Finite Group Databasebeta

← #11803273

Subgroups — #11803273

Order 1152.

1711 conjugacy classes of subgroups.

The subgroup lattice has 1075 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63976C211yesmaximal, characteristic
2C2×D3×#217C211yesmaximal, characteristic, complemented
3C2×#63879C211yesmaximal, characteristic, complemented
4#10592643C211yesmaximal, characteristic, complemented
5C3×#4956C211yesmaximal, characteristic, complemented
6C3×#4955C211yesmaximal, characteristic, complemented
7#10591707C211yesmaximal, characteristic, complemented
8#10591703C211yesmaximal, characteristic, complemented
9#10591385C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591373C211yesmaximal, characteristic, complemented
12#10591368C211yesmaximal, characteristic, complemented
13#10591363C211yesmaximal, characteristic, complemented
14#10591284C211yesmaximal, characteristic, complemented
15#10591281C211yesmaximal, characteristic, complemented
16#74876—31nomaximal
17#73821—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic, complemented
21C22×#625C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3750C2211yescharacteristic, complemented
29C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
37#63976C418yescomplemented
38D3×#217—24no—
39C2×#3724C2211yescharacteristic, complemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47C2×Dic32C2211yescharacteristic, complemented
48C2×Dic32C2211yescharacteristic, complemented
49#63879—24no—
50#63658C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×#953—31no—
57C22×#217—31no—
58C2×#937—31no—
59C2×C4×#67—31no—
60C2×#67⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C3×#386—31no—
63C3×#379—31no—
64#5221—31no—
65#5213—31no—
66#4958—31no—
67#4957—31no—
68#4957—31no—
69#4957—31no—
70#4956—31no—
71#4956—31no—
72#4956D311yescharacteristic, complemented
73#4955D311yescharacteristic, complemented
74#4946—31no—
75#4945—31no—
76#4945—31no—
77#4944—31no—
78#4944—31no—
79#4944—31no—
80#4944—31no—
81#4944—61no—
82Dic3×C22⋊C4—31no—
83#4670—31no—
84#4669—31no—
85#4668—31no—
86#4666—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3—22no—
89C23×C3×D3—22no—
90C23×C3×D3—41no—
91C23×C3×D3—41no—
92C23×C3×D3—41no—
93C23×C3×D3—41no—
94C23×C3×D3C2×C414yescomplemented
95C23×C3×D3C2311yescharacteristic
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C3×#67—41no—
105C2×C3×#67—41no—
106C2×C3×#67C2×C414yescomplemented
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—41no—
114C2×C3×C4×D3—41no—
115C2×#625—22no—
116C2×#625—22no—
117C2×#625—41no—
118C2×#625—41no—
119C2×#625C2×C414yes—
120C2×#625C2×C414yescomplemented
121C2×D3×Dic3—22no—
122C2×D3×Dic3—41no—
123C2×D3×Dic3—41no—
124C2×D3×Dic3—41no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3D414yescomplemented
127C32×C22⋊C4—41no—
128#3757—22no—
129#3757C2×C414yescomplemented
130#3750—22no—
131C4×C3⋊Dic3—41no—
132C3×#217—22no—
133C3×#217—41no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—41no—
137C3×(C2×D3)⋊C4—41no—
138C3×(C2×D3)⋊C4—41no—
139#3724—41no—
140Dic3⋊Dic3—41no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—41no—
145(C2×D3)⋊Dic3C2×C414yescomplemented
146(C2×D3)⋊Dic3C2×C414yescomplemented
147Dic32—22no—
148Dic32—41no—
149#2321—91noSylow
150C25×C3—31no—
151C24×D3C2×D311yescharacteristic
152C22×C3×D4—31no—
