Finite Group Databasebeta

← #11803578

Subgroups — #11803578

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64148C211yesmaximal, characteristic
2C2×#63957C211yesmaximal, characteristic, complemented
3C2×#63952C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic, complemented
7#10591720C211yesmaximal, characteristic, complemented
8#10591704C211yesmaximal, characteristic, complemented
9#10591704C211yesmaximal, characteristic, complemented
10#10591703C211yesmaximal, characteristic, complemented
11#10591693C211yesmaximal, characteristic, complemented
12#10591378C211yesmaximal, characteristic, complemented
13#10591264C211yesmaximal, characteristic, complemented
14#10591243C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#76296—31nomaximal
17#74665—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25#64148C418yescomplemented
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×#3724C2211yescharacteristic
40C2×#3724C2211yescharacteristic
41C2×#3724C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45#63957—24no—
46C2×Dic32C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49#63952—24no—
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#939—31no—
57C2×#939—31no—
58C2×#939—61no—
59C2×C4×#67—31no—
60C2×#67⋊C4—31no—
61C2×#877—31no—
62C2×#877—31no—
63C3×#390—31no—
64C3×#386—31no—
65#5221D311yescharacteristic, complemented
66#5220D311yescharacteristic, complemented
67#5210—31no—
68#4989—31no—
69#4976—31no—
70#4957—31no—
71#4957—31no—
72#4957—31no—
73#4957—31no—
74#4956—31no—
75#4956—31no—
76#4946—31no—
77#4945—31no—
78#4944—31no—
79#4942—31no—
80#4942—31no—
81#4940—31no—
82C4×Dic3⋊C4—31no—
83#4669—31no—
84#4668—31no—
85#4649—31no—
86#4647—31no—
87C24×C32C2311yescharacteristic
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C2×C32×D4—41no—
91C2×C32×D4—41no—
92C2×C32×D4C2×C414yescomplemented
93C22×C32×C4C2311yescharacteristic
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—41no—
97C2×#638—41no—
98C2×#638C2×C414yes—
99C2×#638C2×C414yescomplemented
100C22×C3⋊Dic3—22no—
101C22×C3⋊Dic3—22no—
102C22×C3⋊Dic3C2×C414yescomplemented
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3×Dic3—22no—
107C22×C3×Dic3—41no—
108C22×C3×Dic3—41no—
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×#624—22no—
118C2×#624—41no—
119C2×#624—41no—
120#3757C2×C414yescomplemented
121#3752C2×C414yescomplemented
122#3750C2×C414yescomplemented
123C3×#217—22no—
124C3×#217—22no—
125C3×#217—22no—
126C3×#217—41no—
127C3×#217—41no—
128C3×#217—41no—
129C3×#217—41no—
130C3×C4⋊Dic3—41no—
131C3×C4×Dic3—41no—
132#3724—22no—
133#3724—22no—
134#3724—22no—
135#3724—22no—
136#3724—41no—
137#3722—22no—
138#3722—41no—
139#3722—41no—
140Dic32—22no—
141Dic32—41no—
142Dic32D414yescomplemented
143#2324—91noSylow
144C22×C3×D4—21no—
145C22×C3×D4C2×D311yescharacteristic
146C22×C3×D4C2×D311yescharacteristic
147C23×C3×C4—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—31no—
152C22×#67—61no—
153C22×#67—61no—
154C23×Dic3—31no—
155C23×Dic3—31no—
156C23×Dic3—61no—
157C23×Dic3C2×D311yescharacteristic
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C42—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—61no—
172C2×#217C2×D311yescharacteristic
173C2×#217C2×D311yescharacteristic
174C2×#217C2×D311yescharacteristic
175C2×#217C2×D311yescharacteristic
176C2×#217C2×D311yescharacteristic
177C2×#217C2×D311yescharacteristic
178C2×#217C2×D311yescharacteristic
179#939—38no—
180#939—38no—
181#939—68no—
182C4×#67—64no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—61no—
192C2×C4⋊Dic3C2×D311yescharacteristic
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—61no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3C2×D311yescharacteristic
