Finite Group Databasebeta

← #11784145

Subgroups — #11784145

Order 1152.

717 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic
2C2×C3×#837C211yesmaximal, characteristic
3C3×#5233C211yesmaximal, characteristic
4C2×#63554C211yesmaximal, characteristic, complemented
5#10591057C211yesmaximal, characteristic, complemented
6#10589166C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70370—31nomaximal
9#70290—31nomaximal
10C2×C32×#41C2211yescharacteristic
11#64157—22no—
12#64157C414yescomplemented
13C2×#3748—21no—
14C2×#3748C2211yescharacteristic
15C22×C3⋊(C3⋊C8)—21no—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#837C414yescomplemented
22C3×#835C412yescomplemented
23C3×#832C412yescomplemented
24#63554—21no—
25#63554—22no—
26Dic3×C3⋊C8—21no—
27C2×#948—31no—
28C2×#948—31no—
29C2×#948—61no—
30C2×C3×#104—31no—
31C3×#416—31no—
32C2×#837D311yescharacteristic
33#5233D311yescharacteristic
34#5122—31no—
35C2×#815—31no—
36#4997—31no—
37C2×#803—31no—
38#4558—31no—
39#4552—31no—
40#4532—31no—
41#4523—31no—
42C32×#41—21no—
43C32×#41—21no—
44C32×#41C2×C412yes—
45C32×#41C2×C412yes—
46C2×C32×Q8C2×C411yescharacteristic
47C2×C32×D4—21no—
48C2×C32×D4C2×C411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3×Dic3—21no—
52#3748—21no—
53#3748—24no—
54#3748C2×C412yes—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—24no—
57C2×C3⋊(C3⋊C8)C2×C412yes—
58C2×C3⋊(C3⋊C8)D411yescharacteristic
59C2×C3⋊(C3⋊C8)D411yescharacteristic
60C2×C3⋊(C3⋊C8)D412yes—
61C3×#217—21no—
62C3×C4⋊Dic3C2×C412yes—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3C2×C412yes—
66C3×#208—21no—
67C3×#208C2×C412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8C2×C412yes—
72#1765—91noSylow
73C2×C3×#41—21no—
74C2×C3×#41C2×D311yescharacteristic
75C2×C3×#41C2×D311yescharacteristic
76C2×C3×M16—31no—
77C22×C3×C8—31no—
78C3×#117—31no—
79C2×C3×C42—31no—
80#948—34no—
81#948—34no—
82#948—64no—
83#948—62no—
84#948—62no—
85#948—64no—
86#926C2×D311yescharacteristic
87C2×C4×Dic3C2×D311yescharacteristic
88C2×#208—31no—
89C2×#208—31no—
90C2×#208—61no—
91C2×#208—61no—
92C2×#208—61no—
93C2×#208—62no—
94C2×#208C2×D311yescharacteristic
95C22×C3⋊C8—31no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—61no—
98C22×C3⋊C8—61no—
99C22×C3⋊C8—61no—
100C22×C3⋊C8—62no—
101C22×C3⋊C8C2×D311yescharacteristic
102C3×#104—34no—
103C3×#103—32no—
104C3×#102—32no—
105#837Dic314yescomplemented
106#835Dic312yescomplemented
107#832Dic312yescomplemented
108#815—61no—
109#815—62no—
110C8×Dic3—61no—
111#803—62no—
112#803—61no—
113C4×C3⋊C8—61no—
114C23×C32—21no—
115C23×C32#4111yescharacteristic
116C32×Q8—21no—
117C32×Q8C4212yes—
118C32×D4—22no—
119C32×D4—22no—
120C32×D4—21no—
121C32×D4C4212yes—
122C2×C32×C4—21no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—42no—
134C3⋊(C3⋊C8)—22no—
135C3⋊(C3⋊C8)C22⋊C412yes—
136C3⋊(C3⋊C8)C22⋊C412yes—
137C3×C3⋊C8—22no—
138C3×C3⋊C8—22no—
139C2×#131—91no—
140C2×#104—31no—
141#416—31no—
142#405—91no—
143C2×#97—91no—
144#341—91no—
145#339—91no—
146C3×#41—22no—
147C3×#41—22no—
148C3×#41—21no—
149C3×#41—21no—
150C3×#41—21no—
151C3×#41—21no—
152C3×#41—22no—
153C3×#41—22no—
