Finite Group Databasebeta

← #11798093

Subgroups — #11798093

Order 1152.

581 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 581 conjugacy classes of subgroups — too many to draw. Only its 84 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×Q16×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#828C211yesmaximal, characteristic, complemented
3#10590844C211yesmaximal, characteristic
4C2×#63548C211yesmaximal, characteristic, complemented
5C3×#4564C211yesmaximal, characteristic, complemented
6#10589119C211yesmaximal, characteristic, complemented
7#10589108C211yesmaximal, characteristic, complemented
8#71483—31nomaximal
9#69223—31nomaximal
10C2×Q8×C3⋊D3—21no—
11C2×C32×Q16C2211yescharacteristic
12C2×#3756—21no—
13Q16×C3⋊D3—22no—
14Q16×C3⋊D3—22no—
15C2×#3746C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C2×C3×D24C2211yescharacteristic
18#63916—21no—
19C3×#828—22no—
20C3×#818C2211yescharacteristic
21C2×C3×C3⋊C16C2211yescharacteristic
22C2×C3×C3⋊C16C2211yescharacteristic
23#63562—21no—
24#63548—22no—
25C2×D3×Q16—31no—
26C2×D3×Q16—31no—
27C2×D3×Q16—61no—
28C2×C3×SD32—31no—
29C2×#828D311yescharacteristic, complemented
30#5157—31no—
31C2×#827—31no—
32C2×#800—31no—
33#4883—31no—
34C3×#358—31no—
35#4564D311yescharacteristic, complemented
36(C2×D3)⋊C16—31no—
37(C2×D3)⋊C16—31no—
38#4503—31no—
39#4492—31no—
40C2×C32×Q8—21no—
41Q8×C3⋊D3—24no—
42Q8×C3⋊D3—42no—
43C2×C4×C3⋊D3—41no—
44C2×C4×C3⋊D3D411yescharacteristic
45C2×#634—21no—
46C2×#634—41no—
47C2×C3×D12—21no—
48C2×#626—41no—
49C32×Q16—21no—
50C32×Q16D412yescomplemented
51C2×C32×C8C2311yescharacteristic
52#3756—24no—
53C2×C3⋊(C3⋊C8)D411yescharacteristic
54#3746—21no—
55#3746D412yescomplemented
56C8×C3⋊D3—21no—
57C8×C3⋊D3—21no—
58C3×C4⋊Dic3—21no—
59C3×D24—21no—
60C3×D24—21no—
61(C2×D3)⋊Dic3—41no—
62C3×C3⋊C16—21no—
63C3×C3⋊C16—21no—
64#2185—91noSylow
65C2×D3×Q8—61no—
66C2×D3×Q8—61no—
67C2×D3×Q8—62no—
68C2×C3×Q16—21no—
69C2×C3×Q16C2×D311yescharacteristic
70C2×C3×Q16C2×D311yescharacteristic
71C2×C3×D8—31no—
72C2×#216—61no—
73C2×#216—61no—
74C2×#216—62no—
75#938—61no—
76D3×Q16—62no—
77D3×Q16—62no—
78D3×Q16—64no—
79D3×Q16—64no—
80D3×Q16—62no—
81D3×Q16—62no—
82C2×Dic12—31no—
83C2×Dic12—31no—
84C2×Dic12—61no—
85C2×D24C2×D311yescharacteristic
86C2×D3×C8—31no—
87C2×D3×C8—31no—
88C2×D3×C8—61no—
89#895—61no—
90C3×SD32—62no—
91C2×C3×C16—31no—
92C2×C3×C16—31no—
93C3×#107—31no—
94#832—61no—
95#828—22no—
96#827—62no—
97#818C2×D311yescharacteristic
98C2×C3⋊C16C2×D311yescharacteristic
99C2×C3⋊C16C2×D311yescharacteristic
100#809—61no—
101#800—62no—
102C22×C3⋊D3D811yescharacteristic
103C22×C3×D3—41no—
104C32×Q8—22no—
105C32×Q8—41no—
106C2×C32×C4—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3D811yescharacteristic
110C4×C3⋊D3—21no—
111C4×C3⋊D3—21no—
112C4×C3⋊D3—44no—
113#634—22no—
114#634—44no—
115#634—41no—
116C2×C3×Dic3—41no—
117C3×D12—41no—
118C3×D12—41no—
119#626—82no—
120C32×C8C2×D411yescharacteristic
121C32×C8C2×D411yescharacteristic