213#67⋊C4—64no—
214#877—64no—
215#877—64no—
216C3×#95—31no—
217C3×#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32C22×C412yes—
241C23×C32C22×C412yes—
242C23×C32C2411yescharacteristic
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3C22×C412yes—
250C32×D4—44no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C22×C412yes—
254#638—28no—
255#638—44no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—28no—
261C2×C3⋊Dic3C22×C412yes—
262C2×C3⋊Dic3C22×C412yes—
263C2×C3⋊Dic3C22×C412yes—
264C2×C3⋊Dic3C2×D412yes—
265C2×C3⋊Dic3#4112yes—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—44no—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291#624—44no—
292C2×#121—91no—
293C2×C4×D4—91no—
294C2×#117—91no—
295#390—31no—
296#390—91no—
297#390—91no—
298#389—91no—
299#388—91no—
300#388—91no—
301#386—31no—
302#386—91no—
303#385—91no—
304#385—91no—
305#380—91no—
306C4×C4⋊C4—91no—
307C24×C3—21no—
308C24×C3—21no—
309C24×C3C22×D311yescharacteristic
310C24×C3C22×D311yescharacteristic
311C24×C3C22×D311yescharacteristic
312C24×C3C22×D311yescharacteristic
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—61no—
316C2×C3×D4—24no—
317C2×C3×D4—41no—
318C2×C3×D4—41no—
319C2×C3×D4—41no—
320C2×C3×D4—41no—
321C2×C3×D4—42no—
322C2×C3×D4—42no—
323C2×C3×D4C4×D314yescomplemented
324C2×C3×D4C4×D314yescomplemented
325C22×C3×C4—21no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—62no—
335C22×C3×C4—121no—
336C22×C3×C4—121no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—34no—
340C2×#67—34no—
341C2×#67—34no—
342C2×#67—34no—
343C2×#67—64no—
344C2×#67—64no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—122no—
350C2×#67—122no—
351C2×#67—121no—
352C2×#67—121no—
353C2×#67—121no—
354C2×#67—121no—
355C2×#67—122no—
356C2×#67—122no—
357C22×Dic3—22no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—34no—
361C22×Dic3—34no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—41no—
367C22×Dic3—41no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—64no—
372C22×Dic3—62no—
373C22×Dic3—62no—
374C22×Dic3—62no—
375C22×Dic3—62no—
376C22×Dic3—122no—
377C22×Dic3—122no—
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—121no—
389C2×C4×D3—121no—
390C2×C4×D3—121no—
391C2×C4×D3—121no—
392C3×C4⋊C4—121no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—62no—
396C3×C22⋊C4—121no—
397C3×C22⋊C4—121no—
398C3×C22⋊C4—121no—
399C3×C22⋊C4—121no—
400C3×C42—121no—
401#217—22no—
402#217—22no—
403#217—22no—
404#217—34no—
405#217—34no—
406#217—41no—
407#217—41no—
408#217—41no—
409#217—41no—
410#217—64no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—64no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—121no—
417(C2×D3)⋊C4—121no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4—121no—
420C4⋊Dic3—41no—
421Dic3⋊C4—34no—
422Dic3⋊C4—34no—
423Dic3⋊C4—64no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—121no—
433Dic3⋊C4—121no—
434C4×Dic3—34no—
435C4×Dic3—34no—
436C4×Dic3—41no—
437C4×Dic3—62no—
438C4×Dic3—62no—
439C4×Dic3—121no—
440C4×Dic3—121no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32C23×C411yescharacteristic
456C22×C32C22×D411yescharacteristic
457C22×C32C2×#4111yescharacteristic
458C22×C32H(5,𝔽2)11yescharacteristic
459C22×C32H(5,𝔽2)11yescharacteristic
460C22×C32H(5,𝔽2)11yescharacteristic
461C22×C322−1+411yescharacteristic
462C2×C3⋊D3—22no—
463C2×C3⋊D3—22no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C32×C4—22no—
470C3⋊Dic3—22no—
471C3⋊Dic3—22no—
472C3⋊Dic3C4×D414yes—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C22×D4—91no—
482C22×D4—91no—
483C22×D4D3211yescharacteristic
