Finite Group Databasebeta

← #10689175

Subgroups — #10689175

Order 768.

568 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#73867C211yesmaximal, characteristic
2#69928C211yesmaximal, characteristic
3C2×#4469C211yesmaximal, characteristic
4#69504C211yesmaximal, characteristic
5#69410C211yesmaximal, characteristic
6C3×#1294C211yesmaximal, characteristic
7#67612C211yesmaximal, characteristic
8#8855—31nomaximal, Sylow
9C22×C4⋊Dic3C2211yescharacteristic
10C22×Dic3⋊C4C2211yescharacteristic
11C2×C3×C22⋊C8C2211yescharacteristic
12C3×#380C2211yescharacteristic
13C2×C3×#95C2211yescharacteristic
14#5212C2211yescharacteristic
15C2×C3⋊#95—21no—
16C2×C3⋊#95—21no—
17C2×#830C2211yescharacteristic
18C2×#817—21no—
19#4978—21no—
20#4978—21no—
21C2×#807—21no—
22#4943—21no—
23Dic3×C22⋊C4—21no—
24#4655—21no—
25#4655—21no—
26#4551—21no—
27#4529—21no—
28#4469C414yescomplemented
29#2313—31no—
30#1853—31no—
31#1852—31no—
32C2×#324—31no—
33#1441—31no—
34#1294—31no—
35#1294D311yescharacteristic
36C23×C3×C4—21no—
37C23×C3×C4C2311yescharacteristic
38C23×Dic3—21no—
39C23×Dic3D411yescharacteristic
40C23×Dic3D411yescharacteristic
41C22×C3×C8—21no—
42C2×C3×C4⋊C4D411yescharacteristic
43C2×C3×C4⋊C4D411yescharacteristic
44C2×C3×C22⋊C4—21no—
45C2×#217—21no—
46C2×C4⋊Dic3—21no—
47C2×C4⋊Dic3—21no—
48C2×C4⋊Dic3—42no—
49C2×C4⋊Dic3D411yescharacteristic
50C2×C4⋊Dic3D411yescharacteristic
51C2×Dic3⋊C4—21no—
52C2×Dic3⋊C4—21no—
53C2×Dic3⋊C4—21no—
54C2×Dic3⋊C4—21no—
55C2×Dic3⋊C4C2×C412yes—
56C2×Dic3⋊C4Q812yes—
57C2×C4×Dic3—21no—
58C2×C4×Dic3—21no—
59C22×C3⋊C8—21no—
60C3×C22⋊C8—21no—
61C3×C22⋊C8C2×C412yes—
62C3×#95—21no—
63C3×#95—21no—
64C3×#95—21no—
65C3⋊#95—21no—
66C3⋊#95—21no—
67C3⋊#95—21no—
68C3⋊#95—21no—
69C3⋊#95—21no—
70C3⋊#95—21no—
71C3⋊#95—21no—
72C3⋊#95—42no—
73C3⋊#95—42no—
74#830—21no—
75#830C2×C412yes—
76#817—42no—
77#807—42no—
78C22×C4⋊C4—31no—
79C22×C4⋊C4—31no—
80C2×#107—61no—
81C2×#106—61no—
82C2×C22⋊C8—31no—
83C2×C22⋊C8C2×D311yescharacteristic
84#387—61no—
85#387—61no—
86#387—61no—
87#387—61no—
88#381—61no—
89#380—31no—
90#380C2×D311yescharacteristic
91C4×C22⋊C4—61no—
92C2×#95—61no—
93C2×#95—61no—
94C2×#95C2×D311yescharacteristic
95#340—61no—
96#340—61no—
97#324—34no—
98C24×C3C2×D411yescharacteristic
99C22×C3×C4—22no—
100C22×C3×C4—21no—
101C22×C3×C4—21no—
102C22×C3×C4—41no—
103C22×C3×C4—41no—
104C22×C3×C4—41no—
105C22×C3×C4—41no—
106C22×C3×C4—41no—
107C22×C3×C4—41no—
108C22×C3×C4—41no—
109C22×C3×C4—41no—
110C22×C3×C4C22×C411yescharacteristic
111C22×C3×C4C2×D411yescharacteristic
112C22×C3×C4C2×D411yescharacteristic
113C22×C3×C4C2×Q811yescharacteristic
114C22×C3×C4#4111yescharacteristic
115C22×C3×C4#4111yescharacteristic
116C22×Dic3—21no—
117C22×Dic3—21no—
118C22×Dic3—21no—
119C22×Dic3—21no—
120C22×Dic3—21no—
121C22×Dic3—21no—
122C22×Dic3—21no—
123C22×Dic3—21no—
124C22×Dic3—22no—
125C22×Dic3—21no—
126C22×Dic3—21no—
127C22×Dic3—41no—
128C22×Dic3—41no—
129C22×Dic3—41no—
130C22×Dic3—41no—
131C22×Dic3—41no—
132C22×Dic3—41no—
133C22×Dic3—41no—
134C22×Dic3—41no—
135C22×Dic3C4⋊C412yes—
136C22×Dic3C4⋊C412yes—
137C2×C3×C8—22no—
138C2×C3×C8—41no—
