Finite Group Databasebeta

← #29711085

Subgroups — #29711085

Order 15616.

1794 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519797C211yesmaximal, characteristic, complemented
2C2×#16839922C211yesmaximal, characteristic, complemented
3C2×#16839918C211yesmaximal, characteristic, complemented
4C2×#16839901C211yesmaximal, characteristic, complemented
5#21449164C211yesmaximal, characteristic, complemented
6#21446913C211yesmaximal, characteristic, complemented
7#21446896C211yesmaximal, characteristic, complemented
8#21446822C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446243C211yesmaximal, characteristic, complemented
11#21446174C211yesmaximal, characteristic, complemented
12#21446160C211yesmaximal, characteristic, complemented
13#21446112C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#548C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519797—24no—
18C2×#14519797—24no—
19C2×#14519797—24no—
20C22×#11758202C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×#11758201C2211yescharacteristic
25C22×#11758199C2211yescharacteristic
26C23×#92418C2211yescharacteristic
27C2×#14519756C2211yescharacteristic
28C2×#14519751C2211yescharacteristic
29#16839922—24no—
30#16839918—24no—
31#16839901—24no—
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519697C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43#16839677—21no—
44#16839670—21no—
45#16839668C2211yescharacteristic
46#16839664C2211yescharacteristic
47#16839638—21no—
48#16839633—21no—
49#16839622C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839517C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C23×Q8×C61C2211yescharacteristic
56C61×#548—24no—
57C61×#548—24no—
58C2×#124×C61—21no—
59C2×#124×C61C2211yescharacteristic
60C2×C22⋊Q8×C61—21no—
61C2×C22⋊Q8×C61C2211yescharacteristic
62C2×#121×C61—21no—
63C2×#121×C61C2211yescharacteristic
64C2×C4×Q8×C61C2211yescharacteristic
65C2×C4×D4×C61—21no—
66C2×C4×D4×C61C2211yescharacteristic
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—22no—
71C2×#11758222—41no—
72C2×#11758222—41no—
73C22×Dic122C2311yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C22×C4×D61—21no—
78#14519797—232no—
79C2×#11758202—22no—
80C2×#11758202—22no—
81C2×#11758202—22no—
82C2×#11758202—22no—
83C2×#11758202—41no—
84C2×#11758202D414yescomplemented
85C2×#11758200—22no—
86C2×#11758200—22no—
87C2×#11758200—22no—
88C2×#11758201—22no—
89C2×#11758201—22no—
90C2×#11758201—22no—
91C2×#11758201—22no—
92C2×#11758201—41no—
93C2×#11758201D414yescomplemented
94C2×#11758199—22no—
95C2×#11758199—22no—
96C2×#11758199—22no—
97C22×#92418—22no—
98C22×#92418—22no—
99C22×#92418—22no—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104#14519756—22no—
105#14519756—41no—
106#14519751—22no—
107#14519751—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116#14519701—22no—
117#14519701—22no—
118#14519701—22no—
119#14519701—22no—
120#14519700—22no—
121#14519698—41no—
122#14519698—41no—
123#14519697—22no—
124C22⋊#92418—22no—
125C22⋊#92418—22no—
126C22⋊#92418—22no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130C2×#41×C61—22no—
131C2×#41×C61—22no—
132C2×#41×C61—22no—
133C2×#41×C61—41no—
134C2×#41×C61—41no—
135C2×#41×C61D414yescomplemented
136C22×Q8×C61—22no—
137C22×Q8×C61—22no—
138C22×Q8×C61—21no—
139C22×Q8×C61—22no—
140C22×Q8×C61—22no—
141C22×Q8×C61—41no—
142C22×Q8×C61—41no—
143C22×Q8×C61C2311yescharacteristic
144C22×Q8×C61C2311yescharacteristic
145C22×D4×C61—21no—
146C22×D4×C61—21no—
147C22×D4×C61D411yescharacteristic
148C22×D4×C61C2311yescharacteristic
