Finite Group Databasebeta

← #29727386

Subgroups — #29727386

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×#16839957C211yesmaximal, characteristic, complemented
2C2×#16839896C211yesmaximal, characteristic, complemented
3C2×#16839896C211yesmaximal, characteristic, complemented
4C2×C4×#11758199C211yesmaximal, characteristic, complemented
5#21449407C211yesmaximal, characteristic, complemented
6#21447207C211yesmaximal, characteristic, complemented
7#21447001C211yesmaximal, characteristic, complemented
8#21447001C211yesmaximal, characteristic, complemented
9#21446889C211yesmaximal, characteristic, complemented
10#21446684C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic, complemented
12#21446170C211yesmaximal, characteristic, complemented
13#21446167C211yesmaximal, characteristic, complemented
14#21446066C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C2×#14519774C2211yescharacteristic, complemented
21C2×#14519751C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519750—21no—
24C2×C4×D244C2211yescharacteristic, complemented
25#16839957—24no—
26#16839896—24no—
27#16839896—24no—
28C4×#11758199—24no—
29C2×#14519710C2211yescharacteristic, complemented
30C2×#14519710C2211yescharacteristic, complemented
31C2×C4⋊#92418C2211yescharacteristic, complemented
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519697C2211yescharacteristic, complemented
37C2×#14519697C2211yescharacteristic, complemented
38C2×#14519697C2211yescharacteristic, complemented
39C2×#14519697C2211yescharacteristic, complemented
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C4×#92418C2211yescharacteristic, complemented
43#16839680—21no—
44#16839671—21no—
45#16839664C2211yescharacteristic, complemented
46#16839660C2211yescharacteristic, complemented
47#16839640—21no—
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C23×D4×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C22×C22⋊C4×C61—21no—
56C61×#390C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#386—21no—
59C61×#386—21no—
60C61×#380C2211yescharacteristic
61C61×#379—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C22×D244—21no—
64C22×D244—21no—
65C22×D244C2311yescharacteristic
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C22×C4×D61—21no—
70C2×#11758199—22no—
71C2×#11758199—22no—
72C2×#11758199—22no—
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199—22no—
77C2×#11758199—22no—
78C2×#11758199—22no—
79C2×#11758199—41no—
80C2×#11758199—41no—
81C2×#11758199D414yescomplemented
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519774—22no—
87#14519774—41no—
88#14519751—22no—
89#14519751—22no—
90#14519751—41no—
91#14519751—41no—
92#14519750—44no—
93C4×D244—22no—
94C4×D244—41no—
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103#14519710—22no—
104#14519710—41no—
105C4⋊#92418—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698D414yescomplemented
110#14519697—22no—
111#14519697—22no—
112#14519697—22no—
113#14519697—41no—
114C22⋊#92418—22no—
115C22⋊#92418—22no—
116C4×#92418—22no—
117#14519684—21no—
118C25×C61—21no—
119C22×D4×C61—22no—
120C22×D4×C61—22no—
121C22×D4×C61—22no—
122C22×D4×C61—22no—
123C22×D4×C61—21no—
124C22×D4×C61—41no—
125C22×D4×C61—41no—
126C22×D4×C61C2311yescharacteristic
127C22×D4×C61C2311yescharacteristic
128C23×C4×C61—21no—
129C23×C4×C61—21no—
130C23×C4×C61C2311yescharacteristic
131C4×D4×C61—22no—
132C4×D4×C61—22no—
133C4×D4×C61—41no—
134C4×D4×C61—41no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—44no—
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—24no—
154C24×C61—21no—
155C24×C61—42no—
156C24×C61—42no—
157C24×C61—42no—
158C24×C61—42no—
159C24×C61—81no—
160C24×C61—81no—
161C24×C61C2×D411yescharacteristic
162C23×D61—21no—
163C23×D61—21no—
164C2×D4×C61—24no—
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—42no—
174C2×D4×C61—42no—
175C2×D4×C61—44no—
176C2×D4×C61—44no—
177C2×D4×C61—44no—
178C2×D4×C61—44no—
179C2×D4×C61C2×D412yes—
180C2×D4×C61C2×D412yes—
181C2×D4×C61#4112yes—
182C2×D4×C61#4112yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—42no—
192C22×C4×C61—42no—
193C22×C4×C61—42no—
194C22×C4×C61—42no—
195C22×C4×C61—81no—
196C22×C4×C61—81no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—81no—
208C2×C22⋊D61—81no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—42no—
223C2×D244—42no—
224C2×D244—42no—
225C2×D244—42no—
226C2×D244—81no—
227C2×D244—81no—
228C2×D244C2×D412yes—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—81no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C22⋊C4×C61—41no—
