Finite Group Databasebeta

← #29723813

Subgroups — #29723813

Order 15616.

1204 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839896C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic, complemented
3#21449311C211yesmaximal, characteristic, complemented
4#21447340C211yesmaximal, characteristic, complemented
5#21447250C211yesmaximal, characteristic, complemented
6#21447129C211yesmaximal, characteristic, complemented
7#21447008C211yesmaximal, characteristic, complemented
8#21446505C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446080C211yesmaximal, characteristic, complemented
13#21445829C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic, complemented
20#16839896—24no—
21C4×#11758199—24no—
22C2×#14519710C2211yescharacteristic, complemented
23C2×#14519708C2211yescharacteristic, complemented
24C2×C4⋊#92418C2211yescharacteristic, complemented
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic, complemented
32C2×#14519697C2211yescharacteristic, complemented
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic, complemented
36#16839691—21no—
37#16839677—21no—
38#16839664C2211yescharacteristic, complemented
39#16839660C2211yescharacteristic, complemented
40#16839638—21no—
41#16839628C2211yescharacteristic, complemented
42#16839624—21no—
43#16839622C2211yescharacteristic
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C23×D4×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C22×C22⋊C4×C61—21no—
54C61×#390C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#386—21no—
57C61×#386—21no—
58C61×#380C2211yescharacteristic
59C61×#379—21no—
60C4×C22⋊C4×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C2×#11758199—22no—
65C2×#11758199—22no—
66C2×#11758199—22no—
67C2×#11758199—22no—
68C2×#11758199—41no—
69C2×#11758199D414yes—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519751—22no—
75#14519751—41no—
76C4×D244—22no—
77C4×D244—41no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×C22⋊Dic61—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87#14519710—22no—
88#14519708—41no—
89C4⋊#92418—41no—
90#14519698—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519698—22no—
95#14519698—41no—
96#14519697—22no—
97#14519697—41no—
98C22⋊#92418—22no—
99C22⋊#92418—41no—
100C4×#92418—22no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C25×C61—21no—
106C22×D4×C61—22no—
107C22×D4×C61—22no—
108C22×D4×C61—22no—
109C22×D4×C61—22no—
110C22×D4×C61—21no—
111C22×D4×C61—41no—
112C22×D4×C61—41no—
113C22×D4×C61C2311yescharacteristic
114C22×D4×C61C2311yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61—21no—
117C23×C4×C61C2311yescharacteristic
118C4×D4×C61—22no—
119C4×D4×C61—22no—
120C4×D4×C61—41no—
121C4×D4×C61—41no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—44no—
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C22⋊C4×C61D411yescharacteristic
134C2×C42×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136#95×C61—21no—
137#95×C61D411yescharacteristic
138#95×C61D411yescharacteristic
139C24×C61—21no—
140C24×C61—24no—
141C24×C61—21no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—42no—
145C24×C61—42no—
146C24×C61—81no—
147C24×C61—81no—
148C24×C61C2×D411yescharacteristic
149C23×D61—21no—
150C2×D4×C61—24no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—42no—
160C2×D4×C61—42no—
161C2×D4×C61—44no—
162C2×D4×C61—44no—
163C2×D4×C61—44no—
164C2×D4×C61—44no—
165C2×D4×C61C2×D412yes—
166C2×D4×C61#4112yes—
167C2×D4×C61#4112yes—
168C2×D4×C61#4112yes—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—42no—
178C22×C4×C61—42no—
179C22×C4×C61—42no—
180C22×C4×C61—42no—
181C22×C4×C61—81no—
182C22×C4×C61—81no—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—81no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244C2×D412yes—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—81no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—81no—
216C22⋊C4×C61—81no—
217C42×C61—21no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C22⋊Dic61—81no—
222#11758199—28no—
223#11758199—44no—
224#11758198—42no—
225#11758198—42no—
226#11758198—81no—
227#11758198—81no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234#11758196—81no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418C2×D412yes—
