Finite Group Databasebeta

← #11873314

Subgroups — #11873314

Order 1152.

812 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595989C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic
3C3×#5000C211yesmaximal, characteristic
4#10591186C212yesmaximal
5#10591134C212yesmaximal
6#10590385C212yesmaximal, complemented
7#10590383C212yesmaximal, complemented
8C4×#3719C212yesmaximal, complemented
9#10590302C212yesmaximal, complemented
10#82555—31nomaximal
11#79396—31nomaximal
12C22×C3×Dic6C2211yescharacteristic
13C32×#117C2211yescharacteristic
14#64133C2212yes—
15#64098—22no—
16#64088—22no—
17#64079C2211yescharacteristic
18#64078C2211yescharacteristic
19C4×#634C2212yes—
20C3×#926C2211yescharacteristic
21C3×#887—22no—
22C3×#877—22no—
23C3×C4×Dic6C2212yes—
24C3×C4×Dic6C2212yes—
25C2×#3719C2212yes—
26C2×#3719C2212yes—
27C3×#830C2212yes—
28C3×C4⋊(C3⋊C8)C2212yes—
29C3×#803C2211yescharacteristic
30C3×C4×C3⋊C8C2211yescharacteristic
31#63575C2212yes—
32#63573C2212yes—
33#63567C2212yes—
34#63567C2212yes—
35#63566C2212yes—
36#63566C2212yes—
37C3×#519—31no—
38#5518—31no—
39#5518—31no—
40#5518—61no—
41#5516D311yescharacteristic
42C3×#433—31no—
43#5228—32no—
44#5031—32no—
45#5030—32no—
46C4×#216—32no—
47#5022—32no—
48#5000D311yescharacteristic
49#4996—32no—
50#4849—32no—
51#4829—32no—
52#4739—32no—
53#4723—32no—
54#4716—32no—
55C4×Dic12—32no—
56C22×C32×C4C2311yescharacteristic
57C2×#634C2312yes—
58C22×C3×Dic3—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—24no—
61C2×C3×Dic6C2312yes—
62C32×C4⋊C4D412yes—
63C32×C22⋊C4D412yes—
64C32×C42C2311yescharacteristic
65C32×C42C2311yescharacteristic
66#3757—22no—
67C4⋊(C3⋊Dic3)—22no—
68C4⋊(C3⋊Dic3)C2312yes—
69#3750—22no—
70#3750—22no—
71#3750—22no—
72C4×C3⋊Dic3—22no—
73C3×#217—21no—
74C3×C4⋊Dic3C2312yes—
75C3×Dic3⋊C4—22no—
76C3×Dic3⋊C4—22no—
77C3×C4×Dic3—22no—
78C3×C4×Dic3—22no—
79C3×C4×Dic3—21no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82#3719—24no—
83#3719—24no—
84#3127—91noSylow
85C22×C3×Q8—31no—
86C22×Dic6C2×D311yescharacteristic
87C3×C4×Q8—32no—
88C3×C4×Q8—32no—
89C3×C4×Q8—62no—
90C3×#117—21no—
91C3×#117—31no—
92C3×#117—62no—
93C3×#117C2×D311yescharacteristic
94C3×#117C2×D311yescharacteristic
95C2×#216—32no—
96C2×#216—32no—
97#926C2×D311yescharacteristic
98#924—32no—
99#924—32no—
100#924—62no—
101C2×Dic12—32no—
102C2×Dic12—32no—
103#889—64no—
104#889—62no—
105#889—62no—
106#887—22no—
107#879—64no—
108#879—62no—
109#879—62no—
110#877—22no—
111#870—31no—
112#870—31no—
113#870—61no—
114#869—31no—
115#869—31no—
116#869—61no—
117C4×Dic6—32no—
118C4×Dic6—32no—
119C4×Dic6—62no—
120C4×Dic6C2×D312yes—
121C4×Dic6C2×D312yes—
122C3×C4⋊C8—32no—
123C3×C22⋊C8—32no—
124C3×#97—31no—
125C3×C4×C8—31no—
126#835—32no—
127#835—32no—
128#830C2×D312yes—
129#818—32no—
130#817—32no—
131#816—32no—
132#816—32no—
133#816—32no—
134#816—32no—
135#810—32no—
136#810—32no—
137#808—32no—
138#807—32no—
