Finite Group Databasebeta

← #11792260

Subgroups — #11792260

Order 1152.

1110 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 191 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×C32×#137C211yesmaximal, characteristic, complemented
2#10596304C211yesmaximal, characteristic
3C2×#64151C211yesmaximal, characteristic, complemented
4C2×#63664C211yesmaximal, characteristic, complemented
5#10592928C211yesmaximal, characteristic, complemented
6C2×#63652C211yesmaximal, characteristic, complemented
7#10589420C211yesmaximal, characteristic, complemented
8#72110—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C22×C32×Q8C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C32×#137—22no—
13C32×#137—22no—
14C2×C32×Q16—21no—
15C2×C32×SD16—21no—
16C2×C32×M16C2211yescharacteristic
17#64155—21no—
18C2×#3756—21no—
19#64151—22no—
20#64151—22no—
21C2×#3755—21no—
22#64148—22no—
23#64147—21no—
24#64139—21no—
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26#64133—21no—
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×#3748C2211yescharacteristic
29#63664—22no—
30#63658—22no—
31#63652—22no—
32C2×C3×#137D314yescomplemented
33#5833—34no—
34C2×#942—34no—
35C2×#837—34no—
36#5229—34no—
37C2×#825—34no—
38#4554—34no—
39C32×#41—21no—
40C32×#41—21no—
41C32×#41—21no—
42C32×#41—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8D411yescharacteristic
49C2×C32×Q8D412yescomplemented
50C2×C32×D4—21no—
51C2×C32×D4D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×#638—21no—
56C2×#638—22no—
57C22×C3⋊Dic3—21no—
58C22×C3⋊Dic3D412yes—
59#3828—21no—
60#3828—21no—
61#3828—21no—
62#3828—21no—
63C2×C4⋊(C3⋊D3)D411yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×#634D411yescharacteristic
66C32×Q16—24no—
67C32×SD16—24no—
68C32×M16—21no—
69C32×M16D412yescomplemented
70C2×C32×C8—21no—
71#3757—22no—
72#3756—24no—
73#3755—24no—
74#3752—22no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—21no—
77#3750—22no—
78C4×C3⋊Dic3—21no—
79C4×C3⋊Dic3—21no—
80#3748—21no—
81#3748D412yescomplemented
82C2×C3⋊(C3⋊C8)—21no—
83#2007—91noSylow
84C2×C3×#41C2×D314yes—
85C22×C3×Q8C2×D314yes—
86C2×#235—34no—
87C3×#137—28no—
88C3×#137—28no—
89C2×C3×Q16—24no—
90C2×C3×SD16—24no—
91C2×C3×M16C2×D314yes—
92#946—64no—
93C2×#216—64no—
94#942—68no—
95#942—68no—
96C2×#215—64no—
97#939—68no—
98#938—64no—
99#930—64no—
100C2×C4⋊Dic3—34no—
101#924—64no—
102C2×C4×Dic3—34no—
103C2×#208—34no—
104#837—68no—
105C3⋊#95—68no—
106#825—68no—
107C23×C32—21no—
108C23×C32C2×D411yescharacteristic
109C22×C3⋊D3—21no—
110C32×Q8—22no—
111C32×Q8—22no—
112C32×Q8—21no—
113C32×Q8—21no—
114C32×Q8—41no—
115C32×Q8—41no—
116C32×D4—21no—
117C32×D4—21no—
118C32×D4—41no—
119C32×D4—41no—
120C2×C32×C4—21no—
121C2×C32×C4—22no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132#638—41no—
133#638—41no—
134#638—82no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—42no—
141C4⋊(C3⋊D3)—21no—
142C4⋊(C3⋊D3)—21no—
143C4×C3⋊D3—41no—
144C4×C3⋊D3—41no—
145#634—21no—
146#634—21no—
