Finite Group Databasebeta

← #76347

Subgroups — #76347

Order 384.

760 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#939C211yesmaximal, characteristic, complemented
2C2×#896C211yesmaximal, characteristic, complemented
3C2×#885C211yesmaximal, characteristic, complemented
4C2×#884C211yesmaximal, characteristic, complemented
5C2×#67⋊C4C211yesmaximal, characteristic, complemented
6C2×#878C211yesmaximal, characteristic, complemented
7C3×#390C211yesmaximal, characteristic, complemented
8#5223C211yesmaximal, characteristic, complemented
9#4993C211yesmaximal, characteristic, complemented
10#4960C211yesmaximal, characteristic, complemented
11#4957C211yesmaximal, characteristic, complemented
12#4957C211yesmaximal, characteristic, complemented
13#4949C211yesmaximal, characteristic, complemented
14#4939C211yesmaximal, characteristic, complemented
15C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#2540—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C22×Dic6C2211yescharacteristic
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×C3×C42C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
35#939—24no—
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×(C2×D3)⋊C4C2211yescharacteristic
43C2×C4⋊Dic3C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×Dic3⋊C4C2211yescharacteristic
47C2×Dic3⋊C4C2211yescharacteristic
48C2×Dic3⋊C4C2211yescharacteristic
49C2×C4×Dic3C2211yescharacteristic
50C2×C4×Dic3C2211yescharacteristic
51#896—24no—
52#885—24no—
53#884—24no—
54#67⋊C4—24no—
55#878—24no—
56C3⋊#95C2211yescharacteristic
57C3⋊#95C2211yescharacteristic
58C2×#124—31no—
59C2×C22⋊Q8—31no—
60C2×C22⋊Q8—31no—
61C2×#121—31no—
62C2×#121—31no—
63C2×C4×D4—31no—
64#399—31no—
65#399—31no—
66#392—31no—
67#392—31no—
68#390—31no—
69#390—31no—
70#390—31no—
71#390D311yescharacteristic, complemented
72C4×C4⋊C4—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×#67—41no—
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—41no—
109C2×C4×D3—22no—
110C2×C4×D3—22no—
111C2×C4×D3—22no—
112C2×Dic6—22no—
113C2×Dic6—22no—
114C2×Dic6—22no—
115C3×C4⋊C4—22no—
116C3×C22⋊C4—22no—
117C3×C22⋊C4—22no—
118C3×C22⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C42—41no—
121#217—22no—
122#217—22no—
123#217—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—22no—
130(C2×D3)⋊C4—22no—
131C4⋊Dic3—22no—
132Dic3⋊C4—22no—
133Dic3⋊C4—22no—
134Dic3⋊C4—22no—
135Dic3⋊C4D414yescomplemented
136Dic3⋊C4D414yescomplemented
137C4×Dic3—41no—
138C4×Dic3D414yescomplemented
139C22×Q8—31no—
140C22×D4—31no—
141C22×D4—31no—
142C22×D4—31no—
143C22×D4—31no—
144C22×D4—31no—
145C22×D4C2×D311yescharacteristic
146C23×C4—31no—
147C23×C4—31no—
148#124—64no—
149C22⋊Q8—64no—
150C22⋊Q8—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⋊C4C2×D311yescharacteristic
161C2×C22⋊C4—31no—
162C2×C22⋊C4—31no—
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—
176C2×C42—31no—
177C2×C42C2×D311yescharacteristic
178#95—31no—
179#95—31no—
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×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×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×C4C2×D412yes—
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—44no—
242C2×Dic3C2×D412yes—
243C2×Dic3C2×D412yes—
244C2×Dic3C2×D412yes—
245C2×Dic3C2×D412yes—
246C2×Dic3C2×D412yes—
247C2×Dic3C2×D412yes—
248D12—44no—
249C4×D3—44no—
250Dic6—44no—
251C24—31no—
252C24—31no—
253C24C22×D311yescharacteristic
254C24C22×D311yescharacteristic
255C2×Q8—62no—
256C2×Q8—62no—
257C2×Q8—62no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—41no—
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—
274C2×D4—121no—
275C2×D4—121no—
276C22×C4—31no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—31no—
