Finite Group Databasebeta

← #11906185

Subgroups — #11906185

Order 1152.

2361 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic, complemented
2C3×#5511C212yesmaximal, complemented
3#10595058C212yesmaximal
4C4×#3811C211yesmaximal, characteristic
5#10594993C214yesmaximal, complemented
6#10594981C212yesmaximal, complemented
7#10594925C211yesmaximal, characteristic, complemented
8#10594915C212yesmaximal, complemented
9#10594636C212yesmaximal, complemented
10D3×#897C212yesmaximal, complemented
11#10594537C212yesmaximal, complemented
12#10594401C212yesmaximal, complemented
13#10594397C212yesmaximal, complemented
14#10594396C214yesmaximal, complemented
15#10594383C212yesmaximal, complemented
16#86948—32nomaximal
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×#634C2211yescharacteristic, complemented
19C2×#3811C2211yescharacteristic
20C2×C4×D32C2211yescharacteristic
21C2×#3797C2211yescharacteristic, complemented
22C2×D3×Dic6C2212yescomplemented
23C2×C32×C4⋊C4C2211yescharacteristic, complemented
24C2×#3752C2212yes—
25C2×C4⋊(C3⋊Dic3)C2212yescomplemented
26#64106C2212yes—
27#64106C2212yes—
28#64106C2212yescomplemented
29#64106C2212yescomplemented
30C3×C4×#67C2212yes—
31C3×C4×#67C2214yes—
32C3×#924C2212yescomplemented
33C3×#924C2214yescomplemented
34C3×#897C2212yescomplemented
35C3×#896C2214yescomplemented
36C3×D3×C4⋊C4C2212yescomplemented
37C3×#889C2214yescomplemented
38C3×#888C2212yescomplemented
39C3×#887C2212yescomplemented
40#63982C2214yescomplemented
41#63982C2212yescomplemented
42#63974C2212yes—
43#63974C2211yescharacteristic
44#67⋊Dic3C2214yes—
45#67⋊Dic3C2212yes—
46#63921C2211yescharacteristic
47D3×(C2×D3)⋊C4C2214yes—
48#63918C2214yescomplemented
49#63904C2214yes—
50C4×#626C2212yes—
51#63900C2211yescharacteristic, complemented
52#63896C2214yescomplemented
53#63895C2214yes—
54#63895C2214yescomplemented
55#63893C2214yescomplemented
56#63893C2214yescomplemented
57D3×C4⋊Dic3C2214yescomplemented
58#63888C2214yes—
59#63888C2214yescomplemented
60#63883C2211yescharacteristic
61#63883C2212yescomplemented
62C4×#624C2211yescharacteristic
63#63881C2212yes—
64#63880C2214yes—
65#63871C2212yes—
66#63866C2212yescomplemented
67#63865C2212yes—
68#63857C2212yescomplemented
69#63856C2214yescomplemented
70#63845C2214yescomplemented
71#63845C2214yescomplemented
72#63844C2212yescomplemented
73Dic3×Dic6C2214yescomplemented
74#63840C2214yescomplemented
75#63836C2214yes—
76C3×#554—32no—
77#5730—32no—
78#5728—32no—
79#5690—34no—
80#5689—34no—
81#5635—34no—
82#5635—34no—
83#5634—34no—
84#5634—34no—
85#5632—32no—
86#5632—32no—
87D3×C22⋊Q8—32no—
88D3×C22⋊Q8—32no—
