Finite Group Databasebeta

← #11807675

Subgroups — #11807675

Order 1152.

1141 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#929C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic, complemented
3C3×#5212C211yesmaximal, characteristic, complemented
4#10591721C211yesmaximal, characteristic
5#10591707C211yesmaximal, characteristic
6#10591702C211yesmaximal, characteristic, complemented
7#10591701C211yesmaximal, characteristic, complemented
8#10591379C211yesmaximal, characteristic, complemented
9#10591377C211yesmaximal, characteristic, complemented
10#10591316C211yesmaximal, characteristic, complemented
11#10591307C211yesmaximal, characteristic, complemented
12#10591272C211yesmaximal, characteristic, complemented
13#10591268C211yesmaximal, characteristic, complemented
14#10591265C211yesmaximal, characteristic, complemented
15#10591262C211yesmaximal, characteristic, complemented
16#82840—31nomaximal
17#74013—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C3×#929C418yescomplemented
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×#123—31no—
55C2×#929D311yescharacteristic
56C3×#380—31no—
57#5221—31no—
58#5220—31no—
59#5212—31no—
60#5212—31no—
61#5212—61no—
62#5212D311yescharacteristic, complemented
63#4990—31no—
64#4989—31no—
65#4984—31no—
66#4984—31no—
67#4980—31no—
68#4980—31no—
69#4978—31no—
70#4976—31no—
71#4957—31no—
72#4956—31no—
73#4951—31no—
74#4951—31no—
75#4951—31no—
76#4951—31no—
77#4950—31no—
78#4950—31no—
79#4945—31no—
80#4944—31no—
81#4670—31no—
82#4668—31no—
83#4655—31no—
84#4647—31no—
85C24×C32C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4—41no—
88C22×C32×C4—41no—
89C22×C32×C4C2×C414yescomplemented
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C3×#67—41no—
97C2×C3×#67—41no—
98C2×C3×#67C2×C414yes—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C2×D3×Dic3—41no—
107C2×D3×Dic3—41no—
108C2×D3×Dic3—41no—
109#3757—41no—
110#3757—41no—
111C4⋊(C3⋊Dic3)—41no—
112C4⋊(C3⋊Dic3)—41no—
113C3×#217—41no—
114C3×#217—41no—
115C3×#217C2×C414yescomplemented
116C3×(C2×D3)⋊C4C2×C414yes—
117C3×(C2×D3)⋊C4C2×C414yes—
118C3×C4⋊Dic3—41no—
119C3×C4⋊Dic3—41no—
120C3×Dic3⋊C4C2×C414yescomplemented
121C3×Dic3⋊C4C2×C414yescomplemented
122Dic3⋊Dic3—41no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125(C2×D3)⋊Dic3—41no—
126(C2×D3)⋊Dic3—41no—
127(C2×D3)⋊Dic3—41no—
128Dic32—41no—
129Dic32—41no—
130Dic32—41no—
131#2376—91noSylow
132C22×C3×D4—31no—
133C23×C3×C4—21no—
134C23×C3×C4C2×D311yescharacteristic
135C23×C3×C4C2×D311yescharacteristic
136C22×#67C2×D311yescharacteristic
137C23×Dic3—31no—
138C22×C4×D3—31no—
139C3×#123—38no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—61no—
157C2×#217—61no—
158C2×#217C2×D311yescharacteristic
159C2×#217C2×D311yescharacteristic
160C2×#217C2×D311yescharacteristic
161#929Dic318yescomplemented
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4C2×D311yescharacteristic
166C2×(C2×D3)⋊C4C2×D311yescharacteristic
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—31no—
174C2×C4⋊Dic3—61no—
175C2×C4⋊Dic3—61no—
176C2×C4⋊Dic3C2×D311yescharacteristic
177C2×C4⋊Dic3C2×D311yescharacteristic
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4C2×D311yescharacteristic
182C2×Dic3⋊C4C2×D311yescharacteristic
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—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—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—61no—
208C3⋊#95—61no—
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32C22×C412yes—
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—44no—
231C2×C32×C4C22×C412yes—
232C2×C32×C4C22×C412yes—
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⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C3×#67—44no—
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—21no—
264C2×C3×Dic3C22×C412yes—
265C2×C3×Dic3C22×C412yes—
266C2×C3×Dic3C22×C412yes—
267D3×Dic3—44no—
268C2×#123—31no—
269#390—91no—
270#389—91no—
271#389—91no—
272#388—91no—
273#388—91no—
274#388—91no—
275#388—91no—
276#387—91no—
277#387—91no—
278#386—91no—
279#385—91no—
280#385—91no—
281#380—31no—
282#380—91no—
283C24×C3—21no—
284C24×C3—31no—
285C24×C3C22×D311yescharacteristic
286C24×C3C22×D311yescharacteristic
287C23×D3C22×D311yescharacteristic
288C2×C3×D4—34no—
289C2×C3×D4—121no—
