Finite Group Databasebeta

← #11789921

Subgroups — #11789921

Order 1152.

498 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 73 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×#63777C211yesmaximal, characteristic, complemented
2C2×#63739C211yesmaximal, characteristic
3C2×#63739C211yesmaximal, characteristic
4#10591385C211yesmaximal, characteristic
5#10591328C211yesmaximal, characteristic, complemented
6#10590075C211yesmaximal, characteristic, complemented
7#10590075C211yesmaximal, characteristic, complemented
8C22×#625C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4—21no—
13C2×#3724C2211yescharacteristic
14C2×#3724C2211yescharacteristic
15C2×#3724C2211yescharacteristic
16C2×Dic3⋊Dic3—21no—
17C2×(C2×D3)⋊Dic3—21no—
18#63777—22no—
19#63739—22no—
20#63739C414yescomplemented
21C3×C3⋊#95—21no—
22#4957—61no—
23#4647—61no—
24C23×C3×D3—21no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C22×C3×Dic3—21no—
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C2×#625—21no—
32C2×#625—21no—
33C2×#625—21no—
34C2×#625—21no—
35C2×#625—21no—
36C2×#625C2×C412yes—
37C2×#622—21no—
38C2×#622—21no—
39C2×#622—21no—
40C2×#622—21no—
41C2×#622C2×C412yes—
42C2×#622D412yes—
43C4×C3⋊Dic3—21no—
44C4×C3⋊Dic3—21no—
45C3×(C2×D3)⋊C4—42no—
46#3724—21no—
47#3724—21no—
48#3724—21no—
49#3724—21no—
50#3724—21no—
51#3724C2×C412yes—
52Dic3⋊Dic3—42no—
53(C2×D3)⋊Dic3—42no—
54#1936—91nomaximal, Sylow
55C22×#67—61no—
56C2×C3×C22⋊C4—61no—
57C2×#217—61no—
58C2×(C2×D3)⋊C4—21no—
59C2×(C2×D3)⋊C4—61no—
60C2×C4⋊Dic3—61no—
61C2×Dic3⋊C4—61no—
62C2×Dic3⋊C4—61no—
63C2×Dic3⋊C4—61no—
64C2×Dic3⋊C4—61no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3—61no—
67C3×#95—61no—
68C3⋊#95—21no—
69C23×C32C2×D411yescharacteristic
70C22×C3×D3—22no—
71C22×C3×D3—41no—
72C22×C3×D3—41no—
73C22×C3×D3—41no—
74C22×C3×D3—41no—
75C22×C3×D3—41no—
76C22×C3×D3—41no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3C22×C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C2×C3⋊Dic3#4111yescharacteristic
86C2×C3⋊Dic3#4111yescharacteristic
87C2×C3⋊Dic3#4111yescharacteristic
88C2×C3⋊Dic3#4111yescharacteristic
89C2×C3×Dic3—22no—
90C2×C3×Dic3—41no—
91C2×C3×Dic3—41no—
92C2×C3×Dic3—41no—
93C2×C3×Dic3—41no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98#625—22no—
99#625—22no—
100#625—41no—
101#625—41no—
102#622—22no—
103#622—22no—
104C2×#102—91no—
105C2×#102—91no—
106C2×#97—91no—
107#390—91no—
108#389—91no—
109#340—91no—
110#340—91no—
111C24×C3—61no—
112C23×D3—21no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—61no—
116C22×C3×C4—61no—
117C22×C3×C4—61no—
118C2×#67—62no—
119C2×#67—62no—
120C2×#67—121no—
121C2×#67—121no—
122C2×#67—121no—
123C2×#67—121no—
124C22×Dic3—21no—
125C22×Dic3—21no—
126C22×Dic3—21no—
127C22×Dic3—61no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C3×C22⋊C4—122no—
132#217—122no—
133(C2×D3)⋊C4—42no—
134(C2×D3)⋊C4—122no—
135C4⋊Dic3—122no—
136Dic3⋊C4—62no—
137Dic3⋊C4—62no—
138Dic3⋊C4—121no—
139Dic3⋊C4—121no—
140Dic3⋊C4—121no—
141Dic3⋊C4—121no—
142Dic3⋊C4—122no—
143C4×Dic3—121no—
144C4×Dic3—121no—
145C4×Dic3—121no—
146C4×Dic3—121no—
147C22×C32C4×D411yescharacteristic
148C22×C32#12111yescharacteristic
149C22×C32#12411yescharacteristic
150C22×C32AGL(1,ℤ/8)11yescharacteristic
151C22×C32AGL(1,ℤ/8)11yescharacteristic
152C22×C32AGL(1,ℤ/8)11yescharacteristic
153C22×C32#13711yescharacteristic
154C2×C3×D3—42no—
155C2×C3×D3—42no—
156C2×C3×D3—42no—
157C2×C3×D3—81no—
158C2×C3×D3—81no—
159C2×C3×D3—81no—
160C2×C3×D3—81no—
161C32×C4—41no—
162C3⋊Dic3—41no—
163C3⋊Dic3#11711yescharacteristic
164C3⋊Dic3C4×D411yescharacteristic
165C3⋊Dic3#12311yescharacteristic
166C3⋊Dic3#12611yescharacteristic
167C3×Dic3—42no—
168C3×Dic3—81no—
169C3×Dic3—81no—
170C22×D4—91no—
171C22×C8—91no—
172C22×C8—91no—
173C2×C4⋊C4—91no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—181no—
177C2×C22⋊C4—61no—
178C2×C22⋊C4—181no—
179C2×C42—91no—
180#102—94no—
181#102—182no—
182#97—182no—
183#95—61no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—62no—
