Finite Group Databasebeta

← #11803289

Subgroups — #11803289

Order 1152.

1947 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64146C211yesmaximal, characteristic
2C2×#63974C211yesmaximal, characteristic, complemented
3C2×#63952C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic, complemented
7#10591714C211yesmaximal, characteristic, complemented
8#10591711C211yesmaximal, characteristic, complemented
9#10591704C211yesmaximal, characteristic, complemented
10#10591703C211yesmaximal, characteristic, complemented
11#10591703C211yesmaximal, characteristic, complemented
12#10591378C211yesmaximal, characteristic, complemented
13#10591266C211yesmaximal, characteristic, complemented
14#10591233C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#76429—31nomaximal
17#74876—31nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic, complemented
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26#64146C418yescomplemented
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic, complemented
34C2×C3×#217C2211yescharacteristic, complemented
35C2×C3×#217C2211yescharacteristic, complemented
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38#63974—24no—
39C2×#3724C2211yescharacteristic, complemented
40C2×#3724C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×Dic32C2211yescharacteristic, complemented
48C2×Dic32C2211yescharacteristic, complemented
49#63952—24no—
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×#937—31no—
57C2×#937—31no—
58C2×#937—61no—
59C2×C4×#67—31no—
60C2×#67⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C2×D3×C22⋊C4—31no—
63C3×#390—31no—
64C3×#386—31no—
65#5221D311yescharacteristic, complemented
66#5220D311yescharacteristic, complemented
67#5213—31no—
68#4990—31no—
69#4989—31no—
70#4958—31no—
71#4957—31no—
72#4957—31no—
73#4956—31no—
74#4956—31no—
75#4955—31no—
76#4955—31no—
77#4945—31no—
78#4945—31no—
79#4944—31no—
80#4944—31no—
81#4940—31no—
82C4×(C2×D3)⋊C4—31no—
83#4670—31no—
84#4669—31no—
85#4668—31no—
86#4666—31no—
87C24×C32C2311yescharacteristic
88C24×C32C2311yescharacteristic
89C23×C3⋊D3—22no—
90C23×C3⋊D3—22no—
91C23×C3⋊D3—41no—
92C23×C3⋊D3—41no—
93C23×C3⋊D3—41no—
94C23×C3⋊D3—41no—
95C23×C3⋊D3C2×C414yescomplemented
96C23×C3⋊D3C2311yescharacteristic
97C23×C3⋊D3C2311yescharacteristic
98C2×C32×D4—41no—
99C2×C32×D4—41no—
100C2×C32×D4C2×C414yescomplemented
101C22×C32×C4C2311yescharacteristic
102C2×#638—22no—
103C2×#638—22no—
104C2×#638—41no—
105C2×#638—41no—
106C2×#638C2×C414yes—
107C2×#638C2×C414yescomplemented
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3×Dic3—22no—
111C22×C3×Dic3—41no—
112C22×C3×Dic3—41no—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×#624—22no—
122C2×#624—41no—
123C2×#624—41no—
124C2×#624—41no—
125C2×#624—41no—
126C2×#624D414yescomplemented
127#3757C2×C414yescomplemented
128#3752C2×C414yescomplemented
129#3752C2×C414yescomplemented
130C3×#217—22no—
131C3×#217—22no—
132C3×#217—22no—
133C3×#217—41no—
134C3×#217—41no—
135C3×#217—41no—
136C3×#217—41no—
137C3×C4⋊Dic3—41no—
138C3×C4×Dic3—41no—
139#3724—22no—
140#3724—41no—
141#3722—22no—
142#3722—22no—
143#3722—22no—
144#3722—22no—
145#3722—41no—
