaximal, characteristic
2#10591355C211yesmaximal, characteristic
3#10591152C211yesmaximal, characteristic
4C3×#4538C212yesmaximal, complemented
5#10589154C212yesmaximal, complemented
6#68339—32nomaximal
7C2×Q8×C3⋊D3C411yescharacteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C32×C22⋊Q8C2211yescharacteristic
10#64155C411yescharacteristic, complemented
11#64133C2211yescharacteristic
12#64106C411yescharacteristic, complemented
13#64105—21no—
14C4⋊C4×C3⋊D3—21no—
15C4⋊C4×C3⋊D3C411yescharacteristic, complemented
16C22⋊C4×C3⋊D3—21no—
17#64087—21no—
18C2×#3724—21no—
19C2×#3722—21no—
20C2×#3710—21no—
21C3×C3⋊#95C2212yes—
22C3×#830C2212yes—
23#63557—21no—
24D3×C22⋊Q8—32no—
25D3×C22⋊Q8—61no—
26D3×C22⋊C8—32no—
27#4667—32no—
28C3×#328—32no—
29#4538D312yescomplemented
30#4467—32no—
31#4452—32no—
32C23×C3⋊D3D411yescharacteristic
33C2×C32×Q8C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36Q8×C3⋊D3—42no—
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—42no—
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3C2×C411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×#634—21no—
45C2×#634C2×C411yescharacteristic
46C22×C3×Dic3—22no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50#3757—21no—
51#3752—21no—
52#3752—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56#3750—21no—
57#3750—21no—
58C2×C3×C3⋊C8—22no—
59#3724—42no—
60#3722—42no—
61#3710—42no—
62#1520—91noSylow
63C2×D3×Q8—32no—
64C2×D3×Q8—61no—
65C22×C4×D3—32no—
66C22×C4×D3—61no—
67C3×C22⋊Q8—21no—
68C3×C22⋊Q8C2×D312yes—
69#946—32no—
70#946—61no—
71C2×(C2×D3)⋊C4—62no—
72#924—32no—
73#924—61no—
74C2×Dic3⋊C4—62no—
75C2×D3×C8—62no—
76#897—32no—
77#897—61no—
78#896—62no—
79#896—62no—
80D3×C4⋊C4—32no—
81D3×C4⋊C4—61no—
82D3×C4⋊C4—62no—
83D3×C4⋊C4—62no—
84D3×C22⋊C4—62no—
85D3×C22⋊C4—62no—
86#878—62no—
87#878—62no—
88C3×C22⋊C8—32no—
89C3×#95—32no—
90C3⋊#95C2×D312yes—
91#830C2×D312yes—
92(C2×D3)⋊C8—62no—
93C23×C32C2×D411yescharacteristic
94C22×C3⋊D3—41no—
95C22×C3⋊D3—41no—
96C22×C3⋊D3C22⋊C411yescharacteristic
97C22×C3⋊D3C22⋊C411yescharacteristic
98C22×C3⋊D3SD1612yes—
99C22×C3⋊D3Q1612yes—
100C32×Q8—41no—
101C2×C32×C4—21no—
102C2×C32×C4—21no—
103C2×C32×C4—41no—
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111C4×C3⋊D3—22no—
112C4×C3⋊D3—22no—
113C4×C3⋊D3—41no—
114C4×C3⋊D3—41no—
115C4×C3⋊D3—42no—
116C4×C3⋊D3—42no—
117#634—42no—
118#634—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—42no—
122C3×C3⋊C8—42no—
123C2×C22⋊Q8—91no—
124C2×C22⋊C8—91no—
125#380—91no—
126#328—32no—
127#328—92no—
128C23×D3—32no—
129C23×D3—61no—
130C2×C3×Q8—21no—
131C2×C3×Q8C4×D312yes—
132C22×C3×C4—21no—
133C22×C3×C4—62no—
134C22×C3×C4C22×D312yes—
135C22×Dic3—22no—
136C22×Dic3—32no—
137C22×Dic3—61no—
138D3×Q8—124no—
