Finite Group Databasebeta

← #10690829

Subgroups — #10690829

Order 768.

644 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#83269C211yesmaximal, characteristic
2C2×D3×C4⋊C8C211yesmaximal, characteristic
3C2×C3×#332C211yesmaximal, characteristic, complemented
4C2×#4547C211yesmaximal, characteristic, complemented
5#70475C211yesmaximal, characteristic
6#67702C211yesmaximal, characteristic, complemented
7#67702C211yesmaximal, characteristic, complemented
8#9129—31nomaximal, Sylow
9C2×C3×C4⋊Q8C2211yescharacteristic
10C2×#946—21no—
11C22×D3×C8—21no—
12C2×C42×D3C2211yescharacteristic
13C2×C3×C4⋊C8C2211yescharacteristic
14C2×C3×C4⋊C8C2211yescharacteristic
15#5229—21no—
16C2×(C2×D3)⋊C8—21no—
17C2×Dic3⋊C8—21no—
18#4987—21no—
19#4987C412yes—
20#4972—21no—
21#4972C412yes—
22#4935C2211yescharacteristic
23C2×C4⋊(C3⋊C8)C2211yescharacteristic
24C2×C4⋊(C3⋊C8)C2211yescharacteristic
25D3×C4⋊C8—22no—
26D3×C4⋊C8—22no—
27C3×#332—22no—
28#4550—21no—
29#4547—22no—
30C22×C4⋊C8—31no—
31#2857—31no—
32#1797—31no—
33C2×#332—31no—
34C2×#332D311yescharacteristic, complemented
35#1296—31no—
36#1296—31no—
37C22×C3×Q8—21no—
38C22×C4×D3C2×C411yescharacteristic
39C22×C4×D3D411yescharacteristic
40C22×C4×D3D411yescharacteristic
41C22×C3×C8—21no—
42C22×C3×C8—21no—
43C3×C4⋊Q8—21no—
44C3×C4⋊Q8—21no—
45C3×C4⋊Q8—21no—
46C3×C4⋊Q8—21no—
47C2×C3×C4⋊C4—21no—
48C2×C3×C4⋊C4C2×C412yes—
49C2×C3×C42C2311yescharacteristic
50#946—42no—
51#946—42no—
52C2×(C2×D3)⋊C4—22no—
53C2×C4⋊Dic3—21no—
54C2×C4⋊Dic3—21no—
55C2×C4⋊Dic3C2×C412yes—
56C2×Dic3⋊C4—22no—
57C2×C4×Dic3C2×C411yescharacteristic
58C2×C4×Dic3D411yescharacteristic
59C2×C4×Dic3D411yescharacteristic
60C22×C3⋊C8—21no—
61C22×C3⋊C8—21no—
62C2×D3×C8—24no—
63C2×D3×C8—42no—
64C2×D3×C8—42no—
65C42×D3—21no—
66C42×D3—21no—
67C42×D3—21no—
68C42×D3—21no—
69C3×C4⋊C8—21no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8D412yes—
73C3⋊#95—22no—
74C3⋊#95—22no—
75(C2×D3)⋊C8—42no—
76Dic3⋊C8—24no—
77C4⋊(C3⋊C8)—21no—
78C4⋊(C3⋊C8)—21no—
79C4⋊(C3⋊C8)—21no—
80C4⋊(C3⋊C8)D412yes—
81C23×C8—61no—
82C2×C4⋊Q8C2×D311yescharacteristic
83C2×C22⋊Q8—61no—
84C22×C42—31no—
85C2×C4⋊C8—31no—
86C2×C4⋊C8—31no—
87C2×C4⋊C8—62no—
88C2×C4⋊C8—61no—
89C2×C4⋊C8—62no—
90C2×C4⋊C8C2×D311yescharacteristic
91C2×C4⋊C8C2×D311yescharacteristic
92C2×C22⋊C8—61no—
93#391—61no—
94#389—32no—
95#389—61no—
96#384—31no—
97#380—32no—
98#380—61no—
99#336—61no—
100#332—22no—
101#332—62no—
102C23×D3C22⋊C411yescharacteristic
103C2×C3×Q8—41no—
104C2×C3×Q8—41no—
105C2×C3×Q8—41no—
106C2×C3×Q8—41no—
107C2×C3×Q8—41no—
108C2×C3×Q8—41no—
109C22×C3×C4—22no—
110C22×C3×C4C22×C411yescharacteristic
111C22×C3×C4C2×D411yescharacteristic
112C22×C3×C4C2×D411yescharacteristic
113C22×Dic3—22no—
114C22×Dic3C22⋊C411yescharacteristic
115C22×Dic3C22⋊C411yescharacteristic
116C22×Dic3C22⋊C411yescharacteristic
117C2×C4×D3—21no—
118C2×C4×D3—21no—
119C2×C4×D3—21no—
120C2×C4×D3—21no—
121C2×C4×D3—21no—
122C2×C4×D3—21no—
123C2×C4×D3—21no—
124C2×C4×D3—21no—
125C2×C4×D3—22no—
126C2×C4×D3—21no—
127C2×C4×D3—21no—
128C2×C4×D3—41no—
129C2×C4×D3D812yes—
130C2×C4×D3SD1612yes—
131C2×C4×D3SD1612yes—
132C2×C4×D3Q1612yes—
133C2×C3×C8—22no—
134C2×C3×C8—41no—
135C2×C3×C8—41no—
136C2×C3×C8—41no—
137C2×C3×C8—41no—
138C2×C3×C8—41no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—41no—
142C3×C4⋊C4—41no—
143C3×C42C2×D411yescharacteristic
144C3×C42C2×D411yescharacteristic
