Finite Group Databasebeta

← #29723702

Subgroups — #29723702

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840086C211yesmaximal, characteristic, complemented
2C2×#16839766C211yesmaximal, characteristic, complemented
3#21449175C211yesmaximal, characteristic
4#21447348C211yesmaximal, characteristic, complemented
5#21447223C211yesmaximal, characteristic, complemented
6#21447008C211yesmaximal, characteristic, complemented
7#21447001C211yesmaximal, characteristic, complemented
8#21446446C211yesmaximal, characteristic, complemented
9#21446446C211yesmaximal, characteristic, complemented
10#21446141C211yesmaximal, characteristic, complemented
11#21446117C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445850C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic, complemented
15C61×#2354C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519745—21no—
21#16840086—24no—
22C2×#14519710C2211yescharacteristic, complemented
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519708C2211yescharacteristic, complemented
25C2×#14519708C2211yescharacteristic, complemented
26#16839766—24no—
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic, complemented
37C2×C22⋊#92418C2211yescharacteristic, complemented
38#16839679—21no—
39#16839671—21no—
40#16839664C2211yescharacteristic
41#16839664C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839617—21no—
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C2×C4×D4×C61C2211yescharacteristic
51C2×#117×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic, complemented
53C61×#390—21no—
54C61×#388—21no—
55C61×#388—21no—
56C61×#384C2211yescharacteristic, complemented
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic, complemented
59C4×C4⋊C4×C61—21no—
60C4×C4⋊C4×C61C2211yescharacteristic, complemented
61C24×D61—21no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—21no—
67C22×D244—41no—
68C22×D244—41no—
69C22×D244C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C2×#11758194—22no—
74C2×#11758194—22no—
75C2×#11758194—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80#14519751—22no—
81#14519751—22no—
82#14519751—41no—
83#14519751—41no—
84#14519745—44no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C22⋊Dic61—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94#14519710—22no—
95#14519710—41no—
96#14519708—22no—
97#14519708—41no—
98#14519697—22no—
99#14519697—22no—
100#14519697—22no—
101#14519697—22no—
102#14519697—22no—
103#14519697—41no—
104#14519697—41no—
105#14519697D414yescomplemented
106C22⋊#92418—22no—
107C22⋊#92418—22no—
108C22⋊#92418—41no—
109#14519684—21no—
110C22×D4×C61D411yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C23×C4×C61C2311yescharacteristic
113C4×D4×C61—22no—
114C4×D4×C61—22no—
115#117×C61—22no—
116#117×C61—22no—
117#117×C61—41no—
118#117×C61—41no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61D411yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C42×C61—21no—
133C2×C42×C61—21no—
134C2×C42×C61—21no—
135C2×C42×C61C2311yescharacteristic
136#95×C61—21no—
137#95×C61—21no—
138#95×C61—21no—
139C24×C61C2×D411yescharacteristic
140C24×C61C2×D411yescharacteristic
141C23×D61—21no—
142C23×D61—21no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—42no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61—81no—
149C23×D61—81no—
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—41no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61#4112yes—
172C22×C4×C61#4112yes—
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—42no—
175C2×C22⋊D61—42no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—81no—
179C2×C22⋊D61—81no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C2×D244—28no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—44no—
194C2×D244—44no—
195C2×D244—42no—
196C2×D244—42no—
197C2×D244—44no—
198C2×D244—42no—
199C2×D244C2×D412yes—
200C2×D244#4112yes—
201C4⋊C4×C61—22no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61—81no—
211C4⋊C4×C61C2×D412yes—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—81no—
217C22⋊C4×C61—81no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—42no—
221C42×C61—42no—
222C42×C61—42no—
223C22⋊Dic61—42no—
224#11758198—42no—
225#11758198—42no—
226#11758198—42no—
227#11758198—42no—
228#11758198—81no—
229#11758198—81no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234#11758194—44no—
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—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61#12312yes—