139C4⋊(C3⋊C8)C2×D312yes—
140#803C2×D311yescharacteristic
141C4×C3⋊C8C2×D311yescharacteristic
142C23×C32C2×D411yescharacteristic
143C2×C32×C4—22no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150#634—22no—
151#634—22no—
152C2×C3×Dic3—24no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C3×Dic6—24no—
156C3×Dic6—22no—
157C3×Dic6#4114yes—
158C3×C3⋊C8—22no—
159C3×C3⋊C8—22no—
160#541—91no—
161#519—31no—
162#485—92no—
163#479—92no—
164#462—92no—
165#451—92no—
166#441—92no—
167C4×Q16—92no—
168#433—31no—
169C2×C3×Q8—32no—
170C2×C3×Q8—64no—
171C2×C3×Q8—61no—
172C22×C3×C4—21no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×Dic3—21no—
177C2×Dic6—21no—
178C2×Dic6—24no—
179C2×Dic6—32no—
180C2×Dic6—32no—
181C2×Dic6—62no—
182C2×Dic6C22×D312yes—
183C2×C3×C8—32no—
184C2×C3×C8—32no—
185C3×C4⋊C4—22no—
186C3×C4⋊C4—32no—
187C3×C4⋊C4—62no—
188C3×C4⋊C4—62no—
189C3×C4⋊C4D1212yes—
190C3×C4⋊C4#6712yes—
191C3×C22⋊C4—22no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4D1212yes—
194C3×C22⋊C4#6712yes—
195C3×C42—21no—
196C3×C42—21no—
197C3×C42—61no—
198C3×C42—62no—
199C3×C42—62no—
200C3×C42C22×D311yescharacteristic
201C3×C42C22×D311yescharacteristic
202C3×C42C22×D311yescharacteristic
203C3×C42C22×D311yescharacteristic
204#217—21no—
205#217—64no—
206#217—62no—
207#217—62no—
208#216—64no—
209#216—64no—
210C4⋊Dic3—32no—
211C4⋊Dic3—32no—
212C4⋊Dic3—62no—
213C4⋊Dic3—64no—
214C4⋊Dic3—62no—
215C4⋊Dic3—62no—
216C4⋊Dic3C22×D312yes—
217Dic3⋊C4—22no—
218Dic3⋊C4—22no—
219Dic3⋊C4—64no—
220Dic3⋊C4—64no—
221Dic3⋊C4—64no—
222Dic3⋊C4—62no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—62no—
226Dic3⋊C4—62no—
227Dic3⋊C4—62no—
228C4×Dic3—22no—
229C4×Dic3—22no—
230C4×Dic3—21no—
231C4×Dic3—64no—
232C4×Dic3—62no—
233C4×Dic3—62no—
234C2×C3⋊C8C22×D312yes—
235C2×C3⋊C8C22×D312yes—
236Dic12—64no—
237Dic12—64no—
238C22×C32—21no—
239C22×C32—22no—
240C22×C32C22×D411yescharacteristic
241C32×C4—21no—
242C32×C4—22no—
243C32×C4—22no—
244C32×C4C2×#4112yes—
245C3⋊Dic3—42no—
246C3⋊Dic3—42no—
247C3×Dic3—24no—
248C3×Dic3—42no—
249C22×Q8—31no—
250C2×Q16—92no—
251C2×Q16—92no—
252C4⋊Q8—91no—
253#126—182no—
254#125—91no—
255#125—182no—
256C22⋊Q8—92no—
257C4×Q8—32no—
258C4×Q8—32no—
259C4×Q8—62no—
260C4×Q8—92no—
261#117—31no—
262#117—62no—
263#117D3211yescharacteristic
264#107—92no—
265#106—92no—
266C4⋊C8—32no—
267#103—92no—
268#103—92no—
269#103—92no—
270#103—92no—
271C22⋊C8—32no—
272#97—31no—
273C4×C8—31no—
274C23×C3—21no—
275C23×C3C2×D1211yescharacteristic
276C23×C3C2×#6711yescharacteristic
277C3×Q8—34no—
278C3×Q8—64no—
279C3×Q8—62no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—22no—
286C2×C3×C4—42no—
287C2×C3×C4—64no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4C2×D1212yes—
291C2×C3×C4C2×D1211yescharacteristic
292C2×C3×C4C2×D1212yes—
293C2×C3×C4C2×#6712yes—
294C2×C3×C4C2×#6712yes—
295C2×C3×C4C2×#6711yescharacteristic
296C2×C3×C4C23×D311yescharacteristic