237C22⋊C4×C61—42no—
238C22⋊C4×C61—42no—
239C22⋊C4×C61—42no—
240C22⋊C4×C61—42no—
241C22⋊C4×C61—42no—
242C22⋊C4×C61—81no—
243C22⋊C4×C61—81no—
244C22⋊C4×C61D814yescomplemented
245C42×C61—21no—
246C42×C61—21no—
247C42×C61—21no—
248C42×C61—21no—
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—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61C2×D412yes—
262#11758196—42no—
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—22no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—22no—
285C23×C61—48no—
286C23×C61—48no—
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×C61—41no—
296C23×C61—41no—
297C23×C61—84no—
298C23×C61—84no—
299C23×C61—84no—
300C23×C61—84no—
301C23×C61—84no—
302C23×C61C2×D812yes—
303C23×C61C22×D411yescharacteristic
304C22×D61—22no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—48no—
324D4×C61—41no—
325D4×C61—41no—
326D4×C61#12114yescomplemented
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
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—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
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—84no—
351C2×C4×C61—84no—
352C2×C4×C61C2×D812yes—
353C2×C4×C61C2×D812yes—
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C2×#4111yescharacteristic
357C2×C4×C61C2×#4111yescharacteristic
358C2×C4×C61H(5,𝔽2)11yescharacteristic
359C2×C4×C61H(5,𝔽2)11yescharacteristic
360C22⋊D61—84no—
361C22⋊D61—84no—
362C2×Dic61—22no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368D244—22no—
369D244—22no—
370D244—41no—
371D244—41no—
372D244—41no—
373D244—41no—
374D244—41no—
375D244—41no—
376D244—84no—
377D244—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—24no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—42no—
389C22×C61—41no—
390C22×C61—42no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—42no—
394C22×C61—41no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—816no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61#52511yescharacteristic
407C22×C61D4211yescharacteristic
408C22×C61D4211yescharacteristic
409C22×C61C22×D811yescharacteristic
410C22×C61#57511yescharacteristic
411C22×C61#57611yescharacteristic
412C22×C61#57611yescharacteristic
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—81no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61—81no—
421C2×D61—81no—
422C2×D61—81no—
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—81no—
433C4×C61—81no—
434C4×C61C2×#12111yescharacteristic
435C4×C61#53811yescharacteristic
436C4×C61#54611yescharacteristic
437C4×C61#54611yescharacteristic
438Dic61—42no—
439Dic61—81no—
440C2×#459—611no—
441C2×#447—611no—
442C2×#447—611no—
443C2×C4×D8—611no—
444#2428—611no—
445D4×C22⋊C4D6111yescharacteristic, complemented
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—44no—
457C2×C61—82no—
458C2×C61#242411yescharacteristic
459C2×C61#310011yescharacteristic
460C2×C61#312211yescharacteristic
461C2×C61#326811yescharacteristic
462C2×C61#327311yescharacteristic
463C2×C61D4×D811yescharacteristic
464C2×C61D4×D811yescharacteristic
465D61—82no—
466D61—161no—
467C23×D4C2×D6111yescharacteristic
468C22×D8—611no—
469C22×D8—611no—
470C22×D8—611no—
471C22×D8—611no—
472C2×#127—611no—
473C2×#121—611no—
474C2×#121—611no—
475C2×#121—1221no—
476C2×C4×D4—611no—
477C2×C4×D4C2×D6111yescharacteristic
478C2×C4×D4C2×D6111yescharacteristic
479C22×C22⋊C4—21no—
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—1221no—
499#392—1221no—
500#390—611no—
501#390C2×D6111yescharacteristic
502#390C2×D6111yescharacteristic
503#389—611no—
504#386—21no—
505#386—21no—
506#386—1221no—
507#380C2×D6111yescharacteristic
508#379—21no—
509C4×C22⋊C4C2×D6111yescharacteristic
510#340—611no—
511#340—611no—
512#336—611no—
513#336—611no—
514C61#2514811yescharacteristic, complemented, Sylow
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—611no—
524C22×D4—611no—
525C22×D4—1221no—
526C22×D4—1221no—
527C22×D4—1221no—
528C22×D4—1221no—
529C22×D4C22×D6111yescharacteristic
530C22×D4C22×D6111yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
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—1222no—
552#127—2441no—
553#121—1222no—
554#121—1222no—
555#121—2441no—
556#121—2441no—
557#121—2444no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—1222no—
563C4×D4—2441no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—1221no—
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—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—44no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
