Finite Group Databasebeta

← #11803819

Subgroups — #11803819

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#888C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic
4#10592679C211yesmaximal, characteristic
5C3×#4980C211yesmaximal, characteristic
6#10591272C211yesmaximal, characteristic
7#10591270C211yesmaximal, characteristic
8#10591269C211yesmaximal, characteristic
9#10591262C211yesmaximal, characteristic
10#10591261C211yesmaximal, characteristic
11#10591261C211yesmaximal, characteristic
12#10591239C211yesmaximal, characteristic
13#10591206C211yesmaximal, characteristic
14#10591201C211yesmaximal, characteristic
15#10591192C211yesmaximal, characteristic
16#83227—31nomaximal
17#74948—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#888C418yescomplemented
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic32C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38#63843—24no—
39Dic3×Dic6—24no—
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×C4⋊Q8—31no—
57C2×Q8×Dic3—31no—
58C2×Q8×Dic3—31no—
59C2×#888D311yescharacteristic
60C2×#887—31no—
61C2×C4×Dic6—31no—
62C3×#387—31no—
63#5229—31no—
64#5229—31no—
65#4980—31no—
66#4980—31no—
67#4980—31no—
68#4980—31no—
69#4980—31no—
70#4980—31no—
71#4980—31no—
72#4980—31no—
73#4980—61no—
74#4980D311yescharacteristic
75#4978—31no—
76#4936—31no—
77#4933—31no—
78#4932—31no—
79#4655—31no—
80#4654—31no—
81#4653—31no—
82#4652—31no—
83#4650—31no—
84#4648—31no—
85#4646—31no—
86#4646—31no—
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
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
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×Dic6—22no—
103C2×C3×Dic6—22no—
104C2×C3×Dic6—22no—
105C2×C3×Dic6—22no—
106C2×C3×Dic6C2×C414yes—
107C2×C3×Dic6C2×C414yes—
108C32×C4⋊C4C2×C414yes—
109C4⋊(C3⋊Dic3)—22no—
110C4×C3⋊Dic3—22no—
111C3×C4⋊Dic3—22no—
112C3×C4⋊Dic3C2×C414yes—
113C3×Dic3⋊C4C2×C414yes—
114C3×Dic3⋊C4C2×C414yes—
115C3×C4×Dic3—22no—
116C3×C4×Dic3C2×C414yes—
117Dic3⋊Dic3—22no—
118Dic3⋊Dic3—22no—
119Dic3⋊Dic3—22no—
120Dic3⋊Dic3—22no—
121Dic32—22no—
122Dic32—22no—
123Dic32—22no—
124Dic32D414yes—
125#2327—91noSylow
126C22×C3×Q8—31no—
127C22×C3×Q8—31no—
128C22×Dic6C2×D311yescharacteristic
129C22×Dic6C2×D311yescharacteristic
130C3×C4⋊Q8—38no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4C2×D311yescharacteristic
137C2×C3×C4⋊C4C2×D311yescharacteristic
138C2×C3×C42—31no—
139C2×C3×C42—31no—
140Q8×Dic3—64no—
141Q8×Dic3—64no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—61no—
149C2×C4⋊Dic3C2×D311yescharacteristic
150C2×C4⋊Dic3C2×D311yescharacteristic
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4C2×D311yescharacteristic
156C2×Dic3⋊C4C2×D311yescharacteristic
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—61no—
168C2×C4×Dic3C2×D311yescharacteristic
169C2×C4×Dic3C2×D311yescharacteristic
170#888Dic318yescomplemented
171#887—64no—
172C4×Dic6—64no—
173C3×#95—31no—
174C3×#95—31no—
175C3×#95—31no—
176C3×#95—31no—
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—31no—
200C3⋊#95—31no—
201C3⋊#95—61no—
202C3⋊#95—61no—
203C3⋊#95—61no—
204C3⋊#95—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C23×C32C2411yescharacteristic
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4C22×C412yes—
217C2×C32×C4C22×C412yes—
218C2×C32×C4C22×C412yes—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
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⋊Dic3C2×D412yes—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
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—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C22×C412yes—
249C2×C3×Dic3C22×C412yes—
250C2×C3×Dic3C22×C412yes—
251C2×C3×Dic3C22×C412yes—
