Finite Group Databasebeta

← #29689823

Subgroups — #29689823

Order 15616.

1158 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840292C211yesmaximal, characteristic
2#21448221C211yesmaximal, characteristic, complemented
3#21448214C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal
6#21446276C212yesmaximal, complemented
7#21446274C212yesmaximal, complemented
8#21445807C211yesmaximal, characteristic, complemented
9#21445804C211yesmaximal, characteristic, complemented
10#21445804C211yesmaximal, characteristic, complemented
11C61×#1799C211yesmaximal, characteristic, complemented
12#16840292—21no—
13#16840292—21no—
14#16840292—21no—
15#16840292—21no—
16#16840292—21no—
17#16840292—21no—
18#16840292—21no—
19#16840292—21no—
20C2×#14519772C411yescharacteristic, complemented
21C2×#14519770C411yescharacteristic, complemented
22C2×#14519767C411yescharacteristic, complemented
23C2×#14519763C411yescharacteristic, complemented
24C2×#14519761C2211yescharacteristic
25C2×#14519758C2211yescharacteristic
26C2×#14519754C2211yescharacteristic
27C2×#14519749C2211yescharacteristic
28C2×C4×Dic122C411yescharacteristic, complemented
29C2×C4×C22⋊D61C411yescharacteristic, complemented
30C2×C4×C22⋊D61C2211yescharacteristic
31C2×#14519736C411yescharacteristic, complemented
32C2×#14519734C411yescharacteristic, complemented
33C2×#14519733C2212yes—
34C22×C4×Dic61C2211yescharacteristic
35C2×#14519692C2212yes—
36C2×#14519691C2212yes—
37C2×#14519691C2212yes—
38#16839631—21no—
39#16839629—21no—
40#16839627—21no—
41#16839626—21no—
42#16839623C2212yes—
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839620C2212yes—
46C4⋊C4×Dic61—21no—
47C4⋊C4×Dic61—21no—
48#16839613—21no—
49C22⋊C4×Dic61C2212yes—
50#16839607—21no—
51#16839529C2212yes—
52#16839528C2212yes—
53#16839528C2212yes—
54C2×C4×D4×C61C2211yescharacteristic
55C2×#99×C61C2212yes—
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#342C2212yes—
59C22×Dic122C2×C411yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65#14519772—21no—
66#14519772—21no—
67#14519772—21no—
68#14519772—21no—
69#14519770—21no—
70#14519770—21no—
71#14519770—21no—
72#14519770—21no—
73#14519767—21no—
74#14519767—21no—
75#14519767—21no—
76#14519767—21no—
77#14519763—21no—
78#14519763—21no—
79#14519763—21no—
80#14519763—21no—
81#14519761—21no—
82#14519761—21no—
83#14519761—21no—
84#14519761—21no—
85#14519758—21no—
86#14519758—21no—
87#14519758—21no—
88#14519758—21no—
89#14519754—21no—
90#14519754—21no—
91#14519754—21no—
92#14519754—21no—
93#14519749—21no—
94#14519749—21no—
95#14519749—21no—
96#14519749—21no—
97C4×Dic122—21no—
98C4×Dic122—21no—
99C4×Dic122—21no—
100C4×Dic122—21no—
101C4×C22⋊D61—21no—
102C4×C22⋊D61—21no—
103C4×C22⋊D61—21no—
104C4×C22⋊D61—21no—
105C4×C22⋊D61—21no—
106C4×C22⋊D61—21no—
107C4×C22⋊D61—21no—
108C4×C22⋊D61—21no—
109#14519736—21no—
110#14519736—21no—
111#14519736—21no—
112#14519736—21no—
113#14519734—21no—
114#14519734—21no—
115#14519734—21no—
116#14519734—21no—
117#14519733—42no—
118#14519733—42no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×C4⋊Dic61C2×C411yescharacteristic
123C2×C4⋊Dic61C2×C411yescharacteristic
124C2×#11758196—22no—
125C2×#11758196—22no—
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C2×#11758196C2×C411yescharacteristic
131C2×#11758196C2×C411yescharacteristic
