Finite Group Databasebeta

← #29685365

Subgroups — #29685365

Order 15616.

1318 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840347C211yesmaximal, characteristic
2#21448415C211yesmaximal, characteristic, complemented
3#21448172C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal, complemented
6#21446273C211yesmaximal, characteristic, complemented
7#21446272C211yesmaximal, characteristic, complemented
8#21446270C211yesmaximal, characteristic, complemented
9#99×Dic61C212yesmaximal, complemented
10#21445606C212yesmaximal, complemented
11C61×#1898C211yesmaximal, characteristic, complemented
12#16840347—22no—
13#16840347—22no—
14#16840347—22no—
15#16840347—22no—
16C2×#14519770C411yescharacteristic, complemented
17C2×#14519770C411yescharacteristic, complemented
18C2×#14519764C411yescharacteristic, complemented
19C2×#14519763C411yescharacteristic, complemented
20C2×#14519759C411yescharacteristic, complemented
21C2×#14519758C411yescharacteristic, complemented
22C2×#14519754C2211yescharacteristic
23C2×#14519749C411yescharacteristic, complemented
24C2×#14519749C2211yescharacteristic
25C2×#14519748C411yescharacteristic, complemented
26C2×#14519746C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×#14519737C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C2×#14519692C2212yes—
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34#16839656—22no—
35#16839650—22no—
36#16839620C2212yes—
37#16839618C2211yescharacteristic
38C22⋊C4×Dic61—22no—
39C22⋊C4×Dic61C2212yes—
40C22⋊C4×Dic61C2212yes—
41C22⋊C4×Dic61C2212yes—
42C4×C22⋊Dic61—22no—
43#16839529C2212yes—
44#16839528C2212yes—
45#16839528C2212yes—
46C2×#120×C61C2211yescharacteristic
47C22×C22⋊C4×C61C2211yescharacteristic
48C2×#99×C61C2212yes—
49C61×#379C2211yescharacteristic
50C61×#342C2212yes—
51C22×Dic122C2×C411yescharacteristic, complemented
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic, complemented
55C22×C22⋊D61C2311yescharacteristic
56C23×Dic61—21no—
57C23×Dic61C2×C411yescharacteristic, complemented
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C22×C4×D61C2×C411yescharacteristic, complemented
61#14519770—22no—
62#14519770—22no—
63#14519770—22no—
64#14519770—22no—
65#14519764—22no—
66#14519764—22no—
67#14519763—22no—
68#14519763—22no—
69#14519759—22no—
70#14519759—22no—
71#14519758—22no—
72#14519758—22no—
73#14519754—22no—
74#14519754—22no—
75#14519749—22no—
76#14519749—22no—
77#14519749—22no—
78#14519749—22no—
79#14519748—22no—
80#14519748—22no—
81#14519746—21no—
82#14519746—21no—
83#14519746—21no—
84#14519746—21no—
85D4×Dic61—22no—
86D4×Dic61—22no—
87#14519737—22no—
88#14519737—22no—
89C2×C4⋊Dic61C2×C411yescharacteristic, complemented
90C2×C4⋊Dic61C2×C411yescharacteristic, complemented
91C2×#11758196—22no—
92C2×#11758196C2×C411yescharacteristic, complemented
93C2×#11758196C2×C411yescharacteristic, complemented
94C2×#11758196C2×C411yescharacteristic, complemented
95C2×#11758196C2×C411yescharacteristic, complemented
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—24no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61C2×C411yescharacteristic
101C2×C22⋊Dic61C2×C411yescharacteristic
102C2×C22⋊Dic61C2×C411yescharacteristic
103C2×C22⋊Dic61C2×C411yescharacteristic
104C2×C22⋊Dic61C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic, complemented
107C2×C22⋊Dic61C2×C411yescharacteristic, complemented
108C2×C22⋊Dic61D412yes—
109C2×C22⋊Dic61D412yes—
110C2×C22⋊Dic61D412yes—
111C2×C22⋊Dic61D412yes—
112C2×C22⋊Dic61C2312yes—
113C2×C22⋊Dic61C2311yescharacteristic
114C2×C22⋊Dic61C2312yes—
115C2×#11758198C2×C411yescharacteristic, complemented
116C2×#11758198C2×C411yescharacteristic, complemented
117C2×C4×Dic61—22no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—22no—
120C2×C4×Dic61C2×C411yescharacteristic, complemented
121C2×C4×Dic61C2×C411yescharacteristic, complemented
122#14519692—24no—
123#14519691—24no—
