Finite Group Databasebeta

← #29712219

Subgroups — #29712219

Order 15616.

1332 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839905C211yesmaximal, characteristic, complemented
2C2×#16839756C211yesmaximal, characteristic, complemented
3#21449164C211yesmaximal, characteristic, complemented
4#21446957C211yesmaximal, characteristic, complemented
5#21446952C211yesmaximal, characteristic, complemented
6#21446822C211yesmaximal, characteristic, complemented
7#21446815C211yesmaximal, characteristic, complemented
8#21446248C211yesmaximal, characteristic, complemented
9#21446167C211yesmaximal, characteristic, complemented
10#21446153C211yesmaximal, characteristic, complemented
11#21446141C211yesmaximal, characteristic, complemented
12#21446131C211yesmaximal, characteristic, complemented
13#21446112C211yesmaximal, characteristic, complemented
14#21445914C211yesmaximal, characteristic, complemented
15C2×C61×#555C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22#16839905—24no—
23#16839756—24no—
24C2×#14519700C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35#16839677—21no—
36#16839670—21no—
37#16839668C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839638—21no—
40#16839633—21no—
41#16839622C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C61×#555—24no—
51C61×#555—24no—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×#124×C61—21no—
54C2×#124×C61—21no—
55C2×#121×C61—21no—
56C2×#121×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C2×C4×D4×C61C2211yescharacteristic
60C2×#117×C61—21no—
61C2×#117×C61C2211yescharacteristic
62C2×#117×C61C2211yescharacteristic
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C22×Dic122C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C4×D61—21no—
74C2×#11758200—22no—
75C2×#11758200—22no—
76C2×#11758200—41no—
77C2×#11758199—22no—
78C2×#11758199—22no—
79C2×#11758199—41no—
80C22×#92418—22no—
81C22×#92418—41no—
82C22×#92418—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87#14519756—22no—
88#14519756—41no—
89#14519751—22no—
90#14519751—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99#14519700—22no—
100#14519700—22no—
101#14519700—22no—
102#14519698—41no—
103#14519698—41no—
104#14519697—22no—
105#14519697—22no—
106#14519697—22no—
107C22⋊#92418—22no—
108C22⋊#92418—41no—
109C22⋊#92418—41no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C22×Q8×C61—21no—
114C22×D4×C61—21no—
115C22×D4×C61—21no—
116C22×D4×C61D411yescharacteristic
117C22×D4×C61C2311yescharacteristic
118C23×C4×C61—21no—
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C4⋊Q8×C61—22no—
122C4⋊Q8×C61—22no—
123#124×C61—28no—
124#124×C61—28no—
125#121×C61—28no—
126#121×C61—22no—
127#121×C61—22no—
128#121×C61—22no—
129#121×C61D414yescomplemented
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C4×D4×C61—22no—
133C4×D4×C61—22no—
134#117×C61—28no—
135#117×C61—22no—
136#117×C61—22no—
137#117×C61—22no—
138#117×C61D414yescomplemented
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61D411yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61D411yescharacteristic
150C2×C22⋊C4×C61D411yescharacteristic
151C2×C42×C61—21no—
152C2×C42×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157C23×D61—21no—
158C2×Q8×C61—24no—
159C2×Q8×C61—81no—
160C2×Q8×C61—81no—
161C2×D4×C61—22no—
162C2×D4×C61—24no—
163C2×D4×C61—24no—
164C2×D4×C61—22no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—41no—
171C2×D4×C61—81no—
172C2×D4×C61—81no—
173C2×D4×C61—81no—
174C2×D4×C61—81no—
175C2×D4×C61C2×D412yes—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—24no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
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—42no—
191C22×C4×C61—42no—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2×D412yes—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—42no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—42no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—81no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208#11758222—28no—
209#11758222—44no—
210#11758222—44no—
211#11758222—44no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244#4112yes—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122#4112yes—
227C4⋊C4×C61—24no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C2×D412yes—
233C4⋊C4×C61C2×D412yes—
234C4⋊C4×C61C2×D412yes—
235C22⋊C4×C61—24no—
236C22⋊C4×C61—24no—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—22no—
242C42×C61—24no—
243C42×C61—24no—
244C42×C61—21no—
245C42×C61—21no—
246C22⋊Dic61—42no—
247C22⋊Dic61—81no—
248#11758200—44no—
249#11758199—44no—