153C23×C3×C4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67C2×D311yescharacteristic
159C23×Dic3—31no—
160C23×Dic3—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3C2×D311yescharacteristic, complemented
164C2×C3×C22⋊C4—21no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×C3×C22⋊C4C2×D311yescharacteristic
174#953—38no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—61no—
186C2×#217—61no—
187C2×#217—64no—
188C2×#217C2×D311yescharacteristic
189C2×#217C2×D311yescharacteristic
190#937—38no—
191C4×#67—64no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4C2×D311yescharacteristic
199C2×(C2×D3)⋊C4C2×D311yescharacteristic
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
203C2×C4⋊Dic3—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—61no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—61no—
217#67⋊C4—64no—
218D3×C22⋊C4—64no—
219C3×#95—31no—
220C3×#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—61no—
230C3⋊#95—61no—
231C3⋊#95C2×D311yescharacteristic, complemented
232C3⋊#95C2×D311yescharacteristic, complemented
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32C22×C412yes—
240C23×C32C2411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
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×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—28no—
258C22×C3×D3—44no—
259C22×C3×D3—44no—
260C22×C3×D3—44no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3C22×C412yes—
265C22×C3×D3C22×C412yes—
266C22×C3×D3C22×C412yes—
267C22×C3×D3C2×D412yes—
268C22×C3×D3#4112yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—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⋊Dic3C22×C412yes—
285C2×C3⋊Dic3C22×C412yes—
286C2×C3⋊Dic3C2×D412yes—
287C3×#67—44no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3C22×C412yes—
302C2×C3×Dic3C2×D412yes—
303C3×C4×D3—44no—
304#625—28no—
305#625—44no—
306D3×Dic3—44no—
307D3×Dic3—44no—
308C2×#120—91no—
309C2×C4×D4—91no—
310C22×C22⋊C4—91no—
311#390—91no—
312#390—91no—
313#388—91no—
314#388—91no—
315#388—91no—
316#388—91no—
317#386—31no—
318#386—91no—
319#386—91no—
320#385—91no—
321#379—31no—
322C4×C22⋊C4—91no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3—31no—
326C24×C3—31no—
327C24×C3—34no—
328C24×C3—62no—
329C24×C3—62no—
330C24×C3—121no—
331C24×C3—121no—
332C24×C3—121no—
333C24×C3—121no—
334C24×C3C22×D311yescharacteristic
335C24×C3C22×D311yescharacteristic
336C23×D3—22no—
337C23×D3—22no—
338C23×D3—41no—
339C23×D3—41no—
340C23×D3—41no—
341C23×D3—41no—
342C23×D3C4×D314yescomplemented
343C23×D3C22×D311yescharacteristic
344C23×D3C22×D311yescharacteristic
345C23×D3C22×D311yescharacteristic
346C2×C3×D4—34no—
347C2×C3×D4—121no—
348C2×C3×D4—121no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—62no—
357C22×C3×C4—121no—
358C22×C3×C4—121no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C2×#67—34no—
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—41no—
368C2×#67—41no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—121no—
374C2×#67—121no—
375C2×#67—121no—
376C2×#67—121no—
377C2×#67C4×D314yescomplemented
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—34no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—61no—
391C22×Dic3—62no—
392C22×Dic3—121no—
393C22×Dic3—121no—
394C22×Dic3—121no—
395C22×Dic3—121no—
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C2×C4×D3—22no—