139D3×Q8—124no—
140C2×C4×D3—32no—
141C2×C4×D3—32no—
142C2×C4×D3—32no—
143C2×C4×D3—32no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—124no—
153C2×C4×D3—124no—
154C2×Dic6—32no—
155C2×Dic6—61no—
156C2×Dic6—62no—
157C2×Dic6—62no—
158C2×C3×C8—62no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4C4×D312yes—
163C3×C22⋊C4—22no—
164C3×C22⋊C4—22no—
165#217—62no—
166#217—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—62no—
170(C2×D3)⋊C4—62no—
171(C2×D3)⋊C4—124no—
172C4⋊Dic3—32no—
173C4⋊Dic3—61no—
174C4⋊Dic3—62no—
175C4⋊Dic3—62no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181Dic3⋊C4—62no—
182Dic3⋊C4—124no—
183C2×C3⋊C8—22no—
184D3×C8—124no—
185C22×C32—21no—
186C22×C32—21no—
187C22×C32C2×C22⋊C411yescharacteristic
188C22×C32C2×SD1611yescharacteristic
189C22×C32C2×Q1611yescharacteristic
190C2×C3⋊D3—21no—
191C2×C3⋊D3—21no—
192C2×C3⋊D3—21no—
193C2×C3⋊D3—21no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—42no—
196C2×C3⋊D3#10312yes—
197C2×C3⋊D3#10312yes—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4—41no—
201C32×C4—41no—
202C3⋊Dic3—21no—
203C3⋊Dic3—41no—
204C3⋊Dic3—41no—
205C3⋊Dic3#9912yes—
206C3×Dic3—82no—
207C22×Q8—91no—
208C23×C4—91no—
209C22×C8—181no—
210C22⋊Q8—91no—
211C22⋊Q8—91no—
212C22⋊Q8—91no—
213C22⋊Q8—181no—
214C22⋊Q8—181no—
215C22⋊Q8D3211yescharacteristic
216C2×C4⋊C4—91no—
217C2×C4⋊C4—181no—
218C2×C4⋊C4—181no—
219C2×C22⋊C4—181no—
220C2×C22⋊C4—181no—
221C22⋊C8—32no—
222C22⋊C8—181no—
223#95—32no—
224C23×C3—21no—
225C23×C3D3×D412yes—
226C22×D3—32no—
227C22×D3—32no—
228C22×D3—34no—
229C22×D3—34no—
230C22×D3—61no—
231C22×D3—61no—
232C22×D3—62no—
233C22×D3—62no—
234C22×D3—122no—
235C22×D3—122no—
236C22×D3—122no—
237C22×D3—122no—
238C3×Q8—42no—
239C3×Q8—42no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—42no—
247C2×C3×C4—42no—
248C2×C3×C4—122no—
249C2×C3×C4—122no—
250C2×C3×C4—122no—
251C2×C3×C4C2×C4×D312yes—
252C2×C3×C4D3×D412yes—
253C2×Dic3—32no—
254C2×Dic3—32no—
255C2×Dic3—42no—
256C2×Dic3—42no—
257C2×Dic3—42no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—64no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—122no—
266C4×D3—64no—
267C4×D3—64no—
268C4×D3—64no—
269C4×D3—122no—
270C4×D3—122no—
271C4×D3—122no—
272C4×D3—122no—
273C4×D3—124no—
274C4×D3—124no—
275C4×D3—122no—
276C4×D3—124no—
277C4×D3—124no—
278Dic6—124no—
279Dic6—124no—
280Dic6—122no—
281Dic6—122no—
282C3×C8—122no—
283C3⋊C8—42no—
284C2×C32—21no—
285C2×C32—21no—
286C2×C32C2×#9911yescharacteristic
287C2×C32C2×#10311yescharacteristic
288C2×C32#42111yescharacteristic
289C3⋊D3—22no—
290C3⋊D3—22no—
291C24—91no—
292C2×Q8—91no—
293C2×Q8—181no—
294C2×Q8—362no—
295C2×Q8#62411yescharacteristic
296C22×C4—62no—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—181no—