250#11758198—42no—
251#11758198—42no—
252#11758198—81no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257#11758196—42no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—44no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—22no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61#12012yes—
292C23×C61C22×D411yescharacteristic
293C22×D61—22no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300Q8×C61—84no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—44no—
304D4×C61—41no—
305D4×C61—41no—
306D4×C61—84no—
307D4×C61—84no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—21no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—48no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61#12012yes—
337C2×C4×C61#13512yes—
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C22⋊D61—48no—
345C22⋊D61—84no—
346C2×Dic61—22no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355D244—22no—
356D244—22no—
357D244—41no—
358D244—41no—
359C4×D61—48no—
360Dic122—22no—
361Dic122—22no—
362Dic122—41no—
363Dic122—41no—
364#92418—41no—
365#92418—41no—
366#92418—41no—
367#92418—41no—
368#23965—611nomaximal, Sylow
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—42no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61C2×#12011yescharacteristic
391C22×C61#54611yescharacteristic
392C22×C61#54611yescharacteristic
393C22×C61C2×#13511yescharacteristic
394C22×C61#57511yescharacteristic
395C22×C61#57611yescharacteristic
396C22×C61#57711yescharacteristic
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—81no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61—81no—
404C4×C61—22no—
405C4×C61—22no—
406C4×C61—41no—
407C4×C61—42no—
408C4×C61—41no—
409C4×C61—42no—
410C4×C61—42no—
411C4×C61#52511yescharacteristic
412C4×C61#53511yescharacteristic
413C4×C61#54611yescharacteristic
414C4×C61#54611yescharacteristic
415Dic61—42no—
416Dic61—81no—
417Dic61—81no—
418C2×#555D6111yescharacteristic, complemented
419C2×#449—611no—
420C2×#416—611no—
421#2407—611no—
422#2024—611no—
423#2023—611no—
424#2000—611no—
425#1999—611no—
426#1893—611no—
427#1879—611no—
428#1877—611no—
429#1875—611no—
430#1873—611no—
431#1869—611no—
432#1825—611no—
433C2×C61—42no—
434C2×C61—81no—
435C2×C61—82no—
436C2×C61#240411yescharacteristic
437C2×C61#300211yescharacteristic
438C2×C61#301211yescharacteristic
439C2×C61#330311yescharacteristic
440C2×C61#330511yescharacteristic
441C2×C61#331911yescharacteristic
442C2×C61#332111yescharacteristic
443D61—82no—
444C22×#41—611no—
445C22×SD16—611no—
446C22×D8—611no—
447C23×C8—611no—
448#555—24no—
449#555—24no—
450C2×C4⋊Q8C2×D6111yescharacteristic
451C2×#124—21no—
452C2×#124—21no—
453C2×C22⋊Q8—611no—
454C2×#121—21no—
455C2×#121—611no—
456C2×#121C2×D6111yescharacteristic
457C2×#121C2×D6111yescharacteristic
458C2×C4×D4C2×D6111yescharacteristic
459C2×C4×D4C2×D6111yescharacteristic
460C2×#117—21no—
461C2×#117C2×D6111yescharacteristic
462C2×#117C2×D6111yescharacteristic
463#449—1224no—
464#416—1224no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102—611no—
472C2×#102—611no—
473C2×C22⋊C8—611no—
474C2×C22⋊C8—611no—
475C2×C22⋊C8—611no—
476#394—1221no—
477#392—1221no—
478#391—611no—
479#390—611no—
480#386—1221no—
481#385—1221no—
482#380—611no—
483#340—611no—
484#340—611no—
485#340—611no—
486#340—611no—
487#340—611no—
488#340—611no—
489#336—611no—
490#336—611no—
491C61#2396511yescharacteristic, complemented, Sylow
492C2×#41—1222no—
493C2×#41—1222no—
494C2×#41—1222no—
495C2×#41—1222no—
496C2×#41—2441no—
497C2×#41—2441no—
498C22×Q8—21no—
499C22×Q8—611no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—611no—
503C22×D4—1221no—
504C22×D4—1221no—
505C22×D4C22⋊D6111yescharacteristic
506C22×D4C22×D6111yescharacteristic
507C23×C4—21no—
508C23×C4—1221no—
509C23×C4C22×D6111yescharacteristic
510C23×C4C22×D6111yescharacteristic
511C2×SD16—1222no—
512C2×SD16—1222no—
513C2×SD16—2441no—
514C2×D8—1222no—
515C2×D8—1222no—
516C2×D8—2441no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—611no—
521C22×C8—1222no—
522C22×C8—2441no—
523C22×C8—2441no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526#124—28no—
527#124—28no—
528C22⋊Q8—1222no—
529C22⋊Q8—2441no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—1222no—
535#121—2441no—
536#121C22⋊D6114yescomplemented
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541#117—28no—
542#117—22no—
543#117—22no—
544#117—22no—
545#117C22⋊D6114yescomplemented
546C2×C4⋊C4—21no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4C22⋊D6111yescharacteristic
551C2×C4⋊C4C22×D6111yescharacteristic
552C2×C4⋊C4C22×D6111yescharacteristic
