Finite Group Databasebeta

← #29586341

Subgroups — #29586341

Order 15616.

1234 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519691C211yesmaximal, characteristic
2C22×#14519691C211yesmaximal, characteristic
3#21448394C211yesmaximal, characteristic
4#21448172C211yesmaximal, characteristic, complemented
5C2×#16839528C211yesmaximal, characteristic, complemented
6C2×#16839528C211yesmaximal, characteristic, complemented
7C2×C61×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D61C2211yescharacteristic
9C22×C22⋊Dic61C2211yescharacteristic
10C22×C22⋊Dic61C2211yescharacteristic
11C22×C22⋊Dic61C2211yescharacteristic
12C2×#14519691—22no—
13C2×#14519691—22no—
14C2×#14519691—22no—
15C2×#14519691—22no—
16C2×#14519691C414yescomplemented
17C2×#14519691C414yescomplemented
18#16839641—22no—
19#16839639—22no—
20#16839623C412yescomplemented
21#16839617C412yescomplemented
22C22⋊C4×Dic61—22no—
23C22⋊C4×Dic61—22no—
24C4×C22⋊Dic61—22no—
25#16839528—22no—
26#16839528—22no—
27C22×C22⋊C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2211yescharacteristic
30C61×#342—22no—
31C24×D61C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61—21no—
34C22×C22⋊D61—21no—
35C22×C22⋊D61—21no—
36C22×C22⋊D61—21no—
37C22×C22⋊D61—21no—
38C22×C22⋊D61—21no—
39C22×C22⋊D61—21no—
40C22×C22⋊D61—21no—
41C22×C22⋊D61—21no—
42C22×C22⋊D61—21no—
43C22×C22⋊D61—21no—
44C22×C22⋊D61C2×C412yes—
45C22×C22⋊D61C2×C412yes—
46C23×Dic61—21no—
47C23×Dic61—21no—
48C23×Dic61C2×C411yescharacteristic
49C23×Dic61D412yes—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—21no—
52C2×C22⋊Dic61—21no—
53C2×C22⋊Dic61—21no—
54C2×C22⋊Dic61—21no—
55C2×C22⋊Dic61—21no—
56C2×C22⋊Dic61—21no—
57C2×C22⋊Dic61—21no—
58C2×C22⋊Dic61—21no—
59C2×C22⋊Dic61—21no—
60C2×C22⋊Dic61—21no—
61C2×C22⋊Dic61—21no—
62C2×C22⋊Dic61C2×C412yes—
63C2×C22⋊Dic61C2×C412yes—
64C2×C22⋊Dic61C2×C412yes—
65C2×C22⋊Dic61D412yes—
66C2×C22⋊Dic61D412yes—
67C2×C22⋊Dic61D412yes—
68C2×#11758198—24no—
69C2×C4×Dic61—24no—
70#14519691—28no—
71#14519691—28no—
72#14519684—24no—
73#14519684—24no—
74C25×C61C2311yescharacteristic
75C23×C4×C61—21no—
76C23×C4×C61—21no—
77C23×C4×C61—21no—
78C2×C22⋊C4×C61—21no—
79C2×C22⋊C4×C61—21no—
80C2×C22⋊C4×C61—21no—
81C2×C22⋊C4×C61—21no—
82C2×C22⋊C4×C61—21no—
83C2×C22⋊C4×C61—21no—
84C2×C22⋊C4×C61—21no—
85C2×C22⋊C4×C61—21no—
86C2×C22⋊C4×C61—21no—
87C2×C22⋊C4×C61—21no—
88C2×C22⋊C4×C61—21no—
89C2×C22⋊C4×C61—21no—
90C2×C22⋊C4×C61—21no—
91C2×C22⋊C4×C61C2×C412yes—
92C2×C22⋊C4×C61C2×C412yes—
93C2×C22⋊C4×C61C2×C412yes—
94C2×C22⋊C4×C61D412yes—
95C2×C22⋊C4×C61D412yes—
96C24×C61—82no—
97C24×C61C22×C411yescharacteristic
98C24×C61C22×C411yescharacteristic
99C24×C61C22×C411yescharacteristic
100C24×C61C2×D411yescharacteristic
101C24×C61C2×D411yescharacteristic
102C24×C61C2×D411yescharacteristic
103C24×C61C2×D411yescharacteristic
104C24×C61C2×D411yescharacteristic
105C24×C61C2×D411yescharacteristic
106C24×C61#4111yescharacteristic
107C24×C61#4111yescharacteristic
108C24×C61#4111yescharacteristic
109C24×C61#4111yescharacteristic