149C23×C4×C61—21no—
150C23×C4×C61—21no—
151C23×C4×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153#124×C61—28no—
154#124×C61—22no—
155#124×C61—22no—
156C22⋊Q8×C61—28no—
157C22⋊Q8×C61—22no—
158C22⋊Q8×C61D414yescomplemented
159#121×C61—28no—
160#121×C61—22no—
161#121×C61—22no—
162C4×Q8×C61—22no—
163C4×Q8×C61—22no—
164C4×D4×C61—28no—
165C4×D4×C61—22no—
166C4×D4×C61—22no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61D411yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C22⋊C4×C61—21no—
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61D411yescharacteristic
176C2×C22⋊C4×C61D411yescharacteristic
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179C24×C61—21no—
180C24×C61C2×D411yescharacteristic
181C24×C61C2×D411yescharacteristic
182C23×D61—21no—
183#41×C61—28no—
184#41×C61—44no—
185#41×C61—44no—
186#41×C61—44no—
187C2×Q8×C61—24no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—21no—
193C2×Q8×C61—21no—
194C2×Q8×C61—21no—
195C2×Q8×C61—21no—
196C2×Q8×C61—42no—
197C2×Q8×C61—42no—
198C2×Q8×C61—44no—
199C2×Q8×C61—44no—
200C2×Q8×C61—44no—
201C2×Q8×C61—44no—
202C2×Q8×C61C2×D412yes—
203C2×Q8×C61C2×D412yes—
204C2×Q8×C61C2×D412yes—
205C2×Q8×C61C2×D412yes—
206C2×D4×C61—24no—
207C2×D4×C61—22no—
208C2×D4×C61—24no—
209C2×D4×C61—22no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—41no—
216C2×D4×C61—42no—
217C2×D4×C61—42no—
218C2×D4×C61—42no—
219C2×D4×C61—42no—
220C2×D4×C61C2×D412yes—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—24no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—24no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—42no—
237C22×C4×C61—42no—
238C22×C4×C61—42no—
239C22×C4×C61—42no—
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D412yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2411yescharacteristic
247C2×C22⋊D61—42no—
248C2×C22⋊D61—42no—
249C2×C22⋊D61—42no—
250C2×C22⋊D61—42no—
251C2×C22⋊D61—42no—
252C2×C22⋊D61—81no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256#11758222—28no—
257#11758222—44no—
258#11758222—44no—
259#11758222—44no—
260C2×D244—21no—
261C2×D244—21no—
262C2×D244—21no—
263C2×D244—21no—
264C2×D244—21no—
265C2×D244C2×D412yes—
266C2×C4×D61—42no—
267C2×C4×D61—42no—
268C2×C4×D61—42no—
269C2×Dic122—21no—
270C2×Dic122—21no—
271C2×Dic122—21no—
272C2×Dic122—21no—
273C2×Dic122—21no—
274C2×Dic122C2×D412yes—
275C4⋊C4×C61—24no—
276C4⋊C4×C61—24no—
277C4⋊C4×C61—22no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C2×D412yes—
280C22⋊C4×C61—24no—
281C22⋊C4×C61—24no—
282C22⋊C4×C61—24no—
283C22⋊C4×C61—24no—
284C22⋊C4×C61—22no—
285C22⋊C4×C61—22no—
286C42×C61—24no—
287C42×C61—21no—
288C42×C61—21no—
289C22⋊Dic61—42no—
290C22⋊Dic61—81no—
291#11758202—28no—
292#11758202—44no—
293#11758201—28no—
294#11758201—44no—
295#11758200—28no—
296#11758199—28no—
297#11758198—42no—
298#11758198—42no—
299#11758198—81no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304#11758196—42no—
305C2×#92418—28no—
306C2×#92418—21no—
307C2×#92418—21no—
308C2×#92418—21no—
309C2×#92418—21no—
310C2×#92418—21no—
311C2×#92418—21no—
312C2×#92418—21no—
313C2×#92418—21no—
314C2×#92418—21no—
315C2×#92418—21no—
316C2×#92418C2×D412yes—
317C2×#92418C2×D412yes—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61—21no—
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—22no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61#12012yes—
338C23×C61#13512yescomplemented
339C23×C61C22×D411yescharacteristic
340C22×D61—22no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347Q8×C61—22no—
348Q8×C61—22no—
