Finite Group Databasebeta

← #29685732

Subgroups — #29685732

Order 15616.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839896C211yesmaximal, characteristic
2C2×#16839872C211yesmaximal, characteristic, complemented
3C2×C4×#11758199C211yesmaximal, characteristic, complemented
4#21448512C211yesmaximal, characteristic, complemented
5#21446167C211yesmaximal, characteristic, complemented
6#21446167C211yesmaximal, characteristic, complemented
7#21446141C211yesmaximal, characteristic, complemented
8#21446080C211yesmaximal, characteristic, complemented
9#21446066C211yesmaximal, characteristic, complemented
10#21446018C211yesmaximal, characteristic, complemented
11#21445750C211yesmaximal, characteristic, complemented
12#21445644C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic, complemented
14#21445585C211yesmaximal, characteristic, complemented
15C2×C61×#518C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic, complemented
20#16839896C418yescomplemented
21#16839872—24no—
22C4×#11758199—24no—
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519708C2211yescharacteristic, complemented
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic, complemented
32C2×#14519697C2211yescharacteristic, complemented
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519688C2211yescharacteristic, complemented
36C2×C4×#92418C2211yescharacteristic, complemented
37#16839664C2211yescharacteristic, complemented
38#16839662—21no—
39#16839660C2211yescharacteristic, complemented
40#16839652—21no—
41#16839638—21no—
42#16839633—21no—
43#16839622C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51C23×D4×C61C2211yescharacteristic
52C61×#518—24no—
53C61×#518—24no—
54C2×C4×D4×C61—21no—
55C2×C4×D4×C61—21no—
56C2×C4×D4×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C2×C4×D4×C61C2211yescharacteristic
60C2×#117×C61C2211yescharacteristic
61C2×#117×C61C2211yescharacteristic
62C22×C22⋊C4×C61—21no—
63C22×C22⋊C4×C61—21no—
64C22×D244C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C2×#11758199—22no—
71C2×#11758199C2×C414yescomplemented
72C2×#11758199C2×C414yescomplemented
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519751—22no—
78#14519751C2×C414yescomplemented
79C4×D244—22no—
80C4×D244—22no—
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×C4×Dic61—21no—
91#14519710—22no—
92#14519708—22no—
93#14519698—22no—
94#14519698—22no—
95#14519698—22no—
96#14519698—22no—
97#14519698C2×C414yescomplemented
98#14519698C2×C414yescomplemented
99#14519697—22no—
100#14519697—22no—
101C22⋊#92418—22no—
102C22⋊#92418C2×C414yescomplemented
103#14519688—22no—
104C4×#92418—22no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108C25×C61—21no—
109C22×D4×C61—22no—
110C22×D4×C61—22no—
111C22×D4×C61—22no—
112C22×D4×C61—22no—
113C22×D4×C61—21no—
114C22×D4×C61—22no—
115C22×D4×C61C2×C414yescomplemented
116C22×D4×C61C2311yescharacteristic
117C22×D4×C61C2311yescharacteristic
118C23×C4×C61—21no—
119C23×C4×C61—21no—
120C23×C4×C61—21no—
121C23×C4×C61—21no—
122C23×C4×C61C2311yescharacteristic
123C4×D4×C61—28no—
124C4×D4×C61—28no—
125C4×D4×C61—22no—
126C4×D4×C61—22no—
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C4×D4×C61D414yescomplemented
132C4×D4×C61D414yescomplemented
133#117×C61—22no—
134#117×C61—22no—
135#117×C61—22no—
136#117×C61—22no—
137C2×C4⋊C4×C61D411yescharacteristic
138C2×C4⋊C4×C61D411yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C22⋊C4×C61—28no—
142C2×C22⋊C4×C61—28no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61D411yescharacteristic
149C2×C22⋊C4×C61D411yescharacteristic
150C2×C42×C61—21no—
151C2×C42×C61C2311yescharacteristic
152C2×C42×C61C2311yescharacteristic
153C24×C61—24no—
154C24×C61—24no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—24no—
