Finite Group Databasebeta

← #11920420

Subgroups — #11920420

Order 1152.

570 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C22×#41⋊C9C211yesmaximal, characteristic, complemented
2C2×#63691C211yesmaximal, characteristic, complemented
3#10589529C211yesmaximal, characteristic, complemented
4#10589527C211yesmaximal, characteristic, complemented
5#10589526C211yesmaximal, characteristic, complemented
6#10589523C211yesmaximal, characteristic, complemented
7#10589521C211yesmaximal, characteristic, complemented
8#84080—31nomaximal
9C2×#41⋊C9—22no—
10C2×#41⋊C9C2211yescharacteristic
11C2×#41⋊C9C2211yescharacteristic
12C22×Q8⋊C9C2211yescharacteristic
13#63691—22no—
14C2×#3689C2211yescharacteristic, complemented
15C2×#3688C2211yescharacteristic, complemented
16C4×#611—41nomaximal
17#63421C2211yescharacteristic, complemented
18#63421C2211yescharacteristic, complemented
19C22×C3×#41D311yescharacteristic
20C2×#950—31no—
21C2×#950—31no—
22#5791—31no—
23#5239—31no—
24#5239—31no—
25#5238—31no—
26#5238—31no—
27#5233—31no—
28#5233—31no—
29#5228—31no—
30#5227—31no—
31#5218—31no—
32#5217—31no—
33C2×#830—31no—
34C22×C4×C9—41no—
35C2×#611—41no—
36C2×C4×D9—41no—
37#41⋊C9—21no—
38#41⋊C9D412yescomplemented
39C2×Q8⋊C9—21no—
40C2×Q8⋊C9C2311yescharacteristic
41#3689—21no—
42#3688—21no—
43#3676—41no—
44(C2×D9)⋊C4—41no—
45Dic9⋊C4—41no—
46C4×Dic9—41no—
47#3002—91noSylow
48C2×C3×#41—22no—
49C2×C3×#41—31no—
50C2×C3×#41—31no—
51C2×C3×#41—62no—
52C2×C3×#41C2×D311yescharacteristic
53C2×C3×#41C2×D311yescharacteristic
54C22×C3×Q8C2×D311yescharacteristic
55C22×C3×D4—31no—
56C23×C3×C4—31no—
57C2×#235—31no—
58#953—61no—
59#950—62no—
60#950—64no—
61#950—62no—
62C2×#216—31no—
63C2×#216—31no—
64C2×#215—31no—
65C2×#215—31no—
66C2×#214—31no—
67C2×#214—31no—
68C2×#213—31no—
69C2×#213—31no—
70#930—31no—
71#930—31no—
72#929—61no—
73C4×#67—61no—
74C4×#67—61no—
75#926—31no—
76#924—31no—
77#924—31no—
78C22×C3⋊C8—31no—
79C22×C3⋊C8—31no—
80#835—31no—
81#835—31no—
82#835—31no—
83#835—31no—
84#832—31no—
85#832—31no—
86#832—31no—
87#832—31no—
88#830—31no—
89#830—31no—
90#830—31no—
91#830—31no—
92C23×C9—41no—
93C22×D9—41no—
94C2×C4×C9—41no—
95C2×C4×C9—41no—
96C2×C4×C9—82no—
97#611—44no—
98C2×Dic9—41no—
99C2×Dic9—41no—
100C2×Dic9—41no—
101C4×D9—82no—
102Q8⋊C9C2×D411yescharacteristic
103C22×#41D911yescharacteristic, complemented
104C2×#135—91no—
105C2×#135—91no—
106#525—91no—
107#452—91no—
108#452—91no—
109#451—91no—
110#450—91no—
111#449—91no—
112#449—91no—
113#448—91no—
114#447—91no—
115#416—91no—
116#416—91no—
117C2×C22⋊C8—91no—
118C24×C3—31no—
119C3×#41—21no—
120C3×#41—32no—
121C3×#41—34no—
122C3×#41—62no—
123C3×#41—62no—
124C3×#41—61no—
125C3×#41—62no—
126C3×#41#6712yes—
127C2×C3×Q8—21no—
128C2×C3×Q8—31no—
129C2×C3×Q8—61no—
130C2×C3×Q8C22×D311yescharacteristic
131C2×C3×D4—31no—
132C2×C3×D4—31no—
133C2×C3×D4—61no—
134C2×C3×D4—62no—
135C2×C3×D4—62no—
136C22×C3×C4—31no—
137C22×C3×C4—31no—
138C22×C3×C4—31no—
139C22×C3×C4—31no—
140C22×C3×C4—31no—
141C22×C3×C4—62no—