187C23×C3—121no—
188C23×C3—121no—
189C23×C3—121no—
190C23×C3—121no—
191C23×C3—121no—
192C23×C3—121no—
193C22×D3—22no—
194C22×D3—41no—
195C22×D3—41no—
196C22×D3—41no—
197C22×D3—41no—
198C22×D3—41no—
199C22×D3—41no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—62no—
207C2×C3×C4—121no—
208C2×C3×C4—121no—
209C2×C3×C4—121no—
210C2×C3×C4—121no—
211C2×C3×C4—121no—
212C2×C3×C4—121no—
213C2×C3×C4—121no—
214C2×C3×C4—121no—
215#67—122no—
216#67—122no—
217#67—122no—
218#67—122no—
219C2×Dic3—22no—
220C2×Dic3—41no—
221C2×Dic3—41no—
222C2×Dic3—41no—
223C2×Dic3—41no—
224C2×Dic3—41no—
225C2×Dic3—41no—
226C2×Dic3—41no—
227C2×Dic3—41no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3—61no—
231C2×Dic3—61no—
232C2×Dic3—61no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—121no—
243C2×Dic3—121no—
244C2×Dic3—121no—
245C2×Dic3—121no—
246C2×C32#38811yescharacteristic
247C2×C32#44011yescharacteristic
248C2×C32#44211yescharacteristic
249C2×C32#46811yescharacteristic
250C2×C32#46911yescharacteristic
251C2×C32#48911yescharacteristic
252C2×C32#49011yescharacteristic
253C3×D3—82no—
254C24—61no—
255C2×D4—92no—
256C2×D4—181no—
257C2×D4—181no—
258C2×D4—181no—
259C2×D4—181no—
260C2×D4—181no—
261C22×C4—61no—
262C22×C4—61no—
263C22×C4—61no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4GO+(4,𝔽2)11yescharacteristic
267C2×C8—92no—
268C2×C8—92no—
269C2×C8—181no—
270C2×C8—181no—
271C2×C8—181no—
272C2×C8—181no—
273C4⋊C4—92no—
274C4⋊C4—181no—
275C4⋊C4—181no—
276C4⋊C4—181no—
277C4⋊C4—181no—
278C4⋊C4—181no—
279C4⋊C4—362no—
280C22⋊C4—122no—
281C22⋊C4—362no—
282C42—181no—
283C42—181no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—122no—
299C22×C3—122no—
300C22×C3—122no—
301C22×C3—241no—
302C22×C3—241no—
303C22×C3—241no—
304C22×C3—241no—
305C2×D3—42no—
306C2×D3—42no—
307C2×D3—42no—
308C2×D3—81no—
309C2×D3—81no—
310C2×D3—81no—
311C2×D3—81no—
312C3×C4—42no—
313C3×C4—42no—
314C3×C4—122no—
315C3×C4—241no—
316C3×C4—241no—
317Dic3—42no—
318Dic3—61no—
319Dic3—61no—
320Dic3—61no—
321Dic3—61no—
322Dic3—61no—
323Dic3—61no—
324Dic3—61no—
325Dic3—61no—
326Dic3—81no—
327Dic3—81no—
328Dic3—122no—
329Dic3—122no—
330C32#193611yescharacteristic, complemented, Sylow
331C23—62no—
332C23—121no—
333C23—121no—
334C23—121no—
335C23—121no—
336C23—121no—
337C23—121no—
338C23C2×GO+(4,𝔽2)11yescharacteristic
339D4—182no—
340D4—182no—
341D4—361no—
342D4—361no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—62no—
347C2×C4—91no—
348C2×C4—91no—
349C2×C4—91no—
350C2×C4—91no—
351C2×C4—91no—
352C2×C4—91no—
353C2×C4—121no—
354C2×C4—121no—
355C2×C4—121no—
356C2×C4—121no—
357C2×C4—121no—
358C2×C4—121no—
359C2×C4—121no—
360C2×C4—121no—
361C2×C4—181no—
362C2×C4—181no—
363C2×C4—181no—
364C8—182no—
365C8—182no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—242no—
381D3—82no—
382C22—122no—
383C22—122no—
384C22—122no—
385C22—241no—
386C22—241no—
387C22—241no—
388C22—241no—
389C22#6422111yescharacteristic
390C22#6422411yescharacteristic
391C22#6422411yescharacteristic
392C22C4×GO+(4,𝔽2)11yescharacteristic
393C22#6423611yescharacteristic
394C22#6423911yescharacteristic
395C22#6424211yescharacteristic
396C4—41no—
397C4—91no—
398C4—91no—
399C4—91no—
400C4—91no—
401C4—122no—
402C4—241no—
403C4—241no—
404C4—361no—
405C3—21no—
406C3—21no—
407C2—242no—
408C2#1059335611yescharacteristic
409C2#1059336211yescharacteristic
410C2#1059340011yescharacteristic
411C2#1059341911yescharacteristic
412C2#1059342911yescharacteristic
413C2#1059343211yescharacteristic
414C2#1059349511yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#625C22
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1936
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
1. C2×#63777C2semidirect
5. #10591328C2semidirect
6. #10590075C2semidirect
7. #10590075C2semidirect
20. #63739C4semidirect
330. C32#1936semidirect

Maximal subgroups

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

subgroupindex
C2×#637772
C2×#637392
#105913852
#105913282
#105900752
#19369