158C24×C61—81no—
159C24×C61—81no—
160C24×C61—81no—
161C24×C61—81no—
162C24×C61C2×D411yescharacteristic
163C23×D61—21no—
164C2×D4×C61—24no—
165C2×D4×C61—24no—
166C2×D4×C61—28no—
167C2×D4×C61—28no—
168C2×D4×C61—28no—
169C2×D4×C61—28no—
170C2×D4×C61—24no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61C22×C412yes—
178C2×D4×C61C22×C412yes—
179C2×D4×C61C2×D412yes—
180C2×D4×C61C2×D412yes—
181C2×D4×C61#4112yes—
182C2×D4×C61#4112yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—24no—
190C22×C4×C61—24no—
191C22×C4×C61—24no—
192C22×C4×C61—24no—
193C22×C4×C61—81no—
194C22×C4×C61—81no—
195C22×C4×C61—81no—
196C22×C4×C61—81no—
197C22×C4×C61—81no—
198C22×C4×C61—81no—
199C22×C4×C61—81no—
200C22×C4×C61—81no—
201C22×C4×C61C22×C412yes—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61#4112yes—
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—24no—
210C2×C22⋊D61—81no—
211C2×C22⋊D61—81no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244C22×C412yes—
221C2×C4×D61—42no—
222C2×C4×D61—81no—
223C2×C4×D61—81no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61C2×D412yes—
229C4⋊C4×C61C2×D412yes—
230C22⋊C4×C61—24no—
231C22⋊C4×C61—24no—
232C22⋊C4×C61—24no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—24no—
236C22⋊C4×C61—24no—
237C42×C61—24no—
238C42×C61—21no—
239C42×C61—21no—
240C42×C61C2×D412yes—
241C42×C61C2×D412yes—
242C22⋊Dic61—81no—
243#11758199—28no—
244#11758199—28no—
245#11758198—24no—
246#11758198—42no—
247#11758198—81no—
248#11758198—81no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61C22×C412yes—
255#11758196—81no—
256C4×Dic61—81no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418C22×C412yes—
268C2×#92418C22×C412yes—
269C23×C61—216no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—21no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—21no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—84no—
291C23×C61—84no—
292C23×C61—84no—
293C23×C61—84no—
294C23×C61—84no—
295C23×C61—84no—
296C23×C61C4×D412yes—
297C23×C61C22×D411yescharacteristic
298C22×D61—22no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305D4×C61—216no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61C4×D414yes—
313D4×C61C4×D414yes—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—84no—
337C2×C4×C61—84no—
338C2×C4×C61—84no—
339C2×C4×C61—84no—
340C2×C4×C61C4×D412yes—
341C2×C4×C61#12012yes—
342C2×C4×C61#12012yes—
343C2×C4×C61C23×C411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C2×#4111yescharacteristic
347C2×C4×C61C2×#4111yescharacteristic
348C2×C4×C61C2×#4111yescharacteristic
349C22⋊D61—84no—
350C2×Dic61—22no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359D244—22no—
360D244—22no—
361D244—41no—
362D244—41no—
363C4×D61—84no—
364#92418—22no—
365#92418—22no—
366#92418—41no—
367#92418—41no—
368#21458—611nomaximal, Sylow
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—24no—
373C22×C61—24no—
374C22×C61—41no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—41no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—41no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—41no—
390C22×C61—816no—
391C22×C61C2×C4×D411yescharacteristic
392C22×C61C2×#12011yescharacteristic
393C22×C61#52511yescharacteristic
394C22×C61#57611yescharacteristic
395C22×C61#57611yescharacteristic
396C22×C61#57611yescharacteristic
397C22×C61#57711yescharacteristic
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61—81no—
404C2×D61—81no—
405C4×C61—22no—
406C4×C61—22no—
407C4×C61—22no—
408C4×C61—41no—
409C4×C61—42no—
410C4×C61—41no—
411C4×C61—42no—
412C4×C61C2×C4×D411yescharacteristic
413C4×C61C2×C4×D411yescharacteristic
414C4×C61#52511yescharacteristic
415C4×C61#52511yescharacteristic
416Dic61—42no—