146#3722—41no—
147Dic32—22no—
148Dic32—41no—
149#2321—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C24×D3—61no—
153C22×C3×D4—21no—
154C22×C3×D4C2×D311yescharacteristic
155C22×C3×D4C2×D311yescharacteristic
156C23×C3×C4—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—31no—
160C22×#67—31no—
161C22×#67—61no—
162C22×#67—61no—
163C23×Dic3C2×D311yescharacteristic, complemented
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C42—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—61no—
180C2×#217C2×D311yescharacteristic
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183C2×#217C2×D311yescharacteristic
184C2×#217C2×D311yescharacteristic, complemented
185C2×#217C2×D311yescharacteristic, complemented
186C2×#217C2×D311yescharacteristic, complemented
187#937—38no—
188#937—38no—
189#937—68no—
190C4×#67—64no—
191C2×(C2×D3)⋊C4—31no—
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)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—61no—
208C2×(C2×D3)⋊C4—61no—
209C2×C4⋊Dic3C2×D311yescharacteristic, complemented
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218C2×C4×Dic3C2×D311yescharacteristic, complemented
219#67⋊C4—64no—
220D3×C22⋊C4—64no—
221D3×C22⋊C4—64no—
222C3×#95—31no—
223C3×#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95C2×D311yescharacteristic, complemented
233C3⋊#95C2×D311yescharacteristic, complemented
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32C22×C412yes—
247C23×C32C22×C412yes—
248C23×C32C2411yescharacteristic
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—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3—28no—
260C22×C3⋊D3—44no—
261C22×C3⋊D3—44no—
262C22×C3⋊D3—44no—
263C22×C3⋊D3—44no—
264C22×C3⋊D3—44no—
265C22×C3⋊D3—44no—
266C22×C3⋊D3C22×C412yes—
267C22×C3⋊D3C22×C412yes—
268C22×C3⋊D3C2×D412yes—
269C22×C3⋊D3#4112yes—
270C32×D4—44no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C22×C412yes—
274#638—28no—
275#638—44no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3C22×C412yes—
281C2×C3⋊Dic3C22×C412yes—
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—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×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—44no—
305C2×C3×Dic3C2×D412yes—
306C2×C3×Dic3C2×D412yes—
307#624—44no—
308#624—44no—
309C2×#120—91no—
310C2×C4×D4—91no—
311C22×C22⋊C4—91no—
312#390—31no—
313#390—91no—
314#388—91no—
315#388—91no—
316#388—91no—
317#388—91no—
318#386—31no—
319#386—91no—
320#386—91no—
321#385—91no—
322#379—91no—
323C4×C22⋊C4—91no—
324C24×C3—21no—
325C24×C3—21no—
326C24×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C24×C3C22×D311yescharacteristic
329C24×C3C22×D311yescharacteristic
330C23×D3—31no—
331C23×D3—31no—
332C23×D3—31no—
333C23×D3—31no—
334C23×D3—34no—
335C23×D3—34no—
336C23×D3—61no—
337C23×D3—61no—
338C23×D3—64no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—62no—
343C23×D3—122no—
344C23×D3—122no—
345C23×D3—121no—
346C23×D3—121no—
347C23×D3—121no—
348C23×D3—121no—
349C23×D3—121no—
350C23×D3—121no—
351C23×D3—121no—
352C23×D3—121no—
353C23×D3—122no—
354C23×D3—122no—
355C23×D3—122no—
356C23×D3—122no—
357C2×C3×D4—24no—