139C2×C3×C8—41no—
140C3×C4⋊C4—41no—
141C3×C4⋊C4—41no—
142C3×C22⋊C4—41no—
143C3×C22⋊C4—41no—
144#217—41no—
145#217—41no—
146C4⋊Dic3—22no—
147C4⋊Dic3—22no—
148C4⋊Dic3—41no—
149C4⋊Dic3—41no—
150C4⋊Dic3—41no—
151C4⋊Dic3—41no—
152Dic3⋊C4—22no—
153Dic3⋊C4—22no—
154Dic3⋊C4—22no—
155Dic3⋊C4—22no—
156C4×Dic3—81no—
157C4×Dic3—81no—
158C2×C3⋊C8—22no—
159C2×C3⋊C8—41no—
160C2×C3⋊C8—41no—
161C23×C4—21no—
162C23×C4—31no—
163C23×C4—31no—
164C23×C4—61no—
165C23×C4C22×D311yescharacteristic
166C22×C8—21no—
167C22×C8—61no—
168C2×C4⋊C4—32no—
169C2×C4⋊C4—32no—
170C2×C4⋊C4—31no—
171C2×C4⋊C4—31no—
172C2×C4⋊C4—61no—
173C2×C4⋊C4—61no—
174C2×C4⋊C4—61no—
175C2×C4⋊C4—61no—
176C2×C4⋊C4—61no—
177C2×C4⋊C4—61no—
178C2×C4⋊C4—122no—
179C2×C4⋊C4D1211yescharacteristic
180C2×C4⋊C4D1211yescharacteristic
181C2×C22⋊C4—21no—
182C2×C22⋊C4—61no—
183C2×C42—61no—
184C2×C42—61no—
185#107—122no—
186#106—122no—
187C22⋊C8—21no—
188C22⋊C8—32no—
189C22⋊C8—61no—
190C22⋊C8C4×D312yes—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—61no—
195#95—61no—
196#95—61no—
197#95—61no—
198#95—61no—
199#95—61no—
200#95—61no—
201#95—122no—
202#95—122no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3C2×C4⋊C411yescharacteristic
208C23×C3#12011yescharacteristic
209C23×C3#12311yescharacteristic
210C23×C3#13511yescharacteristic
211C23×C3#13511yescharacteristic
212C23×C3AGL(1,ℤ/8)11yescharacteristic
213C23×C3#13711yescharacteristic
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—42no—
223C2×C3×C4—42no—
224C2×C3×C4—42no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—81no—
232C2×C3×C4—81no—
233C2×C3×C4—81no—
234C2×C3×C4—81no—
235C2×C3×C4C4×D411yescharacteristic
236C2×C3×C4C4×D411yescharacteristic
237C2×C3×C4C22⋊Q811yescharacteristic
238C2×C3×C4C22⋊Q811yescharacteristic
239C2×Dic3—22no—
240C2×Dic3—22no—
241C2×Dic3—22no—
242C2×Dic3—22no—
243C2×Dic3—41no—
244C2×Dic3—41no—
245C2×Dic3—41no—
246C2×Dic3—41no—
247C2×Dic3—41no—
248C2×Dic3—41no—
249C2×Dic3—42no—
250C2×Dic3—42no—
251C2×Dic3—42no—
252C2×Dic3—41no—
253C2×Dic3—41no—
254C2×Dic3—41no—
255C2×Dic3—41no—
256C2×Dic3—41no—
257C2×Dic3—42no—
258C2×Dic3—41no—
259C2×Dic3—81no—
260C2×Dic3—81no—
261C2×Dic3—81no—
262C2×Dic3—81no—
263C2×Dic3—81no—
264C3×C8—42no—
265C3⋊C8—42no—
266C24D3×D411yescharacteristic
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—32no—
271C22×C4—32no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—61no—
281C22×C4—61no—
282C22×C4—61no—
283C22×C4—61no—
284C22×C4—61no—
285C22×C4—61no—
286C22×C4—61no—
287C22×C4—61no—
288C22×C4—62no—
289C22×C4—61no—
290C22×C4—61no—
291C22×C4—121no—
292C22×C4—121no—
293C22×C4—121no—
294C22×C4—121no—
295C22×C4—121no—
296C22×C4—121no—
297C22×C4—121no—
298C22×C4—121no—
299C22×C4C2×C4×D311yescharacteristic
300C22×C4C2×D1211yescharacteristic
301C22×C4#23511yescharacteristic
302C22×C4D3×D411yescharacteristic
303C22×C4#23711yescharacteristic
304C22×C4D3×Q811yescharacteristic
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—62no—
309C2×C8—121no—
310C2×C8—121no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—62no—
314C4⋊C4—62no—
315C4⋊C4—62no—
