Finite Group Databasebeta

← #10697690

Subgroups — #10697690

Order 768.

794 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#459C211yesmaximal, characteristic, complemented
2C2×#5073C211yesmaximal, characteristic, complemented
3C2×#5015C211yesmaximal, characteristic, complemented
4C2×#4544C211yesmaximal, characteristic, complemented
5#71614C211yesmaximal, characteristic, complemented
6C2×#4485C211yesmaximal, characteristic, complemented
7#67703C211yesmaximal, characteristic, complemented
8#10260—31nomaximal, Sylow
9C22×C3×D8—21no—
10C2×C3×#127C2211yescharacteristic
11C2×C3×C4×D4C2211yescharacteristic
12C22×#213—21no—
13C22×#213—22no—
14C2×#874C2211yescharacteristic
15C3×#459—22no—
16C3×#459—22no—
17C2×C3×C4⋊C8C2211yescharacteristic
18C2×C3×#102—21no—
19C2×#830—22no—
20#5073—22no—
21#5073—22no—
22#5015—22no—
23#5015—22no—
24C2×#809—21no—
25C2×C4⋊(C3⋊C8)C2211yescharacteristic
26C2×C4⋊(C3⋊C8)C2211yescharacteristic
27C2×C4×C3⋊C8C2211yescharacteristic
28#4544—22no—
29#4485—22no—
30C2×#493—31no—
31C2×#459—31no—
32C2×#459D311yescharacteristic, complemented
33#1954—31no—
34C2×#331—31no—
35C2×#331—31no—
36#1277—31no—
37C22×C3×D4—21no—
38C22×C3×D4—21no—
39C22×C3×D4—21no—
40C22×C3×D4D411yescharacteristic
41C23×C3×C4—21no—
42C22×D12—21no—
43C22×D12—21no—
44C22×D12—21no—
45C2×C3×D8—24no—
46C2×C3×D8—42no—
47C2×C3×D8—42no—
48C22×C3×C8—21no—
49C3×#127—21no—
50C3×#127—21no—
51C3×#127—21no—
52C3×#127D412yes—
53C3×C4×D4—21no—
54C3×C4×D4—21no—
55C3×C4×D4—21no—
56C3×C4×D4—21no—
57C2×C3×C4⋊C4D411yescharacteristic
58C2×C3×C22⋊C4—21no—
59C2×C3×C42C2311yescharacteristic
60C2×#213—24no—
61C2×#213—28no—
62C2×#213—44no—
63C2×#213—42no—
64C2×#213—42no—
65C2×#213—44no—
66C22×C3⋊C8—21no—
67C22×C3⋊C8—21no—
68C22×C3⋊C8D412yes—
69#874—21no—
70#874—21no—
71#874—21no—
72#874D412yes—
73C3×C4⋊C8—21no—
74C3×C4⋊C8D412yes—
75C3×#102—24no—
76#830—44no—
77#809—24no—
78C4⋊(C3⋊C8)—21no—
79C4⋊(C3⋊C8)—21no—
80C4⋊(C3⋊C8)—21no—
81C4⋊(C3⋊C8)D412yes—
82C4×C3⋊C8—21no—
83C4×C3⋊C8—21no—
84C22×D8—21no—
85C22×D8—62no—
86C22×D8—61no—
87C2×#127—31no—
88C2×#127C2×D311yescharacteristic
89C2×C4×D4C2×D311yescharacteristic
90#493—62no—
91#493—62no—
92#459—22no—
93#459—22no—
94#459—62no—
95#459—62no—
96C2×C4⋊C8—31no—
97C2×C4⋊C8—31no—
98C2×C4⋊C8C2×D311yescharacteristic
99C2×#102—21no—
100C2×#102—61no—
101C2×C22⋊C8—62no—
102C2×C4×C8—31no—
103#331—62no—
104#331—62no—
105C24×C3—21no—
106C24×C3—41no—
107C23×D3—41no—
108C2×C3×D4—21no—
109C2×C3×D4—21no—
110C2×C3×D4—22no—
111C2×C3×D4—22no—
112C2×C3×D4—22no—
113C2×C3×D4—21no—
114C2×C3×D4—21no—
115C2×C3×D4—21no—
116C2×C3×D4—41no—
117C2×C3×D4—41no—
118C2×C3×D4—41no—
119C2×C3×D4—42no—
120C2×C3×D4—41no—
121C2×C3×D4—41no—
122C2×C3×D4—42no—
123C2×C3×D4—41no—
124C2×C3×D4—41no—
125C2×C3×D4—82no—
126C2×C3×D4D812yescomplemented
127C22×C3×C4—21no—
128C22×C3×C4—41no—
129C22×C3×C4—41no—
130C22×C3×C4—42no—
131C22×C3×C4—42no—
132C22×C3×C4C2×D411yescharacteristic
133C22×C3×C4C2×D411yescharacteristic
134C22×C3×C4#4111yescharacteristic
135C2×D12—22no—
136C2×D12—22no—
137C2×D12—22no—
138C2×D12—42no—
139C2×D12—41no—
140C2×D12—41no—
141C2×D12—42no—
142C2×D12—41no—
143C2×D12—41no—
144C2×D12—41no—
145C2×D12—41no—
146C2×D12—41no—
147C2×D12—82no—
148C3×D8—48no—
149C2×C3×C8—22no—
150C2×C3×C8—41no—
151C2×C3×C8—41no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C22⋊C4—41no—