142C22×C3×C4—62no—
143C22×C3×C4S411yescharacteristic
144C2×#67—61no—
145C2×#67—61no—
146C2×#67—61no—
147#235—62no—
148#235—62no—
149C2×D12—31no—
150C2×C4×D3—61no—
151C2×Dic6—31no—
152#217—61no—
153#217—61no—
154#217—61no—
155#216—61no—
156#216—62no—
157#216—61no—
158#215—61no—
159#215—62no—
160#215—61no—
161#214—62no—
162#214—62no—
163#213—62no—
164#213—62no—
165(C2×D3)⋊C4—61no—
166(C2×D3)⋊C4—61no—
167C4⋊Dic3—31no—
168C4⋊Dic3—31no—
169Dic3⋊C4—61no—
170Dic3⋊C4—61no—
171C4×Dic3—61no—
172C2×C3⋊C8—31no—
173C2×C3⋊C8—31no—
174C2×C3⋊C8—31no—
175C2×C3⋊C8—31no—
176C2×C3⋊C8—62no—
177C2×C3⋊C8—62no—
178C22×C9—42no—
179C22×C9—41no—
180C22×C9—81no—
181C22×C9—81no—
182C2×D9—42no—
183C2×D9—81no—
184C2×D9—81no—
185C4×C9—42no—
186C4×C9—81no—
187Dic9—42no—
188Dic9—81no—
189Dic9—81no—
190C2×#41—22no—
191C2×#41—31no—
192C2×#41—31no—
193C2×#41—62no—
194C2×#41—91no—
195C2×#41C2×D911yescharacteristic
196C2×#41C2×D911yescharacteristic
197C22×Q8C2×D911yescharacteristic
198C22×D4—31no—
199C23×C4—31no—
200#135—182no—
201#135—184no—
202#135—182no—
203C2×Q16—91no—
204C2×Q16—91no—
205C2×SD16—91no—
206C2×SD16—91no—
207C2×SD16—91no—
208C2×SD16—91no—
209C2×D8—91no—
210C2×D8—91no—
211C22×C8—91no—
212C22×C8—91no—
213#123—181no—
214C22⋊Q8—91no—
215C22⋊Q8—91no—
216#121—91no—
217#121—91no—
218#120—181no—
219C4×D4—181no—
220C4×D4—181no—
221#117—91no—
222#103—91no—
223#103—91no—
224#103—91no—
225#103—91no—
226#102—91no—
227#102—91no—
228#102—91no—
229#102—91no—
230C22⋊C8—91no—
231C22⋊C8—91no—
232C22⋊C8—91no—
233C22⋊C8—91no—
234C23×C3—31no—
235C23×C3—31no—
236C23×C3—62no—
237C23×C3—62no—
238C23×C3—121no—
239C23×C3C2×S411yescharacteristic
240C22×D3—61no—
241C3×Q8—31no—
242C3×Q8—32no—
243C3×Q8—61no—
244C3×Q8C2×#6711yescharacteristic
245C3×D4—32no—
246C3×D4—32no—
247C3×D4—61no—
248C3×D4—61no—
249C3×D4—64no—
250C2×C3×C4—22no—
251C2×C3×C4—31no—
252C2×C3×C4—32no—
253C2×C3×C4—32no—
254C2×C3×C4—31no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—62no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—62no—
261C2×C3×C4C2×S411yescharacteristic
262C2×C3×C4C2×S411yescharacteristic
263#67—122no—
264#67—122no—
265#67—122no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269D12—61no—
270D12—61no—
271C4×D3—122no—
272Dic6—61no—
273Dic6—61no—
274C3⋊C8—61no—
275C3⋊C8—61no—
276C3⋊C8—61no—
277C3⋊C8—61no—
278C2×C9—41no—
279C2×C9—41no—
280C2×C9—41no—
281C2×C9—82no—
282D9—82no—
283C24—31no—
284#41—21no—
285#41—32no—
286#41—34no—
287#41—62no—
288#41—62no—
289#41—61no—
290#41—62no—
291#41—182no—
292#41—182no—
293#41#61112yescomplemented
294C2×Q8—21no—
295C2×Q8—31no—
296C2×Q8—61no—
297C2×Q8—91no—
298C2×Q8C22×D911yescharacteristic
299C2×D4—31no—
300C2×D4—31no—
301C2×D4—61no—
302C2×D4—62no—
303C2×D4—62no—
304C2×D4—91no—
305C2×D4—181no—
306C2×D4—181no—
307C2×D4—181no—
308C22×C4—31no—
309C22×C4—31no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—31no—
313C22×C4—62no—
314C22×C4—62no—
315C22×C4—181no—
316C22×C4(C22⋊C9)⋊C211yescharacteristic
317Q16—181no—
318Q16—182no—
319Q16—181no—