145C3×C42#4111yescharacteristic
146C3×C42#4111yescharacteristic
147(C2×D3)⋊C4—44no—
148C4⋊Dic3—41no—
149C4⋊Dic3—41no—
150C4⋊Dic3—41no—
151C4⋊Dic3—41no—
152C4⋊Dic3—42no—
153Dic3⋊C4—44no—
154C4×Dic3—21no—
155C4×Dic3—21no—
156C4×Dic3—21no—
157C4×Dic3—21no—
158C4×Dic3—21no—
159C4×Dic3—21no—
160C2×C3⋊C8—22no—
161C2×C3⋊C8—41no—
162C2×C3⋊C8—41no—
163C2×C3⋊C8—41no—
164C2×C3⋊C8—41no—
165C2×C3⋊C8—41no—
166D3×C8—48no—
167C22×Q8—21no—
168C23×C4—31no—
169C23×C4—31no—
170C23×C4—31no—
171C22×C8—21no—
172C22×C8—21no—
173C22×C8—64no—
174C22×C8—61no—
175C22×C8—61no—
176C22×C8—122no—
177C22×C8—122no—
178C4⋊Q8—21no—
179C4⋊Q8—21no—
180C4⋊Q8—21no—
181C4⋊Q8—21no—
182C22⋊Q8—122no—
183C22⋊Q8—122no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—32no—
186C2×C4⋊C4—62no—
187C2×C4⋊C4—61no—
188C2×C4⋊C4—61no—
189C2×C4⋊C4C4×D312yes—
190C2×C22⋊C4—62no—
191C2×C42—31no—
192C2×C42—31no—
193C2×C42—31no—
194C2×C42—61no—
195C2×C42—61no—
196C2×C42—61no—
197C2×C42—61no—
198C2×C42C22×D311yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—32no—
203C4⋊C8—64no—
204C4⋊C8—61no—
205C4⋊C8—61no—
206C4⋊C8—61no—
207C4⋊C8#6712yes—
208C22⋊C8—122no—
209#95—62no—
210#95—62no—
211C23×C3C2×C22⋊C411yescharacteristic
212C22×D3—21no—
213C22×D3—21no—
214C22×D3—21no—
215C22×D3—21no—
216C22×D3#10112yes—
217C22×D3#10212yes—
218C22×D3#10312yes—
219C3×Q8—81no—
220C3×Q8—81no—
221C3×Q8—81no—
222C3×Q8—81no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4C4×D411yescharacteristic
229C2×C3×C4C4×D411yescharacteristic
230C2×C3×C4#12011yescharacteristic
231C2×C3×C4#12111yescharacteristic
232C2×C3×C4#12111yescharacteristic
233C2×C3×C4#12311yescharacteristic
234C2×C3×C4C2×D811yescharacteristic
235C2×C3×C4C2×SD1611yescharacteristic
236C2×C3×C4C2×SD1611yescharacteristic
237C2×C3×C4C2×Q1611yescharacteristic
238C2×C3×C4#13511yescharacteristic
239C2×C3×C4#13511yescharacteristic
240C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
241C2×C3×C4#13711yescharacteristic
242C2×Dic3—21no—
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—42no—
250C2×Dic3—42no—
251C2×Dic3—42no—
252C2×Dic3#10212yes—
253C2×Dic3#10312yes—
254C4×D3—22no—
255C4×D3—22no—
256C4×D3—22no—
257C4×D3—22no—
258C4×D3—22no—
259C4×D3—22no—
260C4×D3—22no—
261C4×D3—22no—
262C4×D3—42no—
263C4×D3—42no—
264C3×C8—42no—
265C3×C8—81no—
266C3⋊C8—42no—
267C3⋊C8—81no—
268C24—31no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C22×C4—22no—
276C22×C4—31no—
277C22×C4—31no—
278C22×C4—32no—
279C22×C4—32no—
280C22×C4—32no—
281C22×C4—32no—
282C22×C4—31no—
283C22×C4—62no—
284C22×C4—61no—
285C22×C4—61no—
286C22×C4—61no—
287C22×C4—61no—
288C22×C4—61no—
289C22×C4—61no—
290C22×C4—61no—
291C22×C4—61no—
292C22×C4—61no—
293C22×C4—61no—
294C22×C4—62no—
295C22×C4—121no—
296C22×C4C2×C4×D311yescharacteristic
297C22×C4D3×D411yescharacteristic
298C22×C4D3×D411yescharacteristic
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—62no—
306C2×C8—128no—
307C2×C8—121no—
308C2×C8—121no—
309C2×C8—121no—
310C2×C8—121no—
311C2×C8—121no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—122no—
317C4⋊C4—124no—
318C4⋊C4—121no—
319C4⋊C4—121no—
320C4⋊C4—121no—
321C4⋊C4—121no—
322C22⋊C4—124no—
323C42—61no—
324C42—61no—
325C42—61no—
326C42—61no—
327C42—61no—
328C42—61no—
329C42#23511yescharacteristic
330C42D3×D411yescharacteristic
331C42#23711yescharacteristic
332C42C2×#6711yescharacteristic
333C22×C3#38611yescharacteristic
