Finite Group Databasebeta

← #11780210

Subgroups — #11780210

Order 1152.

522 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C3×D4×Dic6C211yesmaximal, characteristic
2#10592706C211yesmaximal, characteristic
3#10590385C211yesmaximal, characteristic, complemented
4#10590311C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6#10589093C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71916—31nomaximal
9#68192—31nomaximal
10C22×C3×Dic6—21no—
11C32×C4×D4C2211yescharacteristic
12#64078C2211yescharacteristic
13C3×D4×Dic3—21no—
14C3×#924—21no—
15C3×#888—21no—
16C3×#878—22no—
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C2×#3719—21no—
20#63659—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—22no—
26#63567—21no—
27C3×D4×Q8—31no—
28D4×Dic6D311yescharacteristic
29#5078—31no—
30#5031—31no—
31#5007—31no—
32#5007—31no—
33#5007—61no—
34#4849—31no—
35#4682—31no—
36C3×D4⋊C8—31no—
37#4547—31no—
38#4535—31no—
39D4⋊(C3⋊C8)D311yescharacteristic
40#4482—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#634—21no—
45C22×C3×Dic3—22no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6—42no—
49C2×C3×Dic6—42no—
50C2×C3×Dic6D411yescharacteristic
51C32×C4⋊C4D411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42C2311yescharacteristic
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#217—22no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D412yes—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—22no—
62C3×Dic3⋊C4—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66#3719—42no—
67#1649—91noSylow
68C22×C3×Q8—61no—
69C22×Dic6—21no—
70C3×C4⋊Q8—31no—
71C3×C4⋊Q8—61no—
72C3×C22⋊Q8—62no—
73C3×C22⋊Q8—61no—
74C3×C4×Q8—31no—
75C3×C4×D4—21no—
76C3×C4×D4—61no—
77C3×C4×D4C2×D311yescharacteristic
78C3×C4×D4C2×D311yescharacteristic
79C2×#216—61no—
80D4×Dic3—21no—
81#924—21no—
82C2×Dic12—61no—
83#888—21no—
84#878—22no—
85#869—31no—
86#869—31no—
87#869—61no—
88#869C2×D311yescharacteristic
89C4×Dic6C2×D311yescharacteristic
90C3×C4⋊C8—31no—
91C3×C4×C8—31no—
92#832—62no—
93#832—61no—
94#832—61no—
95#818—62no—
96#816—61no—
97#810—61no—
98#807—62no—
99#807—62no—
100#807—61no—
101#807—61no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—31no—
104C4⋊(C3⋊C8)—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C23×C32—21no—
108C32×D4—21no—
109C32×D4Q1612yescomplemented
110C2×C32×C4—21no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C3⋊Dic3—41no—
117#634—41no—
118#634—41no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—44no—
123C3×Dic6—21no—
124C3×Dic6—44no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127C3×Dic6D812yes—
128C3⋊(C3⋊C8)—41no—
129C3×C3⋊C8—22no—
130C3×C3⋊C8—41no—
131D4×Q8—31no—
132#500—91no—
133#474—91no—
134#462—91no—
135#332—91no—
136Q8⋊C8—91no—
137D4⋊C8—31no—
138C2×C3×Q8—31no—
139C2×C3×Q8—62no—
140C2×C3×Q8—61no—
141C2×C3×Q8—122no—
142C2×C3×Q8—122no—
143C2×C3×D4—21no—
144C2×C3×D4D1211yescharacteristic
145C2×C3×D4#6711yescharacteristic
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—41no—
149C22×C3×C4—62no—
150C22×Dic3—22no—
151C2×Dic6—22no—
152C2×Dic6—21no—
153C2×Dic6—42no—
154C2×Dic6—42no—
155C2×Dic6—61no—
156C2×Dic6—61no—
157C2×Dic6—121no—
158C2×Dic6#6711yescharacteristic
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—32no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4D1211yescharacteristic
168C3×C4⋊C4#6711yescharacteristic
169C3×C22⋊C4—21no—
170C3×C22⋊C4—21no—
171C3×C22⋊C4—41no—
172C3×C22⋊C4—62no—
173C3×C42—21no—
174C3×C42—61no—
175C3×C42C22×D311yescharacteristic
176C3×C42C22×D311yescharacteristic
177#217—22no—
178#216—122no—
179C4⋊Dic3—21no—
180C4⋊Dic3—62no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—121no—
186C4⋊Dic3#6711yescharacteristic
187C4⋊Dic3#6712yes—
188Dic3⋊C4—22no—
189Dic3⋊C4—21no—
190C4×Dic3—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—62no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196Dic12—122no—
197C22×C32—22no—
198C22×C32—41no—
199C22×C32—41no—
200C22×C32#12011yescharacteristic
201C32×C4—21no—
202C32×C4—41no—
203C32×C4C2×D811yescharacteristic
204C32×C4C2×Q1611yescharacteristic
205C32×C4AGL(1,ℤ/8)11yescharacteristic
206C32×C4#13711yescharacteristic
207C3⋊Dic3—81no—
208C3×Dic3—22no—
