Finite Group Databasebeta

← #11805777

Subgroups — #11805777

Order 1152.

1305 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×#67C211yesmaximal, characteristic
2C4×#3757C211yesmaximal, characteristic, complemented
3C3×#5213C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5#10591716C211yesmaximal, characteristic, complemented
6#10591710C211yesmaximal, characteristic
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591368C211yesmaximal, characteristic, complemented
9#10591362C211yesmaximal, characteristic, complemented
10#10591335C211yesmaximal, characteristic, complemented
11#10591287C211yesmaximal, characteristic, complemented
12#10591284C211yesmaximal, characteristic, complemented
13#10591253C211yesmaximal, characteristic, complemented
14#10591252C211yesmaximal, characteristic, complemented
15#10591248C211yesmaximal, characteristic, complemented
16#74674—31nomaximal
17#73336—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30Dic3×#67C418yescomplemented
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×D4×Dic3—31no—
55C2×C4×#67—31no—
56C3×#386—31no—
57C2×C3×#95—31no—
58#5220—31no—
59#5213—31no—
60#5213D311yescharacteristic
61#5212—31no—
62C4×#217—31no—
63C4×#217—31no—
64C4×#217—31no—
65C4×#217—61no—
66C2×C3⋊#95D311yescharacteristic, complemented
67#4945—31no—
68#4944—31no—
69#4943—31no—
70#4942—31no—
71Dic3×C22⋊C4—31no—
72Dic3×C22⋊C4—31no—
73#4670—31no—
74#4670—31no—
75#4666—31no—
76#4664—31no—
77#4655—31no—
78#4655—31no—
79#4654—31no—
80#4653—31no—
81#4651—31no—
82#4651—31no—
83#4648—31no—
84#4648—31no—
85C24×C32C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4—22no—
88C22×C32×C4—22no—
89C22×C32×C4—41no—
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C3×#67—22no—
97C2×C3×#67—22no—
98C2×C3×#67C2×C414yes—
99C22×C3×Dic3—22no—
100C22×C3×Dic3—22no—
101C22×C3×Dic3—41no—
102C22×C3×Dic3—41no—
103C22×C3×Dic3—41no—
104C22×C3×Dic3C2×C414yes—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×D3×Dic3—41no—
113C2×D3×Dic3—41no—
114C2×D3×Dic3C2×C414yescomplemented
115#3757—22no—
116#3757C2×C414yes—
117C4×C3⋊Dic3—22no—
118C4×C3⋊Dic3—41no—
119C3×#217—22no—
120C3×(C2×D3)⋊C4—22no—
121C3×(C2×D3)⋊C4—41no—
122Dic3⋊Dic3—41no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3C2×C414yescomplemented
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—41no—
127(C2×D3)⋊Dic3C2×C414yescomplemented
128Dic32—22no—
129Dic32—41no—
130Dic32C2×C414yescomplemented
131#2353—91noSylow
132C22×C3×D4—31no—
133C23×C3×C4—21no—
134C23×C3×C4—31no—
135C23×C3×C4—31no—
136C23×C3×C4C2×D311yescharacteristic
137C23×C3×C4C2×D311yescharacteristic
138C22×#67C2×D311yescharacteristic
139C23×Dic3—31no—
140C23×Dic3C2×D311yescharacteristic
141C23×Dic3C2×D311yescharacteristic
142C22×C4×D3—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×#217—31no—
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—61no—
154C2×#217—61no—
155C2×#217C2×D311yescharacteristic
156D4×Dic3—38no—
157C4×#67—38no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4C2×D311yescharacteristic
162C2×(C2×D3)⋊C4C2×D311yescharacteristic
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—61no—
180C2×C4×Dic3—61no—
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—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—61no—
204C3⋊#95—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32C22×C412yes—
216C23×C32#4112yes—
217C23×C32#4112yes—
218C23×C32C2411yescharacteristic
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3C22×C412yes—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—44no—
232C2×C32×C4#4112yes—
233C2×C3⋊Dic3—21no—
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⋊Dic3C22×C412yes—
244C2×C3⋊Dic3C22×C412yes—
245C3×#67—28no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—44no—
264C2×C3×Dic3—44no—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3C22×C412yes—
267C2×C3×Dic3C22×C412yes—
268C2×C3×Dic3#4112yes—
269D3×Dic3—44no—
270C2×C4×D4—91no—
271#388—91no—
272#388—91no—
273#387—91no—
274#387—91no—
275#386—31no—
276#386—91no—
277#383—91no—
278#381—91no—
279#380—91no—
280C4×C22⋊C4—91no—
281C4×C22⋊C4—91no—
282C4×C22⋊C4—91no—
283#376—91no—
284C2×#95—31no—
285C24×C3—21no—
286C24×C3—31no—
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C23×D3C22×D311yescharacteristic