484C23×C4—31no—
485C23×C4—91no—
486C23×C4—91no—
487#121—98no—
488C4×D4—184no—
489#117—184no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C42—31no—
510C2×C42—91no—
511C2×C42—91no—
512C2×C42—91no—
513#95—31no—
514#95—31no—
515#95—91no—
516#95—91no—
517#95—91no—
518#95—91no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3C2×C4×D312yes—
559C23×C3C2×C4×D312yes—
560C23×C3C2×C4×D312yes—
561C23×C3C2×C4×D312yes—
562C23×C3C23×D311yescharacteristic
563C23×C3C23×D311yescharacteristic
564C22×D3—32no—
565C22×D3—32no—
566C22×D3—62no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—121no—
580C22×D3—121no—
581C22×D3—121no—
582C22×D3—121no—
583C22×D3—121no—
584C22×D3—121no—
585C3×D4—44no—
586C3×D4—44no—
587C3×D4—48no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—22no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—124no—
620C2×C3×C4C2×C4×D312yes—
621C2×C3×C4C2×C4×D312yes—
622#67—68no—
623#67—68no—
624#67—128no—
625#67—124no—
626#67—124no—
627#67—128no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—44no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—68no—
667C2×Dic3—68no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—128no—
677C2×Dic3—121no—
678C2×Dic3—121no—
679C2×Dic3—121no—
680C2×Dic3—121no—
681C2×Dic3D3×D412yes—
682C2×Dic3D3×D412yes—
683C4×D3—124no—
684C4×D3—124no—
685C2×C32—42no—
686C2×C32—42no—
687C2×C32C2×C4×D411yescharacteristic
688C2×C32#51811yescharacteristic
689C2×C32#52011yescharacteristic
690C2×C32#53511yescharacteristic
691C2×C32#53711yescharacteristic
692C2×C32#54011yescharacteristic
693C2×C32#54211yescharacteristic
694C3⋊D3—42no—
695C24—91no—
696C24C2×D3211yescharacteristic
697C24C2×D3211yescharacteristic
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—94no—
701C2×D4—94no—
702C2×D4—182no—
703C2×D4—182no—
704C2×D4—361no—
705C2×D4—361no—
706C2×D4#62414yescomplemented
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—62no—
716C22×C4—91no—
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—94no—
720C22×C4—121no—
721C22×C4—121no—
722C22×C4—182no—
723C22×C4—182no—
724C22×C4—182no—
725C22×C4—361no—
726C22×C4—361no—
727C22×C4C2×D3211yescharacteristic
728C4⋊C4—94no—
729C4⋊C4—121no—
730C4⋊C4—182no—
731C4⋊C4—182no—
732C4⋊C4—182no—
733C4⋊C4—182no—
734C4⋊C4—361no—
735C22⋊C4—62no—
736C22⋊C4—62no—
737C22⋊C4—62no—
738C22⋊C4—94no—
739C22⋊C4—94no—
740C22⋊C4—121no—
741C22⋊C4—121no—
742C22⋊C4—121no—
743C22⋊C4—121no—
744C22⋊C4—182no—
745C22⋊C4—361no—
746C22⋊C4—361no—
747C42—94no—
748C42—121no—
749C42—182no—
750C42—361no—
751C22×C3—24no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—42no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—42no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—81no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3C22×C4×D311yescharacteristic
801C22×C3C22×C4×D311yescharacteristic
802C22×C3C2×D3×D411yescharacteristic
803C22×C3C2×D3×D411yescharacteristic
804C22×C3#100411yescharacteristic
805C22×C3#100411yescharacteristic
806C22×C3#100411yescharacteristic
807C22×C3#100411yescharacteristic
808C22×C3#100411yescharacteristic
809C22×C3#100411yescharacteristic
810C22×C3D3×#4111yescharacteristic
811C22×C3D3×#4111yescharacteristic
812C22×C3#101011yescharacteristic
813C22×C3#101011yescharacteristic
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—62no—
820C2×D3—122no—
821C2×D3—122no—
822C2×D3—122no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—121no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—121no—
831C2×D3—241no—
832C2×D3—241no—
833C2×D3—241no—
834C2×D3—241no—
835C3×C4—22no—
836C3×C4—22no—
837C3×C4—42no—
838C3×C4—62no—
839C3×C4—62no—
840C3×C4—121no—
841C3×C4—121no—