89#5578—32no—
90Q8×D12—32no—
91#5545—34no—
92C4×D3×D4—32no—
93#5543—34no—
94D4×Dic6—32no—
95#5511—32no—
96#5511D312yescomplemented
97C2×#897—32no—
98C2×#897—32no—
99C2×#897—61no—
100C23×C3⋊D3C2311yescharacteristic
101C22×D32C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2312yes—
104C22×C3⋊Dic3C2312yes—
105C22×C3⋊Dic3C2311yescharacteristic
106C2×C4×C3⋊D3—42no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C4×C3⋊D3C2311yescharacteristic
109C2×C4×C3⋊D3C2311yescharacteristic
110C2×C4×C3⋊D3C2311yescharacteristic
111C2×#634—42no—
112C2×#634C2312yes—
113C2×#634C2312yes—
114C2×C3×#67C2312yes—
115C2×C3×C4×D3C2312yes—
116C2×C3×C4×D3C2314yes—
117C2×C3×Dic6C2312yes—
118C2×C3×Dic6C2314yes—
119#3811Q818yescomplemented
120C2×#627C2314yes—
121C2×#627C2312yes—
122C2×#626C2312yes—
123C2×#624C2312yes—
124C2×#624C2311yescharacteristic
125C2×#624C2311yescharacteristic
126C2×#624C2312yes—
127C2×#624C2311yescharacteristic
128C2×D3×Dic3C2314yes—
129C2×D3×Dic3C2312yes—
130C4×D32—42no—
131#3797—42no—
132D3×Dic6—44no—
133C32×C4⋊C4C2312yes—
134C32×C4⋊C4C2312yes—
135#3752C2314yes—
136#3752C2314yes—
137C4⋊(C3⋊Dic3)C2314yes—
138C4⋊(C3⋊Dic3)C2314yes—
139C3×#217C2312yes—
140C3×#217C2314yes—
141C3×(C2×D3)⋊C4C2312yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×C4⋊Dic3C2312yes—
144C3×C4⋊Dic3C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2312yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×C4×Dic3C2312yes—
151C3×C4×Dic3C2314yes—
152#3724C2314yes—
153#3724C2312yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158Dic3⋊Dic3C2312yes—
159#3722C2314yes—
160#3722C2312yes—
161(C2×D3)⋊Dic3C2312yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yes—
164Dic32C2312yes—
165#3501—91noSylow
166C2×D3×Q8—32no—
167C2×D3×Q8—32no—
168C2×D3×D4—32no—
169C22×C4×D3—32no—
170C22×C4×D3—32no—
171C22×C4×D3—61no—
172C22×Dic6—32no—
173C22×Dic6—32no—
174C22×Dic6—61no—
175C3×C4⋊Q8—32no—
176C3×#125—34no—
177C3×C22⋊Q8—32no—
178C3×C22⋊Q8—34no—
179C3×C22⋊Q8—32no—
180C3×C22⋊Q8—34no—
181C3×C4×Q8—32no—
182C3×C4×D4—32no—
183C3×C4×D4—34no—
184C2×C3×C4⋊C4—21no—
185C2×C3×C4⋊C4—32no—
186C2×C3×C4⋊C4C2×D312yescomplemented
187#946—34no—
188#946—32no—
189#946—34no—
190#946—34no—
191Q8×Dic3—34no—
192#944—32no—
193D4×Dic3—34no—
194D4×Dic3—32no—
195C4×#67—34no—
196C4×#67—32no—
197C4×#67C2×D312yes—
198C4×#67C2×D314yes—
199C2×(C2×D3)⋊C4—34no—
200C2×(C2×D3)⋊C4—34no—
201C2×(C2×D3)⋊C4—62no—
202C2×C4⋊Dic3—34no—
203C2×C4⋊Dic3—34no—
204C2×C4⋊Dic3—62no—
205#924—34no—
206#924—32no—
207#924C2×D314yescomplemented
208#924C2×D312yescomplemented
209#897—32no—
210#897—32no—
211#897—32no—
212#897—34no—
213#897—34no—
