Finite Group Databasebeta

← #11804324

Subgroups — #11804324

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#898C211yesmaximal, characteristic
2#10592679C211yesmaximal, characteristic, complemented
3C3×#4984C211yesmaximal, characteristic, complemented
4#10591377C211yesmaximal, characteristic
5#10591377C211yesmaximal, characteristic
6Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic
7#10591316C211yesmaximal, characteristic
8#10591307C211yesmaximal, characteristic
9#10591286C211yesmaximal, characteristic
10#10591274C211yesmaximal, characteristic, complemented
11#10591269C211yesmaximal, characteristic, complemented
12Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
13#10591265C211yesmaximal, characteristic, complemented
14#10591206C211yesmaximal, characteristic, complemented
15#10591201C211yesmaximal, characteristic, complemented
16#83074—31nomaximal
17#75975—31nomaximal
18C22×D3×Dic3C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#898C418yescomplemented
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×#126—31no—
55C2×#898D311yescharacteristic
56C3×#389—31no—
57#4990—31no—
58#4989—31no—
59#4989—31no—
60#4984—31no—
61#4984D311yescharacteristic, complemented
62#4980—31no—
63#4980—31no—
64#4980—31no—
65#4980—31no—
66#4980—61no—
67#4976—31no—
68Dic3×C4⋊C4—31no—
69Dic3×C4⋊C4—31no—
70Dic3×C4⋊C4—31no—
71#4951—31no—
72#4951—31no—
73#4951—31no—
74#4950—31no—
75#4950—31no—
76Dic3×C22⋊C4—31no—
77C4×(C2×D3)⋊C4—31no—
78#4936—31no—
79C4×C4⋊Dic3—31no—
80#4933—31no—
81#4670—31no—
82#4669—31no—
83#4653—31no—
84#4650—31no—
85C23×C3×D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×D3×Dic3—22no—
101C2×D3×Dic3—41no—
102C2×D3×Dic3—41no—
103C32×C4⋊C4C2×C414yescomplemented
104C4⋊(C3⋊Dic3)—22no—
105C4×C3⋊Dic3—22no—
106C3×(C2×D3)⋊C4C2×C414yes—
107C3×(C2×D3)⋊C4C2×C414yes—
108C3×(C2×D3)⋊C4C2×C414yes—
109C3×C4⋊Dic3—22no—
110C3×C4⋊Dic3—22no—
111C3×C4⋊Dic3—41no—
112C3×C4⋊Dic3C2×C414yescomplemented
113C3×Dic3⋊C4C2×C414yescomplemented
114C3×C4×Dic3—41no—
115C3×C4×Dic3C2×C414yescomplemented
116Dic3⋊Dic3—41no—
117Dic3⋊Dic3—41no—
118Dic3⋊Dic3—41no—
119(C2×D3)⋊Dic3—22no—
120(C2×D3)⋊Dic3—41no—
121(C2×D3)⋊Dic3—41no—
122Dic32—41no—
123Dic32—41no—
124Dic32—41no—
125#2334—91noSylow
126C23×Dic3—31no—
127C22×C4×D3—31no—
128C3×#126—38no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4C2×D311yescharacteristic
136C2×C3×C4⋊C4C2×D311yescharacteristic
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C42—31no—
141C2×C3×C42—31no—
142C2×#217—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4C2×D311yescharacteristic
149C2×(C2×D3)⋊C4C2×D311yescharacteristic
150C2×(C2×D3)⋊C4C2×D311yescharacteristic
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—61no—
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×C4⋊Dic3C2×D311yescharacteristic
159C2×C4⋊Dic3C2×D311yescharacteristic
160C2×C4⋊Dic3C2×D311yescharacteristic
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4C2×D311yescharacteristic
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—61no—
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D311yescharacteristic
176#898Dic318yescomplemented
177C3×#95—31no—
178C3×#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—61no—
200C3⋊#95—61no—
201C3⋊#95—61no—
202C3⋊#95—61no—
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C23×C32C2411yescharacteristic
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3C22×C412yes—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4C22×C412yes—
220C2×C32×C4C22×C412yes—
221C2×C32×C4C22×C412yes—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3#4112yes—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C22×C412yes—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3#4112yes—
255D3×Dic3—44no—
256C2×#126—31no—
257#389—31no—
258#389—91no—
259#388—91no—
260#388—91no—
261#388—91no—
262#387—91no—
263#387—91no—
264#387—91no—
265#385—91no—
266#385—91no—
267#382—91no—
268C4×C4⋊C4—91no—
269C4×C4⋊C4—91no—
270C4×C22⋊C4—91no—
271C24×C3—31no—
272C23×D3C22×D311yescharacteristic