349Q8×C61—22no—
350Q8×C61—22no—
351Q8×C61—22no—
352Q8×C61—48no—
353Q8×C61—41no—
354Q8×C61—41no—
355Q8×C61#12014yes—
356D4×C61—22no—
357D4×C61—22no—
358D4×C61—48no—
359D4×C61—44no—
360D4×C61—48no—
361D4×C61—41no—
362D4×C61—41no—
363C2×C4×C61—22no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—48no—
384C2×C4×C61—48no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61#12012yes—
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D411yescharacteristic
396C2×C4×C61C22×D411yescharacteristic
397C2×C4×C61C22×D411yescharacteristic
398C2×C4×C61H(5,𝔽2)11yescharacteristic
399C2×C4×C61H(5,𝔽2)11yescharacteristic
400C22⋊D61—48no—
401C22⋊D61—84no—
402C2×Dic61—22no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411D244—22no—
412D244—22no—
413D244—41no—
414D244—41no—
415C4×D61—48no—
416Dic122—22no—
417Dic122—22no—
418Dic122—41no—
419Dic122—41no—
420#92418—22no—
421#92418—22no—
422#92418—41no—
423#92418—41no—
424#23854—611nomaximal, Sylow
425C22×C61—22no—
426C22×C61—22no—
427C22×C61—22no—
428C22×C61—22no—
429C22×C61—22no—
430C22×C61—22no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—42no—
440C22×C61—42no—
441C22×C61—42no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61C2×#12011yescharacteristic
447C22×C61D4211yescharacteristic
448C22×C61D4211yescharacteristic
449C22×C61C2×#13511yescharacteristic
450C22×C61#57511yescharacteristic
451C22×C61#57711yescharacteristic
452C22×C61#57811yescharacteristic
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61—81no—
459C2×D61—81no—
460C4×C61—22no—
461C4×C61—24no—
462C4×C61—41no—
463C4×C61—42no—
464C4×C61—41no—
465C4×C61—42no—
466C4×C61—41no—
467C4×C61C2×#12011yescharacteristic
468C4×C61#53411yescharacteristic
469C4×C61D4211yescharacteristic
470C4×C61D4211yescharacteristic
471Dic61—42no—
472Dic61—81no—
473Dic61—81no—
474C22×#135—611no—
475C2×#548D6111yescharacteristic, complemented
476C2×#452—611no—
477C2×#451—611no—
478C2×#448—611no—
479#2407—611no—
480#2015—611no—
481#2012—611no—
482#2000—611no—
483#1999—611no—
484#1892—611no—
485#1880—611no—
486#1878—611no—
487#1869—611no—
488#1788—611no—
489C2×C61—42no—
490C2×C61—42no—
491C2×C61—82no—
492C2×C61#240311yescharacteristic
493C2×C61#300211yescharacteristic
494C2×C61#301311yescharacteristic
495C2×C61#326911yescharacteristic
496C2×C61#327111yescharacteristic
497C2×C61#328211yescharacteristic
498C2×C61#328511yescharacteristic
499D61—82no—
500C22×#41—611no—
501C22×#41C2×D6111yescharacteristic
502C23×Q8C2×D6111yescharacteristic
503C2×#135—1224no—
504C2×#135—1224no—
505C2×#135—1224no—
506C22×Q16—611no—
507C22×Q16—611no—
508C22×SD16—611no—
509C22×SD16—611no—
510C22×SD16—611no—
511C22×D8—611no—
512C23×C8—611no—
513#548—24no—
514#548—24no—
515C2×#124—21no—
516C2×#124C2×D6111yescharacteristic
517C2×C22⋊Q8—21no—
518C2×C22⋊Q8—611no—
519C2×C22⋊Q8C2×D6111yescharacteristic
520C2×#121—21no—
521C2×#121—611no—
522C2×#121C2×D6111yescharacteristic
523C2×C4×Q8C2×D6111yescharacteristic
524C2×C4×D4—21no—
525C2×C4×D4C2×D6111yescharacteristic
526#452—1224no—
527#451—1224no—
528#448—1224no—
529C2×#103—611no—
530C2×#103—611no—
531C2×#103—611no—
532C2×#103—611no—
533C2×#103—611no—
534C2×#102—611no—
535C2×#102—611no—
536C2×#102—611no—
537C2×C22⋊C8—611no—
538C2×C22⋊C8—611no—
539C2×C22⋊C8—611no—
540#394—1221no—
541#392—1221no—
542#391—611no—
543#390—611no—
544#386—1221no—
545#385—1221no—
546#380—611no—
547#340—611no—
548#340—611no—
549#336—611no—
550#336—611no—
551C61#2385411yescharacteristic, complemented, Sylow
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—41no—