214#897—32no—
215#897—32no—
216#897—32no—
217#897—34no—
218#897—34no—
219#897—34no—
220#897—34no—
221#897—62no—
222#897—62no—
223#897—62no—
224#897—62no—
225#897C2×D312yescomplemented
226#896—34no—
227#896—34no—
228#896—34no—
229#896—34no—
230#896—34no—
231#896—34no—
232#896C2×D314yescomplemented
233#893—34no—
234#893—32no—
235#892—34no—
236D3×C4⋊C4—34no—
237D3×C4⋊C4—32no—
238D3×C4⋊C4—34no—
239D3×C4⋊C4—32no—
240D3×C4⋊C4C2×D312yescomplemented
241#890—34no—
242#890—34no—
243#889—34no—
244#889—34no—
245#889C2×D314yescomplemented
246#888—34no—
247#888—34no—
248#888—34no—
249#888C2×D312yescomplemented
250#887—32no—
251#887C2×D312yescomplemented
252#67⋊C4—34no—
253#67⋊C4—32no—
254#67⋊C4—32no—
255#67⋊C4—34no—
256D3×C22⋊C4—34no—
257D3×C22⋊C4—32no—
258D3×C22⋊C4—34no—
259D3×C22⋊C4—32no—
260#878—34no—
261#878—34no—
262#878—34no—
263#878—34no—
264#878—34no—
265#878—34no—
266C4×D12—32no—
267C4×D12—34no—
268#872—34no—
269C42×D3—32no—
270#869—32no—
271#869—34no—
272C4×Dic6—34no—
273C4×Dic6—32no—
274C23×C32C2411yescharacteristic
275C22×C3⋊D3—41no—
276C22×C3⋊D3—41no—
277C22×C3⋊D3C2×Q814yescomplemented
278C22×C3⋊D3C2411yescharacteristic
279C22×C3⋊D3C2411yescharacteristic
280C22×C3×D3C2412yes—
281C2×D32—41no—
282C2×D32—41no—
283C2×D32C2×Q814yescomplemented
284C2×C32×C4—22no—
285C2×C32×C4—42no—
286C2×C32×C4C2414yes—
287C2×C32×C4C2411yescharacteristic
288C2×C32×C4C2411yescharacteristic
289C2×C3⋊Dic3—42no—
290C2×C3⋊Dic3—41no—
291C2×C3⋊Dic3C2411yescharacteristic
292C2×C3⋊Dic3C2414yes—
293C2×C3⋊Dic3C2411yescharacteristic
294C4×C3⋊D3—22no—
295C4×C3⋊D3—22no—
296C4×C3⋊D3—41no—
297C4×C3⋊D3—41no—
298#634—24no—
299#634—42no—
300C3×#67C2×Q818yescomplemented
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2414yes—
303C2×C3×Dic3C2414yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C3×C4×D3—24no—
307C3×C4×D3—44no—
308C3×Dic6—24no—
309C3×Dic6—44no—
310#627—44no—
311#627—42no—
312#626C2×Q818yescomplemented
313#624—42no—
314#624—41no—
315#624—41no—
316#624—42no—
317#624C2×Q814yescomplemented
318D3×Dic3—44no—
319D3×Dic3—42no—
320#554—32no—
321#554—92no—
322#554—94no—
323#554—94no—
324D4×Q8—92no—
325D4×Q8—92no—
326#544—92no—
327#543—92no—
328#543—92no—
329#533—92no—
330C2×C22⋊Q8—92no—
331C2×C22⋊Q8—91no—
332C2×C22⋊Q8—91no—
333#518—92no—
334C2×C4×D4—91no—
335C23×D3—32no—
336C23×D3—32no—
337C23×D3—61no—
338C2×C3×Q8—32no—
339C2×C3×Q8—34no—
340C2×C3×D4—32no—
341C22×C3×C4—21no—
342C22×C3×C4—22no—
343C22×C3×C4—32no—
344C22×C3×C4—34no—
345C22×C3×C4C22×D312yes—
346C22×C3×C4C22×D314yes—
347C2×#67—32no—
348C2×#67C22×D312yes—
349C22×Dic3—32no—
350C22×Dic3—34no—
351C22×Dic3—32no—
352C22×Dic3—34no—