417Dic61—81no—
418Dic61—81no—
419C2×#518D6111yescharacteristic, complemented
420C2×#447—611no—
421C2×#442—611no—
422C2×C4×D8—611no—
423#2324—611no—
424#1879—611no—
425#1879—611no—
426#1875—611no—
427#1864—611no—
428#1862—611no—
429#1854—611no—
430#1786—611no—
431#1762—611no—
432C4×#102—611no—
433#1750—611no—
434C2×C61—42no—
435C2×C61—44no—
436C2×C61—44no—
437C2×C61C4×#12011yescharacteristic
438C2×C61#294611yescharacteristic
439C2×C61#294811yescharacteristic
440C2×C61#300811yescharacteristic
441C2×C61#301211yescharacteristic
442C2×C61#311811yescharacteristic
443C2×C61#312211yescharacteristic
444D61—82no—
445C23×D4C2×D6111yescharacteristic
446C22×D8—611no—
447C22×D8—611no—
448C2×#121—611no—
449#518—24no—
450#518—24no—
451C2×C4×D4—21no—
452C2×C4×D4—21no—
453C2×C4×D4—611no—
454C2×C4×D4C2×D6111yescharacteristic
455C2×C4×D4C2×D6111yescharacteristic
456C2×C4×D4C2×D6111yescharacteristic
457C2×C4×D4C2×D6111yescharacteristic
458C2×#117C2×D6111yescharacteristic
459C2×#117C2×D6111yescharacteristic
460C22×C22⋊C4—21no—
461C22×C22⋊C4—21no—
462#447—618no—
463#442—1224no—
464C4×D8—1224no—
465C2×#107—611no—
466C2×#106—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×C22⋊C8—611no—
476C2×C22⋊C8—611no—
477C2×#97—611no—
478C2×C4×C8—611no—
479#390—611no—
480#390—1221no—
481#389—611no—
482#388—1221no—
483#386—1221no—
484#385—1221no—
485#380—611no—
486C4×C4⋊C4—611no—
487#340—611no—
488#340—611no—
489#340—611no—
490#340—611no—
491#336—611no—
492#336—611no—
493C61#2145811yescharacteristic, complemented, Sylow
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—611no—
502C22×D4—1221no—
503C22×D4C4×D6114yescomplemented
504C22×D4C22×D6111yescharacteristic
505C22×D4C22×D6111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—1221no—
511C23×C4C22×D6111yescharacteristic
512C2×D8—614no—
513C2×D8—614no—
514C2×D8—1222no—
515C2×D8—1222no—
516C2×D8—1222no—
517C2×D8—1222no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—611no—
521C22×C8—611no—
522#121—614no—
523#121—1222no—
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—1222no—
533C4×D4—1222no—
534C4×D4C22⋊D6114yescomplemented
535C4×D4C22⋊D6114yescomplemented
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4C22⋊D6111yescharacteristic
545C2×C4⋊C4C22⋊D6111yescharacteristic
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—28no—
549C2×C22⋊C4—28no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4C22⋊D6111yescharacteristic
561C2×C22⋊C4C22⋊D6111yescharacteristic
562C2×C42—21no—
563C2×C42—1221no—
564C2×C42C22×D6111yescharacteristic
565C2×C42C22×D6111yescharacteristic
566#107—1222no—
567#106—1222no—
568#102—614no—
569#102—614no—
570#102—1222no—
571#102—1222no—
572#102—1222no—
573#102—1222no—
574#102—1222no—
575#102—1222no—
576C22⋊C8—614no—
577C22⋊C8—1222no—
578#97—1222no—
579C4×C8—1222no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—81no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—1221no—
593C24C2×C22⋊D6111yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—612no—
608C2×D4—1224no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—4881no—
615C2×D4—4881no—
616C2×D4C2×C4×D6112yes—
617C2×D4C2×C4×D6112yes—
618C2×D4#1175822212yes—
619C2×D4#1175822212yes—
620C2×D4C2×C22⋊D6112yes—
621C2×D4C2×C22⋊D6112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—4881no—
644C22×C4—4881no—
645C22×C4—2442no—
646C22×C4C2×C4×D6112yes—
647C22×C4#1175822212yes—
648C22×C4C2×C22⋊D6111yescharacteristic
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C2×C22⋊D6111yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C23×D6111yescharacteristic
654D8—1228no—
655D8—1228no—
656C2×C8—612no—
657C2×C8—612no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—612no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—4881no—