402C2×C4×D3—34no—
403C2×C4×D3—41no—
404C2×C4×D3—41no—
405C2×C4×D3—62no—
406C2×C4×D3—121no—
407C2×C4×D3—121no—
408C2×C4×D3—121no—
409C2×C4×D3—121no—
410C3×C22⋊C4—41no—
411C3×C22⋊C4—41no—
412C3×C22⋊C4—42no—
413C3×C22⋊C4—62no—
414C3×C22⋊C4—62no—
415C3×C22⋊C4—62no—
416C3×C22⋊C4—121no—
417C3×C22⋊C4—121no—
418C3×C22⋊C4—121no—
419C3×C22⋊C4—121no—
420#217—22no—
421#217—34no—
422#217—34no—
423#217—34no—
424#217—34no—
425#217—41no—
426#217—64no—
427#217—62no—
428#217—62no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—122no—
433#217—121no—
434(C2×D3)⋊C4—22no—
435(C2×D3)⋊C4—22no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—41no—
439(C2×D3)⋊C4—41no—
440(C2×D3)⋊C4—41no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—121no—
445C4⋊Dic3—121no—
446Dic3⋊C4—62no—
447Dic3⋊C4—62no—
448Dic3⋊C4—122no—
449Dic3⋊C4—121no—
450Dic3⋊C4—121no—
451Dic3⋊C4—121no—
452C4×Dic3—62no—
453C4×Dic3—62no—
454C4×Dic3—121no—
455C4×Dic3—121no—
456C4×Dic3—121no—
457C4×Dic3—121no—
458C4×Dic3—122no—
459C22×C32—22no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C23×C411yescharacteristic
467C22×C32C22×D411yescharacteristic
468C22×C32C2×#4111yescharacteristic
469C22×C32H(5,𝔽2)11yescharacteristic
470C22×C32H(5,𝔽2)11yescharacteristic
471C22×C32H(5,𝔽2)11yescharacteristic
472C22×C32H(5,𝔽2)11yescharacteristic
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—416no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3C4×D414yes—
495C32×C4—41no—
496C32×C4—41no—
497C3⋊Dic3—22no—
498C3⋊Dic3—22no—
499C3⋊Dic3—22no—
500C3⋊Dic3—41no—
501C3×Dic3—22no—
502C3×Dic3—22no—
503C3×Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C25—31no—
507C22×D4—31no—
508C22×D4—91no—
509C22×D4—91no—
510C23×C4—31no—
511C23×C4—91no—
512C23×C4—91no—
513#120—98no—
514C4×D4—184no—
515C2×C4⋊C4—91no—
516C2×C4⋊C4—91no—
517C2×C4⋊C4—91no—
518C2×C22⋊C4—31no—
519C2×C22⋊C4—31no—
520C2×C22⋊C4—31no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—91no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—184no—
534C2×C22⋊C4D3211yescharacteristic
535C2×C42—91no—
536C2×C42—91no—
537C2×C42—91no—
538#95—31no—
539#95—31no—
540#95—91no—
541#95—91no—
542#95—91no—
543#95—91no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—22no—
558C23×C3—32no—
559C23×C3—32no—
560C23×C3—32no—
561C23×C3—32no—
562C23×C3—32no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—68no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—124no—
587C23×C3—124no—
588C23×C3—124no—
589C23×C3—124no—
590C23×C3—124no—
591C23×C3—124no—
592C23×C3C2×C4×D312yes—
593C23×C3C2×C4×D312yes—
594C23×C3C23×D311yescharacteristic
595C23×C3C23×D311yescharacteristic
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—28no—
613C22×D3—44no—
614C22×D3—44no—
615C22×D3—44no—
616C22×D3—44no—
617C22×D3—44no—
618C22×D3—44no—
619C22×D3C2×C4×D312yes—
620C22×D3C2×C4×D312yes—
621C22×D3C2×C4×D312yes—
622C22×D3D3×D412yes—
623C22×D3#23712yes—
624C3×D4—124no—
625C2×C3×C4—22no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—32no—
639C2×C3×C4—32no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—124no—
659#67—44no—
660#67—68no—
661#67—68no—
662#67—124no—
663#67—124no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—121no—
705C2×Dic3—121no—
706C2×Dic3—121no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—124no—
714C2×Dic3—124no—
715C2×Dic3C2×C4×D312yes—
