Finite Group Databasebeta

← #11805194

Subgroups — #11805194

Order 1152.

1293 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63877C211yesmaximal, characteristic
2C2×D3×Dic3⋊C4C211yesmaximal, characteristic
3C2×#63841C211yesmaximal, characteristic
4#10592346C211yesmaximal, characteristic, complemented
5C3×#4664C211yesmaximal, characteristic
6C3×#4655C211yesmaximal, characteristic, complemented
7#10591369C211yesmaximal, characteristic
8#10591368C211yesmaximal, characteristic
9#10591362C211yesmaximal, characteristic
10#10591272C211yesmaximal, characteristic, complemented
11#10591264C211yesmaximal, characteristic, complemented
12#10591257C211yesmaximal, characteristic, complemented
13#10591251C211yesmaximal, characteristic, complemented
14#10591250C211yesmaximal, characteristic, complemented
15#10591243C211yesmaximal, characteristic, complemented
16#74961—31nomaximal
17#74060—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63877—24no—
42D3×Dic3⋊C4C418yescomplemented
43#63841—24no—
44C32×#95C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#926—31no—
57C22×Dic3⋊C4—31no—
58C2×#892—31no—
59C2×D3×C4⋊C4—31no—
60C2×#877—31no—
61C2×#872—31no—
62C3×#387—31no—
63C3×#381—31no—
64#4980—31no—
65#4976—31no—
66#4943—31no—
67#4942—31no—
68Dic3×C22⋊C4—31no—
69C4×Dic3⋊C4—31no—
70#4667—31no—
71#4666—31no—
72#4664—31no—
73#4664D311yescharacteristic
74#4655—31no—
75#4655D311yescharacteristic, complemented
76#4654—31no—
77#4653—31no—
78#4652—31no—
79#4652—31no—
80#4649—31no—
81#4649—31no—
82#4649—31no—
83#4647—31no—
84#4647—31no—
85#4647—31no—
86#4647—61no—
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
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×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3C2×C414yes—
105C2×D3×Dic3—22no—
106C2×D3×Dic3—22no—
107C2×D3×Dic3—22no—
108C2×D3×Dic3—22no—
109C2×D3×Dic3C2×C414yes—
110C2×D3×Dic3C2×C414yes—
111C4⋊(C3⋊Dic3)—22no—
112#3750—22no—
113#3750—22no—
114#3750C2×C414yes—
115C4×C3⋊Dic3—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—22no—
118C3×C4⋊Dic3—22no—
119C3×Dic3⋊C4C2×C414yes—
120C3×C4×Dic3—22no—
121#3724—22no—
122#3724—22no—
123#3724C2×C414yes—
124Dic3⋊Dic3C2×C414yes—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3D414yes—
127Dic32—22no—
128Dic32—22no—
129Dic32—22no—
130Dic32—22no—
131#2344—91noSylow
132C23×C3×C4—31no—
133C23×Dic3—31no—
134C23×Dic3—31no—
135C22×C4×D3—31no—
136C22×C4×D3—31no—
137C22×C4×D3C2×D311yescharacteristic
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C42—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4C2×D311yescharacteristic
148C2×(C2×D3)⋊C4C2×D311yescharacteristic
149#926—64no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—61no—
154C2×C4⋊Dic3C2×D311yescharacteristic
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—38no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—61no—
170C2×Dic3⋊C4—61no—
171C2×Dic3⋊C4—61no—
172C2×Dic3⋊C4C2×D311yescharacteristic
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—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—61no—
184C2×C4×Dic3C2×D311yescharacteristic
185#892—64no—
186D3×C4⋊C4—38no—
187#877—64no—
188#872—64no—
189C3×#95—21no—
190C3×#95—31no—