290C2×C3×D4—121no—
291C22×C3×C4—24no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—41no—
302C22×C3×C4—41no—
303C22×C3×C4—41no—
304C22×C3×C4—41no—
305C22×C3×C4—42no—
306C22×C3×C4—42no—
307C22×C3×C4C4×D314yescomplemented
308C22×C3×C4C2×Dic314yescomplemented
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C2×#67—41no—
314C2×#67—41no—
315C2×#67C2×Dic314yes—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—121no—
329C22×Dic3—121no—
330C22×Dic3—121no—
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C2×C4×D3—121no—
339C2×C4×D3—121no—
340C2×C4×D3—121no—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4—121no—
344C3×C4⋊C4—121no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—121no—
349C3×C22⋊C4—121no—
350#217—41no—
351#217—41no—
352#217—121no—
353#217—121no—
354#217—121no—
355#217—121no—
356#217—121no—
357#217—121no—
358#217—121no—
359#217—122no—
360#217—122no—
361#217C2×Dic314yescomplemented
362(C2×D3)⋊C4—121no—
363(C2×D3)⋊C4—121no—
364(C2×D3)⋊C4—121no—
365(C2×D3)⋊C4C2×Dic314yes—
366(C2×D3)⋊C4C2×Dic314yes—
367C4⋊Dic3—41no—
368C4⋊Dic3—41no—
369C4⋊Dic3—121no—
370C4⋊Dic3—121no—
371C4⋊Dic3—121no—
372C4⋊Dic3—121no—
373C4⋊Dic3—121no—
374C4⋊Dic3—121no—
375C4⋊Dic3—121no—
376C4⋊Dic3—122no—
377C4⋊Dic3—122no—
378Dic3⋊C4—121no—
379Dic3⋊C4—121no—
380Dic3⋊C4—121no—
381Dic3⋊C4C2×Dic314yescomplemented
382Dic3⋊C4C2×Dic314yescomplemented
383C4×Dic3—121no—
384C4×Dic3—121no—
385C4×Dic3—121no—
386C4×Dic3—121no—
387C4×Dic3—121no—
388C4×Dic3—121no—
389C22×C32—22no—
390C22×C32—22no—
391C22×C32—22no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32C23×C411yescharacteristic
397C22×C32H(5,𝔽2)11yescharacteristic
398C22×C32H(5,𝔽2)11yescharacteristic
399C22×C32H(5,𝔽2)11yescharacteristic
400C22×C32H(5,𝔽2)11yescharacteristic
401C22×C322−1+411yescharacteristic
402C22×C322−1+411yescharacteristic
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—22no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C32×C4—22no—
411C32×C4—22no—
412C3⋊Dic3—41no—
413C3⋊Dic3—41no—
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C22×D4—31no—
424C23×C4—91no—
425C23×C4D3211yescharacteristic
426#123—38no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—91no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C42—91no—
447C2×C42—91no—
448C2×C42—91no—
449#95—31no—
450#95—31no—
451#95—91no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459C23×C3—22no—
460C23×C3—22no—
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—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—22no—
475C23×C3—32no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3C2×C4×D312yes—
487C23×C3C22×Dic312yes—
488C23×C3C23×D311yescharacteristic
489C23×C3C23×D311yescharacteristic
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3C22×Dic312yes—
497C3×D4—124no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—44no—
516C2×C3×C4—44no—
517C2×C3×C4—48no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
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×C4C2×C4×D312yes—
537C2×C3×C4C2×C4×D312yes—
538C2×C3×C4C22×Dic312yes—
539C2×C3×C4C22×Dic312yes—
540#67—44no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
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—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
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—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—124no—
596C2×Dic3C22×Dic312yes—
597C2×Dic3C22×Dic312yes—
598C2×Dic3C22×Dic312yes—
599C4×D3—124no—
600C2×C32—42no—
601C2×C32#51811yescharacteristic
602C2×C32#52011yescharacteristic
603C2×C32#52011yescharacteristic
604C2×C32#56011yescharacteristic
605C2×C32#56211yescharacteristic
606C2×C32#56211yescharacteristic
607C2×C32#56311yescharacteristic
608C3×D3—42no—
609C24—31no—
610C24C2×D3211yescharacteristic
611C2×D4—34no—
612C2×D4—121no—
613C2×D4—121no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—91no—
624C22×C4—91no—
625C22×C4—91no—
626C22×C4—91no—
627C22×C4—361no—
628C22×C4—361no—
629C22×C4—361no—
630C22×C4D3×Dic314yescomplemented
631C22×C4C2×D3211yescharacteristic
632C22×C4C2×D3211yescharacteristic
633C4⋊C4—34no—
634C4⋊C4—34no—
635C4⋊C4—121no—
636C4⋊C4—121no—
637C4⋊C4—361no—
638C4⋊C4—361no—
639C4⋊C4—361no—
640C4⋊C4—361no—
641C4⋊C4—361no—
642C22⋊C4—34no—
643C22⋊C4—34no—
