Finite Group Databasebeta

← #29685359

Subgroups — #29685359

Order 15616.

1222 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840292C211yesmaximal, characteristic
2#21448213C211yesmaximal, characteristic, complemented
3C4×#14519733C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal
6#21446276C212yesmaximal, complemented
7#21446274C212yesmaximal, complemented
8C4×#14519691C211yesmaximal, characteristic, complemented
9C4×#14519691C211yesmaximal, characteristic, complemented
10C4×#14519692C211yesmaximal, characteristic, complemented
11C4×#99×C61C211yesmaximal, 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#16839629—21no—
39#16839626—21no—
40#16839623C2212yes—
41#16839620C2212yes—
42C4×#11758196—21no—
43C4×#11758196—21no—
44#16839613—21no—
45C22⋊C4×Dic61C2212yes—
46C4×C22⋊Dic61C2211yescharacteristic
47C4×C22⋊Dic61C2211yescharacteristic
48#16839608—21no—
49#16839607—21no—
50C42×Dic61—21no—
51#16839529C2212yes—
52#16839528C2212yes—
53#16839528C2212yes—
54C2×C4×D4×C61C2211yescharacteristic
55C2×#99×C61C2212yes—
56C4×C22⋊C4×C61C2211yescharacteristic
57C4×C22⋊C4×C61C2211yescharacteristic
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—24no—
118#14519733—24no—
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×C4⋊Dic61C2×C411yescharacteristic
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×#11758196—22no—
123C2×#11758196—22no—
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×C22⋊Dic61C2×C411yescharacteristic
133C2×C22⋊Dic61C2312yes—
134C2×C22⋊Dic61C2311yescharacteristic
135C2×C22⋊Dic61C2312yes—
136C2×#11758198C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
138C2×#11758198C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×C4×Dic61—22no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
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—24no—
158#14519691—24no—
159#14519691—24no—
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×C61C2×C411yescharacteristic
174C2×C22⋊C4×C61C2×C411yescharacteristic
175C2×C22⋊C4×C61C2312yes—
176C2×C22⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61C2312yes—
178C2×C42×C61—21no—
179C2×C42×C61—21no—
180C2×C42×C61C2×C411yescharacteristic
181#99×C61—24no—
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—22no—
190C2×D4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—22no—
195C22×C4×C61—42no—
196C22×C4×C61—42no—
197C22×C4×C61C22×C411yescharacteristic
198C22×C4×C61C22×C411yescharacteristic
199C22×C4×C61C22×C411yescharacteristic
200C22×C4×C61C22×C411yescharacteristic
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208C2×C22⋊D61—22no—
209C2×C22⋊D61—22no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—42no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—42no—
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—42no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—42no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61#4114yes—
249C42×C61—21no—
250C42×C61—21no—
251C42×C61—42no—
252C42×C61—42no—
253C22⋊Dic61—21no—
254C22⋊Dic61—21no—
255C22⋊Dic61—22no—
256C22⋊Dic61—21no—
257C22⋊Dic61—21no—
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—22no—
263C22⋊Dic61—22no—
264C22⋊Dic61#4114yes—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279#11758196—28no—
280#11758196—21no—
281#11758196—21no—
282#11758196—21no—
283#11758196—21no—
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—44no—
293C4×Dic61—28no—
294C4×Dic61—21no—
295C4×Dic61—21no—
296C4×Dic61—44no—
297C4×Dic61—42no—
298C4×Dic61—42no—
299C4×Dic61C22⋊C411yescharacteristic
300C4×Dic61C22⋊C411yescharacteristic
301C4×Dic61C22⋊C411yescharacteristic
302C4×Dic61C22⋊C411yescharacteristic
303C4×Dic61C22⋊C411yescharacteristic
304C4×Dic61C22⋊C411yescharacteristic
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
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61C23×C411yescharacteristic
323C23×C61C22×D411yescharacteristic
324C23×C61C22×D411yescharacteristic
325C23×C61C2×#4112yes—
326C23×C61C2×#4112yes—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—41no—
331C22×D61—41no—
332D4×C61—42no—
333D4×C61—42no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—24no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—42no—
353C2×C4×C61—42no—
354C2×C4×C61—42no—
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C2×C22⋊C411yescharacteristic
359C22⋊D61—42no—
360C22⋊D61—42no—
361C22⋊D61—42no—
