Finite Group Databasebeta

← #11787328

Subgroups — #11787328

Order 1152.

878 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 878 conjugacy classes of subgroups — too many to draw. Only its 91 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×#63912C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic, complemented
3C2×#63778C211yesmaximal, characteristic, complemented
4C2×#63739C212yesmaximal, complemented
5#10590075C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#626—21no—
8C22×#625C2211yescharacteristic
9C22×#624—21no—
10C22×#622C2212yes—
11C2×C3×(C2×D3)⋊C4—21no—
12C2×C3×C4⋊Dic3—21no—
13C2×#3724C2211yescharacteristic
14C2×#3724C2212yes—
15#63912—22no—
16#63912C414yescomplemented
17#63900—24no—
18#63778—22no—
19#63739—24no—
20C2×D3×C4⋊C4—61no—
21C2×#884—61no—
22C23×C3⋊D3D411yescharacteristic
23C23×C3×D3—21no—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3C2×C412yes—
29C2×C4×C3⋊D3D412yes—
30C22×C3×Dic3—22no—
31C22×C3×Dic3—21no—
32C2×#626—24no—
33C2×#626—42no—
34C2×#626—42no—
35C2×#625—22no—
36C2×#625—22no—
37C2×#625—21no—
38C2×#625C2×C412yescomplemented
39C2×#624—24no—
40C2×#624—42no—
41C2×#624—42no—
42C2×#622—22no—
43C2×#622—22no—
44C2×#622—22no—
45C3×(C2×D3)⋊C4—24no—
46C3×C4⋊Dic3—24no—
47#3724—22no—
48#3724—21no—
49#3724C2×C412yescomplemented
50#3724D414yescomplemented
51#1874—91nomaximal, Sylow
52C22×#67—61no—
53C22×#67—61no—
54C22×D12—61no—
55C22×C4×D3—61no—
56C22×C4×D3—61no—
57C22×C4×D3—62no—
58C2×C3×C4⋊C4—61no—
59C2×C3×C22⋊C4—61no—
60C2×(C2×D3)⋊C4—21no—
61C2×C4⋊Dic3—21no—
62C2×Dic3⋊C4—61no—
63C2×Dic3⋊C4—62no—
64D3×C4⋊C4—68no—
65#884—64no—
66#884—64no—
67C23×C32C2×D411yescharacteristic
68C22×C3⋊D3—21no—
69C22×C3⋊D3—21no—
70C22×C3⋊D3—21no—
71C22×C3⋊D3—21no—
72C22×C3⋊D3C22⋊C412yes—
73C22×C3⋊D3D812yes—
74C22×C3⋊D3SD1612yes—
75C22×C3×D3—22no—
76C22×C3×D3—41no—
77C22×C3×D3—41no—
78C22×C3×D3—41no—
79C22×C3×D3—41no—
80C22×C3×D3—41no—
81C22×C3×D3—41no—
82C2×C32×C4—21no—
83C2×C32×C4—21no—
84C2×C32×C4C22⋊C412yes—
85C2×C3⋊Dic3C22×C411yescharacteristic
86C2×C3⋊Dic3C2×D412yes—
87C2×C3⋊Dic3C2×D411yescharacteristic
88C2×C3⋊Dic3#4112yes—
89C4×C3⋊D3—24no—
90C4×C3⋊D3—24no—
91C2×C3×Dic3—22no—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—42no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—42no—
97#626—48no—
98#625—24no—
99#625—42no—
100#624—48no—
101#622—42no—
102C2×#121—91no—
103C22×C4⋊C4—91no—
104C2×#102—92no—
105C2×C22⋊C8—91no—
106#340—92no—
107C24×C3—61no—
108C23×D3—21no—
109C23×D3—61no—
110C23×D3—61no—
111C22×C3×C4—21no—
112C22×C3×C4—21no—
113C22×C3×C4—61no—
114C22×C3×C4—62no—
115C2×#67—62no—
116C2×#67—64no—
117C2×#67—62no—
118C2×#67—122no—
119C2×#67—122no—
120C2×#67—122no—
121C2×#67—122no—
122C22×Dic3—22no—
123C22×Dic3—21no—
124C22×Dic3—61no—
125C22×Dic3—61no—
126C2×D12—64no—
127C2×D12—122no—
