Finite Group Databasebeta

← #29585399

Subgroups — #29585399

Order 15616.

1522 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840235C211yesmaximal, characteristic
2C22×#14519691C211yesmaximal, characteristic
3#21448394C211yesmaximal, characteristic
4C2×#16839528C211yesmaximal, characteristic, complemented
5C2×#16839528C211yesmaximal, characteristic, complemented
6C2×#16839528C211yesmaximal, characteristic, complemented
7C2×C61×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D61C2211yescharacteristic
9#16840235—22no—
10#16840235—22no—
11#16840235—22no—
12#16840235C414yescomplemented
13C2×C4×C22⋊D61—22no—
14C2×#14519737—22no—
15C2×#14519733—21no—
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C22⋊Dic61C2211yescharacteristic
18C22×C22⋊Dic61C2211yescharacteristic
19C2×C22⋊C4×D61—21no—
20C2×#14519691—22no—
21C2×#14519691—22no—
22C2×#14519691C414yescomplemented
23#16839641—22no—
24#16839639C414yescomplemented
25#16839623—21no—
26#16839617—21no—
27#16839528—22no—
28#16839528—22no—
29#16839528—22no—
30C22×C22⋊C4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic
32C22×C22⋊C4×C61C2211yescharacteristic
33C61×#342—22no—
34C24×D61D411yescharacteristic
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⋊D61C2×C412yes—
44C22×C22⋊D61C2×C412yes—
45C22×C22⋊D61C2×C412yes—
46C22×C22⋊D61D412yes—
47C22×C22⋊D61D412yes—
48C22×C22⋊D61Q812yes—
49C23×Dic61—21no—
50C23×Dic61—21no—
51C23×Dic61C2×C412yescomplemented
52C23×Dic61D411yescharacteristic
53C22×C4×D61—22no—
54C4×C22⋊D61—28no—
55C4×C22⋊D61—28no—
56#14519737—28no—
57#14519737—28no—
58#14519733—24no—
59#14519733—24no—
60C2×#11758196—22no—
61C2×C22⋊Dic61—21no—
62C2×C22⋊Dic61—21no—
63C2×C22⋊Dic61—21no—
64C2×C22⋊Dic61—21no—
65C2×C22⋊Dic61—21no—
66C2×C22⋊Dic61—21no—
67C2×C22⋊Dic61—21no—
68C2×C22⋊Dic61—21no—
69C2×C22⋊Dic61—21no—
70C2×C22⋊Dic61—21no—
71C2×C22⋊Dic61—21no—
72C2×C22⋊Dic61—21no—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61C2×C412yes—
76C2×C22⋊Dic61C2×C412yescomplemented
77C2×C22⋊Dic61D412yes—
78C2×C22⋊Dic61D412yes—
79C2×#11758198—22no—
80C2×#11758198—24no—
81C22⋊C4×D61—24no—
82C22⋊C4×D61—24no—
83C2×C4×Dic61—22no—
84#14519691—28no—
85#14519684—24no—
86C25×C61C2311yescharacteristic
87C23×C4×C61—21no—
88C23×C4×C61—21no—
89C23×C4×C61—21no—
90C2×C22⋊C4×C61—21no—
91C2×C22⋊C4×C61—21no—
92C2×C22⋊C4×C61—21no—
93C2×C22⋊C4×C61—21no—
94C2×C22⋊C4×C61—21no—
95C2×C22⋊C4×C61—21no—
96C2×C22⋊C4×C61—21no—
97C2×C22⋊C4×C61—21no—
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61C2×C412yes—
104C2×C22⋊C4×C61C2×C412yescomplemented
105C2×C22⋊C4×C61C2×C412yescomplemented
106C2×C22⋊C4×C61D412yes—
107C2×C22⋊C4×C61D412yes—
108C24×C61—82no—
109C24×C61C22×C411yescharacteristic
110C24×C61C22×C411yescharacteristic
111C24×C61C22×C411yescharacteristic
112C24×C61C2×D411yescharacteristic
113C24×C61C2×D411yescharacteristic
114C24×C61C2×D411yescharacteristic
115C24×C61C2×D411yescharacteristic
116C24×C61C2×D411yescharacteristic
117C24×C61C2×D411yescharacteristic