209C3×Dic3—42no—
210C3×Dic3—41no—
211C22×Q8—61no—
212C2×Q16—181no—
213C4⋊Q8—31no—
214C4⋊Q8—61no—
215C4⋊Q8—91no—
216C22⋊Q8—62no—
217C22⋊Q8—61no—
218C4×Q8—31no—
219C4×D4—61no—
220C4×D4D3211yescharacteristic
221#107—182no—
222#107—181no—
223C4⋊C8—31no—
224C4⋊C8—91no—
225#103—181no—
226#102—181no—
227C4×C8—31no—
228C23×C3—21no—
229C23×C3—21no—
230C23×C3—41no—
231C3×Q8—32no—
232C3×Q8—61no—
233C3×Q8—124no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×D4—21no—
237C3×D4—21no—
238C3×D4—22no—
239C3×D4—41no—
240C3×D4Dic1212yescomplemented
241C3×D4#21612yescomplemented
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—62no—
255C2×C3×C4—81no—
256C2×C3×C4—81no—
257C2×C3×C4—124no—
258C2×C3×C4C2×D1211yescharacteristic
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4C2×#6711yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—22no—
267C2×Dic3—44no—
268C2×Dic3—122no—
269C2×Dic3—121no—
270C2×Dic3—121no—
271Dic6—21no—
272Dic6—44no—
273Dic6—41no—
274Dic6—41no—
275Dic6—121no—
276Dic6—121no—
277Dic6—121no—
278Dic6—121no—
279Dic6—241no—
280Dic6—241no—
281Dic6#21312yes—
282C3×C8—62no—
283C3×C8—121no—
284C3⋊C8—22no—
285C3⋊C8—41no—
286C3⋊C8—122no—
287C3⋊C8—121no—
288C3⋊C8—121no—
289C2×C32—42no—
290C2×C32#44711yescharacteristic
291C2×C32#45111yescharacteristic
292C2×C32#45611yescharacteristic
293C2×Q8—31no—
294C2×Q8—62no—
295C2×Q8—61no—
296C2×Q8—122no—
297C2×Q8—122no—
298C2×Q8—181no—
299C2×D4#62611yescharacteristic
300C22×C4—21no—
301C22×C4—62no—
302Q16—362no—
303C2×C8—61no—
304C2×C8—61no—
305C2×C8—181no—
306C4⋊C4—31no—
307C4⋊C4—32no—
308C4⋊C4—62no—
309C4⋊C4—61no—
310C4⋊C4—61no—
311C4⋊C4—181no—
312C4⋊C4—181no—
313C4⋊C4#62611yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—62no—
316C42—61no—
317C42C2×D3211yescharacteristic
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—21no—
321C22×C3—42no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—81no—
327C22×C3—81no—
328C22×C3#88211yescharacteristic
329C22×C3#95311yescharacteristic
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4—62no—
340C3×C4—81no—
341C3×C4—122no—
342C3×C4—121no—
343C3×C4C2×Dic1211yescharacteristic
344C3×C4#90911yescharacteristic
345C3×C4D3×D811yescharacteristic
346C3×C4#91411yescharacteristic
347C3×C4C2×#21311yescharacteristic
348C3×C4#93211yescharacteristic
349C3×C4#94211yescharacteristic
350C3×C4C2×#21611yescharacteristic
351Dic3—22no—
352Dic3—42no—
353Dic3—41no—
354Dic3—242no—
355Dic3—241no—
356Dic3—241no—
357C32#164911yescharacteristic, complemented, Sylow
358C23—21no—
359Q8—32no—
360Q8—61no—
361Q8—124no—
362Q8—121no—
363Q8—121no—
364Q8—361no—
365Q8—361no—
366D4—21no—
367D4#371912yescomplemented
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—62no—
374C2×C4—124no—
375C2×C4—361no—
376C2×C4C2×#62611yescharacteristic
377C2×C4D3×#6711yescharacteristic
378C2×C4D3×#6711yescharacteristic
379C8—62no—
380C8—121no—
381C8—361no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—42no—
386C2×C3—42no—
387C2×C3—82no—
388C2×C3#473911yescharacteristic
389C2×C3#477311yescharacteristic
390C2×C3#482611yescharacteristic
391C2×C3#521711yescharacteristic
392C2×C3#522811yescharacteristic
393C2×C3#524611yescharacteristic
394C22—22no—
395C22—41no—
396C22—41no—
397C22#6397711yescharacteristic
398C4—21no—
399C4—41no—
400C4—62no—
401C4—121no—
402C4—122no—
403C4—721no—
404C4#6383311yescharacteristic
405C4C2×#371911yescharacteristic
406C4D3×#21311yescharacteristic
407C4#6393411yescharacteristic
408C3—21no—
409C3#6819211yescharacteristic, complemented
410C3#7191611yescharacteristic, complemented
411C2—42no—
412C2#1059118611yescharacteristic
413C2#1059144811yescharacteristic
414C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1649
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10590385C2semidirect
4. #10590311C2semidirect
6. #10589093C2semidirect
7. #10589084C2semidirect
109. C32×D4Q16semidirect
240. C3×D4Dic12semidirect
241. C3×D4#216semidirect
357. C32#1649semidirect
367. D4#3719semidirect
409. C3#68192semidirect
410. C3#71916semidirect

Maximal subgroups

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

subgroupindex
C3×D4×Dic62
#105927062
#105903852
#105903112
C3×D4⋊(C3⋊C8)2
#105890932
#105890842
#719163
#681923