261C23×C61C22×D411yescharacteristic
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—48no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—84no—
278C22×D61—84no—
279C22×D61—84no—
280C22×D61—84no—
281C22×D61—84no—
282C22×D61—84no—
283D4×C61—44no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—22no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
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#12312yes—
315C2×C4×C61AGL(1,ℤ/8)12yes—
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61H(5,𝔽2)11yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C22⋊D61—84no—
323C22⋊D61—84no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330D244—22no—
331D244—22no—
332D244—22no—
333D244—22no—
334D244—48no—
335D244—41no—
336D244—41no—
337D244—41no—
338D244—41no—
339#92418—22no—
340#92418—41no—
341#92418—41no—
342#92418—41no—
343#24890—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61C2×#12311yescharacteristic
359C22×C61D4211yescharacteristic
360C22×C61#54611yescharacteristic
361C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C61#57511yescharacteristic
363C22×C61#57611yescharacteristic
364C22×C61#57711yescharacteristic
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—816no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C2×D61—81no—
377C2×D61—81no—
378C2×D61—81no—
379C2×D61—81no—
380C4×C61—22no—
381C4×C61—22no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61—42no—
385C4×C61—81no—
386C4×C61—81no—
387C4×C61—81no—
388C4×C61#52511yescharacteristic
389C4×C61#53811yescharacteristic
390C4×C61#54611yescharacteristic
391C4×C61#55111yescharacteristic
392Dic61—81no—
393Dic61—81no—
394C2×#482—611no—
395C2×#418—611no—
396#2408—611no—
397#2354D6111yescharacteristic, complemented
398#2093—611no—
399#2071—611no—
400#2034—611no—
401#2033—611no—
402#1926—611no—
403#1926—611no—
404#1875—611no—
405#1870—611no—
406#1854—611no—
407#1809—611no—
408#1786—611no—
409C2×C61—42no—
410C2×C61—81no—
411C2×C61#241811yescharacteristic
412C2×C61#309411yescharacteristic
413C2×C61#309611yescharacteristic
414C2×C61#326711yescharacteristic
415C2×C61#327411yescharacteristic
416C2×C61#331911yescharacteristic
417C2×C61#332411yescharacteristic
418D61—82no—
419D61—82no—
420C23×D4—611no—
421C22×M16—611no—
422C2×#121—611no—
423C2×#121—611no—
424C2×#120—1221no—
425C2×C4×D4C2×D6111yescharacteristic
426C2×#117C2×D6111yescharacteristic
427C2×#117C2×D6111yescharacteristic, complemented
428#482—1224no—
429C2×#107—611no—
430C2×#107—611no—
431C2×#106—611no—
432C2×#106—611no—
433#418—1224no—
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×C22⋊C8—611no—
445#394—1221no—
446#392—1221no—
447#390—21no—
448#390—611no—
449#390—611no—
450#388—21no—
451#388—21no—
452#384C2×D6111yescharacteristic, complemented
453#380—611no—
454#380C2×D6111yescharacteristic
455#380C2×D6111yescharacteristic, complemented
456#379—1221no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2×D6111yescharacteristic, complemented
459#340—611no—
460#340—611no—
461#340—611no—
462#340—611no—
463#336—611no—
464#336—611no—
465C61#2489011yescharacteristic, complemented, Sylow
466C25—1221no—
467C22×D4—611no—
468C22×D4—611no—
469C22×D4—1222no—
470C22×D4—1222no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1222no—
474C22×D4—1222no—
475C22×D4—1221no—
476C22×D4—2441no—
477C22×D4—2441no—
478C22×D4C22⋊D6111yescharacteristic
479C23×C4C22×D6111yescharacteristic
480C23×C4C22×D6111yescharacteristic
481C2×M16—1222no—
482C2×M16—1222no—
483C2×M16—2441no—
484C22×C8—611no—
485C22×C8—611no—
486C22×C8—611no—
487C22×C8—611no—
488#121—1222no—
489#121—1222no—
490#121—2441no—
491#121—2441no—
492#120—2444no—
493C4×D4—22no—
494C4×D4—22no—
495#117—22no—
496#117—22no—
497#117—41no—
498#117—41no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4C22⋊D6111yescharacteristic
504C2×C4⋊C4C22×D6111yescharacteristic
505C2×C4⋊C4C22×D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4C22⋊D6111yescharacteristic
520C2×C22⋊C4C22⋊D6111yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42C22×D6111yescharacteristic
525#107—1222no—
526#107—2441no—
527#106—1222no—
528#106—2441no—
529#102—614no—
530#102—1222no—
531#102—1222no—
532#102—1222no—
533#102—1222no—
534#102—1222no—
535#102—2441no—
536#102—2441no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—2441no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—1221no—
544C24—1221no—
545C24—1221no—
546C24—4881no—
547C24—4881no—
548C24—2442no—
549C24—2442no—
