Finite Group Databasebeta

← #11798201

Subgroups — #11798201

Order 1152.

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

normal subgroups only

This group has 561 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
2C2×C3×#829C211yesmaximal, characteristic, complemented
3#10590857C211yesmaximal, characteristic
4C2×#63551C211yesmaximal, characteristic, complemented
5C3×#4564C211yesmaximal, characteristic, complemented
6#10589119C211yesmaximal, characteristic, complemented
7#10589108C211yesmaximal, characteristic
8#71502—31nomaximal
9#69225—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×Dic12C2211yescharacteristic
18#63871—21no—
19C3×#829—22no—
20C3×#818C2211yescharacteristic
21C2×C3×C3⋊C16C2211yescharacteristic
22C2×C3×C3⋊C16C2211yescharacteristic
23#63565—21no—
24#63551—22no—
25C2×D3×Q16—31no—
26C2×D3×Q16—31no—
27C2×D3×Q16—61no—
28C2×C3×Q32—31no—
29#5188—31no—
30C2×#829—31no—
31C2×#829D311yescharacteristic, complemented
32C2×Dic24—31no—
33#4887—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×Dic6—21no—
48C32×Q16—21no—
49C32×Q16D412yes—
50C2×C32×C8C2311yescharacteristic
51#3756—24no—
52C2×C3⋊(C3⋊C8)D411yescharacteristic
53#3746—21no—
54#3746D412yes—
55C8×C3⋊D3—21no—
56C8×C3⋊D3—21no—
57C3×C4⋊Dic3—21no—
58C3×Dic12—21no—
59C3×Dic12—21no—
60Dic3⋊Dic3—41no—
61#3722—41no—
62C3×C3⋊C16—21no—
63C3×C3⋊C16—21no—
64#2188—91noSylow
65C2×D3×Q8—61no—
66C2×D3×Q8—61no—
67C2×D3×Q8—62no—
68C2×C3×Q16—21no—
69C2×C3×Q16—31no—
70C2×C3×Q16C2×D311yescharacteristic
71C2×C3×Q16C2×D311yescharacteristic
72#946—61no—
73C2×#216—61no—
74C2×#216—61no—
75C2×#216—62no—
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×Dic12C2×D311yescharacteristic
86C2×D3×C8—31no—
87C2×D3×C8—31no—
88C2×D3×C8—61no—
89#897—61no—
90C3×Q32—62no—
91C2×C3×C16—31no—
92C2×C3×C16—31no—
93C3×#107—31no—
94#835—61no—
95#829—22no—
96#829—62no—
97#818C2×D311yescharacteristic
98C2×C3⋊C16C2×D311yescharacteristic
99C2×C3⋊C16C2×D311yescharacteristic
100#810—61no—
101Dic24—62no—
102C22×C3⋊D3D811yescharacteristic
103C32×Q8—22no—
104C32×Q8—41no—
105C2×C32×C4—41no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—41no—
108C2×C3⋊Dic3D811yescharacteristic
109C4×C3⋊D3—21no—
110C4×C3⋊D3—21no—
111C4×C3⋊D3—44no—
112#634—22no—
113#634—44no—
114#634—41no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—41no—
117C3×Dic6—41no—
118C3×Dic6—41no—
119C32×C8C2×D411yescharacteristic
120C32×C8C2×D411yescharacteristic
121C3⋊(C3⋊C8)—21no—
122C22×Q16—91no—
123C2×Q32—31no—
124C2×Q32—91no—
125#467—91no—
126#358—31no—
127#358—91no—
128C22⋊C16—91no—
129C2×C3×Q8—22no—
130C2×C3×Q8—21no—
131C2×C3×Q8—21no—
132C2×C3×Q8—61no—
