Finite Group Databasebeta

← #76898

Subgroups — #76898

Order 384.

788 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#939C211yesmaximal, characteristic, complemented
2C2×#938C211yesmaximal, characteristic, complemented
3C2×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#884C211yesmaximal, characteristic, complemented
5C2×#884C211yesmaximal, characteristic, complemented
6C2×#67⋊C4C211yesmaximal, characteristic, complemented
7C3×#394C211yesmaximal, characteristic, complemented
8#4994C211yesmaximal, characteristic, complemented
9#4961C211yesmaximal, characteristic, complemented
10#4957C211yesmaximal, characteristic, complemented
11#4956C211yesmaximal, characteristic, complemented
12#4948C211yesmaximal, characteristic, complemented
13#4942C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4647C211yesmaximal, characteristic, complemented
16#2416—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C22×C4×D3C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×C3×C22⋊C4C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35#939—24no—
36#938—24no—
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×C4⋊Dic3C2211yescharacteristic
43C2×C4⋊Dic3C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×Dic3⋊C4C2211yescharacteristic
47C2×Dic3⋊C4C2211yescharacteristic
48C2×Dic3⋊C4C2211yescharacteristic
49C2×C4×Dic3C2211yescharacteristic
50D3×C4⋊C4—24no—
51#884—24no—
52#884—24no—
53#67⋊C4—24no—
54C3×#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C3⋊#95C2211yescharacteristic
57C3⋊#95C2211yescharacteristic
58C2×#121—31no—
59C2×#121—31no—
60C2×#121—31no—
61C2×#121—31no—
62C2×C4×D4—31no—
63C22×C4⋊C4—31no—
64#396—31no—
65#396—31no—
66#394—31no—
67#394D311yescharacteristic, complemented
68#390—31no—
69#389—31no—
70#386—31no—
71#386—31no—
72#380—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C23×D3C2311yescharacteristic
76C23×D3C2311yescharacteristic
77C2×C3×D4—22no—
78C2×C3×D4—22no—
79C2×C3×D4—41no—
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C2×#67—22no—
86C2×#67—22no—
87C2×#67—22no—
88C2×#67—22no—
89C2×#67—22no—
90C2×#67—22no—
91C2×#67—22no—
92C2×#67—22no—
93C2×#67—22no—
94C2×#67—22no—
95C2×#67—41no—
96C2×#67D414yescomplemented
97C22×Dic3—22no—
98C22×Dic3—22no—
99C22×Dic3—22no—
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2311yescharacteristic
103C22×Dic3C2311yescharacteristic
104C22×Dic3C2311yescharacteristic
105C22×Dic3C2311yescharacteristic
106C2×D12—22no—
107C2×D12—22no—
108C2×D12—22no—
109C2×C4×D3—22no—
110C2×C4×D3—22no—
111C2×C4×D3—22no—
112C2×C4×D3—22no—
113C2×C4×D3—22no—
114C2×C4×D3—22no—
115C2×C4×D3—41no—
116C2×C4×D3—41no—
117C2×C4×D3D414yescomplemented
118C3×C4⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C22⋊C4—22no—
121C3×C22⋊C4—22no—
122C3×C22⋊C4—41no—
123#217—22no—
124#217—22no—
125#217—22no—
126(C2×D3)⋊C4—22no—
127(C2×D3)⋊C4—22no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—22no—
130(C2×D3)⋊C4—41no—
131C4⋊Dic3—22no—
132C4⋊Dic3—22no—
133Dic3⋊C4—22no—
134Dic3⋊C4—22no—
135Dic3⋊C4—22no—
136Dic3⋊C4—22no—
137Dic3⋊C4D414yescomplemented
138C4×Dic3—22no—
139C22×D4—31no—