553C2×C4⋊C4C22×D6111yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4C22⋊D6111yescharacteristic
565C2×C22⋊C4C22⋊D6111yescharacteristic
566C2×C42—21no—
567C2×C42—21no—
568C2×C42C22×D6111yescharacteristic
569#103—1222no—
570#103—1222no—
571#103—1222no—
572#102—1222no—
573#102—1222no—
574#102—1222no—
575#102—2441no—
576#102—2441no—
577C22⋊C8—1222no—
578C22⋊C8—2441no—
579C22⋊C8—2441no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583C24—21no—
584C24—1221no—
585C24C2×C22⋊D6111yescharacteristic
586C24C2×C22⋊D6111yescharacteristic
587#41—1228no—
588#41—2444no—
589#41—2444no—
590#41—2444no—
591C2×Q8—24no—
592C2×Q8—81no—
593C2×Q8—81no—
594C2×Q8—612no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×D4—22no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—22no—
609C2×D4—41no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—612no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—4881no—
621C2×D4—2442no—
622C2×D4—2442no—
623C2×D4—2442no—
624C2×D4—2442no—
625C2×D4—2442no—
626C2×D4C2×C22⋊D6112yes—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—24no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C2×C22⋊D6112yes—
652C22×C4C2×C22⋊D6112yes—
653C22×C4C2×C22⋊D6111yescharacteristic
654C22×C4C2×C22⋊D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656SD16—2444no—
657D8—2444no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—2444no—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—2442no—
681C4⋊C4C2×C22⋊D6112yes—
682C4⋊C4C2×C22⋊D6112yes—
683C4⋊C4C2×C22⋊D6112yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—22no—
689C22⋊C4—24no—
690C22⋊C4—22no—
691C22⋊C4—4881no—
692C22⋊C4—4881no—
693C22⋊C4—2442no—
694C22⋊C4—2442no—
695C22⋊C4—2442no—
696C42—24no—
697C42—21no—
698C42—21no—
699C42—24no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—1222no—
721C23—2441no—
722C23—2441no—
723C23—2441no—
724C23—2441no—
725C23—2441no—
726C23—2441no—
727C23#1451974612yes—
728C23C22×C22⋊D6111yescharacteristic
729Q8—84no—
730Q8—1222no—
731Q8—1222no—
732Q8—2441no—
733Q8—2441no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—84no—
741D4—1222no—
742D4—1222no—
743D4—4884no—
744D4—2448no—
745D4—2441no—
746D4—2441no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—48no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—1222no—
776C2×C4—2448no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4#1451974612yes—
786C2×C4#1451979712yes—
787C2×C4C22×C22⋊D6111yescharacteristic
788C2×C4C22×C22⋊D6111yescharacteristic
789C2×C4#41×D6111yescharacteristic
790C2×C4#41×D6111yescharacteristic
791C2×C4#1451982311yescharacteristic
792C2×C4#1451982311yescharacteristic
793C8—2441no—
794C8—2441no—
795C8—2441no—
796C8—2441no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—4881no—
819C22—4881no—
820C22—4881no—
821C22—4881no—
822C22—2442no—
823C22—2442no—
824C22—2442no—
825C22C2×#1451974611yescharacteristic
826C22#1684040011yescharacteristic
827C22#1684040011yescharacteristic
828C22C2×#1451979711yescharacteristic
829C22#1684056011yescharacteristic
830C22#1684056511yescharacteristic
831C22#1684057311yescharacteristic
832C4—22no—
833C4—22no—
834C4—41no—
835C4—42no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—4881no—
840C4—4881no—
841C4—2442no—
842C4#1684026911yescharacteristic
843C4#1684032611yescharacteristic
844C4#1684040011yescharacteristic
845C4#1684040011yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—4882no—
850C2#2144913411yescharacteristic
851C2#2145503711yescharacteristic
852C2#2145512311yescharacteristic
853C2#2145774111yescharacteristic
854C2#2145776311yescharacteristic
855C2#2145796911yescharacteristic
856C2#2145799911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#555C2
socleC23×C61C22×D4
hypercenterC2×#555D61
hypocenterC61#23965
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#16839905C2semidirect
2. C2×#16839756C2semidirect
3. #21449164C2semidirect
4. #21446957C2semidirect
5. #21446952C2semidirect
6. #21446822C2semidirect
7. #21446815C2semidirect
8. #21446248C2semidirect
9. #21446167C2semidirect
10. #21446153C2semidirect
11. #21446141C2semidirect
12. #21446131C2semidirect
13. #21446112C2semidirect
14. #21445914C2semidirect
15. C2×C61×#555C2semidirect
129. #121×C61D4semidirect
138. #117×C61D4semidirect
418. C2×#555D61semidirect
491. C61#23965semidirect
536. #121C22⋊D61semidirect
545. #117C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399052
C2×#168397562
#214491642
#214469572
#214469522
#214468222
#214468152
#214462482
#214461672
#214461532
#214461412
#214461312
#214461122
#214459142
C2×C61×#5552
#2396561