353C22×Dic3—61no—
354C22×Dic3—62no—
355D3×Q8—124no—
356D3×Q8—124no—
357D3×D4—316no—
358C2×D12—32no—
359C2×C4×D3—32no—
360C2×C4×D3—32no—
361C2×C4×D3—32no—
362C2×C4×D3—34no—
363C2×C4×D3—32no—
364C2×C4×D3—32no—
365C2×C4×D3—32no—
366C2×C4×D3—32no—
367C2×C4×D3—34no—
368C2×C4×D3—34no—
369C2×C4×D3—32no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—124no—
375C2×C4×D3—124no—
376C2×C4×D3—124no—
377C2×C4×D3C22×D312yes—
378C2×C4×D3C22×D314yes—
379C2×Dic6—32no—
380C2×Dic6—32no—
381C2×Dic6—34no—
382C2×Dic6—34no—
383C2×Dic6—34no—
384C2×Dic6—34no—
385C2×Dic6—62no—
386C2×Dic6—62no—
387C2×Dic6—124no—
388C2×Dic6—124no—
389C2×Dic6—124no—
390C2×Dic6C22×D312yes—
391C2×Dic6C22×D314yes—
392C3×C4⋊C4—22no—
393C3×C4⋊C4—22no—
394C3×C4⋊C4—32no—
395C3×C4⋊C4—32no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4—34no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4—34no—
401C3×C4⋊C4C22×D312yes—
402C3×C4⋊C4C22×D312yes—
403C3×C4⋊C4C22×D314yes—
404C3×C22⋊C4—32no—
405C3×C22⋊C4—34no—
406C3×C22⋊C4—32no—
407C3×C22⋊C4—34no—
408C3×C42—32no—
409C3×C42—34no—
410#217—34no—
411#217—32no—
412#217C22×D312yes—
413#217C22×D314yes—
414(C2×D3)⋊C4—32no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—32no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—32no—
424(C2×D3)⋊C4—64no—
425(C2×D3)⋊C4—64no—
426(C2×D3)⋊C4C22×D314yes—
427(C2×D3)⋊C4C22×D312yes—
428C4⋊Dic3—34no—
429C4⋊Dic3—34no—
430C4⋊Dic3—34no—
431C4⋊Dic3—34no—
432C4⋊Dic3—34no—
433C4⋊Dic3—32no—
434C4⋊Dic3—34no—
435C4⋊Dic3—34no—
436C4⋊Dic3—34no—
437C4⋊Dic3—64no—
438C4⋊Dic3—64no—
439C4⋊Dic3C22×D312yes—
440C4⋊Dic3C22×D314yes—
441Dic3⋊C4—34no—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—32no—
449Dic3⋊C4C22×D314yes—
450Dic3⋊C4C22×D314yes—
451Dic3⋊C4C22×D314yes—
452Dic3⋊C4C22×D314yes—
453Dic3⋊C4C22×D312yes—
454C4×Dic3—32no—
455C4×Dic3—34no—
456C4×Dic3—32no—
457C4×Dic3—34no—
458C4×Dic3C22×D312yes—
459C4×Dic3C22×D314yes—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32C22×Q812yes—
463C22×C32C2511yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—44no—
469C2×C3⋊D3C22×Q812yes—
470C2×C3⋊D3C22×Q812yes—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3C22×Q814yes—
474D32—44no—
475C32×C4—21no—
476C32×C4—24no—
477C32×C4H(5,𝔽2)12yes—
478C3⋊Dic3—21no—
479C3⋊Dic3—24no—
480C3⋊Dic3—21no—
481C3×Dic3—24no—
482C3×Dic3—22no—
483C3×Dic3—22no—
484C3×Dic3—24no—
485C3×Dic3C22×Q814yes—
486C22×Q8—92no—
487C22×Q8—91no—
488C22×Q8—91no—
489C22×D4—91no—
490C23×C4—91no—
491C23×C4—91no—
492C4⋊Q8—32no—
493C4⋊Q8—94no—
494C4⋊Q8—92no—
495C4⋊Q8—94no—
496#125—34no—
497#125—94no—
498#125—94no—
499C22⋊Q8—32no—
500C22⋊Q8—34no—
501C22⋊Q8—32no—