154C3×#41C4×D312yes—
155C3×#41C4×D312yes—
156C3×#41C4×D312yes—
157C3×#41C2×Dic312yes—
158C2×C3×Q8—21no—
159C2×C3×Q8C4×D311yescharacteristic
160C2×C3×Q8C2×Dic311yescharacteristic
161C2×C3×D4—22no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4C4×D311yescharacteristic
166C2×C3×D4C2×Dic311yescharacteristic
167C22×C3×C4—22no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—21no—
175C3×M16—32no—
176C3×M16—61no—
177C2×C3×C8—32no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C2×C3×C8—61no—
181C3×C4⋊C4—32no—
182C3×C22⋊C4—61no—
183C3×C42—32no—
184C3×C42—61no—
185C3×C42—61no—
186#217—21no—
187C4⋊Dic3C2×Dic312yes—
188C4×Dic3—21no—
189C4×Dic3—21no—
190C4×Dic3C2×Dic312yes—
191#208—21no—
192#208—32no—
193#208—32no—
194#208—62no—
195#208—64no—
196#208—64no—
197#208—68no—
198#208—62no—
199#208—61no—
200#208—61no—
201#208C2×Dic312yes—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—32no—
206C2×C3⋊C8—32no—
207C2×C3⋊C8—31no—
208C2×C3⋊C8—31no—
209C2×C3⋊C8—32no—
210C2×C3⋊C8—31no—
211C2×C3⋊C8—31no—
212C2×C3⋊C8—32no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—62no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—64no—
218C2×C3⋊C8—64no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—68no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8C2×Dic312yes—
224C22×C32—22no—
225C22×C32—22no—
226C22×C32—42no—
227C22×C32#11711yescharacteristic
228C22×C32C4×D411yescharacteristic
229C22×C32C4×D411yescharacteristic
230C32×C4—22no—
231C32×C4C2×C4211yescharacteristic
232C32×C4C2×C22⋊C411yescharacteristic
233C32×C4C4×D411yescharacteristic
234C32×C4C4×D411yescharacteristic
235C3×Dic3—42no—
236C3×Dic3—42no—
237C2×#41D3211yescharacteristic
238#131—94no—
239#131—182no—
240C2×M16—31no—
241C2×M16—91no—
242C2×M16—181no—
243C22×C8—31no—
244C22×C8—91no—
245C22×C8—181no—
246#117—31no—
247C2×C42—31no—
248#104—34no—
249#103—32no—
250#102—32no—
251#97—182no—
252#97—181no—
253C4×C8—181no—
254C23×C3—22no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3#23711yescharacteristic
259C23×C3#23711yescharacteristic
260C3×Q8—22no—
261C3×Q8—21no—
262C3×Q8—21no—
263C3×Q8—22no—
264C3×Q8C4×Dic312yes—
265C3×Q8C4×Dic312yes—
266C3×D4—24no—
267C3×D4—24no—
268C3×D4—22no—
269C3×D4—22no—
270C3×D4—22no—
271C3×D4—22no—
272C3×D4—22no—
273C3×D4—21no—
274C3×D4—21no—
275C3×D4—22no—
276C3×D4C4×Dic312yes—
277C3×D4C4×Dic312yes—
278C2×C3×C4—24no—
279C2×C3×C4—22no—
280C2×C3×C4—24no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—122no—
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4C2×C4×D311yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4C22×Dic311yescharacteristic
307C2×C3×C4C22×Dic311yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—42no—
311C3×C8—62no—
312C3×C8—62no—
313C3⋊C8—22no—
314C3⋊C8—22no—
315C3⋊C8—32no—
316C3⋊C8—32no—
317C3⋊C8—32no—
318C3⋊C8—32no—
319C3⋊C8—62no—
320C3⋊C8—62no—
321C3⋊C8—64no—
322C3⋊C8—62no—
323C3⋊C8—62no—
324C2×C32—21no—
325C2×C32—21no—
326C2×C32—42no—
327C2×C32C4×C22⋊C411yescharacteristic
328C2×C32#44412yes—
329#41—21no—
330#41—21no—
331#41D3×Dic312yes—
332#41#62412yes—
333C2×Q8D3×Dic311yescharacteristic
334C2×D4—21no—
