Finite Group Databasebeta

← #74700

Subgroups — #74700

Order 384.

952 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#235C211yesmaximal, characteristic, complemented
2C2×#940C211yesmaximal, characteristic, complemented
3C2×#885C211yesmaximal, characteristic, complemented
4C2×#884C211yesmaximal, characteristic, complemented
5C3×#386C211yesmaximal, characteristic, complemented
6#5223C211yesmaximal, characteristic, complemented
7#5213C211yesmaximal, characteristic, complemented
8#4960C211yesmaximal, characteristic, complemented
9#4960C211yesmaximal, characteristic, complemented
10#4957C211yesmaximal, characteristic, complemented
11#4956C211yesmaximal, characteristic, complemented
12#4671C211yesmaximal, characteristic, complemented
13#4666C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4646C211yesmaximal, characteristic, complemented
16#2431—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic
24C22×#67C2211yescharacteristic
25C2×#235—24no—
26C2×#235—24no—
27C2×#235—24no—
28C22×D12C2211yescharacteristic
29C22×D12C2211yescharacteristic
30C22×D12C2211yescharacteristic
31C22×C4×D3C2211yescharacteristic
32C22×C4×D3C2211yescharacteristic
33C22×Dic6C2211yescharacteristic
34C2×C3×C22⋊C4C2211yescharacteristic
35C2×C3×C22⋊C4C2211yescharacteristic
36C2×C3×C22⋊C4C2211yescharacteristic
37C2×#217C2211yescharacteristic
38C2×#217C2211yescharacteristic
39#940—24no—
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×(C2×D3)⋊C4C2211yescharacteristic
46C2×(C2×D3)⋊C4C2211yescharacteristic
47C2×Dic3⋊C4C2211yescharacteristic
48C2×C4×Dic3C2211yescharacteristic
49C2×C4×Dic3C2211yescharacteristic
50#885—24no—
51#884—24no—
52C3×#95C2211yescharacteristic
53C3×#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C3⋊#95C2211yescharacteristic
57C3⋊#95C2211yescharacteristic
58C22×#41—31no—
59C2×#127—31no—
60C2×#124—31no—
61C2×#121—31no—
62#392—31no—
63#392—31no—
64#392—31no—
65#392—31no—
66#391—31no—
67#390—31no—
68#386—31no—
69#386—31no—
70#386—31no—
71#386D311yescharacteristic, complemented
72C4×C22⋊C4—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C23×D3C2311yescharacteristic
76C23×D3C2311yescharacteristic
77C23×D3C2311yescharacteristic
78C2×C3×D4—22no—
79C2×C3×D4—22no—
80C2×C3×D4—41no—
81C22×C3×C4—22no—
82C22×C3×C4—22no—
83C22×C3×C4—22no—
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C22×C3×C4C2311yescharacteristic
87C22×C3×C4C2311yescharacteristic
88C22×C3×C4C2311yescharacteristic
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—22no—
99C2×#67—22no—
100C2×#67—22no—
101C2×#67—22no—
102C2×#67—41no—
103C2×#67—41no—
104C2×#67—41no—
105C2×#67—41no—
106C2×#67D414yescomplemented
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C22×Dic3C2311yescharacteristic
111C22×Dic3C2311yescharacteristic
112#235—232no—
113C2×D12—22no—
114C2×D12—22no—
115C2×D12—22no—
116C2×D12—22no—
117C2×D12—22no—
118C2×D12—22no—
119C2×D12—41no—
120C2×D12—41no—
121C2×D12—41no—
122C2×C4×D3—22no—
123C2×C4×D3—22no—
124C2×C4×D3—22no—
125C2×C4×D3—22no—
126C2×C4×D3—22no—
127C2×C4×D3D414yescomplemented
128C2×Dic6—22no—
129C2×Dic6—22no—
130C2×Dic6D414yescomplemented
131C3×C22⋊C4—22no—
132C3×C22⋊C4—22no—
133C3×C22⋊C4—41no—
134#217—22no—
135#217—41no—
136(C2×D3)⋊C4—22no—
137(C2×D3)⋊C4—22no—
138(C2×D3)⋊C4—22no—
139(C2×D3)⋊C4—22no—
140(C2×D3)⋊C4—22no—
141(C2×D3)⋊C4—41no—
142(C2×D3)⋊C4—41no—
143Dic3⋊C4—22no—
144C4×Dic3—22no—