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3—62no—
302C22×Dic3—121no—
303C22×Dic3—121no—
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C2×C4×D3—62no—
312C2×C4×D3—121no—
313C2×C4×D3—121no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—34no—
316C3×C4⋊C4—34no—
317C3×C4⋊C4—62no—
318C3×C4⋊C4—62no—
319C3×C4⋊C4—121no—
320C3×C4⋊C4C4×D314yescomplemented
321C3×C4⋊C4C2×Dic314yescomplemented
322C3×C22⋊C4—34no—
323C3×C22⋊C4—34no—
324C3×C22⋊C4—34no—
325C3×C42—34no—
326C3×C42—121no—
327#217—62no—
328#217—121no—
329#217—121no—
330(C2×D3)⋊C4—62no—
331(C2×D3)⋊C4—121no—
332(C2×D3)⋊C4—121no—
333(C2×D3)⋊C4C2×Dic314yes—
334(C2×D3)⋊C4C2×Dic314yes—
335(C2×D3)⋊C4C2×Dic314yes—
336C4⋊Dic3—22no—
337C4⋊Dic3—22no—
338C4⋊Dic3—41no—
339C4⋊Dic3—62no—
340C4⋊Dic3—62no—
341C4⋊Dic3—122no—
342C4⋊Dic3—121no—
343C4⋊Dic3—121no—
344C4⋊Dic3—121no—
345C4⋊Dic3C2×Dic314yescomplemented
346Dic3⋊C4—121no—
347Dic3⋊C4—121no—
348Dic3⋊C4—121no—
349Dic3⋊C4C2×Dic314yescomplemented
350C4×Dic3—41no—
351C4×Dic3—62no—
352C4×Dic3—62no—
353C4×Dic3—122no—
354C4×Dic3—121no—
355C4×Dic3—121no—
356C4×Dic3—121no—
357C4×Dic3—121no—
358C4×Dic3—121no—
359C4×Dic3—121no—
360C4×Dic3C2×Dic314yescomplemented
361C22×C32C23×C411yescharacteristic
362C22×C32C2×#4111yescharacteristic
363C22×C32C2×#4111yescharacteristic
364C22×C32H(5,𝔽2)11yescharacteristic
365C22×C32H(5,𝔽2)11yescharacteristic
366C22×C322−1+411yescharacteristic
367C22×C322−1+411yescharacteristic
368C2×C3×D3—22no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—41no—
372C2×C3×D3—41no—
373C2×C3×D3—41no—
374C2×C3×D3—41no—
375C32×C4—22no—
376C32×C4—22no—
377C32×C4—22no—
378C3⋊Dic3—22no—
379C3⋊Dic3—41no—
380C3⋊Dic3—41no—
381C3⋊Dic3—41no—
382C3×Dic3—22no—
383C3×Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—41no—
387C3×Dic3—41no—
388C3×Dic3—41no—
389C23×C4—91no—
390#126—38no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—91no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4—91no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4D3211yescharacteristic
401C2×C22⋊C4—31no—
402C2×C22⋊C4—31no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—91no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C42—31no—
408C2×C42—31no—
409C2×C42—91no—
410C2×C42—91no—
411C2×C42—91no—
412C2×C42—91no—
413#95—31no—
414#95—31no—
415#95—91no—
416#95—91no—
417#95—91no—
418#95—91no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95—91no—
424#95—91no—
425C23×C3—21no—
426C23×C3—32no—
427C23×C3—61no—
428C23×C3—61no—
429C23×C3—61no—
430C23×C3—61no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3C23×D311yescharacteristic
434C23×C3C23×D311yescharacteristic
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3C22×Dic312yes—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—32no—
460C2×C3×C4—32no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4C2×C4×D312yes—
485C2×C3×C4C2×C4×D312yes—
486C2×C3×C4C2×C4×D312yes—
487C2×C3×C4C22×Dic312yes—
488C2×C3×C4C22×Dic312yes—
489C2×C3×C4C22×Dic312yes—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—32no—
508C2×Dic3—32no—
509C2×Dic3—62no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—62no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—124no—
544C2×Dic3#23712yes—
545C2×Dic3C22×Dic312yes—
546C2×Dic3C22×Dic312yes—
547C2×Dic3C22×Dic312yes—
548C4×D3—124no—
549C2×C32C4×#4111yescharacteristic
550C2×C32#52011yescharacteristic
551C2×C32#52011yescharacteristic
552C2×C32#53811yescharacteristic
553C2×C32#53911yescharacteristic
554C2×C32#54111yescharacteristic
555C2×C32#54211yescharacteristic
556C3×D3—42no—
557C24—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—91no—
566C22×C4—91no—
567C22×C4—91no—
568C22×C4—91no—
569C22×C4—182no—
570C22×C4—361no—
571C22×C4—361no—
572C22×C4C2×D3211yescharacteristic
573C22×C4C2×D3211yescharacteristic
574C22×C4C2×D3211yescharacteristic
575C4⋊C4—34no—
576C4⋊C4—34no—
577C4⋊C4—62no—
578C4⋊C4—62no—
579C4⋊C4—121no—
580C4⋊C4—182no—
581C4⋊C4—361no—
582C4⋊C4—361no—
583C4⋊C4—361no—
584C4⋊C4D3×Dic314yescomplemented
585C22⋊C4—34no—
586C22⋊C4—34no—