358C2×C3×D4—41no—
359C2×C3×D4—41no—
360C2×C3×D4—41no—
361C2×C3×D4—41no—
362C2×C3×D4—42no—
363C2×C3×D4—42no—
364C2×C3×D4C4×D314yescomplemented
365C2×C3×D4C4×D314yescomplemented
366C22×C3×C4—21no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—62no—
376C22×C3×C4—121no—
377C22×C3×C4—121no—
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—34no—
383C2×#67—34no—
384C2×#67—64no—
385C2×#67—64no—
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67—122no—
391C2×#67—122no—
392C2×#67—121no—
393C2×#67—121no—
394C2×#67—121no—
395C2×#67—121no—
396C2×#67—122no—
397C2×#67—122no—
398C22×Dic3—22no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—41no—
404C22×Dic3—41no—
405C22×Dic3—61no—
406C22×Dic3—61no—
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—62no—
418C2×C4×D3—62no—
419C2×C4×D3—121no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
422C2×C4×D3—121no—
423C2×C4×D3—121no—
424C2×C4×D3—121no—
425C2×C4×D3—121no—
426C2×C4×D3—121no—
427C3×C4⋊C4—121no—
428C3×C22⋊C4—62no—
429C3×C22⋊C4—62no—
430C3×C22⋊C4—62no—
431C3×C22⋊C4—121no—
432C3×C22⋊C4—121no—
433C3×C22⋊C4—121no—
434C3×C22⋊C4—121no—
435C3×C42—121no—
436#217—22no—
437#217—22no—
438#217—22no—
439#217—34no—
440#217—34no—
441#217—41no—
442#217—41no—
443#217—41no—
444#217—41no—
445#217—64no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—64no—
451(C2×D3)⋊C4—64no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—62no—
456(C2×D3)⋊C4—62no—
457(C2×D3)⋊C4—62no—
458(C2×D3)⋊C4—62no—
459(C2×D3)⋊C4—62no—
460(C2×D3)⋊C4—121no—
461(C2×D3)⋊C4—121no—
462(C2×D3)⋊C4—121no—
463(C2×D3)⋊C4—121no—
464C4⋊Dic3—41no—
465Dic3⋊C4—62no—
466Dic3⋊C4—62no—
467Dic3⋊C4—121no—
468Dic3⋊C4—121no—
469C4×Dic3—41no—
470C4×Dic3—62no—
471C4×Dic3—62no—
472C4×Dic3—121no—
473C4×Dic3—121no—
474C22×C32—22no—
475C22×C32—22no—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32C23×C411yescharacteristic
489C22×C32C22×D411yescharacteristic
490C22×C32C2×#4111yescharacteristic
491C22×C32H(5,𝔽2)11yescharacteristic
492C22×C32H(5,𝔽2)11yescharacteristic
493C22×C32H(5,𝔽2)11yescharacteristic
494C22×C32H(5,𝔽2)11yescharacteristic
495C2×C3⋊D3—22no—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—22no—
504C2×C3⋊D3—416no—
505C2×C3⋊D3—41no—
506C2×C3⋊D3—41no—
507C2×C3⋊D3—41no—
508C2×C3⋊D3—41no—
509C2×C3⋊D3C4×D414yes—
510C32×C4—22no—
511C3⋊Dic3—22no—
512C3⋊Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3—22no—
515C3×Dic3—41no—
516C3×Dic3—41no—
517C3×Dic3—41no—
518C3×Dic3—41no—
519C3×Dic3—41no—
520C3×Dic3—41no—
521C25—91no—
522C22×D4—91no—
523C22×D4—91no—
524C22×D4D3211yescharacteristic
525C23×C4—31no—
526C23×C4—91no—
527C23×C4—91no—
528#120—98no—
529C4×D4—184no—
530C2×C4⋊C4—31no—
531C2×C4⋊C4—91no—
532C2×C4⋊C4—91no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C22⋊C4—91no—
547C2×C22⋊C4—91no—
548C2×C22⋊C4—91no—
549C2×C22⋊C4—184no—
550C2×C42—31no—
551C2×C42—91no—
552C2×C42—91no—
553#95—31no—
554#95—31no—
555#95—91no—
556#95—91no—
557#95—91no—
558#95—91no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—21no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3C2×C4×D312yes—
599C23×C3C2×C4×D312yes—
600C23×C3C2×C4×D312yes—
601C23×C3C2×C4×D312yes—