147C32×C8—22no—
148C3⋊(C3⋊C8)—22no—
149C2×#137—91no—
150C2×#137C3⋊D311yescharacteristic, complemented
151#537—91no—
152C2×#104—91no—
153C2×#104—91no—
154#391—91no—
155#343—91no—
156C3×#41—24no—
157C3×#41—24no—
158C3×#41—24no—
159C3×#41—24no—
160C2×C3×Q8—24no—
161C2×C3×Q8—24no—
162C2×C3×Q8—24no—
163C2×C3×Q8—24no—
164C2×C3×Q8—24no—
165C2×C3×Q8#6714yes—
166C2×C3×Q8#6718yescomplemented
167C2×C3×D4—24no—
168C2×C3×D4#6714yes—
169C22×C3×C4—24no—
170C22×C3×C4—24no—
171C22×C3×C4C22×D314yes—
172C2×#67—64no—
173C2×#67—68no—
174C22×Dic3—38no—
175C22×Dic3—64no—
176#235—64no—
177#235—64no—
178#235—64no—
179#235—64no—
180C2×D12—34no—
181C2×C4×D3—64no—
182C2×Dic6—34no—
183C3×Q16—216no—
184C3×SD16—216no—
185C3×M16—24no—
186C3×M16#6718yescomplemented
187C2×C3×C8—24no—
188#217—68no—
189#216—616no—
190#215—616no—
191(C2×D3)⋊C4—68no—
192C4⋊Dic3—64no—
193C4⋊Dic3—64no—
194Dic3⋊C4—68no—
195C4×Dic3—64no—
196C4×Dic3—64no—
197#208—38no—
198#208—64no—
199C2×C3⋊C8—64no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32—41no—
203C22×C32—41no—
204C22×C32—41no—
205C22×C32#12011yescharacteristic
206C22×C32#12111yescharacteristic
207C22×C32#12711yescharacteristic
208C2×C3⋊D3—41no—
209C2×C3⋊D3—41no—
210C2×C3⋊D3—41no—
211C32×C4—41no—
212C32×C4—42no—
213C32×C4#12011yescharacteristic
214C32×C4#12011yescharacteristic
215C32×C4#12111yescharacteristic
216C32×C4#12111yescharacteristic
217C3⋊Dic3—42no—
218C3⋊Dic3—41no—
219C3⋊Dic3—42no—
220C2×#41—91no—
221C2×#41C2×C3⋊D311yescharacteristic
222C22×Q8C2×C3⋊D311yescharacteristic
223#137—22no—
224#137—22no—
225#137—182no—
226#137—182no—
227C2×Q16—21no—
228C2×Q16—181no—
229C2×SD16—21no—
230C2×SD16—181no—
231C2×M16—91no—
232C2×M16C2×C3⋊D311yescharacteristic
233C22⋊Q8—181no—
234C22⋊Q8—181no—
235#121—181no—
236#121—182no—
237#121—181no—
238C2×C4⋊C4—91no—
239C2×C42—91no—
240#104—182no—
241#104—182no—
242#95—182no—
243C23×C3—24no—
244C23×C3D3×D414yes—
245C22×D3—64no—
246C3×Q8—28no—
247C3×Q8—24no—
248C3×Q8—28no—
249C3×Q8—24no—
250C3×Q8—44no—
251C3×Q8—44no—
252C3×D4—24no—
253C3×D4—24no—
254C3×D4—44no—
255C3×D4—44no—
256C2×C3×C4—24no—
257C2×C3×C4—28no—
258C2×C3×C4—44no—
259C2×C3×C4—44no—
260C2×C3×C4—44no—
261C2×C3×C4—44no—
262C2×C3×C4D3×D414yes—
263C2×C3×C4D3×D414yes—
264C2×C3×C4#23714yes—
265C2×C3×C4C2×#6714yes—
266C2×C3×C4C2×#6714yes—
267C2×C3×C4C2×#6714yes—
268#67—124no—
269#67—124no—
270#67—248no—
271C2×Dic3—68no—
272C2×Dic3—64no—
273C2×Dic3—68no—
274C2×Dic3—124no—
275C2×Dic3—124no—
276C2×Dic3—128no—
277D12—64no—
278D12—64no—
279C4×D3—124no—
280C4×D3—124no—
281Dic6—64no—
282Dic6—64no—
283C3×C8—28no—
284C3⋊C8—68no—
285C2×C32—21no—
286C2×C32—21no—
287C2×C32—81no—
288C2×C32#39211yescharacteristic
289C2×C32#45511yescharacteristic
290C2×C32#45611yescharacteristic
291C3⋊D3—81no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—21no—
296#41—181no—
297#41—181no—
298#41—181no—
299#41—181no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—91no—
306C2×Q8#63811yescharacteristic
307C2×Q8#63812yescomplemented
308C2×D4—21no—
