Finite Group Databasebeta

← #29727383

Subgroups — #29727383

Order 15616.

1402 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839954C211yesmaximal, characteristic, complemented
2C2×#16839895C211yesmaximal, characteristic, complemented
3C2×#16839895C211yesmaximal, characteristic, complemented
4C2×C4×#11758199C211yesmaximal, characteristic, complemented
5C22⋊C4×D244C211yesmaximal, characteristic, complemented
6#21447204C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446998C211yesmaximal, characteristic, complemented
9#21446890C211yesmaximal, characteristic, complemented
10#21446684C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446170C211yesmaximal, characteristic, complemented
13#21446167C211yesmaximal, characteristic, complemented
14#21446065C211yesmaximal, characteristic, complemented
15C61×#2428C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×C22⋊C4×D61—21no—
24#16839954—24no—
25#16839895—24no—
26#16839895—24no—
27C4×#11758199—24no—
28C2×#14519710C2211yescharacteristic, complemented
29C2×#14519710C2211yescharacteristic, complemented
30C2×C4⋊#92418C2211yescharacteristic, complemented
31C2×#14519698C2211yescharacteristic, complemented
32C2×#14519698C2211yescharacteristic, complemented
33C2×#14519698C2211yescharacteristic, complemented
34C2×#14519698C2211yescharacteristic, complemented
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic, complemented
42#16839664C2211yescharacteristic
43#16839664C2211yescharacteristic
44#16839640—21no—
45#16839640—21no—
46#16839622C2211yescharacteristic
47#16839617—21no—
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C2×#127×C61C2211yescharacteristic, complemented
53C2×#121×C61—21no—
54C2×#121×C61C2211yescharacteristic
55C2×#121×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic, complemented
57C61×#394—21no—
58C61×#392—21no—
59C61×#390C2211yescharacteristic, complemented
60C61×#389C2211yescharacteristic, complemented
61C61×#386—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C24×D61—21no—
64C22×D244—21no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—22no—
69C22×D244—41no—
70C22×D244—41no—
71C22×D244C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758199—22no—
76C2×#11758199—22no—
77C2×#11758199—22no—
78C2×#11758199—22no—
79C2×#11758199—22no—
80C2×#11758199—22no—
81C2×#11758199—22no—
82C2×#11758199—22no—
83C2×#11758199—22no—
84C2×#11758199—41no—
85C2×#11758199—41no—
86C2×#11758199D414yescomplemented
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C4×D244—22no—
92C4×D244—22no—
93C4×D244—41no—
94C4×D244—41no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C22⋊C4×D61—44no—
105#14519710—22no—
106#14519710—41no—
107C4⋊#92418—22no—
108#14519698—22no—
109#14519698—22no—
110#14519698—22no—
111#14519698—41no—
112#14519697—22no—
113#14519697—22no—
114#14519697—22no—
115#14519697D414yescomplemented
116C22⋊#92418—22no—
117C22⋊#92418—22no—
118C4×#92418—22no—
119#14519684—21no—
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61—21no—
123C22×D4×C61—21no—
124C22×D4×C61C2311yescharacteristic
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61C2311yescharacteristic
128#127×C61—22no—
129#127×C61—41no—
130#121×C61—22no—
131#121×C61—22no—
132#121×C61—41no—
133#121×C61—41no—
134#121×C61—44no—
135C4×D4×C61—22no—
136C4×D4×C61—41no—
137C2×C4⋊C4×C61—21no—
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C2×C42×C61C2311yescharacteristic
149#95×C61—21no—
150#95×C61D411yescharacteristic
151#95×C61D411yescharacteristic
152C24×C61—21no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155C23×D61—21no—
156C23×D61—21no—
157C23×D61—24no—
158C23×D61—42no—
159C23×D61—42no—
160C23×D61—42no—
161C23×D61—42no—
162C23×D61—81no—
163C23×D61—81no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—42no—
176C2×D4×C61—42no—
177C2×D4×C61—42no—
178C2×D4×C61—42no—
179C2×D4×C61—42no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61—81no—
184C2×D4×C61—81no—
185C2×D4×C61—81no—
186C2×D4×C61—81no—
187C2×D4×C61C2×D412yes—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—42no—
197C22×C4×C61—42no—
198C22×C4×C61—81no—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2411yescharacteristic
205C22×Dic61—21no—
206C22×Dic61—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—24no—
215C2×D244—21no—
216C2×D244—44no—
217C2×D244—44no—
218C2×D244—44no—
219C2×D244—42no—
220C2×D244—42no—
221C2×D244—44no—
222C2×D244C2×D412yes—
223C2×D244C2×D412yes—
224C2×D244#4112yes—
225C2×D244#4112yes—
226C2×C4×D61—42no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61—81no—
231C2×C4×D61—81no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—42no—
236C4⋊C4×C61C2×D412yes—
