Finite Group Databasebeta

← #10694013

Subgroups — #10694013

Order 768.

656 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4976C211yesmaximal, characteristic
2C2×C3×#324C211yesmaximal, characteristic
3C2×#4528C211yesmaximal, characteristic
4C2×#4469C211yesmaximal, characteristic
5C2×#4469C211yesmaximal, characteristic
6#69908C211yesmaximal, characteristic
7Dic3×C22⋊C8C211yesmaximal, characteristic
8#9650—31nomaximal, Sylow
9C22×C3×C4⋊C4C2211yescharacteristic
10C22×Dic3⋊C4C411yescharacteristic
11C22×Dic3⋊C4C411yescharacteristic
12C22×Dic3⋊C4C2211yescharacteristic
13C22×C4×Dic3C2211yescharacteristic
14C2×C3×C22⋊C8C2211yescharacteristic
15C2×C3×C22⋊C8C2211yescharacteristic
16C2×C3⋊#95C411yescharacteristic
17C2×C3⋊#95C411yescharacteristic
18C2×#830C2211yescharacteristic
19C2×#830C2211yescharacteristic
20C2×Dic3⋊C8—21no—
21C2×C8×Dic3—21no—
22#4976—21no—
23#4976—21no—
24#4976—21no—
25#4976—21no—
26C3×#324—22no—
27#4550—21no—
28#4550—21no—
29#4528—22no—
30#4469—22no—
31#4469—22no—
32C2×#389—31no—
33#1797—31no—
34C4×C22⋊C8—31no—
35C2×#324—31no—
36C2×#324—31no—
37C2×#324—31no—
38C2×#324D311yescharacteristic
39C23×C3×C4C2×C411yescharacteristic
40C23×C3×C4C2×C411yescharacteristic
41C23×C3×C4C2311yescharacteristic
42C23×Dic3C2×C411yescharacteristic
43C23×Dic3C2×C411yescharacteristic
44C23×Dic3C2×C411yescharacteristic
45C23×Dic3C2×C411yescharacteristic
46C22×C3×C8—21no—
47C22×C3×C8—21no—
48C2×C3×C4⋊C4—21no—
49C2×C3×C4⋊C4—21no—
50C2×C3×C4⋊C4—21no—
51C2×C3×C4⋊C4—21no—
52C2×C3×C4⋊C4—21no—
53C2×C3×C4⋊C4—21no—
54C2×Dic3⋊C4—21no—
55C2×Dic3⋊C4—21no—
56C2×Dic3⋊C4—22no—
57C2×Dic3⋊C4—21no—
58C2×Dic3⋊C4—21no—
59C2×Dic3⋊C4—21no—
60C2×Dic3⋊C4—21no—
61C2×Dic3⋊C4—21no—
62C2×Dic3⋊C4—21no—
63C2×Dic3⋊C4—21no—
64C2×Dic3⋊C4—21no—
65C2×Dic3⋊C4—42no—
66C2×Dic3⋊C4C814yescomplemented
67C2×C4×Dic3—42no—
68C2×C4×Dic3D411yescharacteristic
69C2×C4×Dic3D411yescharacteristic
70C2×C4×Dic3D411yescharacteristic
71C2×C4×Dic3D411yescharacteristic
72C22×C3⋊C8—21no—
73C22×C3⋊C8—21no—
74C3×C22⋊C8—21no—
75C3×C22⋊C8—21no—
76C3×C22⋊C8—21no—
77C3×C22⋊C8D412yes—
78C3⋊#95—21no—
79C3⋊#95—21no—
80C3⋊#95—21no—
81C3⋊#95—21no—
82#830—21no—
83#830—21no—
84#830—21no—
85#830D412yes—
86Dic3⋊C8—42no—
87C8×Dic3—42no—
88C22×C4⋊C4—31no—
89C22×C4⋊C4—31no—
90C22×C4⋊C4—31no—
91C22×C4⋊C4C2×D311yescharacteristic
92C22×C42—31no—
93C2×C4⋊C8—61no—
94C2×C22⋊C8—31no—
95C2×C22⋊C8—31no—
96C2×C22⋊C8C2×D311yescharacteristic
97C2×C22⋊C8C2×D311yescharacteristic
98C2×C4×C8—61no—
99#389—61no—
100#389—61no—
101#389—61no—
102#389—61no—
103C2×#95—31no—
104C2×#95—31no—
105#336—61no—
106#336—61no—
107#324—22no—
108#324—62no—
109#324—62no—
110#324—62no—
111C24×C3C22×C411yescharacteristic
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—41no—
122C22×C3×C4—41no—
123C22×C3×C4—41no—
124C22×C3×C4—41no—
125C22×C3×C4C2×C812yes—
126C22×C3×C4C2×D411yescharacteristic
127C22×C3×C4C2×D411yescharacteristic
128C22×C3×C4C2×D411yescharacteristic
129C22×C3×C4C2×D411yescharacteristic
130C22×C3×C4#4111yescharacteristic
131C22×C3×C4#4111yescharacteristic
132C22×Dic3—22no—
133C22×Dic3—22no—
134C22×Dic3—21no—
135C22×Dic3—21no—
136C22×Dic3—21no—
137C22×Dic3—21no—
138C22×Dic3—21no—
139C22×Dic3—21no—
140C22×Dic3—21no—
141C22×Dic3—21no—
142C22×Dic3—22no—
143C22×Dic3—21no—
144C22×Dic3—21no—
145C22×Dic3—21no—
146C22×Dic3—41no—
147C22×Dic3—41no—
148C22×Dic3—41no—
149C22×Dic3C22⋊C411yescharacteristic