320SD16—182no—
321SD16—182no—
322SD16—181no—
323SD16—182no—
324SD16—181no—
325D8—182no—
326D8—182no—
327C2×C8—91no—
328C2×C8—91no—
329C2×C8—91no—
330C2×C8—91no—
331C2×C8—182no—
332C2×C8—182no—
333C4⋊C4—91no—
334C4⋊C4—91no—
335C4⋊C4—181no—
336C4⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C22⋊C4—181no—
341C22⋊C4—181no—
342C42—181no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—32no—
346C22×C3—61no—
347C22×C3—61no—
348C22×C3—61no—
349C22×C3—61no—
350C22×C3—61no—
351C22×C3—124no—
352C22×C3#98512yes—
353C22×C3C22×S411yescharacteristic
354C2×D3—121no—
355C2×D3—121no—
356C2×D3—121no—
357C3×C4—21no—
358C3×C4—31no—
359C3×C4—31no—
360C3×C4—61no—
361C3×C4GL(2,ℤ/4)12yes—
362Dic3—121no—
363Dic3—121no—
364Dic3—121no—
365C9—41noSylow
366C23—31no—
367C23—31no—
368C23—62no—
369C23—62no—
370C23—121no—
371C23—181no—
372C23C2×(C22⋊C9)⋊C211yescharacteristic
373Q8—31no—
374Q8—32no—
375Q8—61no—
376Q8—181no—
377Q8—181no—
378Q8C2×#61111yescharacteristic
379D4—32no—
380D4—32no—
381D4—61no—
382D4—61no—
383D4—64no—
384D4—181no—
385D4—181no—
386D4—362no—
387D4—362no—
388D4—362no—
389C2×C4—22no—
390C2×C4—31no—
391C2×C4—32no—
392C2×C4—32no—
393C2×C4—31no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—62no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—62no—
400C2×C4—181no—
401C2×C4—181no—
402C2×C4—181no—
403C2×C4—362no—
404C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
405C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
406C8—181no—
407C8—181no—
408C8—181no—
409C8—181no—
410C2×C3—22no—
411C2×C3—62no—
412C2×C3—121no—
413C2×C3C2×#98511yescharacteristic
414C2×C3#592311yescharacteristic
415C2×C3C2×GL(2,ℤ/4)11yescharacteristic
416D3—241no—
417C22—21no—
418C22—21no—
419C22—32no—
420C22—61no—
421C22—61no—
422C22—61no—
423C22—61no—
424C22—61no—
425C22—124no—
426C22—361no—
427C22—361no—
428C22—361no—
429C22#6369112yescomplemented
430C22C22×(C22⋊C9)⋊C211yescharacteristic
431C4—21no—
432C4—31no—
433C4—31no—
434C4—61no—
435C4—361no—
436C4—361no—
437C4—361no—
438C4#6369412yes—
439C3#8552111yescharacteristic
440C2—22no—
441C2—62no—
442C2—121no—
443C2—721no—
444C2C2×#6369111yescharacteristic
445C2#1059309811yescharacteristic
446C2C2×#6369411yescharacteristic
subgroupG/H
centerC2×C4C2×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
FittingC22×C3×#41D3
hypercenterC22×C4(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×D4
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×#41⋊C9C2semidirect
2. C2×#63691C2semidirect
3. #10589529C2semidirect
4. #10589527C2semidirect
5. #10589526C2semidirect
6. #10589523C2semidirect
7. #10589521C2semidirect
14. C2×#3689C22semidirect
15. C2×#3688C22semidirect
17. #63421C22semidirect
18. #63421C22semidirect
38. #41⋊C9D4semidirect
103. C22×#41D9semidirect
293. #41#611semidirect
429. C22#63691semidirect

Maximal subgroups

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

subgroupindex
C22×#41⋊C92
C2×#636912
#105895292
#105895272
#105895262
#105895232
#105895212
#840803
C4×#6114