237C22⋊C4×C61—41no—
238C22⋊C4×C61—42no—
239C22⋊C4×C61—42no—
240C22⋊C4×C61—42no—
241C22⋊C4×C61—42no—
242C22⋊C4×C61—81no—
243C22⋊C4×C61D814yescomplemented
244C42×C61—21no—
245C42×C61—21no—
246C42×C61—21no—
247C42×C61—21no—
248C22⋊Dic61—42no—
249#11758199—28no—
250#11758199—44no—
251#11758199—44no—
252#11758199—44no—
253#11758198—42no—
254#11758198—42no—
255#11758198—42no—
256#11758198—42no—
257#11758198—81no—
258#11758198—81no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418C2×D412yes—
274C2×#92418C2×D412yes—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—22no—
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—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61C2×D812yes—
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—48no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—48no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61—84no—
317C22×D61—84no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—41no—
321D4×C61—41no—
322D4×C61—41no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61—41no—
326D4×C61—84no—
327D4×C61—84no—
328D4×C61—84no—
329D4×C61—84no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—22no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—84no—
354C2×C4×C61C2×D812yes—
355C2×C4×C61C2×D812yes—
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C2×#4111yescharacteristic
359C2×C4×C61C2×#4111yescharacteristic
360C2×C4×C61H(5,𝔽2)11yescharacteristic
361C2×C4×C61H(5,𝔽2)11yescharacteristic
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368D244—22no—
369D244—22no—
370D244—22no—
371D244—22no—
372D244—22no—
373D244—48no—
374D244—41no—
375D244—41no—
376D244#12114yescomplemented
377C4×D61—84no—
378C4×D61—84no—
379#92418—22no—
380#92418—22no—
381#92418—41no—
382#92418—41no—
383#25148—611nomaximal, Sylow
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61#52511yescharacteristic
406C22×C61D4211yescharacteristic
407C22×C61D4211yescharacteristic
408C22×C61C22×D811yescharacteristic
409C22×C61#57511yescharacteristic
410C22×C61#57611yescharacteristic
411C22×C61#57611yescharacteristic
412C2×D61—24no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—816no—
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61—81no—
427C4×C61—22no—
428C4×C61—22no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61—41no—
432C4×C61—42no—
433C4×C61—81no—
434C4×C61C2×#12111yescharacteristic
435C4×C61#53811yescharacteristic
436C4×C61#54611yescharacteristic
437C4×C61#54611yescharacteristic
438Dic61—81no—
439Dic61—81no—
440C2×#459—611no—
441C2×#447—611no—
442C2×#447—611no—
443C2×C4×D8—611no—
444#2428D6111yescharacteristic, complemented
445D4×C22⋊C4—611no—
446#2067—611no—
447#2033—611no—
448#2033—611no—
449#2011—611no—
450#1970—611no—
451#1923—611no—
452#1879—611no—
453#1879—611no—
454#1862—611no—
455C2×C61—42no—
456C2×C61—82no—
457C2×C61—161no—
458C2×C61#242411yescharacteristic
459C2×C61#310011yescharacteristic
460C2×C61#312211yescharacteristic
461C2×C61#326811yescharacteristic
462C2×C61#327311yescharacteristic
463C2×C61D4×D811yescharacteristic
464C2×C61D4×D811yescharacteristic
465D61—44no—
466D61—82no—
467C23×D4—611no—
468C22×D8—611no—
469C22×D8—611no—
470C22×D8—611no—
471C22×D8—611no—
472C2×#127C2×D6111yescharacteristic, complemented
473C2×#121—21no—
474C2×#121C2×D6111yescharacteristic
475C2×#121C2×D6111yescharacteristic
476C2×C4×D4—611no—
477C2×C4×D4—611no—
478C2×C4×D4C2×D6111yescharacteristic, complemented
479C22×C22⋊C4—1221no—
480#459—1224no—
481#447—1224no—
482#447—1224no—
483C4×D8—1224no—
484C2×#107—611no—
485C2×#107—611no—
486C2×C4⋊C8—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×C22⋊C8—611no—
496C2×C22⋊C8—611no—
497C2×C4×C8—611no—
498#394—21no—
499#392—21no—
500#390—611no—
501#390—611no—
502#390C2×D6111yescharacteristic, complemented
503#389C2×D6111yescharacteristic, complemented
504#386—21no—
505#386—1221no—
506#386—1221no—
507#380—611no—
508#379—1221no—
509C4×C22⋊C4C2×D6111yescharacteristic
510#340—611no—
511#340—611no—
512#336—611no—
513#336—611no—
514C61#2514811yescharacteristic, complemented, Sylow
515C25—1221no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—611no—
521C22×D4—611no—
522C22×D4—1222no—
523C22×D4—1222no—
524C22×D4—1222no—
525C22×D4—1222no—
526C22×D4—1221no—
527C22×D4—2441no—
528C22×D4—2441no—
529C22×D4C22×D6111yescharacteristic
530C22×D4C22×D6111yescharacteristic
531C23×C4—21no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4C22×D6111yescharacteristic
535C2×D8—614no—
536C2×D8—1222no—
537C2×D8—1222no—
538C2×D8—1222no—
539C2×D8—1222no—
540C2×D8—1222no—
541C2×D8—1222no—
542C2×D8—1222no—
543C2×D8—1222no—
544C2×D8—1222no—
545C2×D8—2441no—