679C4⋊C4C2×C22⋊D6112yes—
680C4⋊C4C2×C22⋊D6112yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—1224no—
689C22⋊C4—4881no—
690C22⋊C4—4881no—
691C22⋊C4—4881no—
692C22⋊C4—2442no—
693C42—24no—
694C42—21no—
695C42—21no—
696C42—4881no—
697C42C2×C22⋊D6112yes—
698C42C2×C22⋊D6112yes—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—1222no—
727C23—2441no—
728C23—2441no—
729C23—2441no—
730C23—2441no—
731C23—2441no—
732C23—2441no—
733C23C4×C22⋊D6112yes—
734C23C22×C22⋊D6111yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—1222no—
743D4—1222no—
744D4—4884no—
745D4—2441no—
746D4—2441no—
747D4C4×C22⋊D6114yes—
748D4C4×C22⋊D6114yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—1222no—
776C2×C4—4884no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4C4×C22⋊D6112yes—
786C2×C4#1451974612yes—
787C2×C4#1451974612yes—
788C2×C4C22×C4×D6111yescharacteristic
789C2×C4C22×C22⋊D6111yescharacteristic
790C2×C4C22×C22⋊D6111yescharacteristic
791C2×C4C2×#1175822211yescharacteristic
792C2×C4C2×#1175822211yescharacteristic
793C2×C4C2×#1175822211yescharacteristic
794C8—1222no—
795C8—1222no—
796C8—2441no—
797C8—2441no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—816no—
820C22—4881no—
821C22—4881no—
822C22—4881no—
823C22—4881no—
824C22—2442no—
825C22—2442no—
826C22—2442no—
827C22C2×C4×C22⋊D6111yescharacteristic
828C22C2×#1451974611yescharacteristic
829C22#1684027311yescharacteristic
830C22#1684056511yescharacteristic
831C22#1684056511yescharacteristic
832C22#1684056511yescharacteristic
833C22#1684057311yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—41no—
838C4—42no—
839C4—41no—
840C4—42no—
841C4—4881no—
842C4—4881no—
843C4—2442no—
844C4C2×C4×C22⋊D6111yescharacteristic
845C4C2×C4×C22⋊D6111yescharacteristic
846C4#1684027311yescharacteristic
847C4#1684027311yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—4882no—
852C2C4×#1451974611yescharacteristic
853C2#2145465111yescharacteristic
854C2#2145466911yescharacteristic
855C2#2145508711yescharacteristic
856C2#2145512311yescharacteristic
857C2#2145600311yescharacteristic
858C2#2145606211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#518C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
cosocleC22×C4×C61C24
hypercenterC2×#518D61
hypocenterC61#21458
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C2×#16839872C2semidirect
3. C2×C4×#11758199C2semidirect
4. #21448512C2semidirect
5. #21446167C2semidirect
6. #21446167C2semidirect
7. #21446141C2semidirect
8. #21446080C2semidirect
9. #21446066C2semidirect
10. #21446018C2semidirect
11. #21445750C2semidirect
12. #21445644C2semidirect
13. C4×#14519698C2semidirect
14. #21445585C2semidirect
15. C2×C61×#518C2semidirect
19. C2×C4×D244C22semidirect
20. #16839896C4semidirect
23. C2×#14519710C22semidirect
24. C2×#14519708C22semidirect
31. C2×#14519697C22semidirect
32. C2×#14519697C22semidirect
35. C2×#14519688C22semidirect
36. C2×C4×#92418C22semidirect
37. #16839664C22semidirect
39. #16839660C22semidirect
44. C4×C4⋊Dic61C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839517C22semidirect
50. #16839517C22semidirect
71. C2×#11758199C2×C4semidirect
72. C2×#11758199C2×C4semidirect
78. #14519751C2×C4semidirect
97. #14519698C2×C4semidirect
98. #14519698C2×C4semidirect
102. C22⋊#92418C2×C4semidirect
115. C22×D4×C61C2×C4semidirect
131. C4×D4×C61D4semidirect
132. C4×D4×C61D4semidirect
419. C2×#518D61semidirect
493. C61#21458semidirect
503. C22×D4C4×D61semidirect
534. C4×D4C22⋊D61semidirect
535. C4×D4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398962
C2×#168398722
C2×C4×#117581992
#214485122
#214461672
#214461412
#214460802
#214460662
#214460182
#214457502
#214456442
C4×#145196982
#214455852
C2×C61×#5182
#2145861