Finite Group Databasebeta

← #77130

Subgroups — #77130

Order 384.

682 conjugacy classes of subgroups.

The subgroup lattice has 492 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×#884C211yesmaximal, characteristic, complemented
4C2×#883C211yesmaximal, characteristic, complemented
5C3×#394C211yesmaximal, characteristic, complemented
6#4993C211yesmaximal, characteristic, complemented
7#4989C211yesmaximal, characteristic, complemented
8#4961C211yesmaximal, characteristic, complemented
9#4960C211yesmaximal, characteristic, complemented
10#4958C211yesmaximal, characteristic, complemented
11#4958C211yesmaximal, characteristic, complemented
12#4946C211yesmaximal, characteristic, complemented
13#4942C211yesmaximal, characteristic, complemented
14#4672C211yesmaximal, characteristic, complemented
15#4657C211yesmaximal, characteristic, complemented
16#2671—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C23×Dic3C2211yescharacteristic
24C22×D12C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33#939—24no—
34#939—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⋊C4C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×Dic3⋊C4C2211yescharacteristic
47C2×Dic3⋊C4C2211yescharacteristic
48#884—24no—
49#883—24no—
50C3×#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C2×#123—31no—
57C2×#121—31no—
58C2×#121—31no—
59C2×#121—31no—
60#399—31no—
61#398—31no—
62#394—31no—
63#394—31no—
64#394D311yescharacteristic, complemented
65#392—31no—
66#386—31no—
67#386—31no—
68#385—31no—
69#385—31no—
70#380—31no—
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C2×C3×D4—22no—
76C2×C3×D4—22no—
77C2×C3×D4—41no—
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C2×#67—22no—
84C2×#67—22no—
85C2×#67—22no—
86C2×#67—22no—
87C2×#67—22no—
88C2×#67—22no—
89C2×#67—41no—
90C2×#67—41no—
91C2×#67—41no—
92C2×#67—41no—
93C2×#67—41no—
94C2×#67D414yescomplemented
95C22×Dic3—22no—
96C22×Dic3—22no—
97C22×Dic3—22no—
98C22×Dic3—41no—
99C22×Dic3—41no—
100C22×Dic3—41no—
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2311yescharacteristic
103C22×Dic3C2311yescharacteristic
104C22×Dic3C2311yescharacteristic
105C22×Dic3C2311yescharacteristic
106C22×Dic3C2311yescharacteristic
107C2×D12—22no—
108C2×D12—41no—
109C2×D12—41no—
110C2×C4×D3—22no—
111C2×C4×D3—22no—
112C2×C4×D3—41no—
113C3×C4⋊C4—41no—
114C3×C22⋊C4—22no—
115C3×C22⋊C4—22no—
116C3×C22⋊C4—41no—
117C3×C22⋊C4—41no—
118#217—22no—
119#217D414yescomplemented
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—41no—
126(C2×D3)⋊C4—41no—
127C4⋊Dic3—22no—
128Dic3⋊C4—22no—
129Dic3⋊C4—22no—
130Dic3⋊C4—22no—
131Dic3⋊C4—22no—
132Dic3⋊C4—41no—
133C22×D4—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4—31no—
137C22×D4—31no—
138C22×D4C2×D311yescharacteristic
139C23×C4—31no—
140C23×C4—31no—
141C23×C4—31no—
142#123—64no—
143#121—64no—
144#121—64no—
145#121—64no—
146C2×C4⋊C4—31no—
147C2×C4⋊C4—31no—
148C2×C4⋊C4—31no—
149C2×C4⋊C4—31no—
150C2×C4⋊C4—31no—
151C2×C4⋊C4—31no—
152C2×C4⋊C4C2×D311yescharacteristic
153C2×C22⋊C4—31no—
154C2×C22⋊C4—31no—
155C2×C22⋊C4—31no—
156C2×C22⋊C4—31no—
157C2×C22⋊C4—31no—
158C2×C22⋊C4—31no—
159C2×C22⋊C4—31no—
160C2×C22⋊C4—31no—
161C2×C22⋊C4—31no—
162C2×C22⋊C4C2×D311yescharacteristic
163C2×C22⋊C4C2×D311yescharacteristic
164C2×C22⋊C4C2×D311yescharacteristic
165C2×C22⋊C4C2×D311yescharacteristic
166#95—31no—
167#95—31no—
168#95—31no—
169#95—31no—
170#95—31no—
171#95C2×D311yescharacteristic
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3C2×D412yes—
185C23×C3C2×D412yes—
186C23×C3C2411yescharacteristic
187C22×D3—21no—
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—21no—
191C22×D3—21no—
192C22×D3—21no—
193C22×D3—21no—
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—21no—
200C22×D3C2×D412yes—
201C3×D4—44no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
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—
217#67—44no—
218#67—44no—
219#67—44no—
220#67—44no—
221C2×Dic3—21no—
222C2×Dic3—21no—
223C2×Dic3—21no—
224C2×Dic3—21no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—44no—