124#14519691—24no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129C25×C61C2311yescharacteristic
130C22×D4×C61C2×C411yescharacteristic
131C22×D4×C61C2×C411yescharacteristic
132C22×D4×C61C2311yescharacteristic
133C23×C4×C61—21no—
134#120×C61—21no—
135#120×C61—21no—
136#120×C61—21no—
137#120×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—24no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C22⋊C4×C61C2×C411yescharacteristic
144C2×C22⋊C4×C61C2312yes—
145C2×C22⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61C2312yes—
147#99×C61—24no—
148C24×C61—22no—
149C24×C61—22no—
150C24×C61—81no—
151C24×C61—81no—
152C24×C61C22×C411yescharacteristic
153C24×C61C22×C411yescharacteristic
154C24×C61C22×C411yescharacteristic
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157C24×C61C2×D411yescharacteristic
158C24×C61C2×D411yescharacteristic
159C24×C61C2411yescharacteristic
160C23×D61C22×C411yescharacteristic
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—81no—
170C2×D4×C61—81no—
171C22×C4×C61—22no—
172C22×C4×C61—24no—
173C22×C4×C61—22no—
174C22×C4×C61—81no—
175C22×C4×C61—81no—
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C22×C4×C61C22×C411yescharacteristic
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61—22no—
183C2×C22⋊D61—21no—
184C2×C22⋊D61—21no—
185C2×C22⋊D61—21no—
186C2×C22⋊D61—21no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—81no—
189C2×C22⋊D61—81no—
190C2×C22⋊D61—81no—
191C22×Dic61—22no—
192C22×Dic61—24no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—81no—
196C22×Dic61—81no—
197C22×Dic61—81no—
198C22×Dic61—81no—
199C22×Dic61—81no—
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202C22×Dic61C22×C411yescharacteristic
203C22×Dic61C22×C411yescharacteristic
204C22×Dic61C22×C411yescharacteristic
205C22×Dic61C22×C411yescharacteristic
206C22×Dic61C22×C411yescharacteristic
207C22×Dic61C2×D412yes—
208C22×Dic61C2×D412yes—
209C22×Dic61C2×D412yes—
210C22×Dic61C2×D412yes—
211C2×C4×D61—22no—
212C2×C4×D61—81no—
213C2×Dic122—22no—
214C2×Dic122—81no—
215C22⋊C4×C61—24no—
216C22⋊C4×C61—21no—
217C22⋊C4×C61—21no—
218C22⋊C4×C61—21no—
219C22⋊C4×C61—21no—
220C22⋊C4×C61—21no—
221C22⋊C4×C61—21no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—81no—
226C22⋊C4×C61—81no—
227C22⋊C4×C61#4114yes—
228C22⋊Dic61—24no—
229C22⋊Dic61—21no—
230C22⋊Dic61—21no—
231C22⋊Dic61—21no—
232C22⋊Dic61—21no—
233C22⋊Dic61—21no—
234C22⋊Dic61—21no—
235C22⋊Dic61—22no—
236C22⋊Dic61—22no—
237C22⋊Dic61—22no—
238C22⋊Dic61—22no—
239C22⋊Dic61—22no—
240C22⋊Dic61—81no—
241C22⋊Dic61—81no—
242C22⋊Dic61C22⋊C412yes—
243C22⋊Dic61C22⋊C412yes—
244C22⋊Dic61C22⋊C412yes—
245C22⋊Dic61C22⋊C412yes—
246C22⋊Dic61C22⋊C412yes—
247C22⋊Dic61C22⋊C412yes—
248C22⋊Dic61C22⋊C412yes—
249C22⋊Dic61C22⋊C412yes—
250C22⋊Dic61#4114yes—
251#11758198—22no—
252#11758198—22no—
253C4⋊Dic61—22no—
254C4⋊Dic61—22no—
255#11758196—22no—
256#11758196—22no—
257#11758196—22no—
258#11758196—22no—
259#11758196—82no—
260C4×Dic61—22no—
261C4×Dic61—22no—
262C4×Dic61—82no—
263C4×Dic61—82no—
264C4×Dic61—82no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—21no—
274C23×C61—22no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
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—41no—
291C23×C61—84no—
292C23×C61—84no—
293C23×C61C2×C22⋊C411yescharacteristic
294C23×C61C2×C22⋊C411yescharacteristic
295C23×C61C2×C22⋊C411yescharacteristic
296C23×C61C2×C22⋊C411yescharacteristic
297C23×C61C23×C411yescharacteristic
298C23×C61C22×D411yescharacteristic
299C23×C61C22×D411yescharacteristic
300C23×C61C2×#4112yes—
301C23×C61C2×#4112yes—
302C22×D61—21no—
303C22×D61—22no—
304C22×D61—41no—
305C22×D61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—42no—
309D4×C61—81no—
310D4×C61—81no—
311D4×C61—81no—
312D4×C61—81no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—22no—
317C2×C4×C61—24no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—84no—