191C3×#95—31no—
192C3×#95—31no—
193C3×#95—31no—
194C3×#95—31no—
195C3×#95—31no—
196C3×#95C2×D311yescharacteristic
197C3×#95C2×D311yescharacteristic
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—31no—
208C3⋊#95—61no—
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C3⋊#95C2×D311yescharacteristic
215C23×C32C2411yescharacteristic
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3C22×C412yes—
221C22×C3×D3C2×D412yes—
222C22×C3×D3#4112yes—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4C22×C412yes—
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⋊Dic3C22×C412yes—
240C2×C3⋊Dic3C22×C412yes—
241C2×C3⋊Dic3C2×D412yes—
242C2×C3⋊Dic3#4112yes—
243C2×C3⋊Dic3#4112yes—
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×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×Dic3C22×C412yes—
262C2×C3×Dic3C22×C412yes—
263C2×C3×Dic3C22×C412yes—
264C2×C3×Dic3C2×D412yes—
265C3×C4×D3—28no—
266D3×Dic3—28no—
267D3×Dic3—28no—
268C2×#117—91no—
269C2×#117—91no—
270C22×C4⋊C4—91no—
271#389—91no—
272#389—91no—
273#387—31no—
274#387—91no—
275#387—91no—
276#387—91no—
277#381—31no—
278#381—91no—
279#380—91no—
280C4×C4⋊C4—91no—
281C4×C4⋊C4—91no—
282C4×C22⋊C4—91no—
283C24×C3—31no—
284C23×D3C22×D311yescharacteristic
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—34no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—62no—
297C22×C3×C4—62no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—34no—
311C22×Dic3—34no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—62no—
319C22×Dic3—62no—
320C22×Dic3—62no—
321C22×Dic3—62no—
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C2×C4×D3—22no—
330C2×C4×D3—22no—
331C2×C4×D3—34no—
332C2×C4×D3—34no—
333C2×C4×D3—62no—
334C2×C4×D3—62no—
335C2×C4×D3—62no—
336C2×C4×D3—62no—
337C2×C4×D3C4×D314yes—
338C3×C4⋊C4—34no—
339C3×C4⋊C4—62no—
340C3×C22⋊C4—62no—
341C3×C22⋊C4—62no—
342C3×C42—62no—
343#217—34no—
344#217—62no—
345(C2×D3)⋊C4—22no—
346(C2×D3)⋊C4—22no—
347(C2×D3)⋊C4—34no—
348(C2×D3)⋊C4—62no—
349C4⋊Dic3—22no—
350C4⋊Dic3—34no—
351C4⋊Dic3—62no—
352C4⋊Dic3—62no—
353C4⋊Dic3—122no—
354Dic3⋊C4—34no—
355Dic3⋊C4—34no—
356Dic3⋊C4—34no—
357Dic3⋊C4—34no—
358Dic3⋊C4—34no—
359Dic3⋊C4—64no—
360Dic3⋊C4—62no—
361Dic3⋊C4—62no—
362Dic3⋊C4—62no—
363Dic3⋊C4—62no—
364Dic3⋊C4—62no—
365Dic3⋊C4—62no—
366Dic3⋊C4—62no—
367Dic3⋊C4—62no—
368Dic3⋊C4—122no—
369Dic3⋊C4—122no—
370Dic3⋊C4C4×D314yes—
371C4×Dic3—22no—
372C4×Dic3—62no—
373C4×Dic3—62no—
374C4×Dic3—62no—
375C4×Dic3—62no—
376C4×Dic3—62no—
377C4×Dic3—62no—
378C4×Dic3—62no—
379C4×Dic3—62no—
380C4×Dic3—62no—
381C4×Dic3—62no—
382C4×Dic3—122no—
383C22×C32C23×C411yescharacteristic
384C22×C32C22×D411yescharacteristic
385C22×C32C2×#4111yescharacteristic
386C22×C32C2×#4111yescharacteristic
387C22×C32C2×#4111yescharacteristic
388C22×C322−1+411yescharacteristic
389C22×C322−1+411yescharacteristic
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—22no—
393C2×C3×D3—22no—
394C2×C3×D3—22no—
395C2×C3×D3—22no—
396C2×C3×D3C4×D414yes—
397C32×C4—22no—
398C32×C4—41no—
399C32×C4—41no—
400C3⋊Dic3—22no—
401C3⋊Dic3—22no—
402C3⋊Dic3—41no—
403C3⋊Dic3#11714yescomplemented
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—22no—