155C3×C22⋊C4—41no—
156C3×C42C2×D411yescharacteristic
157C3×C42C2×D411yescharacteristic
158C3×C42C2×D411yescharacteristic
159C3×C42C2×D411yescharacteristic
160#213—416no—
161#213—48no—
162C2×C3⋊C8—22no—
163C2×C3⋊C8—22no—
164C2×C3⋊C8—22no—
165C2×C3⋊C8—41no—
166C2×C3⋊C8—41no—
167C2×C3⋊C8—41no—
168C2×C3⋊C8—42no—
169C2×C3⋊C8D814yescomplemented
170C22×D4—21no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4—61no—
174C22×D4—61no—
175C22×D4—61no—
176C22×D4#6711yescharacteristic
177C23×C4—21no—
178C2×D8—24no—
179C2×D8—42no—
180C2×D8—42no—
181C2×D8—64no—
182C2×D8—68no—
183C2×D8—124no—
184C2×D8—124no—
185C2×D8—122no—
186C2×D8—122no—
187C22×C8—21no—
188C22×C8—32no—
189C22×C8—61no—
190C22×C8—61no—
191#127—21no—
192#127—21no—
193#127—21no—
194#127—32no—
195#127—61no—
196#127—61no—
197#127—61no—
198#127#6712yes—
199C4×D4—21no—
200C4×D4—21no—
201C4×D4—21no—
202C4×D4—21no—
203C2×C4⋊C4#6711yescharacteristic
204C2×C22⋊C4—21no—
205C2×C42C22×D311yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—32no—
208C4⋊C8—61no—
209C4⋊C8—61no—
210C4⋊C8—61no—
211C4⋊C8#6712yes—
212#102—24no—
213#102—64no—
214C22⋊C8—124no—
215C4×C8—61no—
216C4×C8—61no—
217C23×C3—22no—
218C23×C3—41no—
219C23×C3—42no—
220C23×C3—41no—
221C23×C3—42no—
222C23×C3—42no—
223C23×C3—82no—
224C23×C3—81no—
225C23×C3—81no—
226C23×C3—82no—
227C23×C3#12111yescharacteristic
228C22×D3—42no—
229C22×D3—82no—
230C22×D3—81no—
231C22×D3—81no—
232C22×D3—82no—
233C3×D4—22no—
234C3×D4—22no—
235C3×D4—44no—
236C3×D4—42no—
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—42no—
240C3×D4—82no—
241C3×D4—82no—
242C3×D4—81no—
243C3×D4—81no—
244C3×D4—81no—
245C3×D4—81no—
246C2×C3×C4—22no—
247C2×C3×C4—41no—
248C2×C3×C4—42no—
249C2×C3×C4—82no—
250C2×C3×C4—81no—
251C2×C3×C4—81no—
252C2×C3×C4#12011yescharacteristic
253C2×C3×C4#12011yescharacteristic
254C2×C3×C4#12011yescharacteristic
255C2×C3×C4#12111yescharacteristic
256C2×C3×C4#12111yescharacteristic
257C2×C3×C4#12711yescharacteristic
258C2×C3×C4C2×D812yes—
259C2×C3×C4C2×D811yescharacteristic
260C2×C3×C4#13511yescharacteristic
261C2×C3×C4AGL(1,ℤ/8)12yes—
262C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
263C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
264D12—44no—
265D12—42no—
266D12—42no—
267D12—82no—
268D12—82no—
269D12—81no—
270D12—81no—
271D12—81no—
272D12—81no—
273C3×C8—42no—
274C3⋊C8—24no—
275C3⋊C8—42no—
276C3⋊C8—81no—
277C24—21no—
278C24—41no—
279C24—121no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—22no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—62no—
298C2×D4—62no—
299C2×D4—62no—
300C2×D4—82no—
301C2×D4—122no—
302C2×D4—122no—
303C2×D4—121no—
304C2×D4—121no—
305C2×D4—121no—
306C2×D4—121no—
307C2×D4—121no—
308C2×D4—121no—
309C2×D4—121no—
310C2×D4—242no—
311C2×D4#21312yescomplemented
312C22×C4—21no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4D3×D411yescharacteristic
318C22×C4#23711yescharacteristic
319C22×C4C2×#6711yescharacteristic
320D8—48no—
321D8—1216no—
322D8—128no—
323C2×C8—22no—
324C2×C8—34no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—62no—
328C2×C8—62no—
329C2×C8—62no—
330C2×C8—121no—
331C2×C8—121no—
332C2×C8—122no—
333C2×C8—121no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C42D3×D411yescharacteristic
339C42D3×D411yescharacteristic