335C2×D4D3×Dic311yescharacteristic
336C22×C4—21no—
337C22×C4—61no—
338C22×C4C2×D3211yescharacteristic
339M16—32no—
340M16—61no—
341M16—92no—
342M16—184no—
343M16—181no—
344C2×C8—32no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—61no—
348C2×C8—92no—
349C2×C8—92no—
350C2×C8—91no—
351C2×C8—91no—
352C2×C8—184no—
353C2×C8—181no—
354C4⋊C4—32no—
355C22⋊C4—61no—
356C42—32no—
357C42—61no—
358C42—61no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—24no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—42no—
368C22×C3—44no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3#87711yescharacteristic
372C22×C3#87711yescharacteristic
373C22×C3#67⋊C411yescharacteristic
374C22×C3#67⋊C411yescharacteristic
375C22×C3D4×Dic311yescharacteristic
376C22×C3D4×Dic311yescharacteristic
377C3×C4—24no—
378C3×C4—22no—
379C3×C4—22no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—122no—
385C3×C4—122no—
386C3×C4D3×C22⋊C411yescharacteristic
387C3×C4D3×C22⋊C411yescharacteristic
388C3×C4#67⋊C411yescharacteristic
389C3×C4#67⋊C411yescharacteristic
390C3×C4C2×C4×Dic311yescharacteristic
391C3×C4C2×C4×Dic311yescharacteristic
392C3×C4D4×Dic311yescharacteristic
393C3×C4D4×Dic311yescharacteristic
394Dic3—42no—
395Dic3—42no—
396C32#176511yescharacteristic, complemented, Sylow
397C23—21no—
398C23#380511yescharacteristic
399Q8—21no—
400Q8Dic3212yes—
401D4—22no—
402D4—22no—
403D4—21no—
404D4Dic3212yes—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—122no—
411C2×C4C2×D3×Dic311yescharacteristic
412C2×C4C2×D3×Dic311yescharacteristic
413C2×C4#380511yescharacteristic
414C2×C4C2×#62411yescharacteristic
415C2×C4#381111yescharacteristic
416C2×C4#381111yescharacteristic
417C8—62no—
418C8—62no—
419C8—92no—
420C8—92no—
421C8—182no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—41no—
429C2×C3—41no—
430C2×C3—44no—
431C2×C3—42no—
432C2×C3—42no—
433C2×C3#482312yes—
434C2×C3Dic3×C22⋊C411yescharacteristic
435C2×C3Dic3×C22⋊C411yescharacteristic
436C2×C3#519712yes—
437C22—22no—
438C22—22no—
439C22—42no—
440C22#6395711yescharacteristic
441C22#67⋊Dic311yescharacteristic
442C22#67⋊Dic311yescharacteristic
443C4—22no—
444C4—122no—
445C4—122no—
446C4C2×Dic3211yescharacteristic
447C4#67⋊Dic311yescharacteristic
448C4#67⋊Dic311yescharacteristic
449C4#6397411yescharacteristic
450C3—21no—
451C3#7029011yescharacteristic, complemented
452C3#7037011yescharacteristic, complemented
453C2—21no—
454C2—21no—
455C2—42no—
456C2#1059167612yes—
457C2#1059170511yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C4×D4
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1765
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63554C2semidirect
5. #10591057C2semidirect
6. #10589166C2semidirect
7. #10589161C2semidirect
12. #64157C4semidirect
21. C3×#837C4semidirect
22. C3×#835C4semidirect
23. C3×#832C4semidirect
105. #837Dic3semidirect
106. #835Dic3semidirect
107. #832Dic3semidirect
396. C32#1765semidirect
451. C3#70290semidirect
452. C3#70370semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C2×C3×#8372
C3×#52332
C2×#635542
#105910572
#105891662
#105891612
#703703
#702903