362C22⋊D61—42no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—24no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—42no—
384C2×Dic61—42no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—42no—
388C2×Dic61—42no—
389C2×Dic61—42no—
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C4×D61—42no—
399C4×D61—42no—
400Dic122—42no—
401Dic122—42no—
402#21421—611nomaximal, Sylow
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—42no—
410C22×C61—42no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—81no—
415C22×C61—81no—
416C22×C61C22×C22⋊C411yescharacteristic
417C22×C61C4×#4111yescharacteristic
418C22×C61C4×#4111yescharacteristic
419C22×C61#52512yes—
420C22×C61#53212yes—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61—81no—
425C2×D61—81no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—44no—
430C4×C61—41no—
431C4×C61—41no—
432C4×C61—41no—
433C4×C61—82no—
434C4×C61#41012yes—
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—21no—
441Dic61—21no—
442Dic61—44no—
443Dic61—41no—
444Dic61—41no—
445Dic61—41no—
446Dic61—82no—
447Dic61#41012yes—
448C2×#529—611no—
449#2283—611no—
450C4×#117—611no—
451#1996—612no—
452#1964—612no—
453#1899—612no—
454#1899—612no—
455C4×#99—611no—
456C4×#99—611no—
457C4×#99—611no—
458C4×#99D6111yescharacteristic, complemented
459C2×C61—22no—
460C2×C61—22no—
461C2×C61—21no—
462C2×C61—21no—
463C2×C61—81no—
464C2×C61#229711yescharacteristic
465C2×C61C2×#41011yescharacteristic
466C2×C61C2×#41011yescharacteristic
467D61—81no—
468#529—1221no—
469#529—1221no—
470#529—1221no—
471#529—1221no—
472#529—1221no—
473#529—1221no—
474#529—1221no—
475#529—1221no—
476C2×#126—611no—
477C2×#126—611no—
478C2×#125—611no—
479C2×#124—611no—
480C2×#123—611no—
481C2×#123—611no—
482C2×C22⋊Q8—611no—
483C2×#121—611no—
484C2×C4×Q8—611no—
485C2×C4×D4—611no—
486C2×C4×D4—611no—
487C2×C4×D4C2×D6111yescharacteristic
488C2×#117—611no—
489C2×#117—611no—
490C2×#117—612no—
491C22×C42—611no—
492C2×#99—612no—
493C2×#99—612no—
494C2×#99—612no—
495C2×#99C2×D6112yes—
496#383—1221no—
497#382—1221no—
498#381—612no—
499#380—612no—
500C4×C4⋊C4—1221no—
501C4×C4⋊C4—1221no—
502C4×C4⋊C4—1221no—
503C4×C22⋊C4—611no—
504C4×C22⋊C4—611no—
505C4×C22⋊C4—612no—
506C4×C22⋊C4C2×D6111yescharacteristic
507C4×C22⋊C4C2×D6111yescharacteristic
508#376—1221no—
509#376—1221no—
510C43—1221no—
511#342—612no—
512#342—612no—
513#342—612no—
514#342C2×D6112yes—
515C61#2142111yescharacteristic, complemented, Sylow
516C22×Q8—611no—
517C22×D4—611no—
518C22×D4—611no—
519C22×D4C22×D6111yescharacteristic
520C23×C4—611no—
521C23×C4—611no—
522C23×C4—611no—
523C23×C4C4×D6111yescharacteristic
524C23×C4C22×D6111yescharacteristic
525#126—1221no—
526#126—1221no—
527#126—1221no—
528#126—1221no—
529#126—1221no—
530#126—1221no—
531#126—1221no—
532#126—1221no—
533#125—1221no—
534#125—1221no—
535#125—1221no—
536#125—1221no—
537#124—1221no—
538#124—1221no—
539#124—1221no—
540#124—1221no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545#123—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549C22⋊Q8—1221no—
550C22⋊Q8—1221no—
551C22⋊Q8—1221no—
552C22⋊Q8—1221no—
553#121—1221no—
554#121—1221no—
555#121—1221no—
556#121—1221no—
557C4×Q8—1221no—
558C4×Q8—1221no—
559C4×Q8—1221no—
560C4×Q8—1221no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—1221no—
566C4×D4—1221no—
567C4×D4—1221no—
568C4×D4—1221no—
569C4×D4—1221no—
570C4×D4—1221no—
571C4×D4—1221no—
572C4×D4—1221no—
573#117—1221no—
574#117—1221no—
575#117—1221no—
576#117—1221no—
577#117—1221no—
578#117—1221no—
579#117—1221no—
580#117—1221no—
581#117—1224no—
582#117—1224no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1222no—
593C2×C4⋊C4—1222no—
594C2×C4⋊C4C4×D6111yescharacteristic
595C2×C22⋊C4—612no—
596C2×C22⋊C4—611no—
597C2×C22⋊C4—611no—
598C2×C22⋊C4—611no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4—611no—
601C2×C22⋊C4—611no—
602C2×C22⋊C4—611no—
603C2×C22⋊C4—611no—
604C2×C22⋊C4—612no—
605C2×C22⋊C4C4×D6111yescharacteristic
606C2×C22⋊C4C22×D6112yes—
607C2×C22⋊C4C22×D6111yescharacteristic
608C2×C22⋊C4C22×D6112yes—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—611no—
612C2×C42—611no—
613C2×C42—611no—
614C2×C42—611no—
615C2×C42—611no—
616C2×C42—611no—
617C2×C42—611no—
618C2×C42—611no—
619C2×C42—611no—
620C2×C42—611no—
621C2×C42—611no—
622C2×C42—611no—
623C2×C42—611no—
624C2×C42—1222no—
625C2×C42—1222no—
626C2×C42—1221no—
