Finite Group Databasebeta

← #10690590

Subgroups — #10690590

Order 768.

604 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4978C211yesmaximal, characteristic
2C2×#4719C211yesmaximal, characteristic
3C2×C3×#324C211yesmaximal, characteristic
4C2×#4528C211yesmaximal, characteristic
5#69910C211yesmaximal, characteristic
6#67674C211yesmaximal, characteristic
7#67674C211yesmaximal, characteristic
8#9086—31nomaximal, Sylow
9C22×C3×C4⋊C4C2211yescharacteristic
10C22×Dic3⋊C4C411yescharacteristic
11C22×C4×Dic3C2211yescharacteristic
12C2×C3×C22⋊C8C2211yescharacteristic
13C2×C3×C22⋊C8C2211yescharacteristic
14C2×C3⋊#95C411yescharacteristic
15C2×C3⋊#95C411yescharacteristic
16C2×C3⋊#95C411yescharacteristic
17C2×C3⋊#95C2211yescharacteristic
18C2×#830C2211yescharacteristic
19C2×#830C2211yescharacteristic
20C2×#815—21no—
21C2×Dic3⋊C8—21no—
22#4978—21no—
23#4978—21no—
24#4978—21no—
25#4978—21no—
26#4719—22no—
27#4719—22no—
28C3×#324—22no—
29#4550—21no—
30#4550—21no—
31#4528—22no—
32C2×#432—31no—
33C2×#387—31no—
34#1817—31no—
35C2×#324—31no—
36C2×#324D311yescharacteristic
37#1280—31no—
38#1280—31no—
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—22no—
55C2×Dic3⋊C4—21no—
56C2×Dic3⋊C4—21no—
57C2×Dic3⋊C4—22no—
58C2×C4×Dic3—21no—
59C2×C4×Dic3—21no—
60C2×C4×Dic3—21no—
61C2×C4×Dic3—21no—
62C2×C4×Dic3D411yescharacteristic
63C2×C4×Dic3D411yescharacteristic
64C2×C4×Dic3D411yescharacteristic
65C2×C4×Dic3D411yescharacteristic
66C22×C3⋊C8—21no—
67C22×C3⋊C8—21no—
68C3×C22⋊C8—21no—
69C3×C22⋊C8—21no—
70C3×C22⋊C8—21no—
71C3×C22⋊C8D412yes—
72C3⋊#95—21no—
73C3⋊#95—21no—
74C3⋊#95—21no—
75C3⋊#95—21no—
76C3⋊#95—21no—
77C3⋊#95—21no—
78C3⋊#95—21no—
79C3⋊#95—21no—
80#830—21no—
81#830—21no—
82#830—21no—
83#830D412yes—
84#815—24no—
85Dic3⋊C8—24no—
86C22×C4⋊C4—31no—
87C22×C4⋊C4C2×D311yescharacteristic
88C22×C42—31no—
89#432—62no—
90#432—62no—
91C2×C4⋊C8—61no—
92C2×C22⋊C8—31no—
93C2×C22⋊C8—31no—
94C2×C22⋊C8C2×D311yescharacteristic
95C2×C22⋊C8C2×D311yescharacteristic
96C2×#97—61no—
97#387—61no—
98#387—61no—
99#387—61no—
100#387—61no—
101C2×#95—31no—
102C2×#95—31no—
103C2×#95—31no—
104C2×#95—31no—
105#336—61no—
106#336—61no—
107#324—22no—
108#324—62no—
109C24×C3C22×C411yescharacteristic
110C22×C3×C4—21no—
111C22×C3×C4—21no—
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—41no—
120C22×C3×C4—41no—
121C22×C3×C4—41no—
122C22×C3×C4—41no—
123C22×C3×C4M1612yes—
124C22×C3×C4C2×D411yescharacteristic
125C22×C3×C4C2×D411yescharacteristic
126C22×C3×C4C2×D411yescharacteristic
127C22×C3×C4C2×D411yescharacteristic
128C22×C3×C4#4111yescharacteristic
129C22×C3×C4#4111yescharacteristic
130C22×Dic3—21no—
131C22×Dic3—21no—
132C22×Dic3—21no—
133C22×Dic3—21no—
134C22×Dic3—21no—
135C22×Dic3—21no—
136C22×Dic3—21no—
137C22×Dic3—21no—
138C22×Dic3—21no—
139C22×Dic3—21no—
140C22×Dic3—22no—
141C22×Dic3—21no—
142C22×Dic3—21no—
143C22×Dic3—21no—
144C22×Dic3—41no—
145C22×Dic3—41no—
146C22×Dic3—41no—
147C22×Dic3—41no—
148C22×Dic3—41no—
149C22×Dic3C22⋊C411yescharacteristic
150C22×Dic3C22⋊C411yescharacteristic
151C22×Dic3C22⋊C411yescharacteristic
152C22×Dic3C22⋊C411yescharacteristic