316C4⋊C4—62no—
317C4⋊C4—62no—
318C4⋊C4—62no—
319C4⋊C4—121no—
320C4⋊C4—121no—
321C4⋊C4—121no—
322C4⋊C4—121no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—121no—
326C22⋊C4—121no—
327C42—241no—
328C42—241no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3#38511yescharacteristic
342C22×C3#42711yescharacteristic
343C22×C3#42811yescharacteristic
344C22×C3#44911yescharacteristic
345C22×C3#45211yescharacteristic
346C22×C3#45411yescharacteristic
347C22×C3#45611yescharacteristic
348C22×C3B(4,𝔽2)11yescharacteristic
349C22×C3#45811yescharacteristic
350C22×C3#48211yescharacteristic
351C22×C3#48511yescharacteristic
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—82no—
357C3×C4—81no—
358C3×C4—81no—
359Dic3—42no—
360Dic3—42no—
361Dic3—82no—
362Dic3—81no—
363Dic3—81no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23#88211yescharacteristic
369C23#88311yescharacteristic
370C23D3×C4⋊C411yescharacteristic
371C23#91111yescharacteristic
372C23#91611yescharacteristic
373C23#91611yescharacteristic
374C23#91811yescharacteristic
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—122no—
407C2×C4—122no—
408C2×C4—122no—
409C2×C4—121no—
410C2×C4—122no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4—121no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—241no—
417C2×C4—241no—
418C2×C4—241no—
419C2×C4—241no—
420C2×C4—241no—
421C2×C4C4×D1211yescharacteristic
422C2×C4#67⋊C411yescharacteristic
423C2×C4#89611yescharacteristic
424C2×C4#89711yescharacteristic
425C8—42no—
426C8—122no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3#159711yescharacteristic
432C2×C3#160311yescharacteristic
433C2×C3#160911yescharacteristic
434C2×C3#161511yescharacteristic
435C2×C3#185411yescharacteristic
436C2×C3#185711yescharacteristic
437C2×C3#186711yescharacteristic
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22#466811yescharacteristic
451C22#474111yescharacteristic
452C22#474211yescharacteristic
453C22#477911yescharacteristic
454C22#478111yescharacteristic
455C22#480811yescharacteristic
456C22#481511yescharacteristic
457C22#482611yescharacteristic
458C22#482711yescharacteristic
459C22#486011yescharacteristic
460C22#488111yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—82no—
466C4—81no—
467C4—81no—
468C4—122no—
469C4—122no—
470C4—242no—
471C4—241no—
472C4—241no—
473C3#885511yescharacteristic, complemented, Sylow
474C2—21no—
475C2—21no—
476C2—21no—
477C2—21no—
478C2#6829211yescharacteristic
479C2#6829611yescharacteristic
480C2#6832611yescharacteristic
481C2#6833011yescharacteristic
482C2#6876411yescharacteristic
483C2#6887611yescharacteristic
484C2#6896111yescharacteristic
subgroupG/H
centerC23#882
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC3×#1294C2
socleC23×C3#120
prime radicalC24×C3C2×D4
cosocleC23×C3×C4C23
hypercenter#1294D3
hypocenterC3#8855
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
28. #4469C4semidirect
473. C3#8855semidirect

Maximal subgroups

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

subgroupindex
#738672
#699282
C2×#44692
#695042
#694102
C3×#12942
#676122
#88553