Finite Group Databasebeta

← #74692

Subgroups — #74692

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×#939C211yesmaximal, characteristic, complemented
3C2×#930C211yesmaximal, characteristic, complemented
4C22×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×#884C211yesmaximal, characteristic, complemented
6C2×#67⋊C4C211yesmaximal, characteristic, complemented
7C3×#386C211yesmaximal, characteristic, complemented
8#4959C211yesmaximal, characteristic, complemented
9#4958C211yesmaximal, characteristic, complemented
10#4957C211yesmaximal, characteristic, complemented
11#4948C211yesmaximal, characteristic, complemented
12#4676C211yesmaximal, characteristic, complemented
13#4672C211yesmaximal, characteristic, complemented
14#4667C211yesmaximal, characteristic, complemented
15#4647C211yesmaximal, characteristic, complemented
16#2416—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C23×Dic3C2211yescharacteristic
24C23×Dic3C2211yescharacteristic
25C22×D12C2211yescharacteristic
26C22×C4×D3C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32#939—24no—
33#939—24no—
34#930—24no—
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×C4⋊Dic3C2211yescharacteristic
43C2×Dic3⋊C4—24no—
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×Dic3⋊C4C2211yescharacteristic
47C2×Dic3⋊C4C2211yescharacteristic
48C2×Dic3⋊C4C2211yescharacteristic
49C2×Dic3⋊C4C2211yescharacteristic
50C2×Dic3⋊C4C2211yescharacteristic
51C2×C4×Dic3C2211yescharacteristic
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#394—31no—
68#390—31no—
69#389—31no—
70#386—31no—
71#386D311yescharacteristic, complemented
72#380—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C23×D3C2311yescharacteristic
76C23×D3C2311yescharacteristic
77C2×C3×D4—22no—
78C2×C3×D4—22no—
79C2×C3×D4—22no—
80C22×C3×C4—22no—
81C22×C3×C4—22no—
82C22×C3×C4—41no—
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C2×#67—22no—
89C2×#67—22no—
90C2×#67—22no—
91C2×#67—22no—
92C2×#67—22no—
93C2×#67—22no—
94C2×#67—22no—
95C2×#67—22no—
96C2×#67—22no—
97C2×#67—22no—
98C2×#67—41no—
99C2×#67D414yescomplemented
100C22×Dic3—22no—
101C22×Dic3—22no—
102C22×Dic3—22no—
103C22×Dic3—22no—
104C22×Dic3—41no—
105C22×Dic3D414yescomplemented
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C22×Dic3C2311yescharacteristic
111C22×Dic3C2311yescharacteristic
112C2×D12—22no—
113C2×D12—22no—
114C2×D12—41no—
115C2×C4×D3—22no—
116C2×C4×D3—22no—
117C2×C4×D3—22no—
118C3×C22⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C22⋊C4—41no—
121#217—22no—
122#217—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—22no—
126(C2×D3)⋊C4—22no—
127(C2×D3)⋊C4—22no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—41no—
130C4⋊Dic3—22no—
131Dic3⋊C4—22no—
132Dic3⋊C4—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×C4C2×D311yescharacteristic
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—31no—
162C2×C4⋊C4—64no—
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⋊C4—31no—
172C2×C22⋊C4C2×D311yescharacteristic
173C2×C22⋊C4C2×D311yescharacteristic
174C2×C22⋊C4C2×D311yescharacteristic
175C2×C42—31no—
176#95—31no—
177#95—31no—
178#95C2×D311yescharacteristic
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×C3C2×D412yes—
192C23×C3C2×D412yes—
193C23×C3#4112yes—
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×D3—21no—
207C22×D3—21no—
208C22×D3C2×D412yes—
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×C4—21no—
224C2×C3×C4—44no—
225C2×C3×C4C2×D412yes—
226#67—28no—
227#67—44no—
228#67—44no—
229#67—44no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—28no—
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—44no—
244C2×Dic3C2×D412yes—
245C2×Dic3C2×D412yes—
246C2×Dic3C2×D412yes—
247C2×Dic3C2×D412yes—
248C2×Dic3C2×D412yes—
249C2×Dic3#4112yes—
250D12—44no—
251C4×D3—44no—