133D3×Q8—68no—
134D3×Q8—64no—
135D3×Q8—64no—
136D3×Q8—124no—
137D3×Q8—122no—
138D3×Q8—122no—
139C2×C4×D3—31no—
140C2×C4×D3—31no—
141C2×C4×D3—61no—
142C2×C4×D3—121no—
143C2×C4×D3—121no—
144C2×C4×D3—122no—
145C2×Dic6—21no—
146C2×Dic6—62no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×Dic6—121no—
150C2×Dic6—121no—
151C2×Dic6—122no—
152C3×Q16—22no—
153C3×Q16—21no—
154C3×Q16—21no—
155C3×Q16—22no—
156C3×Q16—61no—
157C3×Q16—61no—
158C3×Q16D1212yes—
159C3×Q16#6712yes—
160C2×C3×C8—21no—
161C2×C3×C8C22×D311yescharacteristic
162C2×C3×C8C22×D311yescharacteristic
163C3×C4⋊C4—61no—
164#216—68no—
165#216—64no—
166#216—64no—
167(C2×D3)⋊C4—121no—
168(C2×D3)⋊C4—121no—
169C4⋊Dic3—21no—
170C4⋊Dic3—121no—
171Dic3⋊C4—121no—
172C2×C3⋊C8—31no—
173C2×C3⋊C8—31no—
174C2×C3⋊C8—61no—
175Dic12—21no—
176Dic12—21no—
177Dic12—32no—
178Dic12—32no—
179Dic12—62no—
180Dic12—62no—
181Dic12—61no—
182Dic12—61no—
183D3×C8—62no—
184D3×C8—62no—
185D3×C8—61no—
186D3×C8—61no—
187D3×C8—61no—
188D3×C8—61no—
189C3×C16—61no—
190C3×C16—61no—
191C3⋊C16—21no—
192C3⋊C16—21no—
193C22×C32C2×D811yescharacteristic
194C2×C3⋊D3—21no—
195C2×C3⋊D3—21no—
196C2×C3⋊D3Q3212yescomplemented
197C32×C4—42no—
198C32×C4#12011yescharacteristic
199C32×C4AGL(1,ℤ/8)11yescharacteristic
200C3⋊Dic3—21no—
201C3⋊Dic3—42no—
202C3×Dic3—81no—
203C3×Dic3—81no—
204C22×Q8—181no—
205C2×Q16—31no—
206C2×Q16—91no—
207C2×Q16—181no—
208C2×Q16—182no—
209C2×Q16—182no—
210C2×Q16D3211yescharacteristic
211C22×C8—91no—
212C22⋊Q8—181no—
213Q32—62no—
214Q32—182no—
215C2×C16—31no—
216C2×C16—31no—
217#107—31no—
218#103—181no—
219C22×D3—31no—
220C22×D3—31no—
221C22×D3—61no—
222C3×Q8—24no—
223C3×Q8—22no—
224C3×Q8—22no—
225C3×Q8—42no—
226C3×Q8—41no—
227C3×Q8—41no—
228C3×Q8—121no—
229C3×Q8—121no—
230C2×C3×C4—21no—
231C2×C3×C4—42no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—121no—
235C2×C3×C4—121no—
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×Dic3—31no—
239C2×Dic3—31no—
240C2×Dic3—41no—
241C2×Dic3—41no—
242C2×Dic3—61no—
243C2×Dic3—122no—
244C2×Dic3—121no—
245C2×Dic3—121no—
246C4×D3—62no—
247C4×D3—62no—
248C4×D3—61no—
249C4×D3—61no—
250C4×D3—61no—
251C4×D3—61no—
252C4×D3—128no—
253C4×D3—124no—
254C4×D3—124no—
255Dic6—41no—
256Dic6—41no—
257Dic6—64no—
258Dic6—62no—
259Dic6—62no—
260Dic6—128no—
261Dic6—124no—
262Dic6—124no—
263Dic6—122no—
264Dic6—121no—
265Dic6—121no—
266C3×C8—21no—
267C3×C8—21no—
268C3×C8C2×D1211yescharacteristic
269C3×C8D3×D411yescharacteristic
270C3×C8D3×D411yescharacteristic
271C3×C8C2×#6711yescharacteristic
272C3⋊C8—62no—
273C3⋊C8—61no—
274C3⋊C8—61no—
275C2×C32#44711yescharacteristic
276C2×C32C2×Q3211yescharacteristic