602C23×C3C23×D311yescharacteristic
603C23×C3C23×D311yescharacteristic
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—32no—
607C22×D3—32no—
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—68no—
617C22×D3—68no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—61no—
629C22×D3—61no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—61no—
635C22×D3—61no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—61no—
640C22×D3—128no—
641C22×D3—121no—
642C22×D3—121no—
643C22×D3—121no—
644C22×D3—121no—
645C22×D3—121no—
646C22×D3—121no—
647C22×D3—121no—
648C22×D3—121no—
649C22×D3—124no—
650C22×D3—124no—
651C22×D3—124no—
652C22×D3—124no—
653C22×D3—128no—
654C22×D3—124no—
655C22×D3—124no—
656C22×D3—124no—
657C22×D3—124no—
658C22×D3—124no—
659C22×D3—124no—
660C22×D3—124no—
661C22×D3—124no—
662C22×D3—128no—
663C22×D3—128no—
664C22×D3—128no—
665C22×D3—128no—
666C22×D3—128no—
667C3×D4—44no—
668C3×D4—44no—
669C3×D4—48no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—22no—
675C2×C3×C4—32no—
676C2×C3×C4—32no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—124no—
702C2×C3×C4C2×C4×D312yes—
703C2×C3×C4C2×C4×D312yes—
704#67—68no—
705#67—68no—
706#67—128no—
707#67—124no—
708#67—124no—
709#67—128no—
710C2×Dic3—21no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—21no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—32no—
733C2×Dic3—32no—
734C2×Dic3—32no—
735C2×Dic3—32no—
736C2×Dic3—44no—
737C2×Dic3—62no—
738C2×Dic3—62no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—121no—
748C2×Dic3—121no—
749C2×Dic3—121no—
750C2×Dic3—121no—
751C2×Dic3D3×D412yes—
752C2×Dic3D3×D412yes—
753C4×D3—124no—
754C4×D3—124no—
755C4×D3—124no—
756C4×D3—124no—
757C2×C32—42no—
758C2×C32—42no—
759C2×C32C2×C4×D411yescharacteristic
760C2×C32#51811yescharacteristic
761C2×C32#51811yescharacteristic
762C2×C32#53411yescharacteristic
763C2×C32#53511yescharacteristic
764C2×C32#53811yescharacteristic
765C2×C32#53811yescharacteristic
766C3⋊D3—24no—
767C3⋊D3—42no—
768C24—91no—
769C24—91no—
770C24—94no—
771C24—182no—
772C24—182no—
773C24—361no—
774C24—361no—
775C24—361no—
776C24—361no—
777C24C2×D3211yescharacteristic
778C24C2×D3211yescharacteristic
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—94no—
782C2×D4—94no—
783C2×D4—182no—
784C2×D4—182no—
785C2×D4—361no—
786C2×D4—361no—
787C2×D4#62414yescomplemented
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—31no—
791C22×C4—31no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—62no—
797C22×C4—94no—
798C22×C4—91no—
799C22×C4—91no—
800C22×C4—121no—
801C22×C4—121no—
802C22×C4—182no—
803C22×C4—361no—
804C22×C4—361no—
805C22×C4—361no—
806C22×C4—361no—
807C22×C4C2×D3211yescharacteristic
808C4⋊C4—121no—
809C4⋊C4—182no—
810C4⋊C4—361no—
811C22⋊C4—62no—
812C22⋊C4—62no—
813C22⋊C4—62no—
814C22⋊C4—94no—
815C22⋊C4—94no—
816C22⋊C4—94no—
817C22⋊C4—121no—
818C22⋊C4—121no—
819C22⋊C4—121no—
820C22⋊C4—121no—
821C22⋊C4—182no—
822C22⋊C4—182no—
823C22⋊C4—182no—
824C22⋊C4—182no—
825C22⋊C4—361no—
826C22⋊C4—361no—
827C42—121no—
828C42—182no—
829C42—361no—
830C22×C3—24no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—41no—
860C22×C3—41no—
861C22×C3—41no—