247C23×C61—21no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—22no—
257C23×C61—48no—
258C23×C61—48no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—84no—
270C23×C61—84no—
271C23×C61—84no—
272C23×C61—84no—
273C23×C61—84no—
274C23×C61#13512yes—
275C23×C61C22×D411yescharacteristic
276C22×D61—22no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—22no—
288D4×C61—48no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61#12314yes—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—84no—
317C2×C4×C61—84no—
318C2×C4×C61AGL(1,ℤ/8)12yes—
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C2×C4×C61C2×#4111yescharacteristic
323C2×C4×C61H(5,𝔽2)11yescharacteristic
324C2×C4×C61H(5,𝔽2)11yescharacteristic
325C22⋊D61—84no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335D244—22no—
336D244—22no—
337D244—41no—
338D244—41no—
339C4×D61—84no—
340#92418—22no—
341#92418—41no—
342#92418—41no—
343#92418—41no—
344#24897—611nomaximal, Sylow
345C22×C61—22no—
346C22×C61—24no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—42no—
350C22×C61—41no—
351C22×C61—42no—
352C22×C61—41no—
353C22×C61—42no—
354C22×C61—41no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—41no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—816no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61#52511yescharacteristic
368C22×C61D4211yescharacteristic
369C22×C61#54611yescharacteristic
370C22×C61C2×#13511yescharacteristic
371C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C61#57611yescharacteristic
373C22×C61#57611yescharacteristic
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—81no—
378C2×D61—81no—
379C2×D61—81no—
380C2×D61—81no—
381C4×C61—22no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61—41no—
385C4×C61—41no—
386C4×C61—81no—
387C4×C61—81no—
388C4×C61C2×#12311yescharacteristic
389C4×C61#53811yescharacteristic
390C4×C61#54611yescharacteristic
391C4×C61#55111yescharacteristic
392Dic61—81no—
393Dic61—81no—
394Dic61—81no—
395C2×#447—611no—
396C2×C4×D8—611no—
397#2420—611no—
398D4×C22⋊C4D6111yescharacteristic, complemented
399#2092—611no—
400#2076—611no—
401#2054—611no—
402#2034—611no—
403#1934—611no—
404#1923—611no—
405#1879—611no—
406#1879—611no—
407#1864—611no—
408#1804—611no—
409#1786—611no—
410C2×C61—42no—
411C2×C61—44no—
412C2×C61—82no—
413C2×C61#241811yescharacteristic
414C2×C61#310511yescharacteristic
415C2×C61#312211yescharacteristic
416C2×C61#326411yescharacteristic
417C2×C61#328011yescharacteristic
418C2×C61#329711yescharacteristic
419C2×C61#332511yescharacteristic
420D61—82no—
421C23×D4C2×D6111yescharacteristic
422C22×D8—611no—
423C22×D8—611no—
424C2×#121—611no—
425C2×C4×D4—611no—
426C2×C4×D4C2×D6111yescharacteristic
427C2×C4×D4C2×D6111yescharacteristic
428C22×C22⋊C4—21no—
429#447—1224no—
430C4×D8—1224no—
431C2×#107—611no—
432C2×#106—611no—
433C2×C4⋊C8—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C4×C8—611no—
445#397—1221no—
446#394—1221no—
447#390—611no—
448#390C2×D6111yescharacteristic
449#390C2×D6111yescharacteristic
450#389—611no—
451#386—21no—
452#386—21no—
453#386—1221no—
454#382—611no—
455#381—1221no—
456#380—611no—
457#380C2×D6111yescharacteristic
458#379—21no—
459C4×C22⋊C4C2×D6111yescharacteristic
460#340—611no—
461#340—611no—
462#340—611no—
463#340—611no—
464#336—611no—
465#336—611no—
466C61#2489711yescharacteristic, complemented, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4—611no—
476C22×D4—1221no—
477C22×D4C22×D6111yescharacteristic
478C22×D4C22×D6111yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—1221no—
482C23×C4C22×D6111yescharacteristic
483C2×D8—614no—
484C2×D8—1222no—
485C2×D8—1222no—
486C2×D8—1222no—
487C2×D8—1222no—
488C2×D8—2441no—
489C22×C8—611no—
490C22×C8—611no—
491C22×C8—611no—
492C22×C8—611no—
493#121—1222no—
494#121—2441no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—41no—
498C4×D4—41no—
499C4×D4—1222no—
500C4×D4—2441no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—44no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4C22⋊D6111yescharacteristic
521C2×C22⋊C4C22⋊D6111yescharacteristic
522C2×C42C22×D6111yescharacteristic
523C2×C42C22×D6111yescharacteristic
524#107—1222no—
525#106—2441no—
526C4⋊C8—2441no—
527#102—1222no—
528#102—1222no—
529#102—1222no—
530#102—1222no—
531#102—1222no—
532#102—1222no—
533#102—2441no—