118C24×C61C2×D411yescharacteristic
119C24×C61C2×Q811yescharacteristic
120C24×C61#4111yescharacteristic
121C24×C61#4111yescharacteristic
122C24×C61#4111yescharacteristic
123C24×C61#4111yescharacteristic
124C23×D61—21no—
125C23×D61—21no—
126C23×D61—21no—
127C23×D61—21no—
128C23×D61—82no—
129C23×D61C22⋊C412yes—
130C23×D61C22⋊C412yes—
131C23×D61C4⋊C412yes—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—41no—
138C22×C4×C61—41no—
139C22×C4×C61—41no—
140C22×C4×C61—41no—
141C22×C4×C61—82no—
142C22×C4×C61—82no—
143C22×C4×C61—82no—
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61C4214yes—
169C2×C22⋊D61C22⋊C414yes—
170C2×C22⋊D61C4⋊C414yes—
171C2×C22⋊D61C4⋊C414yes—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—41no—
184C22×Dic61—41no—
185C22×Dic61—82no—
186C22×Dic61—82no—
187C22×Dic61—82no—
188C22×Dic61C22⋊C412yes—
189C22×Dic61C22⋊C412yes—
190C22×Dic61C4⋊C412yes—
191C2×C4×D61—28no—
192C2×C4×D61—84no—
193C22⋊C4×C61—22no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—22no—
196C22⋊C4×C61—22no—
197C22⋊C4×C61—22no—
198C22⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—41no—
201C22⋊C4×C61—41no—
202C22⋊C4×C61—41no—
203C22⋊C4×C61—41no—
204C22⋊C4×C61C22⋊C414yescomplemented
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209C22⋊Dic61—22no—
210C22⋊Dic61—41no—
211C22⋊Dic61—41no—
212C22⋊Dic61—41no—
213C22⋊Dic61—41no—
214C22⋊Dic61—41no—
215C22⋊Dic61—41no—
216C22⋊Dic61C22⋊C414yescomplemented
217#11758198—28no—
218#11758198—84no—
219#11758196—28no—
220C4×Dic61—28no—
221C23×C61—42no—
222C23×C61—42no—
223C23×C61—42no—
224C23×C61—42no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61—81no—
229C23×C61—81no—
230C23×C61—81no—
231C23×C61—81no—
232C23×C61—81no—
233C23×C61—81no—
234C23×C61—81no—
235C23×C61—81no—
236C23×C61C2×C4211yescharacteristic
237C23×C61C2×C22⋊C411yescharacteristic
238C23×C61C2×C22⋊C411yescharacteristic
239C23×C61C2×C22⋊C411yescharacteristic
240C23×C61C2×C22⋊C411yescharacteristic
241C23×C61C2×C22⋊C411yescharacteristic
242C23×C61C2×C4⋊C411yescharacteristic
243C23×C61C2×C4⋊C411yescharacteristic
244C23×C61C2×C4⋊C411yescharacteristic
245C23×C61#11711yescharacteristic
246C23×C61#11711yescharacteristic
247C23×C61C4×D411yescharacteristic
248C23×C61C4×D411yescharacteristic
249C23×C61C4×D411yescharacteristic
250C23×C61C4×D411yescharacteristic
251C23×C61C4×D411yescharacteristic
252C23×C61C4×D411yescharacteristic
253C23×C61C4×D411yescharacteristic
254C23×C61C4×D411yescharacteristic
255C23×C61#12011yescharacteristic
256C23×C61#12011yescharacteristic
257C23×C61#12011yescharacteristic
258C23×C61#12011yescharacteristic
259C23×C61#12111yescharacteristic
260C23×C61#12111yescharacteristic
261C23×C61#12111yescharacteristic
262C23×C61#12111yescharacteristic
263C23×C61C22⋊Q811yescharacteristic
264C23×C61C22⋊Q811yescharacteristic
265C23×C61C22⋊Q811yescharacteristic
266C23×C61C22⋊Q811yescharacteristic
267C23×C61#12311yescharacteristic
268C23×C61#12311yescharacteristic
269C23×C61#12311yescharacteristic