236C2×Dic3—44no—
237C2×Dic3C2×D412yes—
238C2×Dic3C2×D412yes—
239C2×Dic3C2×D412yes—
240C2×Dic3#4112yes—
241D12—44no—
242C4×D3—44no—
243C24—31no—
244C24—31no—
245C24C22×D311yescharacteristic
246C24C22×D311yescharacteristic
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—34no—
250C2×D4—41no—
251C2×D4—62no—
252C2×D4—62no—
253C2×D4—62no—
254C2×D4—62no—
255C2×D4—62no—
256C2×D4—62no—
257C2×D4—62no—
258C2×D4—121no—
259C2×D4—121no—
260C2×D4—121no—
261C2×D4—121no—
262C2×D4—121no—
263C2×D4—121no—
264C2×D4—121no—
265C22×C4—31no—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—62no—
272C22×C4—62no—
273C22×C4—62no—
274C22×C4—62no—
275C22×C4—62no—
276C22×C4—121no—
277C22×C4—121no—
278C22×C4—121no—
279C22×C4—121no—
280C22×C4C22×D311yescharacteristic
281C22×C4C22×D311yescharacteristic
282C22×C4C22×D311yescharacteristic
283C22×C4C22×D311yescharacteristic
284C22×C4C22×D311yescharacteristic
285C4⋊C4—41no—
286C4⋊C4—62no—
287C4⋊C4—62no—
288C4⋊C4—62no—
289C4⋊C4—62no—
290C4⋊C4—62no—
291C4⋊C4—121no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—34no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C22⋊C4—62no—
303C22⋊C4—121no—
304C22⋊C4—121no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3C22×D411yescharacteristic
320C22×C3C22×D411yescharacteristic
321C22×C3C2×#4111yescharacteristic
322C22×C3H(5,𝔽2)11yescharacteristic
323C22×C3H(5,𝔽2)11yescharacteristic
324C22×C3H(5,𝔽2)11yescharacteristic
325C22×C32−1+411yescharacteristic
326C2×D3—22no—
327C2×D3—22no—
328C2×D3—22no—
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C3×C4—41no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—41no—
345Dic3—22no—
346Dic3—22no—
347Dic3—22no—
348Dic3—22no—
349Dic3—41no—
350Dic3—41no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—32no—
364C23—61no—
365C23—61no—
366C23—61no—
367C23—61no—
368C23—61no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23D3×D412yes—
378C23D3×D412yes—
379C23C23×D311yescharacteristic
380D4—44no—
381D4—124no—
382D4—124no—
383D4—124no—
384D4—124no—
385D4—124no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—32no—
404C2×C4—32no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—124no—
420C2×C4—124no—
421C2×C4—124no—
422C2×C3—42no—
423C2×C3—42no—
424C2×C3#53411yescharacteristic
425C2×C3#53711yescharacteristic
426C2×C3#54011yescharacteristic
427C2×C3D4211yescharacteristic
428C2×C3#54611yescharacteristic
429C2×C3#54711yescharacteristic
430C2×C3#56211yescharacteristic
431D3—42no—
432D3—81no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—62no—
448C22—62no—
449C22—62no—
450C22—121no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22C2×D3×D411yescharacteristic
462C22C2×D3×D411yescharacteristic
463C22#100411yescharacteristic
464C22#100411yescharacteristic
465C22D3×#4111yescharacteristic
466C22#100911yescharacteristic
467C22#101011yescharacteristic
468C4—41no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—62no—
474C4—62no—
475C4—62no—
476C4—62no—
477C4—121no—
478C4—121no—
479C3#267111yescharacteristic, complemented, Sylow
480C2—42no—
481C2—42no—
482C2—122no—
483C2—241no—
484C2#559011yescharacteristic
485C2#559711yescharacteristic
486C2#560511yescharacteristic
487C2#561511yescharacteristic
488C2#565411yescharacteristic
489C2#565511yescharacteristic
490C2#568411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#394C2
hypercenter#394D3
hypocenterC3#2671
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×#939C2semidirect
3. C2×#884C2semidirect
4. C2×#883C2semidirect
5. C3×#394C2semidirect
6. #4993C2semidirect
7. #4989C2semidirect
8. #4961C2semidirect
9. #4960C2semidirect
10. #4958C2semidirect
11. #4958C2semidirect
12. #4946C2semidirect
13. #4942C2semidirect
14. #4672C2semidirect
15. #4657C2semidirect
64. #394D3semidirect
94. C2×#67D4semidirect
119. #217D4semidirect
479. C3#2671semidirect

Maximal subgroups

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

subgroupindex
C2×#9392
C2×#8842
C2×#8832
C3×#3942
#49932
#49892
#49612
#49602
#49582
#49462
#49422
#46722
#46572
#26713