Finite Group Databasebeta

← #11874982

Subgroups — #11874982

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic
3#10592779C211yesmaximal, characteristic, complemented
4C3×#5078C211yesmaximal, characteristic, complemented
5#10590571C214yesmaximal
6#10590413C214yesmaximal, complemented
7C4×D3×C3⋊C8C211yesmaximal, characteristic
8#10590311C211yesmaximal, characteristic, complemented
9#10590309C211yesmaximal, characteristic, complemented
10#83339—31nomaximal
11#81938—31nomaximal
12C32×C4⋊Q8C2211yescharacteristic
13#64078C2211yescharacteristic
14C3×#946—21no—
15C3×Q8×Dic3—21no—
16C3×#897—21no—
17C3×#892C2212yes—
18C3×#890C2212yes—
19C3×#887—21no—
20C3×C42×D3C2211yescharacteristic
21C3×#869C2211yescharacteristic
22C3×#869C2211yescharacteristic
23#63869C2212yes—
24#63857—21no—
25#63856—21no—
26#63844—21no—
27Dic3×Dic6—21no—
28#63841C2212yes—
29C2×D3×C3⋊C8C2212yes—
30#63635C2214yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×#807C2214yes—
33C3×C4×C3⋊C8C2211yescharacteristic
34#63575C2214yes—
35#63574C2214yes—
36Dic3×C3⋊C8C2212yes—
37C3×#533—31no—
38#5728—31no—
39#5728D311yescharacteristic
40#5470—31no—
41C3×#500—31no—
42#5080—31no—
43#5080—31no—
44#5080—31no—
45#5080—31no—
46#5080—61no—
47#5078—31no—
48#5078D311yescharacteristic, complemented
49#5065—34no—
50#4998—34no—
51C2×C4×C3⋊C8—31no—
52#4880—34no—
53#4878—34no—
54C4×D3×C8—31no—
55#4682—31no—
56C2×C32×Q8—21no—
57C2×#634—21no—
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C3×C4×D3C2311yescharacteristic
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C32×C42C2311yescharacteristic
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×(C2×D3)⋊C4—22no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—22no—
73C3×C4⋊Dic3C2312yes—
74C3×C4⋊Dic3C2312yes—
75C3×Dic3⋊C4—22no—
76C3×C4×Dic3—22no—
77C3×C4×Dic3D411yescharacteristic
78C3×C4×Dic3D411yescharacteristic
79C3×C4×Dic3C2311yescharacteristic
80C2×C3×C3⋊C8C2312yes—
81#3724—22no—
82Dic3⋊Dic3—22no—
83(C2×D3)⋊Dic3—22no—
84Dic32—22no—
85D3×C3⋊C8Q818yescomplemented
86#3160—91noSylow
87C3×C4⋊Q8—21no—
88C3×C4⋊Q8—31no—
89C3×C4⋊Q8—31no—
90C3×C4⋊Q8C2×D311yescharacteristic
91C3×C4⋊Q8C2×D311yescharacteristic
92C3×#125—32no—
93C3×C22⋊Q8—61no—
94C3×C22⋊Q8—61no—
95C3×C4×Q8—61no—
96C3×C4×Q8—61no—
97C3×#117—32no—
98C2×C3×C42—31no—
99#946—21no—
100#946—61no—
101Q8×Dic3—21no—
102Q8×Dic3—61no—
103#926—32no—
104#924—61no—
105#924—61no—
106C22×C3⋊C8—32no—
107C2×D3×C8—32no—
108#897—21no—
109#897—61no—
110#892—32no—
111#892C2×D312yes—
112#890—32no—
113#890C2×D312yes—
114#887—21no—
115#887—61no—
116C42×D3C2×D311yescharacteristic
117#870—32no—
118#869—31no—
119#869—31no—
120#869—61no—
121#869C2×D311yescharacteristic
122#869C2×D311yescharacteristic
123C4×Dic6—61no—
124C4×Dic6—61no—
125C3×#107—34no—
126C3×C4×C8—31no—
127#818—34no—
128C8×Dic3—32no—
129#808—34no—
130#808—34no—
131#808—34no—
132#808—34no—
133#808—64no—
134#807—34no—
135#807C2×D314yes—
136C4×C3⋊C8—31no—
137C4×C3⋊C8—31no—
138C4×C3⋊C8—32no—
139C4×C3⋊C8—61no—
140C4×C3⋊C8C2×D311yescharacteristic
141C22×C3×D3C2×D411yescharacteristic