150C22×Dic3C22⋊C411yescharacteristic
151C22×Dic3C22⋊C411yescharacteristic
152C22×Dic3C22⋊C411yescharacteristic
153C22×Dic3C2×C812yes—
154C22×Dic3C2×C812yes—
155C22×Dic3M1612yes—
156C2×C3×C8—22no—
157C2×C3×C8—41no—
158C2×C3×C8—41no—
159C2×C3×C8—41no—
160C2×C3×C8—41no—
161C2×C3×C8—41no—
162C3×C4⋊C4—41no—
163C3×C4⋊C4—41no—
164C3×C4⋊C4—41no—
165C3×C4⋊C4—41no—
166Dic3⋊C4—24no—
167Dic3⋊C4—24no—
168Dic3⋊C4—42no—
169Dic3⋊C4—41no—
170Dic3⋊C4—41no—
171Dic3⋊C4—41no—
172Dic3⋊C4—41no—
173Dic3⋊C4—42no—
174C4×Dic3—22no—
175C4×Dic3—22no—
176C4×Dic3—41no—
177C4×Dic3—41no—
178C2×C3⋊C8—22no—
179C2×C3⋊C8—41no—
180C2×C3⋊C8—41no—
181C2×C3⋊C8—41no—
182C2×C3⋊C8—41no—
183C2×C3⋊C8—41no—
184C23×C4—31no—
185C23×C4—31no—
186C23×C4—31no—
187C23×C4—31no—
188C23×C4C4×D311yescharacteristic
189C23×C4C4×D311yescharacteristic
190C23×C4C22×D311yescharacteristic
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—61no—
194C22×C8—61no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—34no—
202C2×C4⋊C4—61no—
203C2×C4⋊C4—61no—
204C2×C4⋊C4—62no—
205C2×C4⋊C4—61no—
206C2×C4⋊C4—61no—
207C2×C4⋊C4—61no—
208C2×C4⋊C4—61no—
209C2×C4⋊C4—61no—
210C2×C4⋊C4—61no—
211C2×C4⋊C4—61no—
212C2×C4⋊C4—61no—
213C2×C4⋊C4—122no—
214C2×C42—31no—
215C2×C42—31no—
216C2×C42—31no—
217C2×C42—31no—
218C2×C42—122no—
219C4⋊C8—122no—
220C22⋊C8—21no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—32no—
224C22⋊C8—61no—
225C22⋊C8—61no—
226C22⋊C8—61no—
227C22⋊C8#6712yes—
228C4×C8—122no—
229#95—61no—
230#95—61no—
231#95—61no—
232#95—61no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—21no—
236C23×C3—21no—
237C23×C3C2×C22⋊C411yescharacteristic
238C23×C3C4×D411yescharacteristic
239C23×C3C4×D411yescharacteristic
240C23×C3C22×C811yescharacteristic
241C23×C3C2×M1611yescharacteristic
242C23×C3#13111yescharacteristic
243C23×C3#13111yescharacteristic
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—81no—
263C2×C3×C4—81no—
264C2×C3×C4#12111yescharacteristic
265C2×C3×C4#12111yescharacteristic
266C2×C3×C4#12411yescharacteristic
267C2×C3×C4#12711yescharacteristic
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—24no—
273C2×Dic3—24no—
274C2×Dic3—22no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—22no—
279C2×Dic3—22no—
280C2×Dic3—42no—
281C2×Dic3—42no—
282C2×Dic3—41no—
283C2×Dic3—41no—
284C2×Dic3—41no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—41no—
288C2×Dic3—41no—
289C2×Dic3—81no—
290C2×Dic3—81no—
291C2×Dic3C22⋊C812yes—
292C2×Dic3C22⋊C812yes—
293C2×Dic3#9912yes—
294C2×Dic3#10112yes—
295C2×Dic3#10112yes—
296C3×C8—42no—
297C3×C8—81no—
298C3⋊C8—42no—
299C3⋊C8—81no—
300C24C2×C4×D311yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—31no—
313C22×C4—32no—
314C22×C4—32no—
315C22×C4—31no—
316C22×C4—32no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—62no—
322C22×C4—62no—
323C22×C4—62no—
324C22×C4—61no—
325C22×C4—61no—
326C22×C4—61no—
327C22×C4—61no—
328C22×C4—61no—
329C22×C4—61no—
330C22×C4—61no—
331C22×C4—61no—
332C22×C4—61no—
333C22×C4—61no—
334C22×C4—61no—
335C22×C4—121no—
336C22×C4—121no—
337C22×C4—121no—
338C22×C4D3×C812yes—
339C22×C4#23511yescharacteristic
340C22×C4D3×D411yescharacteristic
341C22×C4D3×D411yescharacteristic
342C22×C4D3×D411yescharacteristic
343C22×C4#23711yescharacteristic
344C22×C4C2×#6711yescharacteristic
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—62no—
352C2×C8—121no—
353C2×C8—121no—