153C22×Dic3M1612yes—
154C2×C3×C8—22no—
155C2×C3×C8—41no—
156C2×C3×C8—41no—
157C2×C3×C8—41no—
158C2×C3×C8—41no—
159C2×C3×C8—41no—
160C3×C4⋊C4—41no—
161C3×C4⋊C4—41no—
162C3×C4⋊C4—41no—
163C3×C4⋊C4—41no—
164Dic3⋊C4—24no—
165Dic3⋊C4—24no—
166C4×Dic3—21no—
167C4×Dic3—21no—
168C4×Dic3—21no—
169C4×Dic3—21no—
170C4×Dic3—21no—
171C4×Dic3—21no—
172C4×Dic3—21no—
173C4×Dic3—21no—
174C2×C3⋊C8—22no—
175C2×C3⋊C8—41no—
176C2×C3⋊C8—41no—
177C2×C3⋊C8—41no—
178C2×C3⋊C8—41no—
179C2×C3⋊C8—41no—
180C23×C4—31no—
181C23×C4—31no—
182C23×C4—31no—
183C23×C4—31no—
184C23×C4C4×D311yescharacteristic
185C23×C4C4×D311yescharacteristic
186C23×C4C22×D311yescharacteristic
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—61no—
190C22×C8—61no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—61no—
198C2×C4⋊C4—61no—
199C2×C4⋊C4—62no—
200C2×C4⋊C4—62no—
201C2×C42—31no—
202C2×C42—31no—
203C2×C42—31no—
204C2×C42—31no—
205C2×C42—61no—
206C2×C42—61no—
207C2×C42—61no—
208C2×C42—61no—
209C4⋊C8—64no—
210C22⋊C8—21no—
211C22⋊C8—21no—
212C22⋊C8—21no—
213C22⋊C8—32no—
214C22⋊C8—61no—
215C22⋊C8—61no—
216C22⋊C8—61no—
217C22⋊C8#6712yes—
218#97—64no—
219#95—61no—
220#95—61no—
221#95—61no—
222#95—61no—
223#95—61no—
224#95—61no—
225#95—61no—
226#95—61no—
227C23×C3—21no—
228C23×C3—21no—
229C23×C3—21no—
230C23×C3—21no—
231C23×C3C2×C22⋊C411yescharacteristic
232C23×C3C4×D411yescharacteristic
233C23×C3C4×D411yescharacteristic
234C23×C3C2×M1611yescharacteristic
235C23×C3C2×M1611yescharacteristic
236C23×C3#13111yescharacteristic
237C23×C3#13111yescharacteristic
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—81no—
257C2×C3×C4—81no—
258C2×C3×C4#12011yescharacteristic
259C2×C3×C4#12111yescharacteristic
260C2×C3×C4#12111yescharacteristic
261C2×C3×C4#12311yescharacteristic
262C2×Dic3—21no—
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—21no—
269C2×Dic3—22no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—42no—
275C2×Dic3—42no—
276C2×Dic3—42no—
277C2×Dic3—41no—
278C2×Dic3—41no—
279C2×Dic3—41no—
280C2×Dic3—41no—
281C2×Dic3—41no—
282C2×Dic3—41no—
283C2×Dic3—42no—
284C2×Dic3—41no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—81no—
288C2×Dic3—81no—
289C2×Dic3#10112yes—
290C3×C8—42no—
291C3×C8—81no—
292C3⋊C8—42no—
293C3⋊C8—81no—
294C24C2×C4×D311yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—32no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—62no—
314C22×C4—61no—
315C22×C4—61no—
316C22×C4—61no—
317C22×C4—61no—
318C22×C4—61no—
319C22×C4—61no—
320C22×C4—61no—
321C22×C4—61no—
322C22×C4—61no—
323C22×C4—61no—
324C22×C4—61no—
325C22×C4—61no—
326C22×C4—61no—
327C22×C4—121no—
328C22×C4—121no—
329C22×C4—121no—
330C22×C4—121no—
331C22×C4—121no—
332C22×C4ΓL(1,𝔽25)12yes—
333C22×C4#23511yescharacteristic
334C22×C4D3×D411yescharacteristic
335C22×C4D3×D411yescharacteristic
336C22×C4D3×D411yescharacteristic
337C22×C4#23711yescharacteristic
338C22×C4C2×#6711yescharacteristic
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—62no—
346C2×C8—121no—
347C2×C8—121no—
348C2×C8—121no—
349C2×C8—121no—
350C2×C8—121no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—64no—
356C4⋊C4—64no—