556C2×#41—41no—
557C2×#41—1222no—
558C2×#41—1222no—
559C2×#41—1222no—
560C2×#41—1222no—
561C2×#41—2441no—
562C2×#41—2441no—
563C2×#41C22⋊D6114yescomplemented
564C22×Q8—22no—
565C22×Q8—22no—
566C22×Q8—21no—
567C22×Q8—22no—
568C22×Q8—22no—
569C22×Q8—41no—
570C22×Q8—41no—
571C22×Q8—611no—
572C22×Q8C22×D6111yescharacteristic
573C22×Q8C22×D6111yescharacteristic
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—611no—
577C22×D4—1221no—
578C22×D4—1221no—
579C22×D4C22⋊D6111yescharacteristic
580C22×D4C22×D6111yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—1221no—
584C23×C4C22×D6111yescharacteristic
585C23×C4C22×D6111yescharacteristic
586#135—12232no—
587C2×Q16—614no—
588C2×Q16—1222no—
589C2×Q16—1222no—
590C2×Q16—1222no—
591C2×Q16—1222no—
592C2×Q16—2441no—
593C2×SD16—614no—
594C2×SD16—1222no—
595C2×SD16—1222no—
596C2×SD16—1222no—
597C2×SD16—1222no—
598C2×SD16—1222no—
599C2×SD16—1222no—
600C2×SD16—1222no—
601C2×SD16—2441no—
602C2×D8—1222no—
603C2×D8—1222no—
604C2×D8—1222no—
605C22×C8—611no—
606C22×C8—611no—
607C22×C8—611no—
608C22×C8—611no—
609C22×C8—1222no—
610C22×C8—1222no—
611C22×C8—1222no—
612#124—28no—
613#124—22no—
614#124—22no—
615C22⋊Q8—28no—
616C22⋊Q8—22no—
617C22⋊Q8—1222no—
618C22⋊Q8—2441no—
619C22⋊Q8C22⋊D6114yescomplemented
620#121—28no—
621#121—22no—
622#121—22no—
623#121—1222no—
624#121—2441no—
625C4×Q8—22no—
626C4×Q8—22no—
627C4×D4—28no—
628C4×D4—22no—
629C4×D4—22no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—1221no—
635C2×C4⋊C4C22⋊D6111yescharacteristic
636C2×C4⋊C4C22×D6111yescharacteristic
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4—1221no—
646C2×C22⋊C4C22⋊D6111yescharacteristic
647C2×C22⋊C4C22⋊D6111yescharacteristic
648C2×C42—21no—
649C2×C42C22×D6111yescharacteristic
650#103—1222no—
651#103—1222no—
652#103—1222no—
653#103—1222no—
654#103—1222no—
655#102—1222no—
656#102—2441no—
657#102—2441no—
658C22⋊C8—1222no—
659C22⋊C8—1222no—
660C22⋊C8—1222no—
661#95—1221no—
662#95—1221no—
663#95—1221no—
664C24—21no—
665C24—1221no—
666C24C2×C22⋊D6111yescharacteristic
667C24C2×C22⋊D6111yescharacteristic
668#41—28no—
669#41—44no—
670#41—44no—
671#41—44no—
672#41—1228no—
673#41—2444no—
674#41—2444no—
675#41—2444no—
676C2×Q8—24no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—42no—
686C2×Q8—42no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—612no—
692C2×Q8—1221no—
693C2×Q8—1221no—
694C2×Q8—1221no—
695C2×Q8—1221no—
696C2×Q8—1221no—
697C2×Q8D4×D6112yes—
698C2×Q8D4×D6112yes—
699C2×Q8C2×C22⋊D6112yes—
700C2×Q8C2×C22⋊D6112yes—
701C2×D4—24no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—41no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—42no—
715C2×D4—612no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—4881no—
722C2×D4—2442no—
723C2×D4—2442no—
724C2×D4—2442no—
725C2×D4—2442no—
726C2×D4—2442no—
727C2×D4C2×C22⋊D6112yes—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—24no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—24no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—2442no—
751C22×C4—2442no—
752C22×C4—2442no—
753C22×C4C2×C22⋊D6111yescharacteristic
754C22×C4C2×C22⋊D6111yescharacteristic
755C22×C4C2×C22⋊D6111yescharacteristic
756C22×C4C2×C22⋊D6112yes—
757C22×C4C2×C22⋊D6112yes—
758C22×C4C2×C22⋊D6111yescharacteristic
759C22×C4C23×D6111yescharacteristic
760Q16—1228no—
761Q16—2444no—
762SD16—1228no—
763SD16—1228no—
764SD16—2444no—
765D8—1228no—
766C2×C8—612no—
767C2×C8—612no—
768C2×C8—1228no—
769C2×C8—1221no—
770C2×C8—1221no—
771C2×C8—1221no—
772C2×C8—1221no—
773C2×C8—1221no—