142C32×Q8—42no—
143C2×C32×C4—22no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148#634—42no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3C2×D411yescharacteristic
152C2×C3×Dic3C2×D411yescharacteristic
153C2×C3×Dic3C2×D411yescharacteristic
154C3×C4×D3—22no—
155C3×C4×D3—22no—
156C3×C4×D3C2×Q814yes—
157C3×Dic6—42no—
158C3×Dic6—42no—
159C3⋊(C3⋊C8)C2×Q814yes—
160C3×C3⋊C8C2×Q814yes—
161#533—31no—
162#533—91no—
163#500—31no—
164#500—91no—
165#499—94no—
166#498—91no—
167#498—91no—
168#427—94no—
169C2×C4×C8—91no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—41no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C2×C4×D3#6711yescharacteristic
179C2×C4×D3#6711yescharacteristic
180C2×C4×D3C22×D311yescharacteristic
181C2×Dic6—21no—
182C2×Dic6—21no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—121no—
186C2×C3×C8—32no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—32no—
191C3×C4⋊C4—32no—
192C3×C4⋊C4—41no—
193C3×C4⋊C4—62no—
194C3×C4⋊C4—62no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4C22×D312yes—
198C3×C4⋊C4C22×D312yes—
199C3×C22⋊C4—62no—
200C3×C42—21no—
201C3×C42—31no—
202C3×C42—31no—
203C3×C42—31no—
204C3×C42—62no—
205C3×C42C22×D311yescharacteristic
206C3×C42C22×D311yescharacteristic
207#217—62no—
208(C2×D3)⋊C4—22no—
209(C2×D3)⋊C4—62no—
210C4⋊Dic3—21no—
211C4⋊Dic3—21no—
212C4⋊Dic3—22no—
213C4⋊Dic3—32no—
214C4⋊Dic3—32no—
215C4⋊Dic3—62no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—62no—
219C4⋊Dic3—121no—
220C4⋊Dic3C22×D312yes—
221C4⋊Dic3C22×D312yes—
222Dic3⋊C4—22no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—62no—
226C4×Dic3—22no—
227C4×Dic3—62no—
228C4×Dic3—62no—
229C4×Dic3#6711yescharacteristic
230C4×Dic3#6711yescharacteristic
231C4×Dic3C22×D311yescharacteristic
232C2×C3⋊C8—32no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—38no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8C22×D312yes—
237D3×C8—38no—
238C22×C32C22×D411yescharacteristic
239C2×C3×D3—21no—
240C2×C3×D3—21no—
241C2×C3×D3C4⋊Q812yes—
242C32×C4—42no—
243C32×C4#13512yes—
244C32×C4#13512yes—
245C32×C4C22×Q812yes—
246C3⋊Dic3—42no—
247C3×Dic3—21no—
248C3×Dic3—21no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C3×Dic3C4⋊Q812yes—
252C22×C8—92no—
253C4⋊Q8—31no—
254C4⋊Q8—31no—
255C4⋊Q8—91no—
256C4⋊Q8D3211yescharacteristic
257#125—32no—
258#125—92no—
259C22⋊Q8—61no—
260C22⋊Q8—61no—
261C22⋊Q8—181no—
262C22⋊Q8—181no—
263C4×Q8—61no—
264C4×Q8—61no—
265C4×Q8—181no—
266C4×Q8—181no—
267#117—32no—
268#117—92no—
269C2×C42—31no—
270#107—34no—
271#107—94no—
272#106—94no—
273#106—94no—
274C4×C8—31no—
275C4×C8—92no—
276C4×C8—91no—
277C23×C3—31no—
278C22×D3C2×#6711yescharacteristic
279C3×Q8—42no—
280C3×Q8—42no—
281C3×Q8—82no—
282C3×Q8—122no—
283C3×Q8—122no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—31no—
290C2×C3×C4—34no—
291C2×C3×C4—31no—
292C2×C3×C4—31no—
293C2×C3×C4—42no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C23×D311yescharacteristic
303C2×C3×C4C23×D311yescharacteristic
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—122no—
309C2×Dic3C2×#6711yescharacteristic