110C24×C61#4111yescharacteristic
111C24×C61#4111yescharacteristic
112C23×D61—21no—
113C23×D61—21no—
114C23×D61—21no—
115C23×D61—21no—
116C23×D61—21no—
117C23×D61—21no—
118C23×D61—82no—
119C23×D61C4212yescomplemented
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—41no—
126C22×C4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61—41no—
129C22×C4×C61—82no—
130C22×C4×C61—82no—
131C22×C4×C61—82no—
132C2×C22⋊D61—22no—
133C2×C22⋊D61—22no—
134C2×C22⋊D61—22no—
135C2×C22⋊D61—22no—
136C2×C22⋊D61—22no—
137C2×C22⋊D61—22no—
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—41no—
145C2×C22⋊D61—41no—
146C2×C22⋊D61—41no—
147C2×C22⋊D61—41no—
148C2×C22⋊D61—41no—
149C2×C22⋊D61—41no—
150C2×C22⋊D61—41no—
151C2×C22⋊D61—41no—
152C2×C22⋊D61—41no—
153C2×C22⋊D61—41no—
154C2×C22⋊D61—41no—
155C2×C22⋊D61—41no—
156C2×C22⋊D61—41no—
157C2×C22⋊D61—41no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—41no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—41no—
173C22×Dic61—41no—
174C22×Dic61—82no—
175C22×Dic61—82no—
176C22×Dic61—82no—
177C22×Dic61C4212yescomplemented
178C22×Dic61C22⋊C414yes—
179C22⋊C4×C61—22no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—22no—
186C22⋊C4×C61—41no—
187C22⋊C4×C61—41no—
188C22⋊C4×C61—41no—
189C22⋊C4×C61—41no—
190C22⋊C4×C61C22⋊C414yescomplemented
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—22no—
197C22⋊Dic61—22no—
198C22⋊Dic61—22no—
199C22⋊Dic61—22no—
200C22⋊Dic61—41no—
201C22⋊Dic61—41no—
202C22⋊Dic61C22⋊C414yescomplemented
203#11758198—84no—
204C4×Dic61—84no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—42no—
210C23×C61—42no—
211C23×C61—42no—
212C23×C61—81no—
213C23×C61—81no—
214C23×C61—81no—
215C23×C61—81no—
216C23×C61—81no—
217C23×C61—81no—
218C23×C61—81no—
219C23×C61—81no—
220C23×C61C2×C4211yescharacteristic
221C23×C61C2×C22⋊C411yescharacteristic
222C23×C61C2×C22⋊C411yescharacteristic
223C23×C61C2×C22⋊C411yescharacteristic
224C23×C61#11711yescharacteristic
225C23×C61#11711yescharacteristic
226C23×C61#11711yescharacteristic
227C23×C61C4×D411yescharacteristic
228C23×C61C4×D411yescharacteristic
229C23×C61C4×D411yescharacteristic
230C23×C61C4×D411yescharacteristic
231C23×C61C4×D411yescharacteristic
232C23×C61C4×D411yescharacteristic
233C23×C61C4×D411yescharacteristic
234C23×C61C4×D411yescharacteristic
235C23×C61C4×D411yescharacteristic
236C23×C61C4×D411yescharacteristic
237C23×C61C4×D411yescharacteristic
238C23×C61C4×D411yescharacteristic
239C23×C61#12011yescharacteristic
240C23×C61#12111yescharacteristic
241C23×C61#12111yescharacteristic
242C23×C61#12111yescharacteristic
243C23×C61#12111yescharacteristic
244C23×C61#12111yescharacteristic
245C23×C61#12111yescharacteristic
246C23×C61#12311yescharacteristic
247C23×C61#12311yescharacteristic
248C23×C61#12311yescharacteristic
249C23×C61#12411yescharacteristic
250C23×C61#12411yescharacteristic
251C23×C61#12411yescharacteristic
252C23×C61#12611yescharacteristic
253C23×C61#12611yescharacteristic
254C23×C61#12711yescharacteristic