407C3×Dic3—22no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C23×C4—31no—
412C23×C4—91no—
413C23×C4—91no—
414#117—184no—
415#117—184no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—98no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4—91no—
423C2×C4⋊C4—91no—
424C2×C4⋊C4—91no—
425C2×C4⋊C4—91no—
426C2×C4⋊C4—91no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—31no—
429C2×C22⋊C4—91no—
430C2×C22⋊C4—91no—
431C2×C42—31no—
432C2×C42—91no—
433C2×C42—91no—
434C2×C42—91no—
435C2×C42—91no—
436C2×C42—91no—
437#95—31no—
438#95—31no—
439#95—31no—
440#95—31no—
441#95—31no—
442#95—31no—
443#95—91no—
444#95—91no—
445#95—91no—
446#95—91no—
447#95—91no—
448#95D3211yescharacteristic
449C23×C3—21no—
450C23×C3—32no—
451C23×C3—32no—
452C23×C3—32no—
453C23×C3—61no—
454C23×C3—61no—
455C23×C3—61no—
456C23×C3—61no—
457C23×C3C23×D311yescharacteristic
458C23×C3C23×D311yescharacteristic
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3C2×C4×D312yes—
464C22×D3D3×D412yes—
465C22×D3#23712yes—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—22no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—68no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4C2×C4×D312yes—
514C2×C3×C4C2×C4×D312yes—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—32no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3—62no—
547C2×Dic3—68no—
548C2×Dic3—68no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3—121no—
570C2×Dic3C2×C4×D312yes—
571C2×Dic3C2×C4×D312yes—
572C2×Dic3C2×C4×D312yes—
573C2×Dic3D3×D412yes—
574C4×D3—28no—
575C4×D3—68no—
576C4×D3—68no—
577C2×C32C2×#11711yescharacteristic
578C2×C32C2×C4×D411yescharacteristic
579C2×C32#51911yescharacteristic
580C2×C32#54711yescharacteristic
581C2×C32#54711yescharacteristic
582C2×C32#55211yescharacteristic
583C2×C32#55211yescharacteristic
584C3×D3—24no—
585C24—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—34no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—94no—
597C22×C4—94no—
598C22×C4—91no—
599C22×C4—91no—
600C22×C4—91no—
601C22×C4—91no—
602C22×C4—182no—
603C22×C4—182no—
604C22×C4—182no—
605C22×C4—182no—
606C22×C4C2×D3211yescharacteristic
607C22×C4C2×D3211yescharacteristic
608C22×C4C2×D3211yescharacteristic
609C4⋊C4—34no—
610C4⋊C4—62no—
611C4⋊C4—94no—
612C4⋊C4—94no—
613C4⋊C4—94no—
614C4⋊C4—182no—
615C4⋊C4—182no—
616C4⋊C4—182no—
617C4⋊C4—182no—
618C4⋊C4—182no—
619C22⋊C4—62no—
620C22⋊C4—62no—
621C22⋊C4—94no—
622C22⋊C4—182no—
623C42—62no—
624C42—182no—
625C42—182no—
626C42—182no—
627C42—182no—
628C42—182no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—34no—
637C22×C3—62no—
638C22×C3—62no—
639C22×C3—62no—
640C22×C3—62no—
641C22×C3—62no—
642C22×C3—62no—
643C22×C3C22×C4×D311yescharacteristic
644C22×C3C22×C4×D311yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×#23711yescharacteristic
648C22×C3#100711yescharacteristic
649C22×C3D3×#4111yescharacteristic
650C22×C3D3×#4111yescharacteristic
651C22×C3D3×#4111yescharacteristic
652C22×C3D3×#4111yescharacteristic
653C22×C3D3×#4111yescharacteristic
654C22×C3#101011yescharacteristic
655C22×C3#101011yescharacteristic
656C22×C3#101011yescharacteristic
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—22no—
660C2×D3—22no—
661C2×D3—22no—