326C22⋊D61—41no—
327C22⋊D61—41no—
328C22⋊D61—42no—
329C22⋊D61—82no—
330C22⋊D61—81no—
331C22⋊D61—81no—
332C22⋊D61—81no—
333C22⋊D61—81no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—22no—
338C2×Dic61—24no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—42no—
348C2×Dic61—42no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—42no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—82no—
355C2×Dic61—84no—
356C2×Dic61C2×C22⋊C412yes—
357C2×Dic61C2×C22⋊C412yes—
358C2×Dic61C2×C22⋊C412yes—
359C2×Dic61C2×C22⋊C412yes—
360C4×D61—82no—
361Dic122—82no—
362#21422—611nomaximal, Sylow
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—21no—
369C22×C61—21no—
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—82no—
391C22×C61—82no—
392C22×C61—82no—
393C22×C61—82no—
394C22×C61—82no—
395C22×C61C22×C22⋊C411yescharacteristic
396C22×C61C4×#4112yes—
397C22×C61#52511yescharacteristic
398C22×C61#52511yescharacteristic
399C22×C61#53212yes—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—82no—
404C4×C61—44no—
405C4×C61—41no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—82no—
409Dic61—22no—
410Dic61—22no—
411Dic61—22no—
412Dic61—22no—
413Dic61—44no—
414Dic61—41no—
415Dic61—41no—
416Dic61—41no—
417Dic61—82no—
418C2×#538—611no—
419#2312—611no—
420#2273—611no—
421#1996—612no—
422#1964—612no—
423#1898—611no—
424#1898—611no—
425#1898—611no—
426#1898D6111yescharacteristic, complemented
427C4×#99—612no—
428C4×#99—612no—
429C2×C61—21no—
430C2×C61—22no—
431C2×C61—21no—
432C2×C61—22no—
433C2×C61—41no—
434C2×C61—41no—
435C2×C61—41no—
436C2×C61—41no—
437C2×C61—81no—
438C2×C61#229711yescharacteristic
439C2×C61#288311yescharacteristic
440C2×C61#288311yescharacteristic
441D61—81no—
442#538—1222no—
443#538—1222no—
444#538—1222no—
445#538—1222no—
446C2×#126—611no—
447C2×#126—611no—
448C2×#124—611no—
449C2×#124—611no—
450C2×#123—611no—
451C2×#123—611no—
452C2×C22⋊Q8—611no—
453C2×#121—611no—
454C2×#121—611no—
455C2×#121—611no—
456C2×#120—611no—
457C2×#120C2×D6111yescharacteristic
458C2×C4×D4—611no—
459C2×C4×D4—611no—
460C22×C22⋊C4—611no—
461C22×C22⋊C4—611no—
462C22×C22⋊C4C2×D6111yescharacteristic
463C2×#99—612no—
464C2×#99—612no—
465C2×#99—612no—
466C2×#99C2×D6112yes—
467#388—1222no—
468#388—1222no—
469#380—612no—
470#379—611no—
471#379C2×D6111yescharacteristic
472C4×C22⋊C4—612no—
473C4×C22⋊C4—612no—
474C4×C22⋊C4—612no—
475C4×C22⋊C4—1222no—
476C4×C22⋊C4—1222no—
477#342—612no—
478#342—612no—
479#342—612no—
480#342C2×D6112yes—
481C61#2142211yescharacteristic, complemented, Sylow
482C25C22×D6111yescharacteristic
483C22×Q8—611no—
484C22×D4—611no—
485C22×D4—611no—
486C22×D4—611no—
487C22×D4—611no—
488C22×D4C4×D6111yescharacteristic
489C22×D4C4×D6111yescharacteristic
490C22×D4C22×D6111yescharacteristic
491C23×C4—21no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—1221no—
497#126—1222no—
498#126—1222no—
499#126—1222no—
500#126—1222no—
501#124—1222no—
502#124—1222no—
503#124—1222no—
504#124—1222no—
505#123—1222no—
506#123—1222no—
507#123—1222no—
508#123—1222no—
509C22⋊Q8—1222no—
510C22⋊Q8—1222no—
511#121—1222no—
512#121—1222no—
513#121—1222no—
514#121—1222no—
515#121—1222no—
516#121—1222no—
517#120—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521#120—1221no—
522#120—1221no—
523#120—1221no—
524#120—1221no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—1222no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4—611no—
542C2×C22⋊C4—611no—
543C2×C22⋊C4—611no—
544C2×C22⋊C4—612no—
545C2×C22⋊C4—612no—
546C2×C22⋊C4—612no—
547C2×C22⋊C4—612no—
548C2×C22⋊C4—612no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—611no—
553C2×C22⋊C4—611no—
554C2×C22⋊C4—611no—
555C2×C22⋊C4—611no—
556C2×C22⋊C4—612no—
557C2×C22⋊C4—1224no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4C4×D6111yescharacteristic
562C2×C22⋊C4C4×D6111yescharacteristic
563C2×C22⋊C4C22×D6112yes—
