Finite Group Databasebeta

← #11774009

Subgroups — #11774009

Order 1152.

731 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 731 conjugacy classes of subgroups — too many to draw. Only its 94 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×#64103C211yesmaximal, characteristic
2#10591159C211yesmaximal, characteristic, complemented
3#10591152C211yesmaximal, characteristic, complemented
4C3×#4528C212yesmaximal, complemented
5#10589146C212yesmaximal, complemented
6#68146—32nomaximal
7C22×C4⋊(C3⋊D3)C411yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3752C411yescharacteristic
11C2×#3752C411yescharacteristic
12C2×#3752C2211yescharacteristic
13C2×#3750C411yescharacteristic
14#64103—21no—
15#64103—21no—
16#64103—21no—
17#64103—21no—
18C2×#3712—21no—
19C2×#3710—21no—
20C3×#830C2212yes—
21C3×#830C2212yes—
22#63557—21no—
23#63557—21no—
24C2×#894—32no—
25C2×#894—61no—
26#4726—32no—
27D3×C22⋊C8—32no—
28C3×#324—32no—
29#4528D312yescomplemented
30#4468—32no—
31#4468—32no—
32C23×C3⋊D3C2×C411yescharacteristic
33C23×C3⋊D3C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C22×C3⋊Dic3C2×C411yescharacteristic
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—42no—
42C2×C4×C3⋊D3—42no—
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52#3752—21no—
53#3752—21no—
54#3752—21no—
55#3750—21no—
56#3750—21no—
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8—22no—
59#3712—42no—
60#3710—42no—
61#1468—91noSylow
62C22×D12—32no—
63C22×D12—61no—
64C22×C4×D3—32no—
65C22×C4×D3—61no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4C2×D312yes—
68C2×(C2×D3)⋊C4—32no—
69C2×(C2×D3)⋊C4—32no—
70C2×(C2×D3)⋊C4—32no—
71C2×(C2×D3)⋊C4—61no—
72C2×(C2×D3)⋊C4—61no—
73C2×(C2×D3)⋊C4—61no—
74C2×Dic3⋊C4—32no—
75C2×Dic3⋊C4—61no—
76C2×ΓL(1,𝔽25)—62no—
77C2×D3×C8—62no—
78#894—62no—
79#894—62no—
80#894—62no—
81#894—62no—
82#894—62no—
83#894—62no—
84#894—62no—
85#894—62no—
86C3×C22⋊C8—32no—
87C3×C22⋊C8—32no—
88#830C2×D312yes—
89#830C2×D312yes—
90(C2×D3)⋊C8—62no—
91(C2×D3)⋊C8—62no—
92C23×C32C22×C411yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—21no—
95C22×C3⋊D3—22no—
96C22×C3⋊D3—22no—
97C22×C3⋊D3—41no—
98C22×C3⋊D3—41no—
99C22×C3⋊D3—41no—
100C22×C3⋊D3C22⋊C411yescharacteristic
101C22×C3⋊D3C22⋊C411yescharacteristic
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4—22no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3C22⋊C411yescharacteristic
113C2×C3⋊Dic3C22⋊C411yescharacteristic
114C4⋊(C3⋊D3)—42no—
115C4⋊(C3⋊D3)—42no—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—22no—
118C4×C3⋊D3—41no—
119C4×C3⋊D3—41no—
120C3×C3⋊C8—42no—
121C3×C3⋊C8—42no—
122C2×#123—91no—
123#407—91no—
124C2×C22⋊C8—91no—
125#324—32no—
126#323—92no—
127C23×D3—32no—
128C23×D3—32no—
129C23×D3—61no—
130C23×D3—61no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4C4×D312yes—
135C22×C3×C4C4×D312yes—
136C22×C3×C4C22×D312yes—
137C22×Dic3—32no—
138C22×Dic3—32no—
139C22×Dic3—61no—
140C22×Dic3—61no—
141C2×D12—62no—
142C2×D12—62no—
143C2×D12—62no—
144C2×D12—62no—
145C2×D12—124no—
146C2×D12—124no—
147C2×C4×D3—32no—
148C2×C4×D3—32no—
149C2×C4×D3—32no—
150C2×C4×D3—32no—
151C2×C4×D3—61no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×C4×D3—124no—
156C2×C4×D3—124no—
157C2×C3×C8—62no—
158C2×C3×C8—62no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—22no—
163(C2×D3)⋊C4—62no—
164(C2×D3)⋊C4—62no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—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—62no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—62no—
174(C2×D3)⋊C4—62no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179C2×C3⋊C8—22no—
180C2×C3⋊C8—22no—
181ΓL(1,𝔽25)—124no—
182D3×C8—124no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32C2×C22⋊C411yescharacteristic
186C22×C32#13112yes—
187C2×C3⋊D3—21no—
188C2×C3⋊D3—21no—
189C2×C3⋊D3—21no—
190C2×C3⋊D3—21no—
191C2×C3⋊D3—21no—
192C2×C3⋊D3—44no—
193C2×C3⋊D3—41no—
194C2×C3⋊D3—41no—
195C2×C3⋊D3—41no—
196C2×C3⋊D3—82no—
197C2×C3⋊D3#9912yes—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4—41no—
201C32×C4—41no—
202C3⋊Dic3—21no—
203C3⋊Dic3—21no—
204C3⋊Dic3—41no—
205C22×D4—91no—
206C23×C4—91no—
207C2×M16—181no—
208C22×C8—181no—
209#123—181no—
210#123—181no—