132C2×C22⋊Dic61C2×C411yescharacteristic
133C2×C22⋊Dic61C2×C411yescharacteristic
134C2×C22⋊Dic61C2×C411yescharacteristic
135C2×C22⋊Dic61C2312yes—
136C2×C22⋊Dic61C2312yes—
137C2×C22⋊Dic61C2311yescharacteristic
138C2×#11758198C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C2×C4×Dic61—22no—
143C2×C4×Dic61—22no—
144C2×C4×Dic61C2×C411yescharacteristic
145C2×C4×Dic61C2×C411yescharacteristic
146C2×C4×Dic61C2×C411yescharacteristic
147C2×C4×Dic61C2×C411yescharacteristic
148C2×C4×Dic61C2×C411yescharacteristic
149C2×C4×Dic61D411yescharacteristic
150C2×C4×Dic61D411yescharacteristic
151C2×C4×Dic61D411yescharacteristic
152C2×C4×Dic61D411yescharacteristic
153C2×C4×Dic61D411yescharacteristic
154C2×C4×Dic61D411yescharacteristic
155C2×C4×Dic61D411yescharacteristic
156C2×C4×Dic61D411yescharacteristic
157#14519692—42no—
158#14519691—42no—
159#14519691—42no—
160#14519684—21no—
161#14519684—21no—
162#14519684—22no—
163#14519684—22no—
164#14519684—22no—
165#14519684—22no—
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61C2×C411yescharacteristic
168C23×C4×C61C2311yescharacteristic
169C4×D4×C61—21no—
170C4×D4×C61—21no—
171C4×D4×C61—21no—
172C4×D4×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61C2×C411yescharacteristic
176C2×C22⋊C4×C61C2×C411yescharacteristic
177C2×C22⋊C4×C61C2312yes—
178C2×C22⋊C4×C61C2312yes—
179C2×C22⋊C4×C61C2311yescharacteristic
180C2×C42×C61C2×C411yescharacteristic
181#99×C61—42no—
182#95×C61—21no—
183#95×C61—21no—
184C24×C61C22×C411yescharacteristic
185C24×C61C2411yescharacteristic
186C23×D61C22×C411yescharacteristic
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—22no—
196C22×C4×C61—22no—
197C22×C4×C61—42no—
198C22×C4×C61—42no—
199C22×C4×C61C22×C411yescharacteristic
200C22×C4×C61C22×C411yescharacteristic
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—42no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—42no—
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C22×Dic61C22×C411yescharacteristic
229C22×Dic61C22×C411yescharacteristic
230C22×Dic61C22×C411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—42no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—42no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—42no—
248C4⋊C4×C61—42no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—22no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C42×C61—21no—
258C42×C61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265C22⋊Dic61—21no—
266C22⋊Dic61—21no—
267C22⋊Dic61—22no—
268C22⋊Dic61—22no—
269C22⋊Dic61—22no—
270C22⋊Dic61—22no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—42no—
286C4⋊Dic61—42no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—44no—
300#11758196—44no—
301C4×Dic61—21no—
302C4×Dic61—21no—
303C4×Dic61—44no—
304C4×Dic61—44no—
305C4×Dic61C22⋊C411yescharacteristic
306C4×Dic61C22⋊C411yescharacteristic
307C4×Dic61C22⋊C411yescharacteristic
308C4×Dic61C22⋊C411yescharacteristic
309C4×Dic61C22⋊C411yescharacteristic
310C4×Dic61C22⋊C411yescharacteristic
311C4×Dic61C22⋊C411yescharacteristic
312C4×Dic61C22⋊C411yescharacteristic
313C4×Dic61C22⋊C411yescharacteristic
314C4×Dic61C22⋊C411yescharacteristic
315C4×Dic61C22⋊C411yescharacteristic
316C4×Dic61C22⋊C411yescharacteristic
317C4×Dic61C22⋊C411yescharacteristic
318C4×Dic61C22⋊C411yescharacteristic