340C42C2×#6711yescharacteristic
341C42C2×#6711yescharacteristic
342C22×C3—44no—
343C22×C3—42no—
344C22×C3—82no—
345C22×C3—81no—
346C22×C3—81no—
347C22×C3—82no—
348C22×C3—82no—
349C22×C3—82no—
350C22×C3—162no—
351C22×C3—162no—
352C22×C3#39211yescharacteristic
353C22×C3#45912yes—
354C22×C3#46611yescharacteristic
355C22×C3#46911yescharacteristic
356C22×C3#47212yes—
357C2×D3—82no—
358C2×D3—82no—
359C2×D3—82no—
360C2×D3—162no—
361C2×D3—162no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—81no—
365C3×C4#44712yes—
366C3×C4#44711yescharacteristic
367C3×C4#44711yescharacteristic
368C3×C4#44911yescharacteristic
369C3×C4#44911yescharacteristic
370C3×C4#49311yescharacteristic
371C3×C4#49611yescharacteristic
372C23—22no—
373C23—42no—
374C23—42no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—82no—
379C23—82no—
380C23—81no—
381C23—81no—
382C23—122no—
383C23—242no—
384C23—242no—
385C23—241no—
386C23—241no—
387C23#93911yescharacteristic
388D4—22no—
389D4—22no—
390D4—44no—
391D4—42no—
392D4—41no—
393D4—42no—
394D4—41no—
395D4—82no—
396D4—82no—
397D4—81no—
398D4—81no—
399D4—81no—
400D4—81no—
401D4—124no—
402D4—122no—
403D4—122no—
404D4—242no—
405D4—242no—
406D4—241no—
407D4—241no—
408D4—241no—
409D4—241no—
410C2×C4—22no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—82no—
416C2×C4D3×D812yes—
417C2×C4#91112yes—
418C2×C4C2×#21311yescharacteristic
419C2×C4#93211yescharacteristic
420C2×C4#93711yescharacteristic
421C2×C4#93711yescharacteristic
422C2×C4#93811yescharacteristic
423C2×C4#93911yescharacteristic
424C2×C4#94011yescharacteristic
425C2×C4#94911yescharacteristic
426C2×C4#95011yescharacteristic
427C2×C4#95311yescharacteristic
428C8—42no—
429C8—64no—
430C8—122no—
431C8—241no—
432C2×C3—82no—
433C2×C3—162no—
434C2×C3#166712yes—
435C2×C3#168712yes—
436C2×C3#199911yescharacteristic
437C2×C3#201111yescharacteristic
438C2×C3#201811yescharacteristic
439D3—162no—
440C22—42no—
441C22—44no—
442C22—82no—
443C22—81no—
444C22—81no—
445C22—82no—
446C22—82no—
447C22—82no—
448C22—162no—
449C22—162no—
450C22—242no—
451C22—242no—
452C22—242no—
453C22—482no—
454C22—482no—
455C22#503811yescharacteristic
456C22#503911yescharacteristic
457C22#515012yes—
458C22#519912yes—
459C22#522311yescharacteristic
460C4—21no—
461C4—21no—
462C4—81no—
463C4#503611yescharacteristic
464C4#503711yescharacteristic
465C4#515111yescharacteristic
466C4#515411yescharacteristic
467C4#515612yes—
468C4#521711yescharacteristic
469C4#523811yescharacteristic
470C3#1026011yescharacteristic, complemented, Sylow
471C2—82no—
472C2—162no—
473C2—482no—
474C2#7100512yes—
475C2#7100912yes—
476C2#7168411yescharacteristic
477C2#7204411yescharacteristic
478C2#7209511yescharacteristic
subgroupG/H
centerC23#939
commutator, cosocleC2×C3×C42C23
FrattiniC2×C42C22×D3
FittingC2×C3×#459C2
socleC23×C3#121
hypercenterC2×#459D3
hypocenterC3#10260
LCSG ▷ C2×C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×C3×#459C2semidirect
2. C2×#5073C2semidirect
3. C2×#5015C2semidirect
4. C2×#4544C2semidirect
5. #71614C2semidirect
6. C2×#4485C2semidirect
7. #67703C2semidirect
32. C2×#459D3semidirect
126. C2×C3×D4D8semidirect
169. C2×C3⋊C8D8semidirect
311. C2×D4#213semidirect
470. C3#10260semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4592
C2×#50732
C2×#50152
C2×#45442
#716142
C2×#44852
#677032
#102603