270C23×C61#12311yescharacteristic
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—44no—
278C22×D61—44no—
279C22×D61—82no—
280C22×D61—82no—
281C22×D61—82no—
282C22×D61—82no—
283C22×D61—82no—
284C22×D61#9514yes—
285C2×C4×C61—24no—
286C2×C4×C61—44no—
287C2×C4×C61—44no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—82no—
291C2×C4×C61—82no—
292C2×C4×C61—82no—
293C2×C4×C61—82no—
294C2×C4×C61—82no—
295C2×C4×C61—82no—
296C2×C4×C61—82no—
297C22⋊D61—24no—
298C22⋊D61—24no—
299C22⋊D61—24no—
300C22⋊D61—24no—
301C22⋊D61—24no—
302C22⋊D61—24no—
303C22⋊D61—24no—
304C22⋊D61—24no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—24no—
312C2×Dic61—44no—
313C2×Dic61—44no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—82no—
317C2×Dic61—82no—
318C2×Dic61—82no—
319C2×Dic61—82no—
320C2×Dic61—82no—
321C2×Dic61—82no—
322C2×Dic61—82no—
323C2×Dic61#9514yes—
324C4×D61—88no—
325#10754—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
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×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61C2×#9511yescharacteristic
362C22×C61C4×C22⋊C411yescharacteristic
363C22×C61C4×C22⋊C411yescharacteristic
364C22×C61#37911yescharacteristic
365C22×C61#38011yescharacteristic
366C22×C61#38011yescharacteristic
367C22×C61#38111yescharacteristic
368C22×C61#38511yescharacteristic
369C22×C61#38511yescharacteristic
370C22×C61#38511yescharacteristic
371C22×C61#38511yescharacteristic
372C22×C61#38611yescharacteristic
373C22×C61#38611yescharacteristic
374C22×C61#38611yescharacteristic
375C22×C61#38611yescharacteristic
376C2×D61—24no—
377C2×D61—44no—
378C2×D61—44no—
379C2×D61—44no—
380C2×D61—44no—
381C2×D61—82no—
382C2×D61—82no—
383C2×D61—82no—
384C4×C61—44no—
385C4×C61—82no—
386C4×C61—82no—
387Dic61—24no—
388Dic61—44no—
389Dic61—82no—
390Dic61—82no—
391C2×#518—611no—
392C22×#99—611no—
393#2308—611no—
394C2×#342—611no—
395C2×#342—611no—
396C2×#342—611no—
397C2×#342D6111yescharacteristic, complemented
398C2×C61—21no—
399C2×C61—21no—
400C2×C61—21no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—21no—
404C2×C61—21no—
405C2×C61—21no—
406C2×C61—21no—
407C2×C61—21no—
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61C22⋊#9511yescharacteristic
413C2×C61#191312yes—
414D61—44no—
415C23×D4—611no—
416#518—614no—
417#518—1222no—
418#518—1222no—
419#518—1222no—
420C2×C4×D4—1222no—
421C2×C4×D4—1222no—
422C2×#117—1221no—
423C22×C22⋊C4—611no—
424C22×C22⋊C4—611no—
425C22×C22⋊C4—611no—
426C22×C22⋊C4—1221no—
427C22×C22⋊C4C2×D6111yescharacteristic
428C22×C22⋊C4C2×D6111yescharacteristic
429C22×C22⋊C4C2×D6111yescharacteristic
430C2×#99—614no—
431C2×#99—1222no—
432C2×#99—1222no—
433#386—614no—
434#386—1222no—
435#381—1221no—
436#379—1221no—
437#342—22no—
438#342—1222no—
439#342—1222no—
440#342—1222no—
441C61#1075411yescharacteristic, complemented, Sylow
442C25—611no—
443C25C22×D6111yescharacteristic
444C22×D4—612no—
445C22×D4—612no—
446C22×D4—612no—
447C22×D4—612no—
448C22×D4—612no—
449C22×D4—612no—