282C22×C4—62no—
283C22×C4—62no—
284C22×C4—62no—
285C22×C4—62no—
286C22×C4—62no—
287C22×C4—62no—
288C22×C4C22×D311yescharacteristic
289C22×C4C22×D311yescharacteristic
290C22×C4C22×D311yescharacteristic
291C22×C4C22×D311yescharacteristic
292C22×C4C22×D311yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—34no—
295C4⋊C4—34no—
296C4⋊C4—62no—
297C4⋊C4—62no—
298C4⋊C4—62no—
299C4⋊C4—62no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—62no—
305C22⋊C4—62no—
306C22⋊C4—62no—
307C22⋊C4—62no—
308C22⋊C4—62no—
309C22⋊C4—62no—
310C22⋊C4—62no—
311C22⋊C4—62no—
312C22⋊C4—62no—
313C22⋊C4—62no—
314C42—34no—
315C42—41no—
316C42—121no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—41no—
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×C3C22×D411yescharacteristic
332C22×C3C22×D411yescharacteristic
333C22×C3C22×D411yescharacteristic
334C22×C3C2×#4111yescharacteristic
335C22×C3C2×#4111yescharacteristic
336C22×C3H(5,𝔽2)11yescharacteristic
337C22×C32−1+411yescharacteristic
338C2×D3—22no—
339C2×D3—22no—
340C2×D3—22no—
341C2×D3—41no—
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—
352C3×C4—22no—
353C3×C4—22no—
354C3×C4—22no—
355C3×C4—41no—
356C3×C4—41no—
357Dic3—22no—
358Dic3—22no—
359Dic3—22no—
360Dic3—41no—
361Dic3—41no—
362Dic3#12714yes—
363C23—21no—
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—32no—
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—61no—
390C23#23512yes—
391C23C23×D311yescharacteristic
392Q8—124no—
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—32no—
412C2×C4—32no—
413C2×C4—32no—
414C2×C4—32no—
415C2×C4—32no—
416C2×C4—32no—
417C2×C4—61no—
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—124no—
430C2×C4—124no—
431C2×C4D3×D412yes—
432C2×C4D3×D412yes—
433C2×C4D3×D412yes—
434C2×C3—42no—
435C2×C3—81no—
436C2×C3#52511yescharacteristic
437C2×C3C2×#12711yescharacteristic
438C2×C3#53711yescharacteristic
439C2×C3#54611yescharacteristic
440C2×C3#54611yescharacteristic
441C2×C3#54811yescharacteristic
442C2×C3#54811yescharacteristic
443D3—42no—
444D3—81no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—62no—
460C22—62no—
461C22—62no—
462C22—121no—
463C22—121no—
464C22—121no—
465C22—121no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22C2×#23511yescharacteristic
474C22C2×D3×D411yescharacteristic
475C22C2×D3×D411yescharacteristic
476C22C2×D3×D411yescharacteristic
477C22#100411yescharacteristic
478C22D3×#4111yescharacteristic
479C22#101011yescharacteristic
480C4—22no—
481C4—22no—
482C4—22no—
483C4—34no—
484C4—41no—
485C4—41no—
486C4—62no—
487C4—62no—
488C4—62no—
489C4—121no—
490C4—121no—
491C3#254011yescharacteristic, complemented, Sylow
492C2—42no—
493C2—81no—
494C2—122no—
495C2—241no—
496C2#549011yescharacteristic
497C2#554711yescharacteristic
498C2#555211yescharacteristic
499C2#559711yescharacteristic
500C2#561011yescharacteristic
501C2#567711yescharacteristic
502C2D3×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#390C2
hypercenter#390D3
hypocenterC3#2540
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#939C2semidirect
2. C2×#896C2semidirect
3. C2×#885C2semidirect
4. C2×#884C2semidirect
5. C2×#67⋊C4C2semidirect
6. C2×#878C2semidirect
7. C3×#390C2semidirect
8. #5223C2semidirect
9. #4993C2semidirect
10. #4960C2semidirect
11. #4957C2semidirect
12. #4957C2semidirect
13. #4949C2semidirect
14. #4939C2semidirect
15. C4×Dic3⋊C4C2semidirect
71. #390D3semidirect
135. Dic3⋊C4D4semidirect
136. Dic3⋊C4D4semidirect
138. C4×Dic3D4semidirect
491. C3#2540semidirect

Maximal subgroups

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

subgroupindex
C2×#9392
C2×#8962
C2×#8852
C2×#8842
C2×#67⋊C42
C2×#8782
C3×#3902
#52232
#49932
#49602
#49572
#49492
#49392
C4×Dic3⋊C42
#25403