145C4×Dic3—22no—
146C2×#41—64no—
147C2×#41—64no—
148C2×#41—64no—
149C22×Q8—31no—
150C22×D4—31no—
151C22×D4—31no—
152C22×D4—31no—
153C22×D4—31no—
154C22×D4—31no—
155C22×D4—31no—
156C22×D4—31no—
157C22×D4—31no—
158C22×D4—31no—
159C22×D4C2×D311yescharacteristic
160C23×C4—31no—
161C23×C4—31no—
162C23×C4C2×D311yescharacteristic
163#127—64no—
164#124—64no—
165#121—64no—
166C2×C4⋊C4—31no—
167C2×C22⋊C4—31no—
168C2×C22⋊C4—31no—
169C2×C22⋊C4—31no—
170C2×C22⋊C4—31no—
171C2×C22⋊C4—31no—
172C2×C22⋊C4—31no—
173C2×C22⋊C4—31no—
174C2×C22⋊C4—31no—
175C2×C22⋊C4—31no—
176C2×C22⋊C4C2×D311yescharacteristic
177C2×C22⋊C4C2×D311yescharacteristic
178C2×C22⋊C4C2×D311yescharacteristic
179C2×C42—31no—
180C2×C42—31no—
181#95—31no—
182#95—31no—
183#95—31no—
184#95—31no—
185#95C2×D311yescharacteristic
186#95C2×D311yescharacteristic
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3C2×D412yes—
201C23×C3C2411yescharacteristic
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—21no—
205C22×D3—21no—
206C22×D3—21no—
207C22×D3—21no—
208C22×D3—21no—
209C22×D3—21no—
210C22×D3—21no—
211C22×D3—21no—
212C22×D3—21no—
213C22×D3—21no—
214C22×D3—21no—
215C22×D3—21no—
216C22×D3—21no—
217C22×D3—21no—
218C22×D3—21no—
219C22×D3—21no—
220C22×D3—21no—
221C22×D3C2×D412yes—
222C22×D3C2×D412yes—
223C3×D4—44no—
224C2×C3×C4—28no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4C2×D412yes—
238C2×C3×C4C2×D412yes—
239C2×C3×C4#4112yescomplemented
240#67—28no—
241#67—28no—
242#67—44no—
243#67—44no—
244#67—44no—
245#67—44no—
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3C2×D412yes—
257C2×Dic3C2×D412yes—
258C2×Dic3C2×D412yes—
259C2×Dic3C2×D412yes—
260C2×Dic3#4112yescomplemented
261D12—28no—
262D12—44no—
263D12—44no—
264C4×D3—28no—
265C4×D3—28no—
266Dic6—28no—
267C24—31no—
268C24—31no—
269C24—31no—
270C24C22×D311yescharacteristic
271C24C22×D311yescharacteristic
272#41—632no—
273C2×Q8—34no—
274C2×Q8—62no—
275C2×Q8—62no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—34no—
279C2×D4—41no—
280C2×D4—62no—
281C2×D4—62no—
282C2×D4—62no—
283C2×D4—62no—
284C2×D4—62no—
285C2×D4—62no—
286C2×D4—62no—
287C2×D4—62no—
288C2×D4—62no—
289C2×D4—62no—
290C2×D4—62no—
291C2×D4—62no—
292C2×D4—62no—
293C2×D4—62no—
294C2×D4—62no—
295C2×D4—62no—
296C2×D4—62no—
297C2×D4—62no—
298C2×D4—62no—
299C2×D4—121no—
300C2×D4—121no—
301C2×D4—121no—
302C2×D4—121no—
303C2×D4—121no—
304C2×D4—121no—
305C2×D4—121no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—31no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—34no—
313C22×C4—31no—
314C22×C4—31no—
315C22×C4—62no—
316C22×C4—62no—
317C22×C4—62no—
318C22×C4—62no—
319C22×C4—62no—
320C22×C4C22×D311yescharacteristic
321C22×C4C22×D311yescharacteristic
322C22×C4C22×D311yescharacteristic
323C22×C4C22×D311yescharacteristic
324C22×C4C22×D311yescharacteristic
325C4⋊C4—62no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—41no—
329C22⋊C4—62no—
330C22⋊C4—62no—
331C22⋊C4—62no—
332C22⋊C4—62no—
333C22⋊C4—62no—
334C22⋊C4—62no—
335C22⋊C4—121no—
336C22⋊C4—121no—
337C22⋊C4—121no—
338C42—62no—
339C42—62no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3C22×D411yescharacteristic
355C22×C3C22×D411yescharacteristic
356C22×C3C22×D411yescharacteristic
357C22×C3C2×#4111yescharacteristic
358C22×C3C2×#4111yescharacteristic
359C22×C3H(5,𝔽2)11yescharacteristic
360C22×C3H(5,𝔽2)11yescharacteristic
361C2×D3—22no—
362C2×D3—22no—