546C2×D8—2441no—
547C22×C8—611no—
548C22×C8—611no—
549C22×C8—611no—
550C22×C8—611no—
551#127—22no—
552#127—41no—
553#121—22no—
554#121—22no—
555#121—41no—
556#121—41no—
557#121—44no—
558C4×D4—22no—
559C4×D4—41no—
560C4×D4—1222no—
561C4×D4—1222no—
562C4×D4—2441no—
563C4×D4—2441no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—2444no—
582C2×C22⋊C4C22⋊D6111yescharacteristic
583C2×C22⋊C4C22⋊D6111yescharacteristic
584C2×C42C22×D6111yescharacteristic
585C2×C42C22×D6111yescharacteristic
586#107—1222no—
587#107—2441no—
588C4⋊C8—1222no—
589#102—614no—
590#102—1222no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—1222no—
596#102—2441no—
597C22⋊C8—1222no—
598C22⋊C8—1222no—
599C4×C8—1222no—
600#95—21no—
601#95—1221no—
602#95C22⋊D6111yescharacteristic
603#95C22⋊D6111yescharacteristic
604C24—21no—
605C24—21no—
606C24—1224no—
607C24—1221no—
608C24—1221no—
609C24—4881no—
610C24—4881no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24—2442no—
615C24C2×C22⋊D6111yescharacteristic
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—81no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4—81no—
639C2×D4—612no—
640C2×D4—612no—
641C2×D4—612no—
642C2×D4—612no—
643C2×D4—1224no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—2442no—
653C2×D4—2442no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4—2444no—
657C2×D4—2444no—
658C2×D4D4×D6112yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—81no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—4881no—
673C22×C4—4881no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4C2×C22⋊D6111yescharacteristic
679C22×C4C2×C22⋊D6111yescharacteristic
680C22×C4C2×C22⋊D6111yescharacteristic
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C2×C22⋊D6111yescharacteristic
683C22×C4C23×D6111yescharacteristic
684D8—1228no—
685D8—2444no—
686D8—2444no—
687D8—2444no—
688C2×C8—612no—
689C2×C8—612no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—42no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4D4×D6112yes—
709C22⋊C4—41no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—81no—
715C22⋊C4—4881no—
716C22⋊C4—4881no—
717C22⋊C4—2442no—
718C22⋊C4—2442no—
719C22⋊C4—2442no—
720C22⋊C4—2442no—
721C22⋊C4—2442no—
722C22⋊C4#1175819914yescomplemented
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—1222no—
748C23—1222no—
749C23—1222no—
750C23—1222no—
751C23—4884no—
752C23—4884no—
753C23—4884no—
754C23—4884no—
755C23—4884no—
756C23—2448no—
757C23—2448no—
758C23—2441no—
759C23—2441no—
760C23—2441no—
761C23—2441no—
762C23—2441no—
763C23—2441no—
764C23—2441no—
765C23—2441no—
766C23—2441no—
767C23—2441no—
768C23C2×#1175819912yes—
769C23C22×C22⋊D6111yescharacteristic
770D4—22no—
771D4—22no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—84no—
779D4—84no—
780D4—84no—
781D4—84no—
782D4—614no—
783D4—1222no—
784D4—1222no—
785D4—1222no—
786D4—1222no—
787D4—1222no—
788D4—2448no—
789D4—2441no—
790D4—2441no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—4884no—
816C2×C4—4884no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4C2×#1175819912yes—
824C2×C4C2×#1175819912yes—
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4C2×D4×D6111yescharacteristic
827C2×C4#41×D6111yescharacteristic
828C2×C4#41×D6111yescharacteristic
829C2×C4#1451982211yescharacteristic
830C2×C4#1451982211yescharacteristic
831C8—1222no—
832C8—1222no—
833C8—2441no—
834C8—2441no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—1224no—
857C22—48816no—
858C22—4881no—
859C22—4881no—
860C22—4881no—
861C22—4881no—
862C22—2442no—
863C22—2442no—
864C22—2442no—
865C22—2442no—
866C22—2442no—
867C22—2442no—
868C22—2442no—
869C22—2442no—
870C22—2442no—
871C22#1684026911yescharacteristic
872C22D4×C22⋊D6111yescharacteristic
873C22D4×C22⋊D6111yescharacteristic
874C22C22×#1175819911yescharacteristic
875C22#1684056011yescharacteristic
876C22#1684056511yescharacteristic
877C22#1684056511yescharacteristic
878C4—22no—
879C4—22no—
880C4—41no—
881C4—42no—
882C4—41no—
883C4—41no—
884C4—81no—
885C4—4881no—
886C4—4881no—
887C4#121×D6111yescharacteristic
888C4#1684034411yescharacteristic
889C4#1684040111yescharacteristic
890C4#1684040911yescharacteristic
891C2—42no—
892C2—82no—
893C2—161no—
894C2—4882no—
895C2—2444no—
896C2#2144935211yescharacteristic
897C2#2145581511yescharacteristic
898C2#2145605711yescharacteristic
899C2#2145736011yescharacteristic
900C2#2145742611yescharacteristic
901C2D4×#1175819911yescharacteristic
902C2D4×#1175819911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2428C2
socleC23×C61C22×D4
hypercenter#2428D61
hypocenterC61#25148
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2428