319C4×Dic61C22⋊C411yescharacteristic
320C4×Dic61C22⋊C411yescharacteristic
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61C23×C411yescharacteristic
329C23×C61C22×D411yescharacteristic
330C23×C61C22×D411yescharacteristic
331C23×C61H(5,𝔽2)11yescharacteristic
332C23×C61H(5,𝔽2)11yescharacteristic
333C23×C612−1+411yescharacteristic
334C23×C612−1+411yescharacteristic
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—41no—
339C22×D61—41no—
340D4×C61—41no—
341D4×C61—41no—
342D4×C61—41no—
343D4×C61—41no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—42no—
356C2×C4×C61—42no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—42no—
360C2×C4×C61—42no—
361C2×C4×C61—42no—
362C2×C4×C61—42no—
363C2×C4×C61—42no—
364C2×C4×C61—42no—
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C22⋊D61—42no—
370C22⋊D61—41no—
371C22⋊D61—41no—
372C22⋊D61—41no—
373C22⋊D61—41no—
374C22⋊D61—42no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—42no—
401C2×Dic61—42no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404C2×Dic61—42no—
405C2×Dic61—42no—
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410C2×Dic61C2×C22⋊C411yescharacteristic
411C2×Dic61C2×C22⋊C411yescharacteristic
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C2×C22⋊C411yescharacteristic
414C4×D61—42no—
415C4×D61—42no—
416Dic122—42no—
417Dic122—42no—
418#21875—611nomaximal, Sylow
419C22×C61—21no—
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—81no—
433C22×C61—81no—
434C22×C61C22×C22⋊C411yescharacteristic
435C22×C61#52011yescharacteristic
436C22×C61#52011yescharacteristic
437C22×C61#53511yescharacteristic
438C22×C61#53611yescharacteristic
439C22×C61#53711yescharacteristic
440C22×C61#53711yescharacteristic
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—81no—
445C2×D61—81no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—41no—
450C4×C61—41no—
451C4×C61—41no—
452C4×C61—82no—
453C4×C61—82no—
454C4×C61#41012yes—
455Dic61—21no—
456Dic61—21no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—21no—
461Dic61—21no—
462Dic61—41no—
463Dic61—41no—
464Dic61—41no—
465Dic61—82no—
466Dic61—82no—
467Dic61#41012yes—
468C2×#529—611no—
469#2285—611no—
470#2283—611no—
471#1996—612no—
472#1964—612no—
473#1899—612no—
474#1899—612no—
475#1799—611no—
476#1799—611no—
477#1799—611no—
478#1799D6111yescharacteristic, complemented
479C2×C61—21no—
480C2×C61—21no—
481C2×C61—21no—
482C2×C61—21no—
483C2×C61—21no—
484C2×C61—21no—
485C2×C61—81no—
486C2×C61#231111yescharacteristic
487C2×C61C2×#41011yescharacteristic
488C2×C61C2×#41011yescharacteristic
489D61—81no—
490#529—1221no—
491#529—1221no—
492#529—1221no—
493#529—1221no—
494#529—1221no—
495#529—1221no—
496#529—1221no—
497#529—1221no—
498C2×#126—611no—
499C2×#126—611no—
500C2×#125—611no—
501C2×#124—611no—
502C2×#123—611no—
503C2×#123—611no—
504C2×C22⋊Q8—611no—
505C2×#121—611no—
506C2×C4×Q8—611no—
507C2×C4×D4—611no—
508C2×C4×D4—611no—
509C2×C4×D4C2×D6111yescharacteristic
510C2×#117—611no—
511C2×#117—611no—
512C2×#117—612no—
513C22×C42—611no—
514C2×#99—612no—
515C2×#99—612no—
516C2×#99—612no—
517C2×#99C2×D6112yes—
518#384—1221no—
519#383—1221no—
520#382—1221no—
521#382—1221no—
522#381—612no—
523#380—611no—
524#380—611no—
525#380—612no—
526#380C2×D6111yescharacteristic
527#380C2×D6111yescharacteristic
