Finite Group Databasebeta

← #10691275

Subgroups — #10691275

Order 768.

532 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#82525C211yesmaximal, characteristic
2#41×C3⋊C8C211yesmaximal, characteristic, complemented
3C3×#1806C211yesmaximal, characteristic, complemented
4#70498C211yesmaximal, characteristic, complemented
5#69469C211yesmaximal, characteristic, complemented
6#67714C211yesmaximal, characteristic, complemented
7#67619C211yesmaximal, characteristic, complemented
8#9208—31nomaximal, Sylow
9C3×C4×#41C2211yescharacteristic
10C2×#950—21no—
11#5477C2211yescharacteristic
12C3×#423C2211yescharacteristic
13C2×C3×#104—21no—
14C3×C4×C4⋊C4C2211yescharacteristic
15#5031C411yescharacteristic, complemented
16#5028—21no—
17#5027C411yescharacteristic, complemented
18Q8×C3⋊C8—21no—
19#5019C411yescharacteristic, complemented
20#5016—21no—
21#5015C411yescharacteristic, complemented
22D4×C3⋊C8—21no—
23D4×C3⋊C8—22no—
24#5002—21no—
25#4925—21no—
26#4925C2211yescharacteristic
27C2×C4⋊(C3⋊C8)C2211yescharacteristic
28C2×C4×C3⋊C8—21no—
29C2×C4×C3⋊C8C2211yescharacteristic
30C3×#339—21no—
31#4483—21no—
32#4483—21no—
33#4451—22no—
34#3035—31no—
35C8×#41—31no—
36#1806D311yescharacteristic, complemented
37#1502—31no—
38#1492—31no—
39#1301—31no—
40#1279—31no—
41C2×C3×#41D411yescharacteristic
42C2×#235—21no—
43C2×C3×M16—21no—
44C3×C4×Q8C2×C411yescharacteristic
45C3×C4×Q8D411yescharacteristic
46C3×C4×D4—21no—
47C3×C4×D4—21no—
48C3×C4×D4C2×C411yescharacteristic
49C3×C4×D4D411yescharacteristic
50C3×#117—21no—
51C3×#117D411yescharacteristic
52C2×C3×C4⋊C4—21no—
53C2×C3×C42—21no—
54C2×C3×C42—21no—
55C2×C3×C42C2311yescharacteristic
56#950—42no—
57#950—42no—
58C2×#216—21no—
59C2×#215—21no—
60C2×#214—21no—
61C2×#213—21no—
62#930—21no—
63#930—21no—
64C22×C3⋊C8—22no—
65C22×C3⋊C8—21no—
66C22×C3⋊C8—21no—
67#875—21no—
68#874C2×C411yescharacteristic
69C4×D12—21no—
70C4×D12—21no—
71#869C2×C411yescharacteristic
72C3×C4⋊C8—21no—
73C3×C4⋊C8—21no—
74C3×#104—42no—
75C3×#95—21no—
76#830—22no—
77#830D412yes—
78#810—21no—
79#810—21no—
80#809—21no—
81#809—21no—
82C4⋊(C3⋊C8)—22no—
83C4⋊(C3⋊C8)—21no—
84C4⋊(C3⋊C8)—21no—
85C4⋊(C3⋊C8)C2×C411yescharacteristic
86C4⋊(C3⋊C8)C2×C411yescharacteristic
87C4×C3⋊C8—22no—
88C4×C3⋊C8—21no—
89C4×C3⋊C8—21no—
90C4×C3⋊C8D411yescharacteristic
91C4×C3⋊C8D411yescharacteristic
92C2×#135—61no—
93#532—31no—
94C4×#41C2×D311yescharacteristic
95#464—61no—
96#463—61no—
97#462—31no—
98#461—31no—
99#460—31no—
100#459—31no—
101C8×Q8—61no—
102C8×D4—62no—
103C8×D4—61no—
104#431—31no—
105#431—61no—
106#423C2×D311yescharacteristic
107C2×C4⋊C8—31no—
108C2×#104—21no—
109#416—61no—
110C2×C4×C8—31no—
111C2×C4×C8—61no—
112C4×C4⋊C4C2×D311yescharacteristic
113#339—21no—
114#327—62no—
115D4⋊C8—61no—
116D4⋊C8—61no—
117C3×#41—21no—
118C3×#41—21no—
119C3×#41D812yes—
120C3×#41SD1612yes—
121C2×C3×Q8C22⋊C411yescharacteristic
122C2×C3×D4—21no—
123C2×C3×D4C22⋊C411yescharacteristic
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—41no—
128C22×C3×C4C2×D411yescharacteristic
129C22×C3×C4C2×D411yescharacteristic
130C22×C3×C4#4111yescharacteristic
131C2×#67—41no—
132#235—41no—
133#235—41no—
134#235—41no—
135#235—41no—
136C2×D12—21no—
137C2×D12—21no—
138C2×D12—21no—
139C2×C4×D3—41no—
140C2×Dic6—21no—
141C3×M16—41no—
142C3×M16—41no—