Complements

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

NH ≅ G/Ntype
1. C2×#16839954C2semidirect
2. C2×#16839895C2semidirect
3. C2×#16839895C2semidirect
4. C2×C4×#11758199C2semidirect
5. C22⋊C4×D244C2semidirect
6. #21447204C2semidirect
7. #21446998C2semidirect
8. #21446998C2semidirect
9. #21446890C2semidirect
10. #21446684C2semidirect
11. #21446427C2semidirect
12. #21446170C2semidirect
13. #21446167C2semidirect
14. #21446065C2semidirect
15. C61×#2428C2semidirect
28. C2×#14519710C22semidirect
29. C2×#14519710C22semidirect
30. C2×C4⋊#92418C22semidirect
31. C2×#14519698C22semidirect
32. C2×#14519698C22semidirect
33. C2×#14519698C22semidirect
34. C2×#14519698C22semidirect
41. C2×C4×#92418C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
52. C2×#127×C61C22semidirect
56. C2×C4×D4×C61C22semidirect
59. C61×#390C22semidirect
60. C61×#389C22semidirect
86. C2×#11758199D4semidirect
115. #14519697D4semidirect
243. C22⋊C4×C61D8semidirect
376. D244#121semidirect
444. #2428D61semidirect
472. C2×#127C2×D61semidirect
478. C2×C4×D4C2×D61semidirect
502. #390C2×D61semidirect
503. #389C2×D61semidirect
514. C61#25148semidirect
722. C22⋊C4#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×#168399542
C2×#168398952
C2×C4×#117581992
C22⋊C4×D2442
#214472042
#214469982
#214468902
#214466842
#214464272
#214461702
#214461672
#214460652
C61×#24282
#2514861