310C2×Dic3C2×#6711yescharacteristic
311C2×Dic3C2×#6711yescharacteristic
312C4×D3—22no—
313C4×D3—22no—
314C4×D3D3×Q814yes—
315Dic6—42no—
316Dic6—42no—
317Dic6—122no—
318Dic6—122no—
319Dic6—242no—
320C3×C8—34no—
321C3⋊C8—34no—
322C3⋊C8—34no—
323C3⋊C8—64no—
324C3⋊C8D3×Q814yes—
325C2×C32C2×C4⋊Q811yescharacteristic
326C2×C32C2×#13511yescharacteristic
327C2×C32C2×#13511yescharacteristic
328C3×D3—22no—
329C2×Q8—21no—
330C2×Q8—61no—
331C2×Q8—61no—
332C2×Q8—181no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—31no—
336C2×C8—32no—
337C2×C8—98no—
338C2×C8—92no—
339C4⋊C4—21no—
340C4⋊C4—32no—
341C4⋊C4—32no—
342C4⋊C4—62no—
343C4⋊C4—62no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—92no—
347C4⋊C4—182no—
348C4⋊C4—182no—
349C4⋊C4—181no—
350C4⋊C4C2×D3212yes—
351C22⋊C4—62no—
352C22⋊C4—182no—
353C42—31no—
354C42—31no—
355C42—31no—
356C42—62no—
357C42—182no—
358C42C2×D3211yescharacteristic
359C22×C3—21no—
360C22×C3—32no—
361C22×C3—61no—
362C22×C3—61no—
363C22×C3C2×D3×D411yescharacteristic
364C22×C3C22×#6711yescharacteristic
365C2×D3—21no—
366C2×D3—21no—
367C2×D3#94412yes—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—22no—
371C3×C4—32no—
372C3×C4—42no—
373C3×C4—42no—
374C3×C4—61no—
375C3×C4—61no—
376C3×C4—82no—
377C3×C4—122no—
378C3×C4—122no—
379C3×C4#91212yes—
380C3×C4#91912yes—
381C3×C4#95012yes—
382C3×C4#95012yes—
383C3×C4C2×D3×Q812yes—
384C3×C4C2×D3×Q812yes—
385Dic3—21no—
386Dic3—21no—
387Dic3—42no—
388Dic3—42no—
389Dic3—122no—
390Dic3—122no—
391Dic3—242no—
392Dic3#94412yes—
393C32#316011yescharacteristic, complemented, Sylow
394C23—31no—
395Q8—42no—
396Q8—122no—
397Q8—122no—
398Q8—362no—
399C2×C4—22no—
400C2×C4—31no—
401C2×C4—34no—
402C2×C4—31no—
403C2×C4—31no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—62no—
408C2×C4—182no—
409C2×C4D3×#6711yescharacteristic
410C2×C4D3×#6711yescharacteristic
411C2×C4C22×D3211yescharacteristic
412C8—34no—
413C8—94no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—62no—
418C2×C3D3×C4⋊Q811yescharacteristic
419C2×C3C2×#91211yescharacteristic
420C2×C3C2×#91911yescharacteristic
421C2×C3C2×#94411yescharacteristic
422C2×C3C2×#95011yescharacteristic
423C2×C3C2×#95011yescharacteristic
424D3—22no—
425C22—32no—
426C22—61no—
427C22—61no—
428C22C2×D3×#6711yescharacteristic
429C4—32no—
430C4—42no—
431C4—61no—
432C4—61no—
433C4—122no—
434C4—122no—
435C4—362no—
436C4#6393312yes—
437C4#6394912yes—
438C4D32×Q812yes—
439C3—21no—
440C3#8193811yescharacteristic, complemented
441C3#8333911yescharacteristic, complemented
442C2—62no—
443C2C2×#6393311yescharacteristic
444C2C2×#6394911yescharacteristic
445C2D3×#94411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592779C2semidirect
4. C3×#5078C2semidirect
6. #10590413C2semidirect
8. #10590311C2semidirect
9. #10590309C2semidirect
48. #5078D3semidirect
85. D3×C3⋊C8Q8semidirect
393. C32#3160semidirect
440. C3#81938semidirect
441. C3#83339semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
#105938592
#105927792
C3×#50782
#105905712
#105904132
C4×D3×C3⋊C82
#105903112
#105903092
#833393
#819383