774C2×C8—1221no—
775C2×C8—1221no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—1221no—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—24no—
782C4⋊C4—22no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—2442no—
788C4⋊C4C2×C22⋊D6112yes—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—4881no—
796C22⋊C4—4881no—
797C22⋊C4—2442no—
798C22⋊C4—2442no—
799C22⋊C4—2442no—
800C42—24no—
801C42—21no—
802C42—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—1222no—
823C23—2441no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23#1451974612yes—
830C23#1451979712yescomplemented
831C23C22×C22⋊D6111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—48no—
838Q8—41no—
839Q8—41no—
840Q8—1222no—
841Q8—1222no—
842Q8—2441no—
843Q8—2441no—
844Q8#1451974514yes—
845D4—22no—
846D4—22no—
847D4—48no—
848D4—44no—
849D4—48no—
850D4—41no—
851D4—41no—
852D4—1222no—
853D4—1222no—
854D4—4884no—
855D4—2448no—
856D4—2441no—
857D4—2441no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—48no—
879C2×C4—48no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—1222no—
889C2×C4—2448no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4#1451974612yes—
899C2×C4C2×D4×D6111yescharacteristic
900C2×C4C2×D4×D6111yescharacteristic
901C2×C4C22×C22⋊D6111yescharacteristic
902C2×C4C22×C22⋊D6111yescharacteristic
903C2×C4#1451982211yescharacteristic
904C2×C4#1451982211yescharacteristic
905C8—1222no—
906C8—1222no—
907C8—2441no—
908C8—2441no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—4881no—
931C22—4881no—
932C22—4881no—
933C22—4881no—
934C22—2442no—
935C22—2442no—
936C22—2442no—
937C22C2×#1451974611yescharacteristic
938C22D4×C22⋊D6111yescharacteristic
939C22D4×C22⋊D6111yescharacteristic
940C22C2×#1451979711yescharacteristic
941C22#1684056011yescharacteristic
942C22#1684057011yescharacteristic
943C22#1684057711yescharacteristic
944C4—22no—
945C4—24no—
946C4—41no—
947C4—41no—
948C4—42no—
949C4—41no—
950C4—42no—
951C4—4881no—
952C4—4881no—
953C4—2442no—
954C4C2×#1451974511yescharacteristic
955C4#1684032111yescharacteristic
956C4D4×C22⋊D6111yescharacteristic
957C4D4×C22⋊D6111yescharacteristic
958C2—42no—
959C2—42no—
960C2—82no—
961C2—4882no—
962C2#2144912911yescharacteristic
963C2#2145503711yescharacteristic
964C2#2145513411yescharacteristic
965C2#2145737511yescharacteristic
966C2#2145740511yescharacteristic
967C2#2145752711yescharacteristic
968C2#2145755611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#548C2
socleC23×C61C22×D4
hypercenterC2×#548D61
hypocenterC61#23854
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14519797C2semidirect
2. C2×#16839922C2semidirect
3. C2×#16839918C2semidirect
4. C2×#16839901C2semidirect
5. #21449164C2semidirect
6. #21446913C2semidirect
7. #21446896C2semidirect
8. #21446822C2semidirect
9. #21446815C2semidirect
10. #21446243C2semidirect
11. #21446174C2semidirect
12. #21446160C2semidirect
13. #21446112C2semidirect
14. #21445759C2semidirect
15. C2×C61×#548C2semidirect
84. C2×#11758202D4semidirect
93. C2×#11758201D4semidirect
135. C2×#41×C61D4semidirect
158. C22⋊Q8×C61D4semidirect
338. C23×C61#135semidirect
475. C2×#548D61semidirect
551. C61#23854semidirect
563. C2×#41C22⋊D61semidirect
619. C22⋊Q8C22⋊D61semidirect
830. C23#14519797semidirect

Maximal subgroups

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

subgroupindex
C22×#145197972
C2×#168399222
C2×#168399182
C2×#168399012
#214491642
#214469132
#214468962
#214468222
#214468152
#214462432
#214461742
#214461602
#214461122
#214457592
C2×C61×#5482
#2385461