363C2×D3—22no—
364C2×D3—22no—
365C2×D3—22no—
366C2×D3—22no—
367C2×D3—41no—
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—41no—
371C2×D3—41no—
372C2×D3—41no—
373C2×D3—41no—
374C2×D3—41no—
375C2×D3—41no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—41no—
381C2×D3—41no—
382C3×C4—22no—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—41no—
386C3×C4—41no—
387Dic3—22no—
388Dic3—22no—
389Dic3—41no—
390Dic3—41no—
391Dic3#12014yes—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—32no—
406C23—32no—
407C23—61no—
408C23—61no—
409C23—61no—
410C23—61no—
411C23—61no—
412C23—61no—
413C23—61no—
414C23—61no—
415C23—61no—
416C23—61no—
417C23—61no—
418C23—61no—
419C23—61no—
420C23—61no—
421C23—61no—
422C23—61no—
423C23—61no—
424C23—61no—
425C23—61no—
426C23D3×D412yes—
427C23C23×D311yescharacteristic
428Q8—68no—
429D4—44no—
430D4—68no—
431D4—68no—
432D4—68no—
433D4—124no—
434D4—124no—
435D4—124no—
436D4—124no—
437D4—124no—
438D4—124no—
439C2×C4—28no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—32no—
455C2×C4—32no—
456C2×C4—32no—
457C2×C4—68no—
458C2×C4—68no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4#23512yescomplemented
470C2×C4D3×D412yes—
471C2×C4D3×D412yes—
472C2×C3—42no—
473C2×C3—81no—
474C2×C3C2×#12011yescharacteristic
475C2×C3#53211yescharacteristic
476C2×C3#53511yescharacteristic
477C2×C3#54611yescharacteristic
478C2×C3#54611yescharacteristic
479C2×C3#55011yescharacteristic
480C2×C3#55011yescharacteristic
481D3—42no—
482D3—42no—
483D3—81no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—62no—
499C22—62no—
500C22—62no—
501C22—62no—
502C22—62no—
503C22—62no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22—121no—
509C22—121no—
510C22—121no—
511C22—121no—
512C22—121no—
513C22—121no—
514C22—121no—
515C22—121no—
516C22—121no—
517C22—121no—
518C22—121no—
519C22C2×#23511yescharacteristic
520C22C2×D3×D411yescharacteristic
521C22C2×D3×D411yescharacteristic
522C22C2×D3×D411yescharacteristic
523C22#100411yescharacteristic
524C22D3×#4111yescharacteristic
525C22#100911yescharacteristic
526C4—22no—
527C4—22no—
528C4—22no—
529C4—34no—
530C4—41no—
531C4—41no—
532C4—62no—
533C4—62no—
534C4—121no—
535C4—121no—
536C3#243111yescharacteristic, complemented, Sylow
537C2—42no—
538C2—81no—
539C2—122no—
540C2—122no—
541C2—241no—
542C2#549011yescharacteristic
543C2#554811yescharacteristic
544C2#555311yescharacteristic
545C2D3×#12011yescharacteristic
546C2#559911yescharacteristic
547C2#560711yescharacteristic
548C2#565411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
hypercenter#386D3
hypocenterC3#2431
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#235C2semidirect
2. C2×#940C2semidirect
3. C2×#885C2semidirect
4. C2×#884C2semidirect
5. C3×#386C2semidirect
6. #5223C2semidirect
7. #5213C2semidirect
8. #4960C2semidirect
9. #4960C2semidirect
10. #4957C2semidirect
11. #4956C2semidirect
12. #4671C2semidirect
13. #4666C2semidirect
14. #4665C2semidirect
15. #4646C2semidirect
71. #386D3semidirect
106. C2×#67D4semidirect
127. C2×C4×D3D4semidirect
130. C2×Dic6D4semidirect
239. C2×C3×C4#41semidirect
260. C2×Dic3#41semidirect
469. C2×C4#235semidirect
536. C3#2431semidirect

Maximal subgroups

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

subgroupindex
C22×#2352
C2×#9402
C2×#8852
C2×#8842
C3×#3862
#52232
#52132
#49602
#49572
#49562
#46712
#46662
#46652
#46462
#24313