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—24no—
606C24—21no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24—1221no—
614C24—1221no—
615C24C2×C22⋊D6111yescharacteristic
616C2×D4—24no—
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—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—612no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—4881no—
644C2×D4—4881no—
645C2×D4—4881no—
646C2×D4—4881no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4—2442no—
653C2×D4—2442no—
654C2×D4—2442no—
655C2×D4#1175822212yes—
656C2×D4#1175822212yes—
657C2×D4D4×D6112yes—
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—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—4881no—
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—21no—
704C4⋊C4—612no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—2442no—
709C22⋊C4—41no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—81no—
716C22⋊C4—81no—
717C22⋊C4—4881no—
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—22no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—48no—
738C23—48no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—1222no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
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—22no—
773D4—22no—
774D4—22no—
775D4—48no—
776D4—41no—
777D4—41no—
778D4—1222no—
779D4—1222no—
780D4—4884no—
781D4—4884no—
782D4—4884no—
783D4—4884no—
784D4—2441no—
785D4—2441no—
786D4—2441no—
787D4—2441no—
788D4—2441no—
789D4—2441no—
790D4#1451975014yescomplemented
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—21no—
803C2×C4—21no—
804C2×C4—41no—
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—84no—
816C2×C4—1222no—
817C2×C4—4884no—
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×C4C2×#1175822211yescharacteristic
828C2×C4C2×#1175822211yescharacteristic
829C2×C4#1451982211yescharacteristic
830C2×C4#1451982211yescharacteristic
831C8—1222no—
832C8—1222no—
833C8—2441no—
834C8—2441no—
835C22—22no—
836C22—22no—
837C22—24no—
838C22—22no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—42no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—4881no—
858C22—4881no—
859C22—4881no—
860C22—4881no—
861C22—4881no—
862C22—4881no—
863C22—4881no—
864C22—4881no—
865C22—4881no—
866C22—4881no—
867C22—4881no—
868C22—2442no—
869C22—2442no—
870C22—2442no—
871C22#1684027311yescharacteristic
872C22D4×C22⋊D6111yescharacteristic
873C22D4×C22⋊D6111yescharacteristic
874C22C22×#1175819911yescharacteristic
875C22#1684056011yescharacteristic
876C22#1684056511yescharacteristic
877C22#1684056511yescharacteristic
878C4—22no—
879C4—22no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—4881no—
886C4—2442no—
887C4C2×#1451975011yescharacteristic
888C4#1684035011yescharacteristic
889C4#1684040211yescharacteristic
890C4#1684040211yescharacteristic
891C2—42no—
892C2—44no—
893C2—82no—
894C2—9761no—
895C2—4882no—
896C2#2144935511yescharacteristic
897C2#2145581911yescharacteristic
898C2#2145606211yescharacteristic
899C2#2145735511yescharacteristic
900C2#2145742611yescharacteristic
901C2D4×#1175819911yescharacteristic
902C2D4×#1175819911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
hypercenterD4×C22⋊C4D61
hypocenterC61#25148
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16839957C2semidirect
2. C2×#16839896C2semidirect
3. C2×#16839896C2semidirect
4. C2×C4×#11758199C2semidirect
5. #21449407C2semidirect
6. #21447207C2semidirect
7. #21447001C2semidirect
8. #21447001C2semidirect
9. #21446889C2semidirect
10. #21446684C2semidirect
11. #21446427C2semidirect
12. #21446170C2semidirect
13. #21446167C2semidirect
14. #21446066C2semidirect
15. D4×C22⋊C4×C61C2semidirect
20. C2×#14519774C22semidirect
24. C2×C4×D244C22semidirect
29. C2×#14519710C22semidirect
30. C2×#14519710C22semidirect
31. C2×C4⋊#92418C22semidirect
36. C2×#14519697C22semidirect
37. C2×#14519697C22semidirect
38. C2×#14519697C22semidirect
39. C2×#14519697C22semidirect
42. C2×C4×#92418C22semidirect
45. #16839664C22semidirect
46. #16839660C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
81. C2×#11758199D4semidirect
109. #14519698D4semidirect
244. C22⋊C4×C61D8semidirect
326. D4×C61#121semidirect
445. D4×C22⋊C4D61semidirect
514. C61#25148semidirect
722. C22⋊C4#11758199semidirect
790. D4#14519750semidirect

Maximal subgroups

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

subgroupindex
C2×#168399572
C2×#168398962
C2×C4×#117581992
#214494072
#214472072
#214470012
#214468892
#214466842
#214464272
#214461702
#214461672
#214460662
D4×C22⋊C4×C612
#2514861