644C22⋊C4—34no—
645C22⋊C4—121no—
646C22⋊C4—121no—
647C22⋊C4—361no—
648C22⋊C4—361no—
649C22⋊C4—361no—
650C22⋊C4—361no—
651C22⋊C4—361no—
652C42—361no—
653C42—361no—
654C42—361no—
655C22×C3—24no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—62no—
684C22×C3—62no—
685C22×C3—62no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3C22×C4×D311yescharacteristic
691C22×C3#100411yescharacteristic
692C22×C3#100411yescharacteristic
693C22×C3#100411yescharacteristic
694C22×C3#100411yescharacteristic
695C22×C3#100411yescharacteristic
696C22×C3#100711yescharacteristic
697C22×C3#100911yescharacteristic
698C22×C3#100911yescharacteristic
699C22×C3#100911yescharacteristic
700C22×C3#101011yescharacteristic
701C22×C3#101011yescharacteristic
702C22×C3#101011yescharacteristic
703C22×C3C23×Dic311yescharacteristic
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C3×C4—24no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—42no—
717C3×C4—62no—
718C3×C4—62no—
719C3×C4—62no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4—121no—
724Dic3—22no—
725Dic3—22no—
726Dic3—22no—
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731Dic3—121no—
732Dic3—121no—
733Dic3—121no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738Dic3—121no—
739Dic3—241no—
740Dic3—241no—
741Dic3—241no—
742Dic3—241no—
743C32#237611yescharacteristic, complemented, Sylow
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—32no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23C2×D3×Dic312yes—
758C23C22×D3211yescharacteristic
759D4—124no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—44no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
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—181no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—364no—
799C2×C4C2×D3×Dic312yes—
800C2×C4C2×D3×Dic312yes—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—44no—
809C2×C3—42no—
810C2×C3—42no—
811C2×C3—122no—
812C2×C3#548611yescharacteristic
813C2×C3#550411yescharacteristic
814C2×C3#552311yescharacteristic
815C2×C3#562011yescharacteristic
816C2×C3#562111yescharacteristic
817C2×C3#564611yescharacteristic
818C2×C3#564711yescharacteristic
819C2×C3#565111yescharacteristic
820C2×C3#566611yescharacteristic
821C2×C3#566711yescharacteristic
822C2×C3#566711yescharacteristic
823C2×C3#579811yescharacteristic
824C2×C3#582711yescharacteristic
825C2×C3#582711yescharacteristic
826D3—42no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22#6429711yescharacteristic
842C22#6429811yescharacteristic
843C22#6430711yescharacteristic
844C22#6430811yescharacteristic
845C22C22×D3×Dic311yescharacteristic
846C22#6433011yescharacteristic
847C22#6433011yescharacteristic
848C4—22no—
849C4—22no—
850C4—62no—
851C4—62no—
852C4—62no—
853C4—121no—
854C4—121no—
855C4—121no—
856C4—121no—
857C4—361no—
858C4—361no—
859C4—361no—
860C4—361no—
861C3—21no—
862C3#7401311yescharacteristic, complemented
863C3#8284011yescharacteristic, complemented
864C2—42no—
865C2—122no—
866C2#1059497211yescharacteristic
867C2#1059497511yescharacteristic
868C2#1059497811yescharacteristic
869C2#1059498611yescharacteristic
870C2#1059499211yescharacteristic
871C2#1059509011yescharacteristic
872C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2376
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10592911C2semidirect
3. C3×#5212C2semidirect
6. #10591702C2semidirect
7. #10591701C2semidirect
8. #10591379C2semidirect
9. #10591377C2semidirect
10. #10591316C2semidirect
11. #10591307C2semidirect
12. #10591272C2semidirect
13. #10591268C2semidirect
14. #10591265C2semidirect
15. #10591262C2semidirect
28. C3×#929C4semidirect
62. #5212D3semidirect
89. C22×C32×C4C2×C4semidirect
115. C3×#217C2×C4semidirect
120. C3×Dic3⋊C4C2×C4semidirect
121. C3×Dic3⋊C4C2×C4semidirect
161. #929Dic3semidirect
307. C22×C3×C4C4×D3semidirect
308. C22×C3×C4C2×Dic3semidirect
361. #217C2×Dic3semidirect
381. Dic3⋊C4C2×Dic3semidirect
382. Dic3⋊C4C2×Dic3semidirect
630. C22×C4D3×Dic3semidirect
743. C32#2376semidirect
862. C3#74013semidirect
863. C3#82840semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9292
#105929112
C3×#52122
#105917212
#105917072
#105917022
#105917012
#105913792
#105913772
#105913162
#105913072
#105912722
#105912682
#105912652
#105912622
#828403
#740133