252C2×C3×Dic3C2×D412yes—
253C2×C3×Dic3C2×D412yes—
254C2×C3×Dic3#4112yes—
255C3×Dic6—28no—
256C3×Dic6—28no—
257C2×C4⋊Q8—31no—
258C2×C4×Q8—91no—
259C2×C4×Q8—91no—
260#391—91no—
261#391—91no—
262#387—31no—
263#387—91no—
264#387—91no—
265#387—91no—
266#387—91no—
267#387—91no—
268#387—91no—
269#387—91no—
270#382—91no—
271#376—91no—
272C2×C3×Q8—34no—
273C2×C3×Q8—34no—
274C2×C3×Q8—62no—
275C2×C3×Q8—62no—
276C2×C3×Q8—62no—
277C2×C3×Q8—62no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C2×Dic6—22no—
316C2×Dic6—22no—
317C2×Dic6—22no—
318C2×Dic6—22no—
319C2×Dic6C2×Dic314yes—
320C2×Dic6C2×Dic314yes—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—34no—
323C3×C4⋊C4—34no—
324C3×C4⋊C4—34no—
325C3×C4⋊C4—62no—
326C3×C4⋊C4C4×D314yes—
327C3×C4⋊C4C2×Dic314yes—
328C3×C42—34no—
329C3×C42—62no—
330C4⋊Dic3—22no—
331C4⋊Dic3—62no—
332C4⋊Dic3—62no—
333C4⋊Dic3—62no—
334C4⋊Dic3—62no—
335C4⋊Dic3—62no—
336C4⋊Dic3—62no—
337C4⋊Dic3—122no—
338C4⋊Dic3C2×Dic314yes—
339Dic3⋊C4—62no—
340Dic3⋊C4—62no—
341Dic3⋊C4—62no—
342Dic3⋊C4—62no—
343Dic3⋊C4C2×Dic314yes—
344Dic3⋊C4C2×Dic314yes—
345C4×Dic3—22no—
346C4×Dic3—34no—
347C4×Dic3—34no—
348C4×Dic3—62no—
349C4×Dic3—62no—
350C4×Dic3—62no—
351C4×Dic3—62no—
352C4×Dic3—62no—
353C4×Dic3—62no—
354C4×Dic3—62no—
355C4×Dic3—62no—
356C4×Dic3—122no—
357C4×Dic3C2×Dic314yes—
358C22×C32C23×C411yescharacteristic
359C22×C32C22×D411yescharacteristic
360C22×C32C2×#4111yescharacteristic
361C22×C322−1+411yescharacteristic
362C22×C322−1+411yescharacteristic
363C22×C322−1+411yescharacteristic
364C22×C322−1+411yescharacteristic
365C32×C4—22no—
366C32×C4—22no—
367C32×C4—22no—
368C3⋊Dic3—22no—
369C3⋊Dic3—41no—
370C3⋊Dic3—41no—
371C3⋊Dic3—41no—
372C3×Dic3—22no—
373C3×Dic3—22no—
374C3×Dic3—22no—
375C3×Dic3—22no—
376C3×Dic3—41no—
377C3×Dic3—41no—
378C3×Dic3—41no—
379C3×Dic3C4×D414yes—
380C22×Q8—31no—
381C22×Q8—31no—
382C4⋊Q8—38no—
383C4×Q8—184no—
384C4×Q8—184no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—91no—
390C2×C4⋊C4—91no—
391C2×C4⋊C4—91no—
392C2×C4⋊C4—91no—
393C2×C4⋊C4—91no—
394C2×C4⋊C4D3211yescharacteristic
395C2×C42—31no—
396C2×C42—31no—
397C2×C42—91no—
398C2×C42—91no—
399C2×C42—91no—
400C2×C42—91no—
401C2×C42—91no—
402#95—31no—
403#95—31no—
404#95—31no—
405#95—31no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95—91no—
411#95—91no—
412#95—91no—
413#95—91no—
414#95—91no—
415#95—91no—
416#95—91no—
417#95—91no—
418C23×C3—21no—
419C23×C3C23×D311yescharacteristic
420C23×C3C23×D311yescharacteristic
421C3×Q8—68no—
422C3×Q8—68no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—32no—
439C2×C3×C4—32no—
440C2×C3×C4—32no—
441C2×C3×C4—32no—
442C2×C3×C4—32no—
443C2×C3×C4—32no—
444C2×C3×C4—32no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4C2×C4×D312yes—
469C2×C3×C4C2×C4×D312yes—
470C2×C3×C4C2×C4×D312yes—
471C2×C3×C4C22×Dic312yes—
472C2×C3×C4C22×Dic312yes—
473C2×C3×C4C22×Dic312yes—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—32no—
492C2×Dic3—32no—
493C2×Dic3—62no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—62no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—121no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3D3×D412yes—
528C2×Dic3D3×D412yes—
529C2×Dic3#23712yes—
530C2×Dic3C22×Dic312yes—
531C2×Dic3C22×Dic312yes—
532C2×Dic3C22×Dic312yes—
533C2×Dic3C22×Dic312yes—
534Dic6—28no—
535Dic6—28no—
536C2×C32C2×C4×D411yescharacteristic
537C2×C32#51911yescharacteristic
538C2×C32#51911yescharacteristic
539C2×C32#53611yescharacteristic
540C2×C32#53611yescharacteristic
541C2×C32#54111yescharacteristic
542C2×C32#54111yescharacteristic
543C2×Q8—34no—
544C2×Q8—34no—
545C2×Q8—62no—
546C2×Q8—62no—
547C2×Q8—62no—
548C2×Q8—62no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—91no—