143C2×C3×C8—41no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—41no—
148C3×C4⋊C4C22⋊C411yescharacteristic
149C3×C4⋊C4C22⋊C411yescharacteristic
150C3×C22⋊C4—21no—
151C3×C22⋊C4—21no—
152C3×C22⋊C4—21no—
153C3×C42—21no—
154C3×C42—21no—
155C3×C42—21no—
156C3×C42—41no—
157C3×C42—41no—
158C3×C42C22×C411yescharacteristic
159C3×C42C2×D411yescharacteristic
160C3×C42C2×D411yescharacteristic
161C3×C42#4111yescharacteristic
162#216—42no—
163#215—42no—
164#214—42no—
165#213—42no—
166(C2×D3)⋊C4—41no—
167(C2×D3)⋊C4—41no—
168C4⋊Dic3—21no—
169C4⋊Dic3—21no—
170C2×C3⋊C8—21no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8—21no—
173C2×C3⋊C8—22no—
174C2×C3⋊C8—21no—
175C2×C3⋊C8—42no—
176C2×C3⋊C8—44no—
177C2×C3⋊C8—41no—
178C2×C3⋊C8—41no—
179C2×#41—61no—
180C2×#41#6711yescharacteristic
181#135—122no—
182#135—122no—
183C2×Q16—61no—
184C2×SD16—61no—
185C2×SD16—61no—
186C2×D8—61no—
187C2×M16—21no—
188C22×C8—62no—
189C22×C8—61no—
190C22×C8—61no—
191C4⋊Q8—31no—
192#127—31no—
193#124—61no—
194#121—61no—
195#121—61no—
196C4×Q8C4×D311yescharacteristic
197C4×Q8D1211yescharacteristic
198C4×D4—21no—
199C4×D4—21no—
200C4×D4—61no—
201C4×D4—61no—
202C4×D4C4×D311yescharacteristic
203C4×D4D1211yescharacteristic
204#117—21no—
205#117#6711yescharacteristic
206C2×C4⋊C4—21no—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42C22×D311yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—31no—
213C4⋊C8—31no—
214C4⋊C8—62no—
215C4⋊C8—61no—
216C4⋊C8—61no—
217#104—42no—
218#103—61no—
219#103—61no—
220#102—61no—
221#102—61no—
222C22⋊C8—32no—
223C22⋊C8—62no—
224C4×C8—31no—
225C4×C8—31no—
226C4×C8—62no—
227C4×C8—61no—
228C4×C8—61no—
229#95—21no—
230C23×C3—21no—
231C23×C3#12111yescharacteristic
232C22×D3—41no—
233C3×Q8—21no—
234C3×Q8#10212yes—
235C3×D4—22no—
236C3×D4—22no—
237C3×D4—21no—
238C3×D4#10212yes—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—41no—
247C2×C3×C4—42no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—42no—
251C2×C3×C4—81no—
252C2×C3×C4—81no—
253C2×C3×C4C2×C22⋊C411yescharacteristic
254C2×C3×C4C4×D411yescharacteristic
255C2×C3×C4C4×D411yescharacteristic
256C2×C3×C4#12011yescharacteristic
257C2×C3×C4#12111yescharacteristic
258C2×C3×C4#12311yescharacteristic
259C2×C3×C4C2×D811yescharacteristic
260C2×C3×C4C2×SD1611yescharacteristic
261C2×C3×C4#13511yescharacteristic
262C2×C3×C4#13511yescharacteristic
263#67—81no—
264#67—81no—
265C2×Dic3—41no—
266D12—41no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—81no—
271C4×D3—81no—
272C4×D3—81no—
273Dic6—41no—
274Dic6—41no—
275C3×C8—81no—
276C3⋊C8—22no—
277C3⋊C8—42no—
278C3⋊C8—41no—
279C3⋊C8—41no—
280C3⋊C8—41no—
281#41—21no—
282#41—21no—
283#41—121no—
284#41—121no—
285#41—121no—
286#41—121no—
287#41#21312yes—
288#41#21512yes—
289C2×Q8—61no—
290C2×Q8(C2×D3)⋊C411yescharacteristic
291C2×D4—21no—
292C2×D4—61no—
293C2×D4—61no—
294C2×D4—61no—
295C2×D4—121no—
296C2×D4(C2×D3)⋊C411yescharacteristic
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—121no—
302C22×C4D3×D411yescharacteristic
303C22×C4#23711yescharacteristic
304C22×C4C2×#6711yescharacteristic
305Q16—122no—
306SD16—122no—
307SD16—122no—
308D8—122no—
309M16—41no—
310M16—41no—
311C2×C8—41no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8—62no—
315C2×C8—61no—
316C2×C8—61no—
317C2×C8—122no—
318C2×C8—124no—