528C4×C4⋊C4—1221no—
529C4×C4⋊C4—1221no—
530C4×C4⋊C4—1221no—
531C4×C22⋊C4—612no—
532#376—1221no—
533#342—612no—
534#342—612no—
535#342—612no—
536#342C2×D6112yes—
537C61#2187511yescharacteristic, complemented, Sylow
538C22×Q8—611no—
539C22×D4—611no—
540C22×D4—611no—
541C22×D4C22×D6111yescharacteristic
542C23×C4—611no—
543C23×C4—611no—
544C23×C4—611no—
545C23×C4C4×D6111yescharacteristic
546C23×C4C22×D6111yescharacteristic
547#126—1221no—
548#126—1221no—
549#126—1221no—
550#126—1221no—
551#126—1221no—
552#126—1221no—
553#126—1221no—
554#126—1221no—
555#125—1221no—
556#125—1221no—
557#125—1221no—
558#125—1221no—
559#124—1221no—
560#124—1221no—
561#124—1221no—
562#124—1221no—
563#123—1221no—
564#123—1221no—
565#123—1221no—
566#123—1221no—
567#123—1221no—
568#123—1221no—
569#123—1221no—
570#123—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575#121—1221no—
576#121—1221no—
577#121—1221no—
578#121—1221no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8—1221no—
582C4×Q8—1221no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595#117—1221no—
596#117—1221no—
597#117—1221no—
598#117—1221no—
599#117—1221no—
600#117—1221no—
601#117—1221no—
602#117—1221no—
603#117—2442no—
604#117—2442no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—611no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—611no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—611no—
616C2×C4⋊C4—1222no—
617C2×C4⋊C4—1222no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4—1221no—
620C2×C4⋊C4C4×D6111yescharacteristic
621C2×C22⋊C4—611no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—611no—
624C2×C22⋊C4—611no—
625C2×C22⋊C4—611no—
626C2×C22⋊C4—611no—
627C2×C22⋊C4—611no—
628C2×C22⋊C4—611no—
629C2×C22⋊C4—612no—
630C2×C22⋊C4—612no—
631C2×C22⋊C4C4×D6111yescharacteristic
632C2×C22⋊C4C22×D6112yes—
633C2×C22⋊C4C22×D6112yes—
634C2×C22⋊C4C22×D6111yescharacteristic
635C2×C42—611no—
636C2×C42—611no—
637C2×C42—611no—
638C2×C42—611no—
639C2×C42—611no—
640C2×C42—611no—
641C2×C42—611no—
642C2×C42—611no—
643C2×C42—611no—
644C2×C42—611no—
645C2×C42—611no—
646C2×C42—611no—
647C2×C42—611no—
648C2×C42—1222no—
649C2×C42—1222no—
650C2×C42C4×D6111yescharacteristic
651#99—42no—
652#99—2442no—
653#99—2442no—
654#99—2442no—
655#95—21no—
656#95—21no—
657#95—1222no—
658#95—1222no—
659#95—1222no—
660#95—1222no—
661#95—1221no—
662#95—1221no—
663C24—611no—
664C24C2×C4×D6111yescharacteristic
665C24C23×D6111yescharacteristic
666C2×Q8—1221no—
667C2×Q8—1221no—
668C2×Q8—2442no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—1221no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—2442no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1222no—
712C22×C4—1222no—
713C22×C4—2442no—
714C22×C4—2442no—
715C22×C4C2×C4×D6111yescharacteristic
716C22×C4C2×C4×D6111yescharacteristic
717C22×C4C2×C4×D6111yescharacteristic
718C22×C4C2×C4×D6111yescharacteristic
719C22×C4C2×C4×D6111yescharacteristic
720C22×C4D4×D6111yescharacteristic
721C22×C4D4×D6111yescharacteristic
722C22×C4D4×D6111yescharacteristic
723C22×C4D4×D6111yescharacteristic
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—2442no—
747C4⋊C4—2442no—
748C4⋊C4—2444no—
749C4⋊C4—2444no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4—1221no—
774C22⋊C4—1222no—
775C22⋊C4—1222no—
776C22⋊C4—1222no—