564C2×C22⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4C22×D6112yes—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—1222no—
569C2×C42—1222no—
570C2×C42—1222no—
571#99—24no—
572#99—1224no—
573#99—1224no—
574#99—1224no—
575#95—1222no—
576#95—1222no—
577#95—1222no—
578#95—1222no—
579C24—22no—
580C24—22no—
581C24—81no—
582C24—81no—
583C24—611no—
584C24C2×C4×D6111yescharacteristic
585C24C2×C4×D6111yescharacteristic
586C24C2×C4×D6111yescharacteristic
587C24D4×D6111yescharacteristic
588C24D4×D6111yescharacteristic
589C24D4×D6111yescharacteristic
590C24D4×D6111yescharacteristic
591C24C23×D6111yescharacteristic
592C2×Q8—1222no—
593C2×Q8—4881no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4—1222no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1222no—
612C2×D4—1222no—
613C2×D4—4881no—
614C2×D4—4881no—
615C2×D4—4881no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—612no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1224no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—4881no—
638C22×C4—4881no—
639C22×C4—4881no—
640C22×C4—4881no—
641C22×C4—4881no—
642C22×C4—4881no—
643C22×C4C2×C4×D6111yescharacteristic
644C22×C4C2×C4×D6111yescharacteristic
645C22×C4C2×C4×D6111yescharacteristic
646C4⋊C4—1222no—
647C4⋊C4—1222no—
648C4⋊C4—1222no—
649C4⋊C4—1222no—
650C4⋊C4—1222no—
651C4⋊C4—1222no—
652C4⋊C4—4882no—
653C22⋊C4—24no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—22no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—612no—
666C22⋊C4—612no—
667C22⋊C4—612no—
668C22⋊C4—612no—
669C22⋊C4—612no—
670C22⋊C4—612no—
671C22⋊C4—612no—
672C22⋊C4—612no—
673C22⋊C4—614no—
674C22⋊C4—1222no—
675C22⋊C4—1222no—
676C22⋊C4—1222no—
677C22⋊C4—1222no—
678C22⋊C4—1224no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1222no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4—4881no—
689C22⋊C4—4881no—
690C22⋊C4#1175822414yes—
691C42—1222no—
692C42—1222no—
693C42—4882no—
694C42—4882no—
695C42—4882no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—21no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—84no—
723C23—84no—
724C23—1222no—
725C23—1221no—
726C23—2441no—
727C23—2441no—
728C23C22⋊C4×D6111yescharacteristic
729C23C22⋊C4×D6111yescharacteristic
730C23C22⋊C4×D6111yescharacteristic
731C23C22⋊C4×D6111yescharacteristic
732C23C22×C4×D6111yescharacteristic
733C23C2×D4×D6111yescharacteristic
734C23C2×D4×D6111yescharacteristic
735C23#41×D6112yes—
736C23C2×#1175822412yes—
737Q8—4882no—
738D4—41no—
739D4—41no—
740D4—42no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—4882no—
746D4—4881no—
747D4—4881no—
748D4—4881no—
749D4—4881no—
750D4—2441no—
751D4—2441no—
752D4—2442no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—612no—
767C2×C4—612no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1222no—
774C2×C4—1224no—
775C2×C4—4882no—
776C2×C4—4882no—
777C2×C4—4884no—
778C2×C4—2442no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4—2442no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2441no—
792C2×C4—2441no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—4882no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22C2×C22⋊C4×D6111yescharacteristic
830C22C4×#1175822412yes—
831C22#1684026811yescharacteristic
832C22#1684027011yescharacteristic
833C22#1684030712yes—
834C4—44no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—82no—
839C4—1222no—
840C4—1222no—
841C4—1222no—
842C4—1222no—
843C4—4882no—
844C4—2444no—
845C4—2441no—
846C4—2441no—
847C4—2441no—
848C2—21no—
849C2—22no—
850C2—21no—
851C2—22no—
852C2—41no—
853C2—41no—
854C2—41no—
855C2—41no—
856C2—81no—
857C2—4881no—
858C2#2144830411yescharacteristic
859C2#2145427711yescharacteristic
860C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1898C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840347C2
cosocleC24×C61C24
hypercenter#1898D61
hypocenterC61#21422
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #1898