357C42—61no—
358C42—61no—
359C42—61no—
360C42—61no—
361C42—61no—
362C42—61no—
363C42—61no—
364C42—61no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3#38611yescharacteristic
378C22×C3#40711yescharacteristic
379C22×C3#40811yescharacteristic
380C22×C3#41011yescharacteristic
381C22×C3#41011yescharacteristic
382C22×C3C2×#10111yescharacteristic
383C22×C3#41311yescharacteristic
384C22×C3#43511yescharacteristic
385C22×C3#43511yescharacteristic
386C22×C3#43611yescharacteristic
387C22×C3#43611yescharacteristic
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—42no—
393C3×C4—81no—
394Dic3—22no—
395Dic3—41no—
396Dic3—41no—
397Dic3—41no—
398Dic3—42no—
399Dic3—81no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23D3×C22⋊C411yescharacteristic
405C23#67⋊C411yescharacteristic
406C23C2×ΓL(1,𝔽25)11yescharacteristic
407C23#90111yescharacteristic
408C23D3×M1611yescharacteristic
409C23#90711yescharacteristic
410C23C4×#6711yescharacteristic
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—32no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—62no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—122no—
445C2×C4—122no—
446C2×C4—122no—
447C2×C4—121no—
448C2×C4—121no—
449C2×C4—121no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4—121no—
453C2×C4—122no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—241no—
458C2×C4—241no—
459C2×C4#88311yescharacteristic
460C2×C4#88411yescharacteristic
461C2×C4#93711yescharacteristic
462C2×C4#93811yescharacteristic
463C8—42no—
464C8—81no—
465C8—122no—
466C8—241no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3#146411yescharacteristic
472C2×C3#146711yescharacteristic
473C2×C3#147011yescharacteristic
474C2×C3#147311yescharacteristic
475C2×C3#187011yescharacteristic
476C2×C3#189911yescharacteristic
477C2×C3#190111yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22#472611yescharacteristic
491C22#472711yescharacteristic
492C22#472911yescharacteristic
493C22#473011yescharacteristic
494C22#474011yescharacteristic
495C22#474011yescharacteristic
496C22D3×#10111yescharacteristic
497C22#475111yescharacteristic
498C22#495611yescharacteristic
499C22#511111yescharacteristic
500C22#512811yescharacteristic
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—42no—
506C4—62no—
507C4—81no—
508C4—122no—
509C4—121no—
510C4—121no—
511C4—121no—
512C4—241no—
513C3#908611yescharacteristic, complemented, Sylow
514C2—21no—
515C2—21no—
516C2—21no—
517C2—21no—
518C2#6812611yescharacteristic
519C2#6812711yescharacteristic
520C2#6812811yescharacteristic
521C2#6812911yescharacteristic
522C2#6995811yescharacteristic
523C2#7002911yescharacteristic
524C2#7011511yescharacteristic
subgroupG/H
centerC23D3×C22⋊C4
commutator, prime radicalC24×C3C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#324C2
socleC23×C3C2×C22⋊C4
cosocleC23×C3×C4C23
hypercenterC2×#324D3
hypocenterC3#9086
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
513. C3#9086semidirect

Maximal subgroups

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

subgroupindex
C2×#49782
C2×#47192
C2×C3×#3242
C2×#45282
#699102
#676742
#90863