560C22×C4—91no—
561C22×C4C2×D3211yescharacteristic
562C22×C4C2×D3211yescharacteristic
563C22×C4C2×D3211yescharacteristic
564C4⋊C4—34no—
565C4⋊C4—34no—
566C4⋊C4—34no—
567C4⋊C4—62no—
568C4⋊C4—182no—
569C4⋊C4—182no—
570C4⋊C4—182no—
571C4⋊C4—182no—
572C4⋊C4—182no—
573C4⋊C4D3×Dic314yes—
574C42—34no—
575C42—62no—
576C42—94no—
577C42—182no—
578C42—182no—
579C42—182no—
580C42—182no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3C22×C4×D311yescharacteristic
589C22×C3C2×D3×D411yescharacteristic
590C22×C3C2×D3×D411yescharacteristic
591C22×C3C2×#23711yescharacteristic
592C22×C3#100711yescharacteristic
593C22×C3#100711yescharacteristic
594C22×C3#100711yescharacteristic
595C22×C3#100711yescharacteristic
596C22×C3#100711yescharacteristic
597C22×C3D3×#4111yescharacteristic
598C22×C3#101011yescharacteristic
599C22×C3#101011yescharacteristic
600C22×C3#101011yescharacteristic
601C22×C3C23×Dic311yescharacteristic
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—34no—
609C3×C4—42no—
610C3×C4—42no—
611C3×C4—42no—
612C3×C4—62no—
613C3×C4—62no—
614C3×C4—62no—
615C3×C4—62no—
616C3×C4—121no—
617C3×C4—121no—
618C3×C4—121no—
619Dic3—22no—
620Dic3—22no—
621Dic3—22no—
622Dic3—22no—
623Dic3—41no—
624Dic3—41no—
625Dic3—41no—
626Dic3—62no—
627Dic3—62no—
628Dic3—122no—
629Dic3—122no—
630Dic3—121no—
631Dic3—121no—
632Dic3—121no—
633Dic3—121no—
634Dic3—121no—
635Dic3—121no—
636Dic3—241no—
637Dic3—241no—
638Dic3D4×Dic314yes—
639C32#232711yescharacteristic, complemented, Sylow
640C23C22×D3211yescharacteristic
641Q8—68no—
642Q8—68no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—32no—
650C2×C4—32no—
651C2×C4—32no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—92no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—181no—
677C2×C4—181no—
678C2×C4—181no—
679C2×C4—181no—
680C2×C4—181no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4—181no—
684C2×C4—181no—
685C2×C4C2×D3×Dic312yes—
686C2×C4C2×D3×Dic312yes—
687C2×C4C2×D3×Dic312yes—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3#551611yescharacteristic
696C2×C3C4×D3×D411yescharacteristic
697C2×C3#557211yescharacteristic
698C2×C3#562811yescharacteristic
699C2×C3#564811yescharacteristic
700C2×C3#569611yescharacteristic
701C2×C3#570111yescharacteristic
702C2×C3#572411yescharacteristic
703C2×C3#572411yescharacteristic
704C2×C3#573111yescharacteristic
705C2×C3#573111yescharacteristic
706C2×C3C2×D4×Dic311yescharacteristic
707C2×C3#581211yescharacteristic
708C2×C3#581211yescharacteristic
709C22#6429711yescharacteristic
710C22#6429711yescharacteristic
711C22D32×D411yescharacteristic
712C22D3×#23711yescharacteristic
713C22#6431511yescharacteristic
714C22#6431611yescharacteristic
715C22C22×D3×Dic311yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—34no—
720C4—62no—
721C4—62no—
722C4—62no—
723C4—62no—
724C4—121no—
725C4—121no—
726C4—121no—
727C4—182no—
728C4—361no—
729C4—361no—
730C4—361no—
731C3—21no—
732C3#7494811yescharacteristic, complemented
733C3#8322711yescharacteristic, complemented
734C2#1059431611yescharacteristic
735C2#1059432811yescharacteristic
736C2#1059436611yescharacteristic
737C2#1059444611yescharacteristic
738C2#1059481811yescharacteristic
739C2D3×D4×Dic311yescharacteristic
740C2#1059534711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2327
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
29. C3×#888C4semidirect
170. #888Dic3semidirect
639. C32#2327semidirect
732. C3#74948semidirect
733. C3#83227semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8882
C2×#638432
C2×Dic3×Dic62
#105926792
C3×#49802
#105912722
#105912702
#105912692
#105912622
#105912612
#105912392
#105912062
#105912012
#105911922
#832273
#749483