550C24—2442no—
551C24—2442no—
552C24—2442no—
553C24C2×C22⋊D6111yescharacteristic
554C24C2×C22⋊D6111yescharacteristic
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—41no—
558C2×D4—612no—
559C2×D4—612no—
560C2×D4—1228no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—4881no—
572C2×D4—4881no—
573C2×D4—2444no—
574C2×D4—2444no—
575C2×D4—2442no—
576C2×D4—2442no—
577C2×D4—2444no—
578C2×D4—2442no—
579C2×D4—2442no—
580C2×D4—2442no—
581C2×D4—2442no—
582C2×D4—2442no—
583C22×C4—21no—
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—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4#1175822212yes—
600C22×C4#1175822212yes—
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C23×D6111yescharacteristic
606M16—2444no—
607C2×C8—612no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—42no—
628C4⋊C4—81no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C4⋊C4D4×D6112yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—4881no—
641C22⋊C4—4881no—
642C22⋊C4—2442no—
643C22⋊C4—2442no—
644C22⋊C4—2442no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C42—21no—
648C42—21no—
649C42—42no—
650C42—42no—
651C42—42no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—1222no—
666C23—1222no—
667C23—4884no—
668C23—4884no—
669C23—4884no—
670C23—4884no—
671C23—4884no—
672C23—4884no—
673C23—2448no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23#1451976012yes—
687C23C22×C22⋊D6111yescharacteristic
688D4—44no—
689D4—1222no—
690D4—1222no—
691D4—1222no—
692D4—1222no—
693D4—4884no—
694D4—4884no—
695D4—2448no—
696D4—2441no—
697D4—2441no—
698D4—2441no—
699D4—2441no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
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—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4#1451976012yes—
737C2×C4#1451980212yes—
738C2×C4C2×D4×D6111yescharacteristic
739C2×C4#41×D6111yescharacteristic
740C2×C4C2×#1175822211yescharacteristic
741C2×C4C2×#1175822211yescharacteristic
742C2×C4#1451982211yescharacteristic
743C2×C4#1451982311yescharacteristic
744C8—1222no—
745C8—2441no—
746C8—2441no—
747C8—2441no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—48816no—
763C22—4881no—
764C22—4881no—
765C22—4881no—
766C22—4881no—
767C22—4881no—
768C22—4881no—
769C22—4881no—
770C22—4881no—
771C22—2442no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22C2×#1451976011yescharacteristic
778C22D4×C22⋊D6111yescharacteristic
779C22#1684040011yescharacteristic
780C22C2×#1451980211yescharacteristic
781C22#1684056011yescharacteristic
782C22#1684056511yescharacteristic
783C22#1684057011yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—42no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—4881no—
793C4—4881no—
794C4#1684027111yescharacteristic
795C4#1684034511yescharacteristic
796C4#1684040811yescharacteristic
797C4#1684044111yescharacteristic
798C2—42no—
799C2—81no—
800C2—4882no—
801C2—4882no—
802C2#2144927511yescharacteristic
803C2#2145575911yescharacteristic
804C2#2145577711yescharacteristic
805C2#2145734511yescharacteristic
806C2#2145743911yescharacteristic
807C2#2145796911yescharacteristic
808C2#2145804411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2354C2
socleC23×C61C22×D4
prime radical#21449175C2
hypercenter#2354D61
hypocenterC61#24890
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. C2×#16840086C2semidirect
2. C2×#16839766C2semidirect
4. #21447348C2semidirect
5. #21447223C2semidirect
6. #21447008C2semidirect
7. #21447001C2semidirect
8. #21446446C2semidirect
9. #21446446C2semidirect
10. #21446141C2semidirect
11. #21446117C2semidirect
12. #21446018C2semidirect
13. #21445850C2semidirect
14. #21445749C2semidirect
15. C61×#2354C2semidirect
22. C2×#14519710C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519708C22semidirect
25. C2×#14519708C22semidirect
36. C2×C22⋊#92418C22semidirect
37. C2×C22⋊#92418C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
52. C2×#117×C61C22semidirect
56. C61×#384C22semidirect
58. C61×#380C22semidirect
60. C4×C4⋊C4×C61C22semidirect
105. #14519697D4semidirect
397. #2354D61semidirect
427. C2×#117C2×D61semidirect
452. #384C2×D61semidirect
455. #380C2×D61semidirect
458. C4×C4⋊C4C2×D61semidirect
465. C61#24890semidirect

Maximal subgroups

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

subgroupindex
C2×#168400862
C2×#168397662
#214491752
#214473482
#214472232
#214470082
#214470012
#214464462
#214461412
#214461172
#214460182
#214458502
#214457492
C61×#23542
#2489061