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—44no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—82no—
264C22×D61—82no—
265C22×D61—82no—
266C22×D61—82no—
267C22×D61—82no—
268C22×D61—82no—
269C2×C4×C61—24no—
270C2×C4×C61—44no—
271C2×C4×C61—44no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—82no—
275C2×C4×C61—82no—
276C2×C4×C61—82no—
277C2×C4×C61—82no—
278C2×C4×C61—82no—
279C2×C4×C61—82no—
280C2×C4×C61—82no—
281C22⋊D61—42no—
282C22⋊D61—42no—
283C22⋊D61—42no—
284C22⋊D61—42no—
285C22⋊D61—42no—
286C22⋊D61—42no—
287C22⋊D61—42no—
288C22⋊D61—42no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—24no—
293C2×Dic61—24no—
294C2×Dic61—44no—
295C2×Dic61—44no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—44no—
301C2×Dic61—42no—
302C2×Dic61—82no—
303C2×Dic61—82no—
304C2×Dic61—82no—
305C2×Dic61—82no—
306C2×Dic61—82no—
307C2×Dic61—82no—
308#10938—611nomaximal, Sylow
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61C4×C22⋊C411yescharacteristic
345C22×C61C4×C22⋊C411yescharacteristic
346C22×C61C4×C22⋊C411yescharacteristic
347C22×C61#38611yescharacteristic
348C22×C61#38611yescharacteristic
349C22×C61#38611yescharacteristic
350C22×C61#38811yescharacteristic
351C22×C61#38811yescharacteristic
352C22×C61#38811yescharacteristic
353C22×C61#38811yescharacteristic
354C22×C61#38811yescharacteristic
355C22×C61#38811yescharacteristic
356C22×C61#39011yescharacteristic
357C22×C61#39011yescharacteristic
358C22×C61#39011yescharacteristic
359C2×D61—44no—
360C2×D61—42no—
361C2×D61—82no—
362C2×D61—82no—
363C2×D61—82no—
364C2×D61—82no—
365C2×D61—82no—
366C2×D61—82no—
367C4×C61—44no—
368C4×C61—82no—
369C4×C61—82no—
370Dic61—44no—
371Dic61—44no—
372Dic61—42no—
373Dic61—82no—
374C22×#99—611no—
375C22×#99—611no—
376#2308—611no—
377#2273—611no—
378C2×#342—611no—
379C2×#342—611no—
380C2×#342D6111yescharacteristic, complemented
381C2×C61—21no—
382C2×C61—21no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—21no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—21no—
391C2×C61—21no—
392C2×C61—21no—
393C2×C61—21no—
394C2×C61—21no—
395C2×C61#143711yescharacteristic
396C2×C61#191312yes—
397D61—82no—
398C23×D4—611no—
399C22×C22⋊C4—611no—
400C22×C22⋊C4—611no—
401C22×C22⋊C4—611no—
402C22×C22⋊C4C2×D6111yescharacteristic
403C22×C22⋊C4C2×D6111yescharacteristic
404C22×C22⋊C4C2×D6111yescharacteristic
405C2×#99—614no—
406C2×#99—614no—
407C2×#99—1222no—
408C2×#99—1222no—
409C2×#99—1222no—
410C2×#99—1222no—
411#386—1222no—
412#386—1222no—
413#381—612no—
414#379—612no—
415C4×C22⋊C4—1222no—
416C4×C22⋊C4—1222no—
417C4×C22⋊C4—1222no—
418#342—22no—
419#342—1222no—
420#342—1222no—
421C61#1093811yescharacteristic, complemented, Sylow
422C25—611no—
423C25C22×D6111yescharacteristic
424C22×D4—612no—
425C22×D4—612no—
426C22×D4—1221no—
427C22×D4—1221no—
428C22×D4—1221no—
429C22×D4—1221no—
430C22×D4—1221no—
431C22×D4—1221no—
432C22×D4—1221no—
433C22×D4—1221no—
434C22×D4—1221no—
435C22×D4—1221no—
436C22×D4—1221no—
437C22×D4—1221no—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—611no—
442C23×C4—612no—
443C23×C4—1221no—