450C22×D4—1221no—
451C22×D4—1221no—
452C22×D4—1221no—
453C22×D4—1221no—
454C22×D4—1221no—
455C22×D4—1221no—
456C22×D4—1221no—
457C22×D4—1221no—
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—611no—
462C23×C4—612no—
463C23×C4—1222no—
464C23×C4—1221no—
465C23×C4—1221no—
466C4×D4—1228no—
467C4×D4—1228no—
468C4×D4—1228no—
469C4×D4—1228no—
470#117—1224no—
471#117—1224no—
472C2×C4⋊C4—1222no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—612no—
487C2×C22⋊C4—612no—
488C2×C22⋊C4—612no—
489C2×C22⋊C4—612no—
490C2×C22⋊C4—1224no—
491C2×C22⋊C4—1224no—
492C2×C22⋊C4—1222no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4C4×D6112yes—
509C2×C22⋊C4C4×D6112yescomplemented
510C2×C22⋊C4C4×D6112yescomplemented
511C2×C22⋊C4D24412yes—
512C2×C22⋊C4C22⋊D6112yes—
513C2×C42—1222no—
514#99—1228no—
515#95—1224no—
516C24—82no—
517C24—612no—
518C24—612no—
519C24—612no—
520C24—1221no—
521C24—1221no—
522C24—1221no—
523C24—1221no—
524C24—4882no—
525C24C2×C4×D6111yescharacteristic
526C24C2×C4×D6111yescharacteristic
527C24C2×C4×D6111yescharacteristic
528C24C2×D24411yescharacteristic
529C24#1175822211yescharacteristic
530C24#1175822211yescharacteristic
531C24D4×D6111yescharacteristic
532C24D4×D6111yescharacteristic
533C24D4×D6111yescharacteristic
534C24D4×D6111yescharacteristic
535C24D4×D6111yescharacteristic
536C24#1175822411yescharacteristic
537C24Q8×D6111yescharacteristic
538C24#1175822611yescharacteristic
539C24C2×C22⋊D6111yescharacteristic
540C2×D4—614no—
541C2×D4—614no—
542C2×D4—614no—
543C2×D4—614no—
544C2×D4—1222no—
545C2×D4—1222no—
546C2×D4—1222no—
547C2×D4—1222no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1222no—
551C2×D4—1222no—
552C2×D4—1222no—
553C2×D4—1222no—
554C2×D4—1222no—
555C2×D4—1222no—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1222no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—1228no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—4884no—
596C22×C4—4882no—
597C22×C4—4882no—
598C22×C4—4882no—
599C22×C4—2441no—
600C22×C4—2441no—
601C4⋊C4—1228no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—614no—
614C22⋊C4—1228no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—4884no—
621C22⋊C4—2441no—
622C22⋊C4—2441no—
623C22⋊C4—2441no—
624C22⋊C4—2441no—
625C22⋊C4—2441no—
626C22⋊C4—2441no—
627C22⋊C4#1175819814yescomplemented
628C42—1228no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—614no—
645C23—1222no—
646C23—1222no—
647C23—1222no—
648C23—1222no—
649C23—1222no—
650C23—1222no—
651C23—4882no—
652C23—4882no—
653C23—4882no—
654C23—4882no—
655C23—4882no—
656C23—2444no—
657C23—2444no—
658C23C42×D6111yescharacteristic
659C23C22⋊C4×D6111yescharacteristic
660C23C22⋊C4×D6111yescharacteristic
661C23C22⋊C4×D6111yescharacteristic
662C23C22⋊C4×D6111yescharacteristic
663C23C2×#1175819811yescharacteristic
664C23C4⋊C4×D6111yescharacteristic
665C23C4⋊C4×D6111yescharacteristic
666C23C4⋊C4×D6111yescharacteristic
667C23#1451973411yescharacteristic
668C23#1451973511yescharacteristic