122C3⋊(C3⋊C8)—21no—
123C22×Q16—91no—
124C2×SD32—31no—
125C2×SD32—91no—
126#466—91no—
127#358—31no—
128#358—91no—
129C22⋊C16—91no—
130C2×C3×Q8—22no—
131C2×C3×Q8—21no—
132C2×C3×Q8—21no—
133C2×C3×D4—61no—
134C2×#67—121no—
135D3×Q8—68no—
136D3×Q8—64no—
137D3×Q8—64no—
138D3×Q8—124no—
139D3×Q8—122no—
140D3×Q8—122no—
141C2×D12—21no—
142C2×D12—121no—
143C2×C4×D3—31no—
144C2×C4×D3—31no—
145C2×C4×D3—61no—
146C2×C4×D3—121no—
147C2×C4×D3—121no—
148C2×C4×D3—122no—
149C2×Dic6—62no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C2×Dic6—121no—
153C2×Dic6—121no—
154C2×Dic6—122no—
155C3×Q16—22no—
156C3×Q16—21no—
157C3×Q16—21no—
158C3×Q16—22no—
159C3×Q16D1212yescomplemented
160C3×Q16#6712yescomplemented
161C3×D8—61no—
162C3×D8—61no—
163C2×C3×C8—21no—
164C2×C3×C8C22×D311yescharacteristic
165C2×C3×C8C22×D311yescharacteristic
166C3×C4⋊C4—61no—
167#217—121no—
168#216—68no—
169#216—64no—
170#216—64no—
171(C2×D3)⋊C4—121no—
172C4⋊Dic3—21no—
173C2×C3⋊C8—31no—
174C2×C3⋊C8—31no—
175C2×C3⋊C8—61no—
176Dic12—32no—
177Dic12—32no—
178Dic12—62no—
179Dic12—62no—
180Dic12—61no—
181Dic12—61no—
182D24—21no—
183D24—21no—
184D3×C8—62no—
185D3×C8—62no—
186D3×C8—61no—
187D3×C8—61no—
188D3×C8—61no—
189D3×C8—61no—
190C3×C16—61no—
191C3×C16—61no—
192C3⋊C16—21no—
193C3⋊C16—21no—
194C22×C32C2×D811yescharacteristic
195C2×C3⋊D3—21no—
196C2×C3⋊D3—21no—
197C2×C3⋊D3SD3212yescomplemented
198C2×C3×D3—81no—
199C2×C3×D3—81no—
200C2×C3×D3—81no—
201C32×C4—42no—
202C32×C4#12011yescharacteristic
203C32×C4AGL(1,ℤ/8)11yescharacteristic
204C3⋊Dic3—21no—
205C3⋊Dic3—42no—
206C3×Dic3—81no—
207C22×Q8—181no—
208C2×Q16—91no—
209C2×Q16—181no—
210C2×Q16—182no—
211C2×Q16—182no—
212C2×Q16D3211yescharacteristic
213C2×D8—31no—
214C22×C8—91no—
215#121—181no—
216SD32—62no—
217SD32—182no—
218C2×C16—31no—
219C2×C16—31no—
220#107—31no—
221#102—181no—
222C23×C3—121no—
223C22×D3—31no—
224C22×D3—31no—
225C22×D3—41no—
226C22×D3—61no—
227C3×Q8—24no—
228C3×Q8—22no—
229C3×Q8—22no—
230C3×Q8—42no—
231C3×Q8—41no—
232C3×Q8—41no—
233C3×D4—121no—
234C3×D4—121no—
235C2×C3×C4—21no—
236C2×C3×C4—42no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—121no—
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242#67—242no—
243C2×Dic3—31no—
244C2×Dic3—31no—
245C2×Dic3—41no—
246C2×Dic3—61no—
247C2×Dic3—122no—
248C2×Dic3—121no—
249C2×Dic3—121no—
250D12—41no—
251D12—41no—
252D12—242no—
253C4×D3—62no—
254C4×D3—62no—
255C4×D3—61no—
256C4×D3—61no—
257C4×D3—61no—
258C4×D3—61no—
259C4×D3—128no—
260C4×D3—124no—
261C4×D3—124no—
262Dic6—64no—
263Dic6—62no—
264Dic6—62no—
265Dic6—128no—
266Dic6—124no—
267Dic6—124no—
268Dic6—122no—
269Dic6—121no—
270Dic6—121no—
271C3×C8—21no—
272C3×C8—21no—
273C3×C8C2×D1211yescharacteristic
274C3×C8D3×D411yescharacteristic
275C3×C8D3×D411yescharacteristic
276C3×C8C2×#6711yescharacteristic
277C3⋊C8—62no—
278C3⋊C8—61no—
279C3⋊C8—61no—
280C2×C32#44711yescharacteristic
281C2×C32C2×SD3211yescharacteristic
282C2×C32#51011yescharacteristic