444C23×C4—1221no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—612no—
459C2×C22⋊C4—612no—
460C2×C22⋊C4—612no—
461C2×C22⋊C4—612no—
462C2×C22⋊C4—612no—
463C2×C22⋊C4—612no—
464C2×C22⋊C4—1221no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4—1221no—
468C2×C22⋊C4—1221no—
469C2×C22⋊C4—1221no—
470C2×C22⋊C4—1221no—
471C2×C22⋊C4—1221no—
472C2×C22⋊C4—1221no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1224no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4C4×D6112yes—
478C2×C22⋊C4C4×D6112yes—
479C2×C22⋊C4C4×D6112yes—
480C2×C22⋊C4D24412yes—
481C2×C22⋊C4C22⋊D6112yes—
482C2×C42—1224no—
483#99—1228no—
484#99—1228no—
485#95—1224no—
486#95—1224no—
487C24—82no—
488C24—612no—
489C24—1221no—
490C24—1221no—
491C24—1221no—
492C24—1221no—
493C24—1221no—
494C24—1221no—
495C24—4882no—
496C24C2×C4×D6111yescharacteristic
497C24C2×C4×D6111yescharacteristic
498C24C2×C4×D6111yescharacteristic
499C24C2×D24411yescharacteristic
500C24#1175822211yescharacteristic
501C24#1175822211yescharacteristic
502C24D4×D6111yescharacteristic
503C24D4×D6111yescharacteristic
504C24D4×D6111yescharacteristic
505C24D4×D6111yescharacteristic
506C24#1175822411yescharacteristic
507C24#1175822411yescharacteristic
508C24#1175822611yescharacteristic
509C24#1175822611yescharacteristic
510C24C2×C22⋊D6111yescharacteristic
511C2×D4—1222no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—1222no—
518C2×D4—1222no—
519C2×D4—1222no—
520C2×D4—1222no—
521C2×D4—1222no—
522C2×D4—1222no—
523C2×D4—2441no—
524C2×D4—2441no—
525C2×D4—2441no—
526C2×D4—2441no—
527C2×D4—2441no—
528C2×D4—2441no—
529C2×D4—2441no—
530C2×D4—2441no—
531C2×D4—2441no—
532C2×D4—2441no—
533C2×D4—2441no—
534C2×D4—2441no—
535C2×D4—2441no—
536C2×D4—2441no—
537C2×D4—2441no—
538C2×D4—2441no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4—612no—
552C22×C4—614no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—4882no—
566C22×C4—4882no—
567C22×C4—4882no—
568C22×C4—2441no—
569C22×C4—2441no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—614no—
582C22⋊C4—1222no—
583C22⋊C4—1222no—
584C22⋊C4—1222no—
585C22⋊C4—1222no—
586C22⋊C4—1222no—
587C22⋊C4—1222no—
588C22⋊C4—1222no—
589C22⋊C4—1222no—
590C22⋊C4—1222no—
591C22⋊C4—4884no—
592C22⋊C4—2441no—
593C22⋊C4—2441no—
594C22⋊C4#1175819814yescomplemented
595C42—4884no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—81no—
604C23—81no—
605C23—81no—
606C23—81no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—1222no—
612C23—1222no—
613C23—1222no—
614C23—4882no—
615C23—4882no—
616C23—4882no—
617C23—4882no—
618C23—4882no—
619C23—4882no—
620C23—2444no—
621C23—2441no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23C42×D6111yescharacteristic
626C23C22⋊C4×D6111yescharacteristic
627C23C22⋊C4×D6111yescharacteristic
628C23C2×#1175819811yescharacteristic
629C23#1451973411yescharacteristic
630C23#1451973511yescharacteristic
631C23#1451973511yescharacteristic
632C23#1451973711yescharacteristic
633C23#1451973711yescharacteristic
634C23#1451973711yescharacteristic
635C23#1451973711yescharacteristic