669C23#1451973711yescharacteristic
670C23#1451973711yescharacteristic
671C23C4×C22⋊D6111yescharacteristic
672C23C4×C22⋊D6111yescharacteristic
673C23#1451973911yescharacteristic
674C23#1451973911yescharacteristic
675C23C4×D24411yescharacteristic
676C23C4×D24411yescharacteristic
677C23#1451974511yescharacteristic
678C23#1451974511yescharacteristic
679C23#1451974711yescharacteristic
680C23#1451974711yescharacteristic
681C23#1451974811yescharacteristic
682C23#1451975011yescharacteristic
683C23#1451975011yescharacteristic
684C23#1451975211yescharacteristic
685C23#1451975311yescharacteristic
686C23#1451975511yescharacteristic
687C23#1451975511yescharacteristic
688C23#1451975711yescharacteristic
689C23#1451975911yescharacteristic
690C23#1451975911yescharacteristic
691C23#1451976211yescharacteristic
692C23#1451976211yescharacteristic
693D4—1224no—
694D4—1224no—
695D4—1224no—
696D4—1224no—
697D4—1224no—
698D4—1224no—
699D4—1224no—
700D4—1224no—
701C2×C4—24no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4—614no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1224no—
721C2×C4—4888no—
722C2×C4—4882no—
723C2×C4—4882no—
724C2×C4—4882no—
725C2×C4—4882no—
726C2×C4—4882no—
727C2×C4—4882no—
728C2×C4—4882no—
729C2×C4—2444no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2444no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—1224no—
769C22—4882no—
770C22—4882no—
771C22—4882no—
772C22—2444no—
773C22—2444no—
774C22—2444no—
775C22—2444no—
776C22#95×D6111yescharacteristic
777C22#1683960911yescharacteristic
778C22C4×#1175819811yescharacteristic
779C22#1683961711yescharacteristic
780C22#1683961911yescharacteristic
781C22#1683962111yescharacteristic
782C22#1683962411yescharacteristic
783C22#1683963311yescharacteristic
784C22#1683963311yescharacteristic
785C22#1683963611yescharacteristic
786C22#1683963611yescharacteristic
787C22#1683963811yescharacteristic
788C22#1683963811yescharacteristic
789C22#1683964011yescharacteristic
790C22#1683964011yescharacteristic
791C4—44no—
792C4—82no—
793C4—82no—
794C4—1224no—
795C4—4882no—
796C4—4882no—
797C4—2444no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—21no—
809C2—21no—
810C2—21no—
811C2—21no—
812C2—2444no—
813C2#2144404011yescharacteristic
814C2#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#10754
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. C2×#16839528C2semidirect
5. C2×#16839528C2semidirect
6. C2×#16839528C2semidirect
7. C2×C61×#342C2semidirect
12. #16840235C4semidirect
22. C2×#14519691C4semidirect
24. #16839639C4semidirect
51. C23×Dic61C2×C4semidirect
76. C2×C22⋊Dic61C2×C4semidirect
104. C2×C22⋊C4×C61C2×C4semidirect
105. C2×C22⋊C4×C61C2×C4semidirect
204. C22⋊C4×C61C22⋊C4semidirect
216. C22⋊Dic61C22⋊C4semidirect
397. C2×#342D61semidirect
441. C61#10754semidirect
509. C2×C22⋊C4C4×D61semidirect
510. C2×C22⋊C4C4×D61semidirect
627. C22⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C2×#168402352
C22×#145196912
#214483942
C2×#168395282
C2×C61×#3422
#1075461