842C3×C4—121no—
843C3×C4—121no—
844C3×C4—121no—
845C3×C4—121no—
846Dic3—22no—
847Dic3—22no—
848Dic3—34no—
849Dic3—34no—
850Dic3—41no—
851Dic3—41no—
852Dic3—41no—
853Dic3—41no—
854Dic3—41no—
855Dic3—41no—
856Dic3—64no—
857Dic3—62no—
858Dic3—62no—
859Dic3—62no—
860Dic3—62no—
861Dic3—122no—
862Dic3—122no—
863C32#232411yescharacteristic, complemented, Sylow
864C23—21no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—92no—
877C23—181no—
878C23—181no—
879C23—181no—
880C23—181no—
881C23—181no—
882C23—181no—
883C23C2×#62412yes—
884C23C2×#62412yes—
885C23C22×D3211yescharacteristic
886D4—44no—
887D4—188no—
888D4—364no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—32no—
892C2×C4—32no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—92no—
916C2×C4—92no—
917C2×C4—92no—
918C2×C4—92no—
919C2×C4—92no—
920C2×C4—124no—
921C2×C4—188no—
922C2×C4—181no—
923C2×C4—181no—
924C2×C4—181no—
925C2×C4—181no—
926C2×C4—364no—
927C2×C4C2×#62412yes—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—44no—
936C2×C3—42no—
937C2×C3—42no—
938C2×C3—42no—
939C2×C3—42no—
940C2×C3—82no—
941C2×C3#548611yescharacteristic
942C2×C3#548611yescharacteristic
943C2×C3C4×D3×D411yescharacteristic
944C2×C3C4×D3×D411yescharacteristic
945C2×C3#554611yescharacteristic
946C2×C3#554611yescharacteristic
947C2×C3#559211yescharacteristic
948C2×C3#559711yescharacteristic
949C2×C3#560811yescharacteristic
950C2×C3#561511yescharacteristic
951C2×C3#561511yescharacteristic
952C2×C3#566211yescharacteristic
953C2×C3#566911yescharacteristic
954C2×C3#571511yescharacteristic
955D3—122no—
956D3—122no—
957D3—242no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—182no—
973C22—182no—
974C22—182no—
975C22—361no—
976C22—361no—
977C22—361no—
978C22—361no—
979C22#6430911yescharacteristic
980C22D32×D411yescharacteristic
981C22#6431211yescharacteristic
982C22#6431311yescharacteristic
983C22C22×#62411yescharacteristic
984C22#6433011yescharacteristic
985C22#6433011yescharacteristic
986C4—22no—
987C4—62no—
988C4—62no—
989C4—94no—
990C4—121no—
991C4—121no—
992C4—121no—
993C4—121no—
994C4—121no—
995C4—121no—
996C4—182no—
997C4—182no—
998C3—21no—
999C3#7466511yescharacteristic, complemented
1000C3#7629611yescharacteristic, complemented
1001C2—42no—
1002C2—42no—
1003C2—362no—
1004C2#1059513211yescharacteristic
1005C2D4×#62411yescharacteristic
1006C2#1059520511yescharacteristic
1007C2#1059521111yescharacteristic
1008C2#1059521911yescharacteristic
1009C2#1059528611yescharacteristic
1010C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×#64148C2
hypercenterC22×D4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63957C2semidirect
3. C2×#63952C2semidirect
4. C3×#5221C2semidirect
5. C3×#5220C2semidirect
6. #10591722C2semidirect
7. #10591720C2semidirect
8. #10591704C2semidirect
9. #10591704C2semidirect
10. #10591703C2semidirect
11. #10591693C2semidirect
12. #10591378C2semidirect
13. #10591264C2semidirect
14. #10591243C2semidirect
15. #10591202C2semidirect
25. #64148C4semidirect
65. #5221D3semidirect
66. #5220D3semidirect
92. C2×C32×D4C2×C4semidirect
99. C2×#638C2×C4semidirect
102. C22×C3⋊Dic3C2×C4semidirect
120. #3757C2×C4semidirect
121. #3752C2×C4semidirect
122. #3750C2×C4semidirect
142. Dic32D4semidirect
323. C2×C3×D4C4×D3semidirect
324. C2×C3×D4C4×D3semidirect
706. C2×D4#624semidirect
863. C32#2324semidirect
999. C3#74665semidirect
1000. C3#76296semidirect

Maximal subgroups

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

subgroupindex
C2×#641482
C2×#639572
C2×#639522
C3×#52212
C3×#52202
#105917222
#105917202
#105917042
#105917032
#105916932
#105913782
#105912642
#105912432
#105912022
#762963
#746653