627C2×C42—1221no—
628C2×C42C4×D6111yescharacteristic
629#99—24no—
630#99—1224no—
631#99—1224no—
632#99—1224no—
633#95—21no—
634#95—21no—
635#95—1222no—
636#95—1222no—
637#95—1222no—
638#95—1222no—
639#95—1221no—
640#95—1221no—
641C24—611no—
642C24C2×C4×D6111yescharacteristic
643C24C23×D6111yescharacteristic
644C2×Q8—1221no—
645C2×Q8—1221no—
646C2×Q8—2442no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1222no—
656C2×D4—1222no—
657C2×D4—2442no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—1222no—
680C22×C4—1222no—
681C22×C4—1222no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1222no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4C2×C4×D6111yescharacteristic
688C22×C4C2×C4×D6111yescharacteristic
689C22×C4C2×C4×D6111yescharacteristic
690C22×C4C2×C4×D6111yescharacteristic
691C22×C4C2×C4×D6111yescharacteristic
692C22×C4D4×D6111yescharacteristic
693C22×C4D4×D6111yescharacteristic
694C22×C4D4×D6111yescharacteristic
695C22×C4D4×D6111yescharacteristic
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1228no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—2444no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—22no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—614no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1222no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4—1222no—
744C22⋊C4—1222no—
745C22⋊C4#1175822214yes—
746C42—21no—
747C42—21no—
748C42—42no—
749C42—42no—
750C42—611no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—611no—
757C42—611no—
758C42—611no—
759C42—611no—
760C42—611no—
761C42—611no—
762C42—611no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—1228no—
767C42—1221no—
768C42—1221no—
769C42—2442no—
770C42—2442no—
771C42—2444no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—1221no—
780C23—1221no—
781C23—1221no—
782C23—2441no—
783C23—2441no—
784C23C22×C4×D6111yescharacteristic
785C23C2×D4×D6111yescharacteristic
786C23C2×D4×D6111yescharacteristic
787C23#41×D6112yes—
788C23C2×#1175822212yes—
789Q8—2442no—
790Q8—2442no—
791D4—42no—
792D4—42no—
793D4—2442no—
794D4—2442no—
795D4—2442no—
796D4—2442no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—24no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—611no—
823C2×C4—611no—
824C2×C4—611no—
825C2×C4—611no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1224no—
843C2×C4—2442no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2442no—
848C2×C4—2442no—
849C2×C4—2442no—
850C2×C4—2442no—
851C2×C4—2442no—
852C2×C4—2442no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4C22⋊C4×D6111yescharacteristic
856C2×C4C22⋊C4×D6111yescharacteristic
857C2×C4C22⋊C4×D6111yescharacteristic
858C2×C4C22⋊C4×D6111yescharacteristic
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—42no—
866C22—42no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—81no—
871C22—81no—
872C22—4881no—
873C22—4881no—
874C22—2441no—
875C22—2441no—
876C22—2441no—
877C22C2×C22⋊C4×D6111yescharacteristic
878C22#1684023011yescharacteristic
879C22C4×#1175822211yescharacteristic
880C22#1684027112yes—
881C22#1684030912yes—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—44no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—82no—
890C4—612no—
891C4—1221no—
892C4—1221no—
893C4—1221no—
894C4—1221no—
895C4—1221no—
896C4—1221no—
897C4—1221no—
898C4—4882no—
899C4—2444no—
900C4—2441no—
901C4—2441no—
902C4—2441no—
903C4#1683973412yes—
904C2—22no—
905C2—22no—
906C2—21no—
907C2—21no—
908C2—81no—
909C2—4881no—
910C2#2144830511yescharacteristic
911C2#410×D6111yescharacteristic
912C2C2×#1683973411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#99×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519749C22
cosocleC24×C61C24
hypercenterC4×#99D61
hypocenterC61#21421
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #21448213C2semidirect
3. C4×#14519733C2semidirect
4. #21446802C2semidirect
6. #21446276C2semidirect
7. #21446274C2semidirect
8. C4×#14519691C2semidirect
9. C4×#14519691C2semidirect
10. C4×#14519692C2semidirect
11. C4×#99×C61C2semidirect
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
458. C4×#99D61semidirect
515. C61#21421semidirect

Maximal subgroups

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

subgroupindex
C2×#168402922
#214482132
C4×#145197332
#214468022
#214466532
#214462762
#214462742
C4×#145196912
C4×#145196922
C4×#99×C612
#2142161