502C22⋊Q8—34no—
503C22⋊Q8—92no—
504C22⋊Q8—94no—
505C22⋊Q8—94no—
506C22⋊Q8—94no—
507C22⋊Q8—94no—
508C22⋊Q8—92no—
509C22⋊Q8—94no—
510C22⋊Q8—94no—
511C22⋊Q8—92no—
512C22⋊Q8—92no—
513C22⋊Q8—94no—
514C22⋊Q8—94no—
515C22⋊Q8—94no—
516C22⋊Q8—92no—
517C22⋊Q8—92no—
518C22⋊Q8—92no—
519C22⋊Q8—92no—
520C4×Q8—32no—
521C4×Q8—92no—
522C4×Q8—94no—
523C4×D4—32no—
524C4×D4—34no—
525C4×D4—94no—
526C4×D4—92no—
527C4×D4—92no—
528C4×D4—92no—
529C4×D4—94no—
530C4×D4—94no—
531#117—94no—
532C2×C4⋊C4—32no—
533C2×C4⋊C4—91no—
534C2×C4⋊C4—91no—
535C2×C4⋊C4—92no—
536C2×C4⋊C4—94no—
537C2×C4⋊C4—92no—
538C2×C4⋊C4D3211yescharacteristic, complemented
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—92no—
542C2×C22⋊C4—94no—
543C2×C22⋊C4—92no—
544C2×C42—91no—
545C23×C3—21no—
546C23×C3—32no—
547C23×C3C23×D312yes—
548C22×D3—32no—
549C22×D3—32no—
550C22×D3—38no—
551C22×D3—38no—
552C22×D3—64no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3C23×D312yes—
562C3×Q8—64no—
563C3×Q8—124no—
564C3×D4—38no—
565C2×C3×C4—24no—
566C2×C3×C4—24no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—24no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—34no—
573C2×C3×C4—34no—
574C2×C3×C4—32no—
575C2×C3×C4—44no—
576C2×C3×C4—44no—
577C2×C3×C4—64no—
578C2×C3×C4—124no—
579C2×C3×C4C23×D314yes—
580C2×C3×C4C23×D312yes—
581C2×C3×C4C23×D314yes—
582C2×C3×C4C23×D312yes—
583#67—38no—
584#67D3×Q818yescomplemented
585C2×Dic3—32no—
586C2×Dic3—34no—
587C2×Dic3—34no—
588C2×Dic3—32no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—64no—
592C2×Dic3—124no—
593C2×Dic3—122no—
594C2×Dic3—124no—
595C2×Dic3—122no—
596C2×Dic3—124no—
597C2×Dic3—122no—
598C2×Dic3C23×D312yes—
599C2×Dic3C23×D314yes—
600C2×Dic3C23×D314yes—
601C2×Dic3C23×D312yes—
602C2×Dic3C23×D312yes—
603D12—38no—
604C4×D3—24no—
605C4×D3—38no—
606C4×D3—44no—
607C4×D3—64no—
608C4×D3—64no—
609C4×D3—122no—
610C4×D3—122no—
611C4×D3—122no—
612C4×D3—124no—
613C4×D3—122no—
614C4×D3—124no—
615C4×D3—122no—
616C4×D3—122no—
617C4×D3—122no—
618C4×D3—124no—
619C4×D3—122no—
620C4×D3—122no—
621Dic6—24no—
622Dic6—44no—
623Dic6—64no—
624Dic6—64no—
625Dic6—124no—
626Dic6—124no—
627Dic6—124no—
628Dic6—124no—
629Dic6—124no—
630Dic6—124no—
631C2×C32—22no—
632C2×C32C23×Q811yescharacteristic
633C2×C32C2×H(5,𝔽2)11yescharacteristic
634C2×C32#58511yescharacteristic
635C3⋊D3—22no—
636C3⋊D3—22no—
637C3×D3—24no—
638C24—91no—
639C24—91no—
640C2×Q8—32no—
641C2×Q8—34no—
642C2×Q8—92no—
643C2×Q8—94no—
644C2×Q8—92no—
645C2×Q8—92no—
646C2×Q8—362no—
647C2×Q8—364no—
648C2×Q8—362no—
649C2×D4—32no—
650C2×D4—92no—
651C2×D4—98no—
652C22×C4—32no—
653C22×C4—34no—
654C22×C4—91no—
655C22×C4—91no—