290C2×C3×D4—34no—
291C2×C3×D4—62no—
292C2×C3×D4—62no—
293C22×C3×C4—24no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—34no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—42no—
309C22×C3×C4—41no—
310C22×C3×C4—41no—
311C22×C3×C4—42no—
312C22×C3×C4—62no—
313C22×C3×C4—62no—
314C22×C3×C4—121no—
315C22×C3×C4—121no—
316C22×C3×C4—121no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—22no—
322C2×#67—22no—
323C2×#67C4×D314yes—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—34no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—41no—
336C22×Dic3—41no—
337C22×Dic3—41no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—121no—
343C22×Dic3—121no—
344C22×Dic3C4×D314yes—
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C2×C4×D3—34no—
353C2×C4×D3—121no—
354C2×C4×D3—121no—
355C3×C22⋊C4—62no—
356C3×C22⋊C4—62no—
357C3×C22⋊C4—121no—
358#217—22no—
359#217—34no—
360#217—34no—
361#217—34no—
362#217—64no—
363#217—64no—
364#217—62no—
365#217—62no—
366#217—62no—
367#217—121no—
368(C2×D3)⋊C4—22no—
369(C2×D3)⋊C4—34no—
370(C2×D3)⋊C4—41no—
371(C2×D3)⋊C4—62no—
372(C2×D3)⋊C4—121no—
373C4⋊Dic3—34no—
374C4⋊Dic3—121no—
375C4⋊Dic3—121no—
376Dic3⋊C4—34no—
377Dic3⋊C4—121no—
378Dic3⋊C4—121no—
379C4×Dic3—34no—
380C4×Dic3—34no—
381C4×Dic3—62no—
382C4×Dic3—62no—
383C4×Dic3—62no—
384C4×Dic3—62no—
385C4×Dic3—122no—
386C4×Dic3—121no—
387C4×Dic3—121no—
388C4×Dic3—121no—
389C4×Dic3—121no—
390C4×Dic3—122no—
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32#11714yes—
398C22×C32C23×C411yescharacteristic
399C22×C32C2×#4111yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32H(5,𝔽2)11yescharacteristic
404C22×C32H(5,𝔽2)11yescharacteristic
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C32×C4—22no—
413C32×C4—41no—
414C3⋊Dic3—22no—
415C3⋊Dic3—22no—
416C3⋊Dic3—41no—
417C3⋊Dic3—41no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—31no—
426C23×C4—31no—
427C23×C4—31no—
428C23×C4—91no—
429C23×C4D3211yescharacteristic
430C4×D4—98no—
431C2×C4⋊C4—91no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—91no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4—91no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C42—91no—
443C2×C42—91no—
444C2×C42—91no—
445C2×C42—91no—
446C2×C42—91no—
447#95—31no—
448#95—31no—
449#95—31no—
450#95—31no—
451#95—31no—
452#95—31no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95—91no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—32no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—61no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3C2×C4×D312yes—
485C23×C3C2×C4×D312yes—
486C23×C3#23712yes—
487C23×C3#23712yes—
488C23×C3#23712yes—
489C23×C3#23912yes—
490C23×C3C23×D311yescharacteristic
491C23×C3C23×D311yescharacteristic
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3C2×C4×D312yes—
499C3×D4—68no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—44no—
521C2×C3×C4—44no—
522C2×C3×C4—48no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—124no—
541C2×C3×C4—124no—
542C2×C3×C4#23512yes—
543C2×C3×C4#23712yes—
544#67—28no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—32no—
563C2×Dic3—32no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—44no—
567C2×Dic3—44no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—62no—
579C2×Dic3—62no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—124no—
601C2×Dic3C2×C4×D312yes—
602C2×Dic3C2×C4×D312yes—
603C2×Dic3C2×C4×D312yes—
604C2×Dic3#23512yes—
605C4×D3—124no—
606C2×C32—24no—
607C2×C32C2×#11711yescharacteristic
608C2×C32C4×#4111yescharacteristic
609C2×C32#51811yescharacteristic
610C2×C32#55111yescharacteristic
611C2×C32#55111yescharacteristic
612C2×C32#55311yescharacteristic
613C2×C32#55311yescharacteristic
614C3×D3—42no—
615C24—31no—
616C24C2×D3211yescharacteristic
617C2×D4—34no—
618C2×D4—62no—
619C2×D4—62no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—34no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—41no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—94no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4—91no—
637C22×C4—91no—
638C22×C4—121no—
639C22×C4—121no—
640C22×C4—121no—
641C22×C4—361no—
642C22×C4—361no—
643C22×C4C2×D3211yescharacteristic
644C22×C4C2×D3211yescharacteristic