862C22×C3—41no—
863C22×C3—41no—
864C22×C3—41no—
865C22×C3—41no—
866C22×C3—41no—
867C22×C3—41no—
868C22×C3—41no—
869C22×C3—41no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—41no—
875C22×C3—81no—
876C22×C3—81no—
877C22×C3—81no—
878C22×C3—81no—
879C22×C3C22×C4×D311yescharacteristic
880C22×C3C22×C4×D311yescharacteristic
881C22×C3C2×D3×D411yescharacteristic
882C22×C3C2×D3×D411yescharacteristic
883C22×C3#100411yescharacteristic
884C22×C3#100411yescharacteristic
885C22×C3#100411yescharacteristic
886C22×C3#100411yescharacteristic
887C22×C3#100411yescharacteristic
888C22×C3#100411yescharacteristic
889C22×C3D3×#4111yescharacteristic
890C22×C3D3×#4111yescharacteristic
891C22×C3#100911yescharacteristic
892C22×C3#100911yescharacteristic
893C2×D3—34no—
894C2×D3—34no—
895C2×D3—64no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—62no—
901C2×D3—62no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—62no—
905C2×D3—62no—
906C2×D3—62no—
907C2×D3—62no—
908C2×D3—64no—
909C2×D3—62no—
910C2×D3—62no—
911C2×D3—62no—
912C2×D3—62no—
913C2×D3—62no—
914C2×D3—62no—
915C2×D3—122no—
916C2×D3—122no—
917C2×D3—122no—
918C2×D3—122no—
919C2×D3—122no—
920C2×D3—122no—
921C2×D3—122no—
922C2×D3—122no—
923C2×D3—1216no—
924C2×D3—1216no—
925C2×D3—122no—
926C2×D3—122no—
927C2×D3—122no—
928C2×D3—122no—
929C2×D3—1232no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—121no—
934C2×D3—121no—
935C2×D3—121no—
936C2×D3—121no—
937C2×D3—121no—
938C3×C4—22no—
939C3×C4—22no—
940C3×C4—42no—
941C3×C4—62no—
942C3×C4—62no—
943C3×C4—121no—
944C3×C4—121no—
945C3×C4—121no—
946C3×C4—121no—
947C3×C4—121no—
948C3×C4—121no—
949Dic3—22no—
950Dic3—22no—
951Dic3—41no—
952Dic3—41no—
953Dic3—41no—
954Dic3—41no—
955Dic3—41no—
956Dic3—41no—
957Dic3—62no—
958Dic3—62no—
959Dic3—62no—
960Dic3—62no—
961Dic3—122no—
962Dic3—122no—
963C32#232111yescharacteristic, complemented, Sylow
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—92no—
977C23—92no—
978C23—92no—
979C23—92no—
980C23—188no—
981C23—181no—
982C23—181no—
983C23—181no—
984C23—181no—
985C23—181no—
986C23—181no—
987C23—181no—
988C23—181no—
989C23—181no—
990C23—181no—
991C23—364no—
992C23—364no—
993C23—364no—
994C23—364no—
995C23—364no—
996C23—364no—
997C23C2×#62412yes—
998C23C2×#62412yes—
999C23C22×D3211yescharacteristic
1000D4—44no—
1001D4—188no—
1002D4—364no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—61no—
1012C2×C4—61no—
1013C2×C4—61no—
1014C2×C4—61no—
1015C2×C4—61no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—61no—
1029C2×C4—92no—
1030C2×C4—92no—
1031C2×C4—124no—
1032C2×C4—181no—
1033C2×C4—181no—
1034C2×C4—181no—
1035C2×C4—181no—
1036C2×C4—364no—
1037C2×C4—364no—
1038C2×C4C2×#62412yes—
1039C2×C3—21no—
1040C2×C3—21no—
1041C2×C3—21no—
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—44no—
1047C2×C3—42no—
1048C2×C3—42no—
1049C2×C3—42no—
1050C2×C3—42no—
1051C2×C3—82no—
1052C2×C3#548611yescharacteristic
1053C2×C3#548611yescharacteristic
1054C2×C3C4×D3×D411yescharacteristic
1055C2×C3C4×D3×D411yescharacteristic
1056C2×C3#554511yescharacteristic
1057C2×C3#554511yescharacteristic
1058C2×C3#558911yescharacteristic
1059C2×C3#560511yescharacteristic