777C22⋊C4—1222no—
778C42—21no—
779C42—21no—
780C42—611no—
781C42—611no—
782C42—611no—
783C42—611no—
784C42—611no—
785C42—611no—
786C42—611no—
787C42—611no—
788C42—611no—
789C42—611no—
790C42—611no—
791C42—611no—
792C42—611no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—1221no—
797C42—1221no—
798C42—2444no—
799C42—2444no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—1221no—
808C23—1221no—
809C23—1221no—
810C23—2441no—
811C23—2441no—
812C23C22×C4×D6111yescharacteristic
813C23C2×D4×D6111yescharacteristic
814C23C2×D4×D6111yescharacteristic
815C23#1451982211yescharacteristic
816C23#1451982311yescharacteristic
817C23#1451982411yescharacteristic
818C23#1451982511yescharacteristic
819Q8—2442no—
820Q8—2442no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—2442no—
826D4—2442no—
827D4—2441no—
828D4—2441no—
829D4—2441no—
830D4—2441no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—611no—
853C2×C4—611no—
854C2×C4—611no—
855C2×C4—611no—
856C2×C4—611no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—611no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—2442no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2442no—
885C2×C4—2442no—
886C2×C4—2442no—
887C2×C4—2442no—
888C2×C4—2442no—
889C2×C4—2442no—
890C2×C4—2442no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4C22⋊C4×D6111yescharacteristic
894C2×C4C22⋊C4×D6111yescharacteristic
895C2×C4C22⋊C4×D6111yescharacteristic
896C2×C4C22⋊C4×D6111yescharacteristic
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—4881no—
913C22—4881no—
914C22—2441no—
915C22—2441no—
916C22—2441no—
917C22C2×C22⋊C4×D6111yescharacteristic
918C22#1684024211yescharacteristic
919C22#1684024311yescharacteristic
920C22#1684032811yescharacteristic
921C22#1684033511yescharacteristic
922C22#1684034111yescharacteristic
923C22#1684034211yescharacteristic
924C4—21no—
925C4—21no—
926C4—21no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—82no—
931C4—82no—
932C4—612no—
933C4—1221no—
934C4—1221no—
935C4—1221no—
936C4—1221no—
937C4—1221no—
938C4—1221no—
939C4—1221no—
940C4—4882no—
941C4—4882no—
942C4—2441no—
943C4—2441no—
944C4—2441no—
945C4#1683973412yes—
946C2—21no—
947C2—21no—
948C2—21no—
949C2—21no—
950C2—21no—
951C2—21no—
952C2—81no—
953C2—4881no—
954C2#2144840811yescharacteristic
955C2#410×D6111yescharacteristic
956C2C2×#1683973411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1799C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519749C22
cosocleC24×C61C24
hypercenter#1799D61
hypocenterC61#21875
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #21448221C2semidirect
3. #21448214C2semidirect
4. #21446802C2semidirect
6. #21446276C2semidirect
7. #21446274C2semidirect
8. #21445807C2semidirect
9. #21445804C2semidirect
10. #21445804C2semidirect
11. C61×#1799C2semidirect
20. C2×#14519772C4semidirect
21. C2×#14519770C4semidirect
22. C2×#14519767C4semidirect
23. C2×#14519763C4semidirect
28. C2×C4×Dic122C4semidirect
29. C2×C4×C22⋊D61C4semidirect
31. C2×#14519736C4semidirect
32. C2×#14519734C4semidirect
478. #1799D61semidirect
537. C61#21875semidirect

Maximal subgroups

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

subgroupindex
C2×#168402922
#214482212
#214482142
#214468022
#214466532
#214462762
#214462742
#214458072
#214458042
C61×#17992
#2187561