303C22×C4—181no—
304C22×C4—362no—
305C22×C4C2×D3211yescharacteristic
306C2×C8—62no—
307C2×C8—362no—
308C4⋊C4—21no—
309C4⋊C4—91no—
310C4⋊C4—181no—
311C4⋊C4—181no—
312C4⋊C4—181no—
313C4⋊C4—181no—
314C4⋊C4—362no—
315C4⋊C4#62411yescharacteristic
316C22⋊C4—21no—
317C22⋊C4—181no—
318C22⋊C4—181no—
319C22⋊C4—181no—
320C22⋊C4—362no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3D3×C22⋊C412yes—
329C22×C3D3×SD1612yes—
330C22×C3D3×Q1612yes—
331C2×D3—34no—
332C2×D3—34no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—62no—
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—62no—
339C2×D3—62no—
340C2×D3—62no—
341C2×D3—121no—
342C2×D3—121no—
343C2×D3—124no—
344C2×D3—124no—
345C2×D3—124no—
346C2×D3—124no—
347C3×C4—22no—
348C3×C4—22no—
349C3×C4—22no—
350C3×C4—41no—
351C3×C4—42no—
352C3×C4—42no—
353C3×C4—42no—
354C3×C4—42no—
355C3×C4—242no—
356Dic3—34no—
357Dic3—62no—
358Dic3—62no—
359Dic3—82no—
360Dic3—121no—
361Dic3—122no—
362Dic3—122no—
363Dic3—122no—
364Dic3—122no—
365C32#152011yescharacteristic, complemented, Sylow
366C23—91no—
367C23—91no—
368C23—92no—
369C23—92no—
370C23—361no—
371C23—361no—
372C23#381111yescharacteristic
373Q8—41no—
374Q8—361no—
375Q8—362no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—91no—
380C2×C4—91no—
381C2×C4—122no—
382C2×C4—122no—
383C2×C4—122no—
384C2×C4—182no—
385C2×C4—182no—
386C2×C4—182no—
387C2×C4—181no—
388C2×C4—181no—
389C2×C4—361no—
390C2×C4—361no—
391C2×C4—362no—
392C2×C4—362no—
393C2×C4C2×#62411yescharacteristic
394C2×C4#381111yescharacteristic
395C8—122no—
396C2×C3—22no—
397C2×C3—22no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—41no—
402C2×C3—41no—
403C2×C3D3×#9912yes—
404C2×C3D3×#10312yes—
405C2×C3#482112yes—
406D3—64no—
407D3—64no—
408D3—64no—
409D3—122no—
410C22—21no—
411C22—21no—
412C22—92no—
413C22—92no—
414C22—181no—
415C22—181no—
416C22—181no—
417C22—181no—
418C22—362no—
419C22—362no—
420C22#6394011yescharacteristic
421C22#6394411yescharacteristic
422C22#6397411yescharacteristic
423C4—21no—
424C4—21no—
425C4—41no—
426C4—41no—
427C4—92no—
428C4—181no—
429C4—242no—
430C4—361no—
431C4—361no—
432C3—21no—
433C3#6833912yescomplemented
434C2—21no—
435C2—21no—
436C2—182no—
437C2—182no—
438C2#1059152711yescharacteristic
439C2#1059155211yescharacteristic
440C2#1059167211yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1520
LCSG ▷ C2×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
4. C3×#4538C2semidirect
5. #10589154C2semidirect
7. C2×Q8×C3⋊D3C4semidirect
10. #64155C4semidirect
12. #64106C4semidirect
15. C4⋊C4×C3⋊D3C4semidirect
29. #4538D3semidirect
365. C32#1520semidirect
433. C3#68339semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
#105913552
#105911522
C3×#45382
#105891542
#683393