252C24—31no—
253C24—31no—
254C24C22×D311yescharacteristic
255C24C22×D311yescharacteristic
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—34no—
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—121no—
273C2×D4—121no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—31no—
277C22×C4—34no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—31no—
282C22×C4—31no—
283C22×C4—41no—
284C22×C4—62no—
285C22×C4—62no—
286C22×C4—62no—
287C22×C4—62no—
288C22×C4—62no—
289C22×C4—62no—
290C22×C4—62no—
291C22×C4—121no—
292C22×C4C22×D311yescharacteristic
293C22×C4C22×D311yescharacteristic
294C22×C4C22×D311yescharacteristic
295C22×C4C22×D311yescharacteristic
296C22×C4C22×D311yescharacteristic
297C4⋊C4—34no—
298C4⋊C4—62no—
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—41no—
308C22⋊C4—62no—
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—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3#12114yescomplemented
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—41no—
343C2×D3—41no—
344C2×D3—41no—
345C2×D3—41no—
346C2×D3—41no—
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—41no—
352C2×D3—41no—
353C3×C4—22no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—41no—
358Dic3—22no—
359Dic3—22no—
360Dic3—22no—
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—32no—
376C23—61no—
377C23—61no—
378C23—61no—
379C23—61no—
380C23—61no—
381C23—61no—
382C23—61no—
383C23—61no—
384C23—61no—
385C23—61no—
386C23—61no—
387C23—61no—
388C23—61no—
389C23#23512yes—
390C23D3×D412yes—
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—21no—
413C2×C4—32no—
414C2×C4—32no—
415C2×C4—32no—
416C2×C4—32no—
417C2×C4—32no—
418C2×C4—32no—
419C2×C4—44no—
420C2×C4—68no—
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—61no—
432C2×C4—61no—
433C2×C4—124no—
434C2×C4—124no—
435C2×C4D3×D412yes—
436C2×C3—24no—
437C2×C3—81no—
438C2×C3C2×#12111yescharacteristic
439C2×C3C2×#12111yescharacteristic
440C2×C3#53711yescharacteristic
441C2×C3D4211yescharacteristic
442C2×C3#54711yescharacteristic
443C2×C3#54811yescharacteristic
444C2×C3#55311yescharacteristic
445D3—42no—
446D3—81no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—62no—
461C22—62no—
462C22—62no—
463C22—121no—
464C22—121no—
465C22—121no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22—121no—
474C22#88414yescomplemented
475C22C2×#23511yescharacteristic
476C22C2×D3×D411yescharacteristic
477C22C2×D3×D411yescharacteristic
478C22C2×D3×D411yescharacteristic
479C22#100411yescharacteristic
480C22D3×#4111yescharacteristic
481C22#101011yescharacteristic
482C4—22no—
483C4—34no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—62no—
489C4—62no—
490C4—62no—
491C4—121no—
492C4—121no—
493C3#241611yescharacteristic, complemented, Sylow
494C2—24no—
495C2—81no—
496C2—122no—
497C2—241no—
498C2C2×#88411yescharacteristic
499C2#554011yescharacteristic
500C2#555211yescharacteristic
501C2#559011yescharacteristic
502C2#559711yescharacteristic
503C2D3×#12111yescharacteristic
504C2#565511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
hypercenter#386D3
hypocenterC3#2416
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#939C2semidirect
2. C2×#939C2semidirect
3. C2×#930C2semidirect
4. C22×Dic3⋊C4C2semidirect
5. C2×#884C2semidirect
6. C2×#67⋊C4C2semidirect
7. C3×#386C2semidirect
8. #4959C2semidirect
9. #4958C2semidirect
10. #4957C2semidirect
11. #4948C2semidirect
12. #4676C2semidirect
13. #4672C2semidirect
14. #4667C2semidirect
15. #4647C2semidirect
71. #386D3semidirect
99. C2×#67D4semidirect
105. C22×Dic3D4semidirect
137. Dic3⋊C4D4semidirect
331. C22×C3#121semidirect
363. Dic3#121semidirect
474. C22#884semidirect
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×#9302
C22×Dic3⋊C42
C2×#8842
C2×#67⋊C42
C3×#3862
#49592
#49582
#49572
#49482
#46762
#46722
#46672
#46472
#24163