716C2×Dic3D3×D412yes—
717C4×D3—44no—
718C4×D3—124no—
719C4×D3—124no—
720C2×C32—42no—
721C2×C32C2×C4×D411yescharacteristic
722C2×C32#51811yescharacteristic
723C2×C32#51811yescharacteristic
724C2×C32#53411yescharacteristic
725C2×C32#53511yescharacteristic
726C2×C32#53811yescharacteristic
727C2×C32#53811yescharacteristic
728C3×D3—24no—
729C3×D3—42no—
730C3×D3—42no—
731C24—31no—
732C24—31no—
733C24—31no—
734C24—34no—
735C24—62no—
736C24—62no—
737C24—121no—
738C24—121no—
739C24—121no—
740C24—121no—
741C24C2×D3211yescharacteristic
742C2×D4—34no—
743C2×D4—94no—
744C2×D4—94no—
745C2×D4—121no—
746C2×D4—121no—
747C2×D4—182no—
748C2×D4—182no—
749C2×D4—361no—
750C2×D4—361no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—62no—
757C22×C4—94no—
758C22×C4—91no—
759C22×C4—91no—
760C22×C4—91no—
761C22×C4—91no—
762C22×C4—121no—
763C22×C4—121no—
764C22×C4—182no—
765C22×C4—361no—
766C22×C4—361no—
767C22×C4—361no—
768C22×C4—361no—
769C22×C4C2×D3211yescharacteristic
770C22×C4C2×D3211yescharacteristic
771C4⋊C4—182no—
772C4⋊C4—361no—
773C4⋊C4—361no—
774C22⋊C4—41no—
775C22⋊C4—62no—
776C22⋊C4—62no—
777C22⋊C4—62no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—94no—
781C22⋊C4—121no—
782C22⋊C4—121no—
783C22⋊C4—121no—
784C22⋊C4—121no—
785C22⋊C4—182no—
786C22⋊C4—182no—
787C22⋊C4—182no—
788C22⋊C4—182no—
789C22⋊C4—361no—
790C42—182no—
791C42—361no—
792C42—361no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—34no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—81no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3—1216no—
835C22×C3—121no—
836C22×C3—121no—
837C22×C3—121no—
838C22×C3—121no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3C22×C4×D311yescharacteristic
844C22×C3C22×C4×D311yescharacteristic
845C22×C3C2×D3×D411yescharacteristic
846C22×C3C2×D3×D411yescharacteristic
847C22×C3C2×#23711yescharacteristic
848C22×C3#100411yescharacteristic
849C22×C3#100411yescharacteristic
850C22×C3#100411yescharacteristic
851C22×C3#100411yescharacteristic
852C22×C3#100411yescharacteristic
853C22×C3#100411yescharacteristic
854C22×C3#100411yescharacteristic
855C22×C3D3×#4111yescharacteristic
856C22×C3#100911yescharacteristic
857C2×D3—22no—
858C2×D3—22no—
859C2×D3—22no—
860C2×D3—22no—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—416no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3#67⋊C414yes—
879C3×C4—42no—
880C3×C4—41no—
881C3×C4—41no—
882C3×C4—41no—
883C3×C4—41no—
884C3×C4—62no—
885C3×C4—62no—
886C3×C4—81no—
887C3×C4—121no—
888C3×C4—121no—
889C3×C4—121no—
890Dic3—22no—
891Dic3—22no—
892Dic3—41no—
893Dic3—41no—
894Dic3—41no—
895Dic3—62no—
896Dic3—62no—
897Dic3—62no—
898Dic3—62no—
899Dic3—62no—
900Dic3—62no—
901Dic3—122no—
902Dic3—122no—
903Dic3—122no—
904Dic3—121no—
905Dic3—121no—
906Dic3—241no—
907C32#232111yescharacteristic, complemented, Sylow
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23—32no—
915C23—32no—
916C23—32no—
917C23—32no—
918C23—32no—
919C23—68no—
920C23—61no—
921C23—61no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—124no—
937C23—124no—
938C23—124no—
939C23—124no—
940C23—124no—
941C23—124no—
942C23C4×D3212yes—
943C23C22×D3211yescharacteristic
944D4—124no—
945D4—188no—
946D4—364no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—32no—
954C2×C4—32no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—92no—