645C4⋊C4—94no—
646C4⋊C4—361no—
647C4⋊C4—361no—
648C22⋊C4—62no—
649C22⋊C4—62no—
650C22⋊C4—94no—
651C22⋊C4—94no—
652C22⋊C4—121no—
653C22⋊C4—182no—
654C22⋊C4—182no—
655C22⋊C4—361no—
656C42—94no—
657C42—182no—
658C42—182no—
659C42—361no—
660C42—361no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—24no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3#87714yes—
695C22×C3#89214yes—
696C22×C3C22×C4×D311yescharacteristic
697C22×C3C22×C4×D311yescharacteristic
698C22×C3C2×#23511yescharacteristic
699C22×C3C2×#23511yescharacteristic
700C22×C3C2×#23711yescharacteristic
701C22×C3C2×#23711yescharacteristic
702C22×C3C2×#23711yescharacteristic
703C22×C3C2×#23711yescharacteristic
704C22×C3#100411yescharacteristic
705C22×C3#100411yescharacteristic
706C22×C3#100411yescharacteristic
707C22×C3C2×#23911yescharacteristic
708C22×C3D3×#4111yescharacteristic
709C22×C3#100911yescharacteristic
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C3×C4—24no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—42no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—62no—
724C3×C4—62no—
725C3×C4—62no—
726C3×C4—62no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4—121no—
730Dic3—22no—
731Dic3—22no—
732Dic3—22no—
733Dic3—22no—
734Dic3—41no—
735Dic3—41no—
736Dic3—41no—
737Dic3—62no—
738Dic3—62no—
739Dic3—62no—
740Dic3—62no—
741Dic3—122no—
742Dic3—122no—
743Dic3—122no—
744Dic3—122no—
745Dic3—121no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749C32#235311yescharacteristic, complemented, Sylow
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—32no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23#379612yes—
762C23C4×D3212yes—
763C23#380512yes—
764C23C22×D3211yescharacteristic
765D4—68no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—44no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—92no—
794C2×C4—92no—
795C2×C4—124no—
796C2×C4—124no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—364no—
808C2×C4#380412yes—
809C2×C3—24no—
810C2×C3—24no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—44no—
819C2×C3—122no—
820C2×C3C4×#23511yescharacteristic
821C2×C3C2×#87711yescharacteristic
822C2×C3#548611yescharacteristic
823C2×C3#549511yescharacteristic
824C2×C3#549511yescharacteristic
825C2×C3C2×#89211yescharacteristic
826C2×C3#551411yescharacteristic
827C2×C3#551411yescharacteristic
828C2×C3C4×#23711yescharacteristic
829C2×C3#554511yescharacteristic
830C2×C3#558711yescharacteristic
831C2×C3#560111yescharacteristic
832C2×C3#561811yescharacteristic
833C2×C3#565811yescharacteristic
834D3—42no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22#6387814yes—
849C22C2×#379611yescharacteristic
850C22C2×C4×D3211yescharacteristic
851C22D3×#23511yescharacteristic
852C22#6430711yescharacteristic
853C22C2×#380411yescharacteristic
854C22C2×#380511yescharacteristic
855C22#6433011yescharacteristic
856C4—22no—
857C4—41no—
858C4—62no—
859C4—62no—
860C4—62no—
861C4—62no—
862C4—121no—
863C4—121no—
864C4—121no—
865C4—182no—
866C4—182no—
867C4—361no—
868C4—361no—
869C3—21no—
870C3#7333611yescharacteristic, complemented
871C3#7467411yescharacteristic, complemented
872C2—24no—
873C2—122no—
874C2C2×#6387811yescharacteristic
875C2C4×#380411yescharacteristic
876C2#1059494011yescharacteristic
877C2#1059495311yescharacteristic
878C2#1059498911yescharacteristic
879C2#1059505611yescharacteristic
880C2#1059550911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C4×#3757C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. #10591716C2semidirect
7. Dic3×#217C2semidirect
8. #10591368C2semidirect
9. #10591362C2semidirect
10. #10591335C2semidirect
11. #10591287C2semidirect
12. #10591284C2semidirect
13. #10591253C2semidirect
14. #10591252C2semidirect
15. #10591248C2semidirect
30. Dic3×#67C4semidirect
66. C2×C3⋊#95D3semidirect
114. C2×D3×Dic3C2×C4semidirect
124. Dic3⋊Dic3C2×C4semidirect
127. (C2×D3)⋊Dic3C2×C4semidirect
130. Dic32C2×C4semidirect
749. C32#2353semidirect
870. C3#73336semidirect
871. C3#74674semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×#672
C4×#37572
C3×#52132
C2×C3×C3⋊#952
#105917162
#105917102
Dic3×#2172
#105913682
#105913622
#105913352
#105912872
#105912842
#105912532
#105912522
#105912482
#746743
#733363