656C22×C4—92no—
657C22×C4—92no—
658C22×C4—91no—
659C22×C4—94no—
660C22×C4—92no—
661C22×C4—92no—
662C22×C4—91no—
663C22×C4—91no—
664C22×C4—91no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—362no—
668C22×C4—362no—
669C22×C4C2×D3211yescharacteristic
670C22×C4C2×D3212yes—
671C4⋊C4—32no—
672C4⋊C4—34no—
673C4⋊C4—32no—
674C4⋊C4—34no—
675C4⋊C4—34no—
676C4⋊C4—34no—
677C4⋊C4—34no—
678C4⋊C4—94no—
679C4⋊C4—92no—
680C4⋊C4—92no—
681C4⋊C4—94no—
682C4⋊C4—94no—
683C4⋊C4—94no—
684C4⋊C4—94no—
685C4⋊C4—94no—
686C4⋊C4—94no—
687C4⋊C4C2×D3212yes—
688C4⋊C4C2×D3212yes—
689C22⋊C4—32no—
690C22⋊C4—34no—
691C22⋊C4—32no—
692C22⋊C4—34no—
693C22⋊C4—94no—
694C22⋊C4—92no—
695C22⋊C4—92no—
696C22⋊C4—94no—
697C22⋊C4—94no—
698C22⋊C4—94no—
699C42—32no—
700C42—34no—
701C42—92no—
702C42—94no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—21no—
709C22×C3—34no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3C2×D3×Q814yes—
713C22×C3C24×D312yes—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—34no—
717C2×D3—34no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—62no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—128no—
729C2×D3—128no—
730C2×D3—128no—
731C2×D3C2×D3×Q814yes—
732C3×C4—22no—
733C3×C4—22no—
734C3×C4—24no—
735C3×C4—24no—
736C3×C4—22no—
737C3×C4—34no—
738C3×C4—44no—
739C3×C4—62no—
740C3×C4—64no—
741C3×C4—64no—
742C3×C4—62no—
743C3×C4#100914yes—
744Dic3—24no—
745Dic3—22no—
746Dic3—22no—
747Dic3—24no—
748Dic3—64no—
749Dic3—64no—
750Dic3—62no—
751Dic3—62no—
752Dic3—124no—
753Dic3—121no—
754Dic3—121no—
755Dic3C2×D3×Q814yes—
756C32#350111yescharacteristic, complemented, Sylow
757C23—32no—
758C23—94no—
759C23—91no—
760C23—91no—
761C23—94no—
762C23—361no—
763C23—361no—
764C23—361no—
765C23—361no—
766C23C22×D3211yescharacteristic
767Q8—64no—
768Q8—124no—
769Q8—184no—
770Q8—362no—
771Q8—364no—
772Q8—362no—
773D4—38no—
774D4—98no—
775C2×C4—22no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—34no—
779C2×C4—34no—
780C2×C4—32no—
781C2×C4—42no—
782C2×C4—64no—
783C2×C4—94no—
784C2×C4—91no—
785C2×C4—94no—
786C2×C4—91no—
787C2×C4—124no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—361no—
791C2×C4—361no—
792C2×C4—361no—
793C2×C4—362no—
794C2×C4—362no—
795C2×C4—361no—
796C2×C4—362no—
797C2×C4—364no—
798C2×C4—361no—
799C2×C4—362no—
800C2×C4C22×D3214yes—
801C2×C4C22×D3211yescharacteristic
802C2×C4C22×D3211yescharacteristic
803C2×C3—24no—
804C2×C3—24no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—64no—
809C2×C3C22×D3×Q812yes—
810C2×C3C2×#100912yes—
811C2×C3#596612yes—
812D3—24no—
813D3—64no—
814D3—64no—
815D3—122no—
816D3—122no—
817C22—21no—
818C22—21no—