128C2×D12—122no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—62no—
132C2×C4×D3—62no—
133C2×C4×D3—64no—
134C2×C4×D3—64no—
135C2×C4×D3—68no—
136C2×C4×D3—122no—
137C2×C4×D3—122no—
138C2×C4×D3—124no—
139C2×C4×D3—124no—
140C3×C4⋊C4—64no—
141C3×C22⋊C4—64no—
142(C2×D3)⋊C4—24no—
143C4⋊Dic3—24no—
144Dic3⋊C4—62no—
145Dic3⋊C4—64no—
146Dic3⋊C4—62no—
147Dic3⋊C4—64no—
148C22×C32C2×C22⋊C411yescharacteristic
149C22×C32#12011yescharacteristic
150C22×C32#12311yescharacteristic
151C22×C32C2×D811yescharacteristic
152C22×C32C2×SD1611yescharacteristic
153C22×C32AGL(1,ℤ/8)11yescharacteristic
154C22×C32#13711yescharacteristic
155C2×C3⋊D3—22no—
156C2×C3⋊D3—22no—
157C2×C3⋊D3—22no—
158C2×C3⋊D3—22no—
159C2×C3⋊D3—22no—
160C2×C3⋊D3—22no—
161C2×C3⋊D3#10214yescomplemented
162C2×C3×D3—42no—
163C2×C3×D3—42no—
164C2×C3×D3—42no—
165C2×C3×D3—81no—
166C2×C3×D3—81no—
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C32×C4—22no—
170C3⋊Dic3C4×D412yes—
171C3⋊Dic3#12112yes—
172C3×Dic3—42no—
173C3×Dic3—44no—
174C22×D4—91no—
175C22×D4—181no—
176C23×C4—91no—
177C23×C4—181no—
178C22×C8—92no—
179#121—94no—
180#121—182no—
181C2×C4⋊C4—61no—
182C2×C4⋊C4—92no—
183C2×C4⋊C4—91no—
184C2×C4⋊C4—184no—
185C2×C22⋊C4—61no—
186#102—184no—
187C22⋊C8—182no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—62no—
191C23×C3—121no—
192C23×C3—121no—
193C23×C3—121no—
194C23×C3—121no—
195C23×C3—121no—
196C23×C3—121no—
197C22×D3—22no—
198C22×D3—41no—
199C22×D3—41no—
200C22×D3—41no—
201C22×D3—41no—
202C22×D3—41no—
203C22×D3—41no—
204C22×D3—62no—
205C22×D3—62no—
206C22×D3—62no—
207C22×D3—62no—
208C22×D3—62no—
209C22×D3—62no—
210C22×D3—62no—
211C22×D3—62no—
212C22×D3—62no—
213C22×D3—62no—
214C22×D3—121no—
215C22×D3—121no—
216C22×D3—121no—
217C22×D3—121no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—62no—
225C2×C3×C4—64no—
226C2×C3×C4—122no—
227C2×C3×C4—122no—
228C2×C3×C4—121no—
229C2×C3×C4—121no—
230#67—124no—
231#67—128no—
232#67—124no—
233C2×Dic3—24no—
234C2×Dic3—22no—
235C2×Dic3—42no—
236C2×Dic3—42no—
237C2×Dic3—41no—
238C2×Dic3—41no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—62no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247D12—128no—
248C4×D3—68no—
249C4×D3—68no—
250C4×D3—124no—
251C4×D3—124no—
252C4×D3—1216no—
253C2×C32#38611yescharacteristic
254C2×C32C2×#10211yescharacteristic
255C2×C32#41711yescharacteristic
256C2×C32#44711yescharacteristic
257C2×C32#44811yescharacteristic
258C2×C32#48011yescharacteristic
259C2×C32#48111yescharacteristic
260C3⋊D3—24no—
261C3×D3—82no—
262C24—61no—
263C24—91no—
264C2×D4—92no—
265C2×D4—184no—
266C2×D4—182no—
267C2×D4—182no—
268C2×D4—181no—
269C2×D4—362no—
270C2×D4—362no—
271C22×C4—61no—
272C22×C4—62no—
273C22×C4—91no—
274C22×C4—92no—
275C22×C4—92no—
276C22×C4—182no—
277C22×C4—182no—
278C22×C4—184no—
279C22×C4—362no—
280C22×C4—362no—
281C22×C4GO+(4,𝔽2)11yescharacteristic