587C22⋊C4—34no—
588C22⋊C4—182no—
589C22⋊C4—361no—
590C22⋊C4—361no—
591C42—34no—
592C42—121no—
593C42—182no—
594C42—361no—
595C42—361no—
596C42—361no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—62no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—121no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3C22×C4×D311yescharacteristic
612C22×C3C2×#23711yescharacteristic
613C22×C3#100411yescharacteristic
614C22×C3#100711yescharacteristic
615C22×C3#100711yescharacteristic
616C22×C3D3×#4111yescharacteristic
617C22×C3D3×#4111yescharacteristic
618C22×C3D3×#4111yescharacteristic
619C22×C3#100911yescharacteristic
620C22×C3#100911yescharacteristic
621C22×C3#100911yescharacteristic
622C22×C3#101011yescharacteristic
623C22×C3#101011yescharacteristic
624C22×C3C23×Dic311yescharacteristic
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—62no—
642C3×C4—62no—
643C3×C4—62no—
644C3×C4—62no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4—121no—
648Dic3—22no—
649Dic3—22no—
650Dic3—22no—
651Dic3—22no—
652Dic3—41no—
653Dic3—41no—
654Dic3—41no—
655Dic3—62no—
656Dic3—62no—
657Dic3—122no—
658Dic3—122no—
659Dic3—121no—
660Dic3—121no—
661Dic3—121no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—241no—
666Dic3—241no—
667C32#233411yescharacteristic, complemented, Sylow
668C23—32no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23C22×D3211yescharacteristic
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—32no—
683C2×C4—32no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—92no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—364no—
716C2×C4C2×D3×Dic312yes—
717C2×C4C2×D3×Dic312yes—
718C2×C4C2×D3×Dic312yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—122no—
727C2×C3#550411yescharacteristic
728C2×C3C4×#23711yescharacteristic
729C2×C3#557411yescharacteristic
730C2×C3#561711yescharacteristic
731C2×C3#564011yescharacteristic
732C2×C3#569211yescharacteristic
733C2×C3#570111yescharacteristic
734C2×C3#570411yescharacteristic
735C2×C3#570711yescharacteristic
736C2×C3#571011yescharacteristic
737C2×C3#573111yescharacteristic
738C2×C3Dic3×#4111yescharacteristic
739C2×C3#582711yescharacteristic
740C2×C3#582711yescharacteristic
741D3—42no—
742C22—62no—
743C22—62no—
744C22—62no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22#6429711yescharacteristic
750C22#6430711yescharacteristic
751C22D3×#23711yescharacteristic
752C22#6431211yescharacteristic
753C22#6431511yescharacteristic
754C22#6432011yescharacteristic
755C22C22×D3×Dic311yescharacteristic
756C4—22no—
757C4—22no—
758C4—22no—
759C4—62no—
760C4—62no—
761C4—62no—
762C4—62no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—182no—
767C4—361no—
768C4—361no—
769C4—361no—
770C3—21no—
771C3#7597511yescharacteristic, complemented
772C3#8307411yescharacteristic, complemented
773C2—122no—
774C2#1059444611yescharacteristic
775C2#1059448111yescharacteristic
776C2#1059457711yescharacteristic
777C2#1059464611yescharacteristic
778C2#1059498611yescharacteristic
779C2Dic3×#23711yescharacteristic
780C2#1059539411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2334
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592679C2semidirect
3. C3×#4984C2semidirect
10. #10591274C2semidirect
11. #10591269C2semidirect
12. Dic3×C4⋊Dic3C2semidirect
13. #10591265C2semidirect
14. #10591206C2semidirect
15. #10591201C2semidirect
32. C3×#898C4semidirect
61. #4984D3semidirect
103. C32×C4⋊C4C2×C4semidirect
112. C3×C4⋊Dic3C2×C4semidirect
113. C3×Dic3⋊C4C2×C4semidirect
115. C3×C4×Dic3C2×C4semidirect
176. #898Dic3semidirect
320. C3×C4⋊C4C4×D3semidirect
321. C3×C4⋊C4C2×Dic3semidirect
345. C4⋊Dic3C2×Dic3semidirect
349. Dic3⋊C4C2×Dic3semidirect
360. C4×Dic3C2×Dic3semidirect
584. C4⋊C4D3×Dic3semidirect
667. C32#2334semidirect
771. C3#75975semidirect
772. C3#83074semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8982
#105926792
C3×#49842
#105913772
Dic3×(C2×D3)⋊C42
#105913162
#105913072
#105912862
#105912742
#105912692
Dic3×C4⋊Dic32
#105912652
#105912062
#105912012
#830743
#759753