819C22—34no—
820C22—62no—
821C22—62no—
822C22—92no—
823C22—92no—
824C22—181no—
825C22—181no—
826C22—181no—
827C22—181no—
828C22—364no—
829C22—364no—
830C22D32×Q812yes—
831C22C23×D3211yescharacteristic
832C4—21no—
833C4—24no—
834C4—34no—
835C4—62no—
836C4—64no—
837C4—64no—
838C4—62no—
839C4—181no—
840C4—181no—
841C4—184no—
842C4#6430812yes—
843C3—21no—
844C3#8694812yescomplemented
845C2—22no—
846C2—64no—
847C2—182no—
848C2—182no—
849C2C2×#6430811yescharacteristic
850C2#1059667911yescharacteristic
851C2C2×D32×Q811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
prime radicalC2×#3811C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64106C2semidirect
2. C3×#5511C2semidirect
5. #10594993C2semidirect
6. #10594981C2semidirect
7. #10594925C2semidirect
8. #10594915C2semidirect
9. #10594636C2semidirect
10. D3×#897C2semidirect
11. #10594537C2semidirect
12. #10594401C2semidirect
13. #10594397C2semidirect
14. #10594396C2semidirect
15. #10594383C2semidirect
18. C22×#634C22semidirect
21. C2×#3797C22semidirect
22. C2×D3×Dic6C22semidirect
23. C2×C32×C4⋊C4C22semidirect
25. C2×C4⋊(C3⋊Dic3)C22semidirect
28. #64106C22semidirect
29. #64106C22semidirect
32. C3×#924C22semidirect
33. C3×#924C22semidirect
34. C3×#897C22semidirect
35. C3×#896C22semidirect
36. C3×D3×C4⋊C4C22semidirect
37. C3×#889C22semidirect
38. C3×#888C22semidirect
39. C3×#887C22semidirect
40. #63982C22semidirect
41. #63982C22semidirect
48. #63918C22semidirect
51. #63900C22semidirect
52. #63896C22semidirect
54. #63895C22semidirect
55. #63893C22semidirect
56. #63893C22semidirect
57. D3×C4⋊Dic3C22semidirect
59. #63888C22semidirect
61. #63883C22semidirect
66. #63866C22semidirect
68. #63857C22semidirect
69. #63856C22semidirect
70. #63845C22semidirect
71. #63845C22semidirect
72. #63844C22semidirect
73. Dic3×Dic6C22semidirect
74. #63840C22semidirect
96. #5511D3semidirect
119. #3811Q8semidirect
186. C2×C3×C4⋊C4C2×D3semidirect
207. #924C2×D3semidirect
208. #924C2×D3semidirect
225. #897C2×D3semidirect
232. #896C2×D3semidirect
240. D3×C4⋊C4C2×D3semidirect
245. #889C2×D3semidirect
249. #888C2×D3semidirect
251. #887C2×D3semidirect
277. C22×C3⋊D3C2×Q8semidirect
283. C2×D32C2×Q8semidirect
300. C3×#67C2×Q8semidirect
312. #626C2×Q8semidirect
317. #624C2×Q8semidirect
538. C2×C4⋊C4D32semidirect
584. #67D3×Q8semidirect
756. C32#3501semidirect
844. C3#86948semidirect

Maximal subgroups

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

subgroupindex
C2×#641062
C3×#55112
#105950582
C4×#38112
#105949932
#105949812
#105949252
#105949152
#105946362
D3×#8972
#105945372
#105944012
#105943972
#105943962
#105943832
#869483