Complements

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

NH ≅ G/Ntype
2. #21448415C2semidirect
3. #21448172C2semidirect
4. #21446802C2semidirect
5. #21446653C2semidirect
6. #21446273C2semidirect
7. #21446272C2semidirect
8. #21446270C2semidirect
9. #99×Dic61C2semidirect
10. #21445606C2semidirect
11. C61×#1898C2semidirect
16. C2×#14519770C4semidirect
17. C2×#14519770C4semidirect
18. C2×#14519764C4semidirect
19. C2×#14519763C4semidirect
20. C2×#14519759C4semidirect
21. C2×#14519758C4semidirect
23. C2×#14519749C4semidirect
25. C2×#14519748C4semidirect
51. C22×Dic122C2×C4semidirect
54. C22×C22⋊D61C2×C4semidirect
57. C23×Dic61C2×C4semidirect
60. C22×C4×D61C2×C4semidirect
89. C2×C4⋊Dic61C2×C4semidirect
90. C2×C4⋊Dic61C2×C4semidirect
92. C2×#11758196C2×C4semidirect
93. C2×#11758196C2×C4semidirect
94. C2×#11758196C2×C4semidirect
95. C2×#11758196C2×C4semidirect
106. C2×C22⋊Dic61C2×C4semidirect
107. C2×C22⋊Dic61C2×C4semidirect
115. C2×#11758198C2×C4semidirect
116. C2×#11758198C2×C4semidirect
120. C2×C4×Dic61C2×C4semidirect
121. C2×C4×Dic61C2×C4semidirect
426. #1898D61semidirect
481. C61#21422semidirect

Maximal subgroups

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

subgroupindex
C2×#168403472
#214484152
#214481722
#214468022
#214466532
#214462732
#214462722
#214462702
#99×Dic612
#214456062
C61×#18982
#2142261