354C2×C8—121no—
355C2×C8—121no—
356C2×C8—121no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—64no—
362C4⋊C4—64no—
363C4⋊C4—122no—
364C4⋊C4—122no—
365C4⋊C4—121no—
366C4⋊C4—121no—
367C4⋊C4—121no—
368C4⋊C4—121no—
369C42—62no—
370C42—62no—
371C42—121no—
372C42—121no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3#39011yescharacteristic
386C22×C3C2×C22⋊C811yescharacteristic
387C22×C3#40811yescharacteristic
388C22×C3C2×#9911yescharacteristic
389C22×C3#41011yescharacteristic
390C22×C3C2×#10111yescharacteristic
391C22×C3C2×#10111yescharacteristic
392C22×C3C8×D411yescharacteristic
393C22×C3C8×D411yescharacteristic
394C22×C3#43611yescharacteristic
395C22×C3#43611yescharacteristic
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—42no—
401C3×C4—81no—
402Dic3—22no—
403Dic3—22no—
404Dic3—42no—
405Dic3—41no—
406Dic3—81no—
407Dic3#32414yescomplemented
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23D3×C22⋊C411yescharacteristic
413C23#67⋊C411yescharacteristic
414C23C2×D3×C811yescharacteristic
415C23#90111yescharacteristic
416C23D3×M1611yescharacteristic
417C23#90711yescharacteristic
418C23C4×#6711yescharacteristic
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—32no—
427C2×C4—32no—
428C2×C4—32no—
429C2×C4—32no—
430C2×C4—32no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—64no—
443C2×C4—64no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—62no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—122no—
457C2×C4—122no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—241no—
466C2×C4—241no—
467C2×C4#88411yescharacteristic
468C2×C4#88511yescharacteristic
469C2×C4#93911yescharacteristic
470C2×C4#94011yescharacteristic
471C8—42no—
472C8—81no—
473C8—122no—
474C8—241no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3C2×#32411yescharacteristic
480C2×C3#146111yescharacteristic
481C2×C3#147011yescharacteristic
482C2×C3#147211yescharacteristic
483C2×C3#195411yescharacteristic
484C2×C3#196411yescharacteristic
485C2×C3#196611yescharacteristic
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22D3×C22⋊C811yescharacteristic
499C22#67⋊C811yescharacteristic
500C22#472711yescharacteristic
501C22#472911yescharacteristic
502C22#474011yescharacteristic
503C22D3×#9911yescharacteristic
504C22D3×#10111yescharacteristic
505C22D3×#10111yescharacteristic
506C22#495711yescharacteristic
507C22C8×#6711yescharacteristic
508C22#512811yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—34no—
514C4—42no—
515C4—62no—
516C4—62no—
517C4—81no—
518C4—122no—
519C4—121no—
520C4—241no—
521C3#965011yescharacteristic, complemented, Sylow
522C2—21no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2#6812511yescharacteristic
527C2#6812811yescharacteristic
528C2D3×#32411yescharacteristic
529C2#6814711yescharacteristic
530C2#6991611yescharacteristic
531C2#7003011yescharacteristic
532C2#7009811yescharacteristic
subgroupG/H
centerC23D3×C22⋊C4
commutatorC23×C3C22×C8
FrattiniC23×C4C22×D3
FittingC2×C3×#324C2
socleC23×C3C2×C22⋊C4
prime radicalC24×C3C22×C4
cosocleC23×C3×C4C23
hypercenterC2×#324D3
hypocenterC3#9650
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
66. C2×Dic3⋊C4C8semidirect
407. Dic3#324semidirect
521. C3#9650semidirect

Maximal subgroups

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

subgroupindex
C2×#49762
C2×C3×#3242
C2×#45282
C2×#44692
#699082
Dic3×C22⋊C82
#96503