636C23C4×C22⋊D6111yescharacteristic
637C23C4×C22⋊D6111yescharacteristic
638C23#1451973911yescharacteristic
639C23#1451973911yescharacteristic
640C23#1451973911yescharacteristic
641C23#1451973911yescharacteristic
642C23C4×D24411yescharacteristic
643C23C4×D24411yescharacteristic
644C23#1451974711yescharacteristic
645C23#1451974911yescharacteristic
646C23#1451974911yescharacteristic
647C23#1451975011yescharacteristic
648C23#1451975011yescharacteristic
649C23#1451975211yescharacteristic
650C23#1451975211yescharacteristic
651C23#1451976111yescharacteristic
652C23#1451976211yescharacteristic
653C23#1451976211yescharacteristic
654C23#1451976311yescharacteristic
655C23#1451976311yescharacteristic
656C23#1451976611yescharacteristic
657C23#1451977211yescharacteristic
658C23#1451977211yescharacteristic
659C23#1451977311yescharacteristic
660D4—2442no—
661D4—2442no—
662D4—2442no—
663D4—2442no—
664D4—2442no—
665D4—2442no—
666D4—2442no—
667D4—2442no—
668C2×C4—24no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—82no—
674C2×C4—82no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1224no—
684C2×C4—1224no—
685C2×C4—4882no—
686C2×C4—4882no—
687C2×C4—4882no—
688C2×C4—4882no—
689C2×C4—4882no—
690C2×C4—4882no—
691C2×C4—2442no—
692C2×C4—2444no—
693C2×C4—2444no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2444no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—4882no—
735C22—4882no—
736C22—4882no—
737C22—4882no—
738C22—4882no—
739C22—4882no—
740C22—2444no—
741C22—2442no—
742C22#1683960911yescharacteristic
743C22#1683960911yescharacteristic
744C22C4×#1175819811yescharacteristic
745C22#1683963911yescharacteristic
746C22#1683964011yescharacteristic
747C22#1683964011yescharacteristic
748C22#1683965111yescharacteristic
749C22#1683965111yescharacteristic
750C22#1683965211yescharacteristic
751C22#1683965211yescharacteristic
752C22#1683965411yescharacteristic
753C22#1683965411yescharacteristic
754C22#1683966211yescharacteristic
755C22#1683966211yescharacteristic
756C22#1683966311yescharacteristic
757C4—44no—
758C4—82no—
759C4—82no—
760C4—4882no—
761C4—2444no—
762C4—2442no—
763C4—2444no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—4882no—
779C2#2144405511yescharacteristic
780C2#2144636012yes—
subgroupG/H
centerC22#16839640
commutatorC23×C61C2×C42
FrattiniC25C22×D61
FittingC2×C61×#342C2
socleC22×C61#386
prime radicalC23×C22⋊D61C22
cosocleC25×C61C23
hypercenterC2×#342D61
hypocenterC61#10938
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. #21448172C2semidirect
5. C2×#16839528C2semidirect
6. C2×#16839528C2semidirect
7. C2×C61×#342C2semidirect
16. C2×#14519691C4semidirect
17. C2×#14519691C4semidirect
20. #16839623C4semidirect
21. #16839617C4semidirect
119. C23×D61C42semidirect
177. C22×Dic61C42semidirect
190. C22⋊C4×C61C22⋊C4semidirect
202. C22⋊Dic61C22⋊C4semidirect
380. C2×#342D61semidirect
421. C61#10938semidirect
594. C22⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145196912
#214483942
#214481722
C2×#168395282
C2×C61×#3422
#1093861