282C2×C8—182no—
283C2×C8—182no—
284C2×C8—182no—
285C4⋊C4—64no—
286C4⋊C4—94no—
287C4⋊C4—92no—
288C4⋊C4—182no—
289C4⋊C4—181no—
290C22⋊C4—64no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—122no—
306C22×C3—122no—
307C22×C3—122no—
308C22×C3—241no—
309C22×C3—241no—
310C22×C3—241no—
311C22×C3—241no—
312C2×D3—42no—
313C2×D3—42no—
314C2×D3—42no—
315C2×D3—64no—
316C2×D3—64no—
317C2×D3—64no—
318C2×D3—64no—
319C2×D3—64no—
320C2×D3—64no—
321C2×D3—64no—
322C2×D3—64no—
323C2×D3—81no—
324C2×D3—81no—
325C2×D3—81no—
326C2×D3—81no—
327C2×D3—122no—
328C2×D3—122no—
329C2×D3—122no—
330C2×D3—122no—
331C2×D3—122no—
332C2×D3—122no—
333C3×C4—24no—
334C3×C4—42no—
335C3×C4—124no—
336C3×C4—122no—
337Dic3—44no—
338Dic3—42no—
339Dic3—62no—
340Dic3—62no—
341Dic3—62no—
342Dic3—62no—
343C32#187411yescharacteristic, complemented, Sylow
344C23—62no—
345C23—92no—
346C23—92no—
347C23—92no—
348C23—121no—
349C23—121no—
350C23—121no—
351C23—121no—
352C23—121no—
353C23—121no—
354C23—181no—
355C23—181no—
356C23—181no—
357C23—181no—
358C23C2×GO+(4,𝔽2)11yescharacteristic
359D4—184no—
360D4—362no—
361D4—368no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—62no—
365C2×C4—64no—
366C2×C4—91no—
367C2×C4—91no—
368C2×C4—92no—
369C2×C4—92no—
370C2×C4—122no—
371C2×C4—122no—
372C2×C4—121no—
373C2×C4—121no—
374C2×C4—184no—
375C2×C4—184no—
376C2×C4—368no—
377C2×C4D32⋊C412yes—
378C8—362no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—242no—
394D3—68no—
395D3—82no—
396D3—124no—
397C22—94no—
398C22—122no—
399C22—122no—
400C22—122no—
401C22—182no—
402C22—182no—
403C22—182no—
404C22—182no—
405C22—182no—
406C22—182no—
407C22—241no—
408C22—241no—
409C22—241no—
410C22—241no—
411C22#6422411yescharacteristic
412C22#6422511yescharacteristic
413C22#6422611yescharacteristic
414C22#6422711yescharacteristic
415C22C2×D32⋊C411yescharacteristic
416C22#6423311yescharacteristic
417C22#6424111yescharacteristic
418C4—22no—
419C4—92no—
420C4—92no—
421C4—122no—
422C4—124no—
423C3—21no—
424C3—21no—
425C2—184no—
426C2—242no—
427C2#1059336011yescharacteristic
428C2#1059336111yescharacteristic
429C2#1059336511yescharacteristic
430C2#1059336811yescharacteristic
431C2#1059342511yescharacteristic
432C2#1059343611yescharacteristic
433C2#1059351411yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC2×#63912C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1874
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63900C2semidirect
3. C2×#63778C2semidirect
4. C2×#63739C2semidirect
5. #10590075C2semidirect
16. #63912C4semidirect
38. C2×#625C2×C4semidirect
49. #3724C2×C4semidirect
50. #3724D4semidirect
161. C2×C3⋊D3#102semidirect
343. C32#1874semidirect

Maximal subgroups

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

subgroupindex
C2×#639122
C2×#639002
C2×#637782
C2×#637392
#105900752
#18749