140C22×D4—31no—
141C22×D4—31no—
142C22×D4—31no—
143C22×D4—31no—
144C22×D4C2×D311yescharacteristic
145C23×C4—31no—
146C23×C4—31no—
147C23×C4—31no—
148C23×C4—31no—
149#121—64no—
150#121—64no—
151#121—64no—
152#121—64no—
153C4×D4—64no—
154C2×C4⋊C4—31no—
155C2×C4⋊C4—31no—
156C2×C4⋊C4—31no—
157C2×C4⋊C4—31no—
158C2×C4⋊C4—31no—
159C2×C4⋊C4—31no—
160C2×C4⋊C4—31no—
161C2×C4⋊C4—64no—
162C2×C4⋊C4C2×D311yescharacteristic
163C2×C22⋊C4—31no—
164C2×C22⋊C4—31no—
165C2×C22⋊C4—31no—
166C2×C22⋊C4—31no—
167C2×C22⋊C4—31no—
168C2×C22⋊C4—31no—
169C2×C22⋊C4—31no—
170C2×C22⋊C4—31no—
171C2×C22⋊C4C2×D311yescharacteristic
172C2×C22⋊C4C2×D311yescharacteristic
173C2×C22⋊C4C2×D311yescharacteristic
174C2×C22⋊C4C2×D311yescharacteristic
175C2×C42—31no—
176#95—31no—
177#95—31no—
178#95—31no—
179#95C2×D311yescharacteristic
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—21no—
185C23×C3—21no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3C2×D412yes—
194C23×C3C2411yescharacteristic
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—21no—
200C22×D3—21no—
201C22×D3—21no—
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—21no—
205C22×D3—21no—
206C22×D3C2×D412yes—
207C22×D3C2×D412yes—
208C22×D3#4112yes—
209C3×D4—44no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4C2×D412yes—
224C2×C3×C4C2×D412yes—
225#67—28no—
226#67—44no—
227#67—44no—
228#67—44no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—44no—
243C2×Dic3C2×D412yes—
244C2×Dic3C2×D412yes—
245C2×Dic3C2×D412yes—
246C2×Dic3C2×D412yes—
247C2×Dic3#4112yes—
248D12—44no—
249C4×D3—28no—
250C4×D3—44no—
251C4×D3—44no—
252C24—31no—
253C24—31no—
254C24C22×D311yescharacteristic
255C24C22×D311yescharacteristic
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—34no—
259C2×D4—41no—
260C2×D4—62no—
261C2×D4—62no—
262C2×D4—62no—
263C2×D4—62no—
264C2×D4—62no—
265C2×D4—62no—
266C2×D4—62no—
267C2×D4—62no—
268C2×D4—62no—
269C2×D4—62no—
270C2×D4—62no—
271C2×D4—62no—
272C2×D4—62no—
273C2×D4—121no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—31no—
277C22×C4—34no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—62no—
282C22×C4—62no—
283C22×C4—62no—
284C22×C4—62no—
285C22×C4—62no—
286C22×C4—62no—
287C22×C4—62no—
288C22×C4—62no—
289C22×C4—62no—
290C22×C4—121no—
291C22×C4—121no—
292C22×C4C22×D311yescharacteristic
293C22×C4C22×D311yescharacteristic
294C22×C4C22×D311yescharacteristic
295C22×C4C22×D311yescharacteristic
296C22×C4C22×D311yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—34no—
299C4⋊C4—62no—
300C4⋊C4—62no—
301C4⋊C4—62no—
302C4⋊C4—62no—
303C4⋊C4—62no—
304C4⋊C4—62no—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—41no—
309C22⋊C4—62no—
310C22⋊C4—62no—
311C22⋊C4—62no—
312C22⋊C4—62no—
313C22⋊C4—62no—
314C22⋊C4—62no—
315C22⋊C4—62no—
316C22⋊C4—121no—
317C42—62no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3C22×D411yescharacteristic
333C22×C3C22×D411yescharacteristic
334C22×C3C22×D411yescharacteristic
335C22×C3C2×#4111yescharacteristic
336C22×C3C2×#4111yescharacteristic
337C22×C3H(5,𝔽2)11yescharacteristic
338C22×C32−1+411yescharacteristic
339C2×D3—22no—