1060C2×C3#560711yescharacteristic
1061C2×C3#561311yescharacteristic
1062C2×C3#561311yescharacteristic
1063C2×C3#565711yescharacteristic
1064C2×C3#567811yescharacteristic
1065C2×C3#571511yescharacteristic
1066D3—64no—
1067D3—64no—
1068D3—124no—
1069D3—124no—
1070D3—122no—
1071D3—122no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—41no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—41no—
1084C22—41no—
1085C22—41no—
1086C22—94no—
1087C22—182no—
1088C22—182no—
1089C22—182no—
1090C22—182no—
1091C22—182no—
1092C22—182no—
1093C22—182no—
1094C22—182no—
1095C22—182no—
1096C22—3616no—
1097C22—361no—
1098C22—361no—
1099C22—361no—
1100C22—361no—
1101C22D32×D411yescharacteristic
1102C22#6431211yescharacteristic
1103C22#6431411yescharacteristic
1104C22#6431411yescharacteristic
1105C22C22×#62411yescharacteristic
1106C22#6433011yescharacteristic
1107C22#6433011yescharacteristic
1108C4—22no—
1109C4—62no—
1110C4—62no—
1111C4—121no—
1112C4—121no—
1113C4—121no—
1114C4—121no—
1115C4—121no—
1116C4—121no—
1117C4—182no—
1118C4—182no—
1119C3—21no—
1120C3#7487611yescharacteristic, complemented
1121C3#7642911yescharacteristic, complemented
1122C2—42no—
1123C2—42no—
1124C2—184no—
1125C2—362no—
1126C2D4×#62411yescharacteristic
1127C2#1059520711yescharacteristic
1128C2#1059522311yescharacteristic
1129C2#1059525511yescharacteristic
1130C2#1059528111yescharacteristic
1131C2#1059529911yescharacteristic
1132C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×#64146C2
hypercenterC22×D4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63974C2semidirect
3. C2×#63952C2semidirect
4. C3×#5221C2semidirect
5. C3×#5220C2semidirect
6. #10591722C2semidirect
7. #10591714C2semidirect
8. #10591711C2semidirect
9. #10591704C2semidirect
10. #10591703C2semidirect
11. #10591703C2semidirect
12. #10591378C2semidirect
13. #10591266C2semidirect
14. #10591233C2semidirect
15. #10591202C2semidirect
22. C23×C3×Dic3C22semidirect
26. #64146C4semidirect
33. C2×C3×#217C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×#217C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C2×C3×C4×Dic3C22semidirect
39. C2×#3724C22semidirect
40. C2×#3724C22semidirect
47. C2×Dic32C22semidirect
48. C2×Dic32C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
65. #5221D3semidirect
66. #5220D3semidirect
95. C23×C3⋊D3C2×C4semidirect
100. C2×C32×D4C2×C4semidirect
107. C2×#638C2×C4semidirect
126. C2×#624D4semidirect
127. #3757C2×C4semidirect
128. #3752C2×C4semidirect
129. #3752C2×C4semidirect
163. C23×Dic3C2×D3semidirect
184. C2×#217C2×D3semidirect
185. C2×#217C2×D3semidirect
186. C2×#217C2×D3semidirect
209. C2×C4⋊Dic3C2×D3semidirect
218. C2×C4×Dic3C2×D3semidirect
232. C3⋊#95C2×D3semidirect
233. C3⋊#95C2×D3semidirect
364. C2×C3×D4C4×D3semidirect
365. C2×C3×D4C4×D3semidirect
787. C2×D4#624semidirect
963. C32#2321semidirect
1120. C3#74876semidirect
1121. C3#76429semidirect

Maximal subgroups

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

subgroupindex
C2×#641462
C2×#639742
C2×#639522
C3×#52212
C3×#52202
#105917222
#105917142
#105917112
#105917042
#105917032
#105913782
#105912662
#105912332
#105912022
#764293
#748763