309C2×D4—91no—
310C2×D4—181no—
311C2×D4—182no—
312C2×D4#63811yescharacteristic
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—92no—
316C22×C4—181no—
317C22×C4—181no—
318C22×C4C22×C3⋊D311yescharacteristic
319Q16—24no—
320Q16—184no—
321SD16—24no—
322SD16—184no—
323M16—21no—
324M16—92no—
325M16—181no—
326M16#63812yescomplemented
327C2×C8—21no—
328C2×C8—181no—
329C4⋊C4—182no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C22⋊C4—182no—
333C22⋊C4—182no—
334C42—181no—
335C42—181no—
336C22×C3—24no—
337C22×C3—24no—
338C22×C3—44no—
339C22×C3—44no—
340C22×C3—44no—
341C22×C3#93714yes—
342C22×C3#93914yes—
343C22×C3#94014yes—
344C2×D3—124no—
345C2×D3—124no—
346C2×D3—124no—
347C3×C4—44no—
348C3×C4—48no—
349C3×C4#93714yes—
350C3×C4#93814yes—
351C3×C4#93914yes—
352C3×C4#95314yes—
353Dic3—128no—
354Dic3—128no—
355Dic3—124no—
356C32#200711yescharacteristic, complemented, Sylow
357C23—21no—
358C23—181no—
359C23D4×C3⋊D311yescharacteristic
360Q8—22no—
361Q8—21no—
362Q8—22no—
363Q8—21no—
364Q8—41no—
365Q8—41no—
366Q8—181no—
367Q8—181no—
368D4—21no—
369D4—21no—
370D4—41no—
371D4—41no—
372D4—181no—
373D4—181no—
374D4—361no—
375D4—361no—
376D4—722no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—182no—
384C2×C4—182no—
385C2×C4—181no—
386C2×C4—361no—
387C2×C4—361no—
388C2×C4—361no—
389C2×C4—361no—
390C2×C4—362no—
391C2×C4D4×C3⋊D311yescharacteristic
392C2×C4D4×C3⋊D311yescharacteristic
393C2×C4#383011yescharacteristic
394C2×C4C2×#63811yescharacteristic
395C2×C4C2×#63811yescharacteristic
396C2×C4C2×#63811yescharacteristic
397C8—22no—
398C8—182no—
399C2×C3—24no—
400C2×C3—24no—
401C2×C3—84no—
402C2×C3#520214yes—
403C2×C3#520514yes—
404C2×C3#522314yes—
405D3—244no—
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—361no—
412C22—361no—
413C22—361no—
414C22#6414611yescharacteristic
415C22#6414811yescharacteristic
416C22#6414911yescharacteristic
417C4—41no—
418C4—42no—
419C4—362no—
420C4—362no—
421C4—361no—
422C4#6414611yescharacteristic
423C4#6414711yescharacteristic
424C4#6414811yescharacteristic
425C4#6416211yescharacteristic
426C3#7211014yescomplemented
427C2—21no—
428C2—21no—
429C2—81no—
430C2—721no—
431C2#1059290111yescharacteristic
432C2#1059290411yescharacteristic
433C2#1059292211yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#137C2
socleC22×C32#120
prime radical#10596304C2
hypercenterC2×#137C3⋊D3
hypocenterC32#2007
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C32×#137C2semidirect
3. C2×#64151C2semidirect
4. C2×#63664C2semidirect
5. #10592928C2semidirect
6. C2×#63652C2semidirect
7. #10589420C2semidirect
32. C2×C3×#137D3semidirect
49. C2×C32×Q8D4semidirect
69. C32×M16D4semidirect
81. #3748D4semidirect
150. C2×#137C3⋊D3semidirect
166. C2×C3×Q8#67semidirect
186. C3×M16#67semidirect
307. C2×Q8#638semidirect
326. M16#638semidirect
356. C32#2007semidirect
426. C3#72110semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
#105963042
C2×#641512
C2×#636642
#105929282
C2×#636522
#105894202
#721103