297C2×C3×C4C23×D311yescharacteristic
298C2×Dic3—24no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—64no—
302C2×Dic3—64no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307Dic6—24no—
308Dic6—22no—
309Dic6—62no—
310Dic6—62no—
311Dic6—62no—
312Dic6—62no—
313Dic6—122no—
314Dic6—122no—
315Dic6#23514yes—
316C3×C8—62no—
317C3×C8—62no—
318C3⋊C8—22no—
319C3⋊C8—22no—
320C2×C32—41no—
321C2×C32#52511yescharacteristic
322C2×C32#57812yes—
323C2×Q8—32no—
324C2×Q8—64no—
325C2×Q8—61no—
326C2×Q8—92no—
327C22×C4—61no—
328C22×C4C2×D3211yescharacteristic
329Q16—184no—
330Q16—184no—
331C2×C8—32no—
332C2×C8—32no—
333C4⋊C4—32no—
334C4⋊C4—62no—
335C4⋊C4—62no—
336C4⋊C4—92no—
337C4⋊C4—182no—
338C4⋊C4—182no—
339C4⋊C4—182no—
340C4⋊C4—182no—
341C4⋊C4#62612yes—
342C22⋊C4—61no—
343C22⋊C4—182no—
344C22⋊C4#62612yes—
345C42—61no—
346C42—62no—
347C42—62no—
348C42—182no—
349C42C2×D3211yescharacteristic
350C42C2×D3211yescharacteristic
351C22×C3—22no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—22no—
355C22×C3—21no—
356C22×C3—41no—
357C22×C3—42no—
358C22×C3C22×D1211yescharacteristic
359C22×C3C22×#6711yescharacteristic
360C3×C4—22no—
361C3×C4—22no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—22no—
365C3×C4—22no—
366C3×C4—22no—
367C3×C4—41no—
368C3×C4—42no—
369C3×C4—42no—
370C3×C4—64no—
371C3×C4—122no—
372C3×C4C2×#23512yes—
373C3×C4D3×#4112yes—
374Dic3—24no—
375Dic3—42no—
376Dic3—124no—
377Dic3—124no—
378Dic3—122no—
379Dic3—122no—
380Dic3—122no—
381Dic3—122no—
382C32#312711yescharacteristic, complemented, Sylow
383C23C2×#62611yescharacteristic
384Q8—34no—
385Q8—64no—
386Q8—62no—
387Q8—182no—
388Q8—182no—
389C2×C4—22no—
390C2×C4—64no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—182no—
394C2×C4—182no—
395C2×C4C2×#62612yes—
396C2×C4C2×#62612yes—
397C2×C4C2×#62611yescharacteristic
398C2×C4C22×D3211yescharacteristic
399C8—62no—
400C8—62no—
401C2×C3—22no—
402C2×C3—21no—
403C2×C3—41no—
404C2×C3—41no—
405C2×C3—81no—
406C2×C3#552411yescharacteristic
407C2×C3#575312yes—
408C2×C3#579111yescharacteristic
409C2×C3#583812yes—
410C22—22no—
411C22—21no—
412C22C22×#62611yescharacteristic
413C4—22no—
414C4—22no—
415C4—21no—
416C4—64no—
417C4—122no—
418C4—362no—
419C4—362no—
420C4D3×#23512yes—
421C3—21no—
422C3#7939611yescharacteristic, complemented
423C3#8255511yescharacteristic, complemented
424C2—41no—
425C2#1059502311yescharacteristic
426C2#1059545012yes—
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#117D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
6. #10590385C2semidirect
7. #10590383C2semidirect
8. C4×#3719C2semidirect
9. #10590302C2semidirect
382. C32#3127semidirect
422. C3#79396semidirect
423. C3#82555semidirect

Maximal subgroups

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

subgroupindex
#105959892
C3×#55162
C3×#50002
#105911862
#105911342
#105903852
#105903832
C4×#37192
#105903022
#825553
#793963