534#102—2441no—
535C22⋊C8—1222no—
536C22⋊C8—2441no—
537C4×C8—1222no—
538#95—21no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543#95C22⋊D6111yescharacteristic
544#95C22⋊D6111yescharacteristic
545C24—21no—
546C24—24no—
547C24—21no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24—1221no—
555C24C2×C22⋊D6111yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—612no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—4881no—
578C2×D4—2442no—
579C2×D4—2442no—
580C2×D4#1175822212yes—
581C2×D4#1175822212yes—
582C2×D4D4×D6112yes—
583C2×D4#1175822412yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—81no—
597C22×C4—81no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—4881no—
602C22×C4—2442no—
603C22×C4—2442no—
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C2×C22⋊D6111yescharacteristic
606C22×C4C2×C22⋊D6111yescharacteristic
607C22×C4C2×C22⋊D6111yescharacteristic
608C22×C4C2×C22⋊D6111yescharacteristic
609C22×C4C23×D6111yescharacteristic
610D8—1228no—
611D8—2444no—
612C2×C8—612no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—4881no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—4881no—
645C22⋊C4—4881no—
646C22⋊C4—4881no—
647C22⋊C4—2442no—
648C22⋊C4—2442no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—21no—
660C23—22no—
661C23—21no—
662C23—22no—
663C23—48no—
664C23—48no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—1222no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23#1451979712yes—
688C23C22×C22⋊D6111yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—41no—
696D4—41no—
697D4—1222no—
698D4—1222no—
699D4—4884no—
700D4—2441no—
701D4—2441no—
702D4#1451975914yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—4884no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4#1451980312yes—
740C2×C4C2×D4×D6111yescharacteristic
741C2×C4C2×#1175822411yescharacteristic
742C2×C4C2×#1175822211yescharacteristic
743C2×C4C2×#1175822211yescharacteristic
744C2×C4#1451982211yescharacteristic
745C2×C4#1451982211yescharacteristic
746C8—1222no—
747C8—2441no—
748C8—2441no—
749C8—2441no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—816no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—4881no—
773C22—4881no—
774C22—4881no—
775C22—4881no—
776C22—2442no—
777C22—2442no—
778C22—2442no—
779C22#1684027311yescharacteristic
780C22D4×C22⋊D6111yescharacteristic
781C22#1684040611yescharacteristic
782C22C2×#1451979711yescharacteristic
783C22C2×#1451980311yescharacteristic
784C22#1684056511yescharacteristic
785C22#1684056511yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—4881no—
794C4—4881no—
795C4—4881no—
796C4C2×#1451975911yescharacteristic
797C4#1684035011yescharacteristic
798C4#1684040211yescharacteristic
799C4#1684043811yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—4882no—
804C2#2144928111yescharacteristic
805C2#2145586611yescharacteristic
806C2#2145606211yescharacteristic
807C2#2145729511yescharacteristic
808C2#2145750011yescharacteristic
809C2#2145766911yescharacteristic
810C2#2145806111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingD4×C22⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
hypercenterD4×C22⋊C4D61
hypocenterC61#24897
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
2. C2×C4×#11758199C2semidirect
3. #21449311C2semidirect
4. #21447340C2semidirect
5. #21447250C2semidirect
6. #21447129C2semidirect
7. #21447008C2semidirect
8. #21446505C2semidirect
9. #21446427C2semidirect
10. #21446170C2semidirect
11. #21446167C2semidirect
12. #21446080C2semidirect
13. #21445829C2semidirect
14. #21445750C2semidirect
15. D4×C22⋊C4×C61C2semidirect
19. C2×C4×D244C22semidirect
22. C2×#14519710C22semidirect
23. C2×#14519708C22semidirect
24. C2×C4⋊#92418C22semidirect
31. C2×#14519697C22semidirect
32. C2×#14519697C22semidirect
35. C2×C4×#92418C22semidirect
38. #16839664C22semidirect
39. #16839660C22semidirect
41. #16839628C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
398. D4×C22⋊C4D61semidirect
466. C61#24897semidirect

Maximal subgroups

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

subgroupindex
C2×#168398962
C2×C4×#117581992
#214493112
#214473402
#214472502
#214471292
#214470082
#214465052
#214464272
#214461702
#214461672
#214460802
#214458292
#214457502
D4×C22⋊C4×C612
#2489761