211#123—181no—
212#123—181no—
213C2×C4⋊C4—91no—
214C2×C4⋊C4D3211yescharacteristic
215C2×C22⋊C4—91no—
216C2×C22⋊C4—91no—
217C2×C22⋊C4—91no—
218C22⋊C8—32no—
219C22⋊C8—32no—
220C22⋊C8—181no—
221C22⋊C8—181no—
222C23×C3—21no—
223C23×C3C2×C4×D312yes—
224C22×D3—32no—
225C22×D3—32no—
226C22×D3—61no—
227C22×D3—61no—
228C22×D3—64no—
229C22×D3—64no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—62no—
233C22×D3—62no—
234C22×D3—62no—
235C22×D3—62no—
236C22×D3—122no—
237C22×D3—122no—
238C22×D3—122no—
239C22×D3—122no—
240C22×D3—122no—
241C22×D3—122no—
242C22×D3—122no—
243C22×D3—122no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—42no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4D3×D412yes—
258C2×C3×C4D3×D412yes—
259C2×Dic3—32no—
260C2×Dic3—32no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—122no—
266C2×Dic3—122no—
267C2×Dic3—122no—
268C2×Dic3—122no—
269D12—124no—
270D12—124no—
271D12—124no—
272D12—124no—
273C4×D3—64no—
274C4×D3—64no—
275C4×D3—122no—
276C4×D3—122no—
277C4×D3—122no—
278C4×D3—122no—
279C4×D3—122no—
280C4×D3—122no—
281C3×C8—122no—
282C3×C8—122no—
283C3⋊C8—42no—
284C3⋊C8—42no—
285C2×C32—22no—
286C2×C32#40811yescharacteristic
287C2×C32C2×#9911yescharacteristic
288C2×C32#41311yescharacteristic
289C3⋊D3—22no—
290C3⋊D3—41no—
291C3⋊D3—81no—
292C24—91no—
293C24—91no—
294C2×D4—181no—
295C2×D4—181no—
296C2×D4—362no—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—362no—
304C22×C4#62411yescharacteristic
305C22×C4#62411yescharacteristic
306C22×C4C2×D3211yescharacteristic
307M16—362no—
308C2×C8—62no—
309C2×C8—62no—
310C2×C8—362no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—181no—
314C4⋊C4—181no—
315C22⋊C4—181no—
316C22⋊C4—181no—
317C22⋊C4—181no—
318C22⋊C4—181no—
319C22⋊C4—181no—
320C22⋊C4—181no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—21no—
327C22×C3D3×C22⋊C412yes—
328C22×C3#90112yes—
329C22×C3#90712yes—
330C2×D3—34no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—62no—
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—121no—
339C2×D3—121no—
340C2×D3—121no—
341C2×D3—121no—
342C2×D3—124no—
343C2×D3—124no—
344C2×D3—128no—
345C2×D3—122no—
346C2×D3—122no—
347C2×D3—122no—
348C2×D3—122no—
349C2×D3—122no—
350C2×D3—122no—
351C2×D3—244no—
352C2×D3—242no—
353C2×D3—242no—
354C3×C4—22no—
355C3×C4—22no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—42no—
359C3×C4—42no—
360C3×C4—42no—
361C3×C4—42no—
362Dic3—62no—
363Dic3—62no—
364Dic3—121no—
365Dic3—121no—
366Dic3—122no—
367Dic3—122no—
368C32#146811yescharacteristic, complemented, Sylow
369C23—91no—
370C23—91no—
371C23—182no—
372C23—182no—
373C23—181no—
374C23—182no—
375C23—361no—
376C23—361no—
377C23—361no—
378C23C2×#62411yescharacteristic
379D4—362no—
380D4—362no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—91no—
387C2×C4—91no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4—181no—
391C2×C4—361no—
392C2×C4—361no—
393C2×C4—361no—
394C2×C4—361no—
395C2×C4#381111yescharacteristic
396C2×C4#381111yescharacteristic
397C8—122no—
398C8—122no—
399C2×C3—24no—
400C2×C3—22no—
401C2×C3—22no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3#472712yes—
406C2×C3D3×#9912yes—
407C2×C3#475112yes—
408D3—64no—
409D3—122no—
410D3—122no—
411D3—122no—
412D3—242no—
413D3—242no—
414C22—21no—
415C22—21no—
416C22—92no—
417C22—181no—
418C22—181no—
419C22—181no—
420C22—181no—
421C22—181no—
422C22—364no—
423C22—361no—
424C22—361no—
425C22—361no—
426C22—722no—
427C22#6381712yes—
428C22#6397411yescharacteristic
429C4—21no—
430C4—21no—
431C4—41no—
432C4—41no—
433C4—181no—
434C4—181no—
435C4—361no—
436C3—21no—
437C3#6814612yescomplemented
438C2—22no—
439C2—182no—
440C2—361no—
441C2—721no—
442C2#1059115311yescharacteristic
443C2#1059152711yescharacteristic
444C2#1059164011yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1468
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
2. #10591159C2semidirect
3. #10591152C2semidirect
4. C3×#4528C2semidirect
5. #10589146C2semidirect
29. #4528D3semidirect
368. C32#1468semidirect
437. C3#68146semidirect

Maximal subgroups

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

subgroupindex
C2×#641032
#105911592
#105911522
C3×#45282
#105891462
#681463