969C2×C4—92no—
970C2×C4—92no—
971C2×C4—124no—
972C2×C4—181no—
973C2×C4—181no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—364no—
982C2×C4—364no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—42no—
991C2×C3—42no—
992C2×C3—64no—
993C2×C3—82no—
994C2×C3—122no—
995C2×C3—122no—
996C2×C3C2×#67⋊C411yescharacteristic
997C2×C3#548611yescharacteristic
998C2×C3#548611yescharacteristic
999C2×C3#548611yescharacteristic
1000C2×C3C4×D3×D411yescharacteristic
1001C2×C3#554511yescharacteristic
1002C2×C3#558911yescharacteristic
1003C2×C3#558911yescharacteristic
1004C2×C3#559211yescharacteristic
1005C2×C3#559311yescharacteristic
1006C2×C3#559311yescharacteristic
1007C2×C3#560711yescharacteristic
1008C2×C3#561311yescharacteristic
1009C2×C3#565711yescharacteristic
1010D3—24no—
1011D3—42no—
1012D3—42no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—34no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—1216no—
1034C22—121no—
1035C22—121no—
1036C22—121no—
1037C22—121no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22C2×C4×D3211yescharacteristic
1043C22#6430711yescharacteristic
1044C22D32×D411yescharacteristic
1045C22D3×#23711yescharacteristic
1046C22#6431311yescharacteristic
1047C22#6431311yescharacteristic
1048C22#6433011yescharacteristic
1049C4—41no—
1050C4—41no—
1051C4—62no—
1052C4—62no—
1053C4—121no—
1054C4—121no—
1055C4—121no—
1056C4—182no—
1057C4—182no—
1058C4—182no—
1059C4—361no—
1060C3—21no—
1061C3#7382111yescharacteristic, complemented
1062C3#7487611yescharacteristic, complemented
1063C2—42no—
1064C2—64no—
1065C2—122no—
1066C2—122no—
1067C2#1059418111yescharacteristic
1068C2#1059421311yescharacteristic
1069C2D3×#67⋊C411yescharacteristic
1070C2#1059426911yescharacteristic
1071C2#1059505611yescharacteristic
1072C2#1059518011yescharacteristic
1073C2#1059528011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63976C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#217C2semidirect
3. C2×#63879C2semidirect
4. #10592643C2semidirect
5. C3×#4956C2semidirect
6. C3×#4955C2semidirect
7. #10591707C2semidirect
8. #10591703C2semidirect
9. #10591385C2semidirect
10. #10591381C2semidirect
11. #10591373C2semidirect
12. #10591368C2semidirect
13. #10591363C2semidirect
14. #10591284C2semidirect
15. #10591281C2semidirect
20. C22×C3×C4×D3C22semidirect
28. C2×#3750C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. #63976C4semidirect
39. C2×#3724C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×Dic32C22semidirect
48. C2×Dic32C22semidirect
50. #63658C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
72. #4956D3semidirect
73. #4955D3semidirect
94. C23×C3×D3C2×C4semidirect
106. C2×C3×#67C2×C4semidirect
120. C2×#625C2×C4semidirect
126. C2×D3×Dic3D4semidirect
129. #3757C2×C4semidirect
145. (C2×D3)⋊Dic3C2×C4semidirect
146. (C2×D3)⋊Dic3C2×C4semidirect
163. C22×C4×D3C2×D3semidirect
202. C2×(C2×D3)⋊C4C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
342. C23×D3C4×D3semidirect
377. C2×#67C4×D3semidirect
907. C32#2321semidirect
1061. C3#73821semidirect
1062. C3#74876semidirect

Maximal subgroups

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

subgroupindex
C2×#639762
C2×D3×#2172
C2×#638792
#105926432
C3×#49562
C3×#49552
#105917072
#105917032
#105913852
#105913812
#105913732
#105913682
#105913632
#105912842
#105912812
#748763
#738213