277C2×C32#51011yescharacteristic
278C3⋊D3—22no—
279C2×Q8—21no—
280C2×Q8—61no—
281C2×Q8—184no—
282C2×Q8—181no—
283C2×Q8—361no—
284C2×Q8—362no—
285C22×C4—91no—
286C22×C4—361no—
287Q16—21no—
288Q16—61no—
289Q16—61no—
290Q16—92no—
291Q16—184no—
292Q16—181no—
293Q16#62612yes—
294C2×C8—91no—
295C2×C8—181no—
296C2×C8—181no—
297C2×C8C2×D3211yescharacteristic
298C4⋊C4—61no—
299C4⋊C4—361no—
300C22⋊C4—361no—
301C16—61no—
302C16—61no—
303C22×C3—21no—
304C22×C3D3×D811yescharacteristic
305C22×C3D3×D811yescharacteristic
306C2×D3—32no—
307C2×D3—32no—
308C2×D3—62no—
309C2×D3—62no—
310C2×D3—62no—
311C2×D3—61no—
312C2×D3—61no—
313C2×D3—61no—
314C2×D3—61no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—44no—
318C3×C4—42no—
319C3×C4—42no—
320C3×C4—241no—
321C3×C4—241no—
322C3×C4#88211yescharacteristic
323C3×C4#91111yescharacteristic
324C3×C4#91411yescharacteristic
325C3×C4#93711yescharacteristic
326Dic3—62no—
327Dic3—61no—
328Dic3—61no—
329Dic3—81no—
330Dic3—81no—
331Dic3—124no—
332Dic3—122no—
333Dic3—122no—
334C32#218811yescharacteristic, complemented, Sylow
335C23—91no—
336Q8—22no—
337Q8—41no—
338Q8—121no—
339Q8—121no—
340Q8—182no—
341Q8—364no—
342Q8—361no—
343C2×C4—41no—
344C2×C4—91no—
345C2×C4—121no—
346C2×C4—121no—
347C2×C4—181no—
348C2×C4—181no—
349C2×C4—364no—
350C2×C4—361no—
351C2×C4#381111yescharacteristic
352C8—181no—
353C8C2×#62611yescharacteristic
354C8#381111yescharacteristic
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3#477311yescharacteristic
359C2×C3#491511yescharacteristic
360C2×C3D3×Q3211yescharacteristic
361C2×C3D3×Q3211yescharacteristic
362C2×C3#491811yescharacteristic
363C2×C3#515611yescharacteristic
364D3—64no—
365D3—62no—
366D3—62no—
367C22—92no—
368C22—181no—
369C22—181no—
370C22#6392611yescharacteristic
371C4—42no—
372C4—181no—
373C4—241no—
374C4—241no—
375C4—362no—
376C4#6393711yescharacteristic
377C4#6398111yescharacteristic
378C3—21no—
379C3#6922511yescharacteristic, complemented
380C3#7150211yescharacteristic, complemented
381C2—182no—
382C2#1059104311yescharacteristic
383C2#1059105011yescharacteristic
384C2#1059145611yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC22×C3⋊D3D8
hypercenterC2×Q16D32
hypocenterC32#2188
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
2. C2×C3×#829C2semidirect
4. C2×#63551C2semidirect
5. C3×#4564C2semidirect
6. #10589119C2semidirect
31. C2×#829D3semidirect
35. #4564D3semidirect
196. C2×C3⋊D3Q32semidirect
334. C32#2188semidirect
379. C3#69225semidirect
380. C3#71502semidirect

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×#8292
#105908572
C2×#635512
C3×#45642
#105891192
#105891082
#715023
#692253