340C2×D3—22no—
341C2×D3—22no—
342C2×D3—22no—
343C2×D3—22no—
344C2×D3—22no—
345C2×D3—41no—
346C2×D3—41no—
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—41no—
352C2×D3#12114yescomplemented
353C3×C4—22no—
354C3×C4—22no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—41no—
358Dic3—22no—
359Dic3—22no—
360Dic3—41no—
361Dic3—41no—
362Dic3—41no—
363Dic3#12114yescomplemented
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—32no—
378C23—32no—
379C23—32no—
380C23—61no—
381C23—61no—
382C23—61no—
383C23—61no—
384C23—61no—
385C23—61no—
386C23—61no—
387C23—61no—
388C23—61no—
389C23—61no—
390C23—61no—
391C23D3×D412yes—
392C23C23×D311yescharacteristic
393D4—44no—
394D4—68no—
395D4—124no—
396D4—124no—
397D4—124no—
398D4—124no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—32no—
413C2×C4—32no—
414C2×C4—32no—
415C2×C4—32no—
416C2×C4—32no—
417C2×C4—68no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—124no—
432C2×C4—124no—
433C2×C4—124no—
434C2×C4D3×D412yes—
435C2×C4D3×D412yes—
436C2×C3—42no—
437C2×C3—81no—
438C2×C3C2×#12111yescharacteristic
439C2×C3C2×#12111yescharacteristic
440C2×C3#53711yescharacteristic
441C2×C3D4211yescharacteristic
442C2×C3#54711yescharacteristic
443C2×C3#54811yescharacteristic
444C2×C3#55311yescharacteristic
445D3—24no—
446D3—81no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—34no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—62no—
463C22—62no—
464C22—62no—
465C22—62no—
466C22—62no—
467C22—62no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22—121no—
474C22—121no—
475C22C2×D3×D411yescharacteristic
476C22C2×D3×D411yescharacteristic
477C22C2×D3×D411yescharacteristic
478C22#100411yescharacteristic
479C22D3×#4111yescharacteristic
480C22D3×#4111yescharacteristic
481C22#101011yescharacteristic
482C4—22no—
483C4—22no—
484C4—34no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—62no—
489C4—62no—
490C4—121no—
491C4—121no—
492C4—121no—
493C3#241611yescharacteristic, complemented, Sylow
494C2—42no—
495C2—64no—
496C2—81no—
497C2—241no—
498C2#559011yescharacteristic
499C2D3×#12111yescharacteristic
500C2D3×#12111yescharacteristic
501C2#560811yescharacteristic
502C2#565511yescharacteristic
503C2#566111yescharacteristic
504C2#567711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#394C2
hypercenter#394D3
hypocenterC3#2416
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#939C2semidirect
2. C2×#938C2semidirect
3. C2×D3×C4⋊C4C2semidirect
4. C2×#884C2semidirect
5. C2×#884C2semidirect
6. C2×#67⋊C4C2semidirect
7. C3×#394C2semidirect
8. #4994C2semidirect
9. #4961C2semidirect
10. #4957C2semidirect
11. #4956C2semidirect
12. #4948C2semidirect
13. #4942C2semidirect
14. #4665C2semidirect
15. #4647C2semidirect
67. #394D3semidirect
96. C2×#67D4semidirect
117. C2×C4×D3D4semidirect
137. Dic3⋊C4D4semidirect
352. C2×D3#121semidirect
363. Dic3#121semidirect
493. C3#2416semidirect

Maximal subgroups

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

subgroupindex
C2×#9392
C2×#9382
C2×D3×C4⋊C42
C2×#8842
C2×#67⋊C42
C3×#3942
#49942
#49612
#49572
#49562
#49482
#49422
#46652
#46472
#24163