283C3⋊D3—22no—
284C3×D3—161no—
285C2×Q8—21no—
286C2×Q8—184no—
287C2×Q8—181no—
288C2×Q8—361no—
289C2×Q8—362no—
290C2×D4—61no—
291C2×D4—361no—
292C22×C4—91no—
293C22×C4—361no—
294Q16—21no—
295Q16—92no—
296Q16—184no—
297Q16—181no—
298Q16#62612yescomplemented
299D8—61no—
300D8—61no—
301C2×C8—91no—
302C2×C8—181no—
303C2×C8—181no—
304C2×C8C2×D3211yescharacteristic
305C4⋊C4—61no—
306C22⋊C4—361no—
307C16—61no—
308C16—61no—
309C22×C3—21no—
310C22×C3—241no—
311C22×C3—241no—
312C22×C3—241no—
313C22×C3D3×D811yescharacteristic
314C22×C3D3×D811yescharacteristic
315C2×D3—32no—
316C2×D3—32no—
317C2×D3—62no—
318C2×D3—62no—
319C2×D3—62no—
320C2×D3—61no—
321C2×D3—61no—
322C2×D3—61no—
323C2×D3—61no—
324C2×D3—81no—
325C2×D3—81no—
326C2×D3—81no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—44no—
330C3×C4—42no—
331C3×C4—42no—
332C3×C4—241no—
333C3×C4#88211yescharacteristic
334C3×C4#91111yescharacteristic
335C3×C4#91411yescharacteristic
336C3×C4#93711yescharacteristic
337Dic3—62no—
338Dic3—61no—
339Dic3—61no—
340Dic3—81no—
341Dic3—124no—
342Dic3—122no—
343Dic3—122no—
344C32#218511yescharacteristic, complemented, Sylow
345C23—91no—
346C23—121no—
347Q8—22no—
348Q8—41no—
349Q8—182no—
350Q8—364no—
351Q8—361no—
352D4—121no—
353D4—121no—
354D4—722no—
355C2×C4—41no—
356C2×C4—91no—
357C2×C4—121no—
358C2×C4—181no—
359C2×C4—181no—
360C2×C4—364no—
361C2×C4—361no—
362C2×C4#381111yescharacteristic
363C8—181no—
364C8C2×#62611yescharacteristic
365C8#381111yescharacteristic
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—481no—
370C2×C3#477311yescharacteristic
371C2×C3D3×SD3211yescharacteristic
372C2×C3D3×SD3211yescharacteristic
373C2×C3#491511yescharacteristic
374C2×C3#491811yescharacteristic
375C2×C3#515611yescharacteristic
376D3—64no—
377D3—62no—
378D3—62no—
379D3—161no—
380C22—92no—
381C22—181no—
382C22—181no—
383C22—241no—
384C22—241no—
385C22—241no—
386C22#6392611yescharacteristic
387C4—42no—
388C4—181no—
389C4—241no—
390C4—362no—
391C4#6393711yescharacteristic
392C4#6398111yescharacteristic
393C3—21no—
394C3#6922311yescharacteristic, complemented
395C3#7148311yescharacteristic, complemented
396C2—182no—
397C2—481no—
398C2#1059103911yescharacteristic
399C2#1059105011yescharacteristic
400C2#1059145611yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radical#10590844C2
hypercenterC2×Q16D32
hypocenterC32#2185
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×Q16×C3⋊D3C2semidirect
2. C2×C3×#828C2semidirect
4. C2×#63548C2semidirect
5. C3×#4564C2semidirect
6. #10589119C2semidirect
7. #10589108C2semidirect
29. C2×#828D3semidirect
35. #4564D3semidirect
50. C32×Q16D4semidirect
55. #3746D4semidirect
159. C3×Q16D12semidirect
160. C3×Q16#67semidirect
197. C2×C3⋊D3SD32semidirect
298. Q16#626semidirect
344. C32#2185semidirect
394. C3#69223semidirect
395. C3#71483semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×C3⋊D32
C2×C3×#8282
#105908442
C2×#635482
C3×#45642
#105891192
#105891082
#714833
#692233