319C2×C8—121no—
320C2×C8—121no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—61no—
326C4⋊C4—61no—
327C4⋊C4(C2×D3)⋊C411yescharacteristic
328C4⋊C4(C2×D3)⋊C411yescharacteristic
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—121no—
333C22⋊C4—121no—
334C42—21no—
335C42—21no—
336C42—21no—
337C42—41no—
338C42—41no—
339C42C2×C4×D311yescharacteristic
340C42C2×D1211yescharacteristic
341C42D3×D411yescharacteristic
342C42#23711yescharacteristic
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—22no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3#38611yescharacteristic
349C22×C3#46511yescharacteristic
350C22×C3#46611yescharacteristic
351C2×D3—81no—
352C2×D3—81no—
353C2×D3—81no—
354C3×C4—21no—
355C3×C4—22no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—82no—
361C3×C4C2×#10211yescharacteristic
362C3×C4#41611yescharacteristic
363C3×C4#44311yescharacteristic
364C3×C4#44411yescharacteristic
365C3×C4#46511yescharacteristic
366C3×C4#46611yescharacteristic
367Dic3—81no—
368C23—21no—
369C23—121no—
370C23#93911yescharacteristic
371Q8—21no—
372Q8—121no—
373Q8—121no—
374Q8#80912yes—
375D4—22no—
376D4—22no—
377D4—21no—
378D4—121no—
379D4—121no—
380D4—121no—
381D4—121no—
382D4—241no—
383D4—241no—
384D4—241no—
385D4#80912yes—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—121no—
401C2×C4—241no—
402C2×C4—241no—
403C2×C4#67⋊C411yescharacteristic
404C2×C4#67⋊C411yescharacteristic
405C2×C4#88211yescharacteristic
406C2×C4#88611yescharacteristic
407C2×C4C2×(C2×D3)⋊C411yescharacteristic
408C2×C4C2×#21311yescharacteristic
409C2×C4#93911yescharacteristic
410C2×C4C2×#21511yescharacteristic
411C2×C4#95011yescharacteristic
412C2×C4#95011yescharacteristic
413C8—62no—
414C8—81no—
415C8—121no—
416C8—122no—
417C8—121no—
418C8—121no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—42no—
422C2×C3#187611yescharacteristic
423C2×C3#189311yescharacteristic
424C2×C3#190611yescharacteristic
425D3—161no—
426C22—21no—
427C22—21no—
428C22—22no—
429C22—41no—
430C22—41no—
431C22—241no—
432C22—241no—
433C22—241no—
434C22#495811yescharacteristic
435C22#503811yescharacteristic
436C22#504811yescharacteristic
437C4—22no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—41no—
443C4—82no—
444C4—241no—
445C4#482311yescharacteristic
446C4#482411yescharacteristic
447C4C2×#80911yescharacteristic
448C4#500211yescharacteristic
449C4#503811yescharacteristic
450C4#504811yescharacteristic
451C3#920811yescharacteristic, complemented, Sylow
452C2—21no—
453C2—21no—
454C2—42no—
455C2—481no—
456C2#6951511yescharacteristic
457C2#7037711yescharacteristic
458C2#7039511yescharacteristic
subgroupG/H
centerC2×C4#939
commutatorC3×C42C22×C4
FrattiniC2×C42C22×D3
FittingC3×#1806C2
socleC22×C3#386
prime radical#82525C2
cosocleC2×C3×C42C23
hypercenter#1806D3
hypocenterC3#9208
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #41×C3⋊C8C2semidirect
3. C3×#1806C2semidirect
4. #70498C2semidirect
5. #69469C2semidirect
6. #67714C2semidirect
7. #67619C2semidirect
15. #5031C4semidirect
17. #5027C4semidirect
19. #5019C4semidirect
21. #5015C4semidirect
36. #1806D3semidirect
451. C3#9208semidirect

Maximal subgroups

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

subgroupindex
#825252
#41×C3⋊C82
C3×#18062
#704982
#694692
#677142
#676192
#92083