334C22×C3C2×#10111yescharacteristic
335C22×C3#41311yescharacteristic
336C22×C3C2×#10211yescharacteristic
337C22×C3C2×#10311yescharacteristic
338C22×C3#41611yescharacteristic
339C22×C3#41711yescharacteristic
340C2×D3—22no—
341C2×D3—22no—
342C2×D3—22no—
343C2×D3—22no—
344C2×D3—22no—
345C2×D3—22no—
346C2×D3#33214yescomplemented
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—82no—
350C3×C4#45011yescharacteristic
351C3×C4#45111yescharacteristic
352C3×C4#46511yescharacteristic
353C3×C4#46511yescharacteristic
354C3×C4#46611yescharacteristic
355C3×C4#46611yescharacteristic
356C3×C4#48311yescharacteristic
357C3×C4#48411yescharacteristic
358Dic3—22no—
359Dic3—22no—
360Dic3—41no—
361Dic3—82no—
362C23—32no—
363C23—32no—
364C23—32no—
365C23—61no—
366C23—61no—
367C23—61no—
368C23—61no—
369C23D3×C22⋊C411yescharacteristic
370Q8—81no—
371Q8—81no—
372Q8—81no—
373Q8—81no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—32no—
377C2×C4—32no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—122no—
397C2×C4—122no—
398C2×C4—122no—
399C2×C4—122no—
400C2×C4—122no—
401C2×C4#67⋊C411yescharacteristic
402C2×C4#88311yescharacteristic
403C2×C4#88411yescharacteristic
404C2×C4D3×D811yescharacteristic
405C2×C4#91211yescharacteristic
406C2×C4D3×SD1611yescharacteristic
407C2×C4D3×SD1611yescharacteristic
408C2×C4#91411yescharacteristic
409C2×C4#91611yescharacteristic
410C2×C4D3×Q1611yescharacteristic
411C2×C4#91811yescharacteristic
412C2×C4C4×#6711yescharacteristic
413C2×C4#93711yescharacteristic
414C2×C4#93811yescharacteristic
415C8—42no—
416C8—81no—
417C8—122no—
418C8—241no—
419C2×C3C2×#33211yescharacteristic
420C2×C3#154211yescharacteristic
421C2×C3#154711yescharacteristic
422C2×C3#155211yescharacteristic
423C2×C3#187211yescharacteristic
424C2×C3#189311yescharacteristic
425C2×C3#190111yescharacteristic
426D3—24no—
427C22—34no—
428C22—62no—
429C22—62no—
430C22—62no—
431C22—62no—
432C22—62no—
433C22—62no—
434C22D3×#10111yescharacteristic
435C22#475111yescharacteristic
436C22D3×#10211yescharacteristic
437C22#477211yescharacteristic
438C22D3×#10311yescharacteristic
439C22#480311yescharacteristic
440C22#495611yescharacteristic
441C4—21no—
442C4—21no—
443C4—62no—
444C4—62no—
445C4—82no—
446C4—121no—
447C4—242no—
448C4#477511yescharacteristic
449C4#477811yescharacteristic
450C4#480511yescharacteristic
451C4#481111yescharacteristic
452C4#515711yescharacteristic
453C4#516911yescharacteristic
454C4#517111yescharacteristic
455C4#518611yescharacteristic
456C3#912911yescharacteristic, complemented, Sylow
457C2—64no—
458C2D3×#33211yescharacteristic
459C2#6841811yescharacteristic
460C2#6842111yescharacteristic
461C2#6842411yescharacteristic
462C2#7011511yescharacteristic
463C2#7020211yescharacteristic
464C2#7026811yescharacteristic
subgroupG/H
centerC23D3×C22⋊C4
commutatorC22×C3×C4C22×C4
FrattiniC2×C42C22×D3
FittingC2×C3×#332C2
socleC23×C3C2×C22⋊C4
prime radicalC23×D3C22⋊C4
cosocleC2×C3×C42C23
hypercenterC2×#332D3
hypocenterC3#9129
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. C2×C3×#332C2semidirect
4. C2×#4547C2semidirect
6. #67702C2semidirect
7. #67702C2semidirect
34. C2×#332D3semidirect
346. C2×D3#332semidirect
456. C3#9129semidirect

Maximal subgroups

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

subgroupindex
#832692
C2×D3×C4⋊C82
C2×C3×#3322
C2×#45472
#704752
#677022
#91293