662C2×D3—22no—
663C2×D3#67⋊C414yes—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—42no—
667C3×C4—42no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—62no—
673C3×C4—62no—
674C3×C4—62no—
675C3×C4—62no—
676C3×C4—81no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680Dic3—22no—
681Dic3—22no—
682Dic3—22no—
683Dic3—22no—
684Dic3—34no—
685Dic3—34no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—64no—
690Dic3—62no—
691Dic3—62no—
692Dic3—62no—
693Dic3—62no—
694Dic3—122no—
695Dic3—122no—
696Dic3—121no—
697Dic3—121no—
698Dic3—241no—
699C32#234411yescharacteristic, complemented, Sylow
700C23—32no—
701C23—32no—
702C23—32no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23C22×D3211yescharacteristic
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—32no—
717C2×C4—32no—
718C2×C4—32no—
719C2×C4—32no—
720C2×C4—68no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—92no—
739C2×C4—92no—
740C2×C4—92no—
741C2×C4—92no—
742C2×C4—92no—
743C2×C4—188no—
744C2×C4—188no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4C4×D3212yes—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—64no—
761C2×C3C2×#67⋊C411yescharacteristic
762C2×C3#551611yescharacteristic
763C2×C3D3×#11711yescharacteristic
764C2×C3D3×#11711yescharacteristic
765C2×C3C4×D3×D411yescharacteristic
766C2×C3#557211yescharacteristic
767C2×C3#563111yescharacteristic
768C2×C3#565011yescharacteristic
769C2×C3#565011yescharacteristic
770C2×C3#565511yescharacteristic
771C2×C3#565511yescharacteristic
772C2×C3#565511yescharacteristic
773C2×C3#569311yescharacteristic
774C2×C3#570811yescharacteristic
775D3—24no—
776C22—34no—
777C22—62no—
778C22—62no—
779C22—62no—
780C22—62no—
781C22—62no—
782C22—62no—
783C22#6429711yescharacteristic
784C22#6429811yescharacteristic
785C22C2×C4×D3211yescharacteristic
786C22D32×D411yescharacteristic
787C22D3×#23711yescharacteristic
788C22#6431211yescharacteristic
789C22#6431911yescharacteristic
790C4—22no—
791C4—41no—
792C4—41no—
793C4—62no—
794C4—62no—
795C4—62no—
796C4—62no—
797C4—94no—
798C4—121no—
799C4—121no—
800C4—121no—
801C4—182no—
802C4—182no—
803C4—361no—
804C3—21no—
805C3#7406011yescharacteristic, complemented
806C3#7496111yescharacteristic, complemented
807C2—64no—
808C2#1059388511yescharacteristic
809C2#1059406411yescharacteristic
810C2#1059411611yescharacteristic
811C2D3×#67⋊C411yescharacteristic
812C2#1059442911yescharacteristic
813C2#1059451411yescharacteristic
814C2#1059460211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32#2344
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #10592346C2semidirect
6. C3×#4655C2semidirect
10. #10591272C2semidirect
11. #10591264C2semidirect
12. #10591257C2semidirect
13. #10591251C2semidirect
14. #10591250C2semidirect
15. #10591243C2semidirect
42. D3×Dic3⋊C4C4semidirect
75. #4655D3semidirect
403. C3⋊Dic3#117semidirect
699. C32#2344semidirect
805. C3#74060semidirect
806. C3#74961semidirect

Maximal subgroups

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

subgroupindex
C2×#638772
C2×D3×Dic3⋊C42
C2×#638412
#105923462
C3×#46642
C3×#46552
#105913692
#105913682
#105913622
#105912722
#105912642
#105912572
#105912512
#105912502
#105912432
#749613
#740603