Finite Group Databasebeta

← #29688943

Subgroups — #29688943

Order 15616.

1426 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840309C211yesmaximal, characteristic
2C2×#16839730C211yesmaximal, characteristic, complemented
3C2×#16839727C211yesmaximal, characteristic, complemented
4#21446116C211yesmaximal, characteristic, complemented
5#21446115C211yesmaximal, characteristic, complemented
6#21446113C211yesmaximal, characteristic, complemented
7#21446112C211yesmaximal, characteristic, complemented
8#21446110C211yesmaximal, characteristic, complemented
9#21446109C211yesmaximal, characteristic, complemented
10#21446108C211yesmaximal, characteristic, complemented
11#21445886C211yesmaximal, characteristic, complemented
12#21445886C211yesmaximal, characteristic, complemented
13#21445730C211yesmaximal, characteristic, complemented
14#21445730C211yesmaximal, characteristic, complemented
15C61×#1870C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758222C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840309—24no—
22#16840309—24no—
23C2×#14519776C411yescharacteristic
24C2×#14519773C411yescharacteristic
25C2×#14519763C411yescharacteristic
26C2×#14519763C411yescharacteristic
27C2×#14519752C411yescharacteristic
28C2×#14519750C411yescharacteristic
29C2×#14519750C411yescharacteristic
30C2×#14519748C411yescharacteristic
31C2×C4×D244C2211yescharacteristic
32C2×C4×C22⋊D61C2211yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×C42×D61C2211yescharacteristic
35#16839730—24no—
36#16839727—24no—
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48C2×#14519689C2211yescharacteristic
49C2×#14519689C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222—41no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222—41no—
71C2×#11758222—41no—
72C2×#11758222—41no—
73C2×#11758222D414yes—
74C2×#11758222D414yes—
75C22×Dic122C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×D244C2×C411yescharacteristic
78C22×D244C2×C411yescharacteristic
79C22×D244C2×C411yescharacteristic
80C22×C22⋊D61C2×C411yescharacteristic
81C22×C22⋊D61C2×C411yescharacteristic
82C22×C22⋊D61C2×C411yescharacteristic
83C22×C22⋊D61C2×C411yescharacteristic
84C22×C22⋊D61C2×C411yescharacteristic
85C22×C22⋊D61C2×C411yescharacteristic
86C22×C4×D61C2×C411yescharacteristic
87C22×C4×D61C2×C411yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C2×#11758189—22no—
92C2×#11758189—41no—
93C2×#11758189—41no—
94C22×#92418—22no—
95C22×#92418—41no—
96C22×#92418—41no—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C2×C8×D61—22no—
102C2×C8×D61—41no—
103C2×C8×D61—41no—
104#14519776—24no—
105#14519773—24no—
106#14519763—24no—
107#14519763—24no—
108#14519752—24no—
109#14519750—24no—
110#14519750—24no—
111#14519748—24no—
112C4×D244—22no—
113C4×D244—22no—
114C4×C22⋊D61—22no—
115C4×C22⋊D61—22no—
116C4×C22⋊D61—22no—
117C4×C22⋊D61—22no—
118C2×C4⋊Dic61C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×C22⋊Dic61C2×C411yescharacteristic
122C2×C22⋊Dic61C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×C4×Dic61C2×C411yescharacteristic
128C2×C4×Dic61C2×C411yescharacteristic
129C2×C4×Dic61C2311yescharacteristic
130C42×D61—22no—
131C42×D61—22no—
132C22⋊#92418—22no—
133C22⋊#92418—41no—
134C22⋊#92418—41no—
135#14519689—22no—
136#14519689—22no—
137#14519689—22no—
138#14519689—22no—
139#14519689—22no—
140#14519689—22no—
141#14519689—41no—
142#14519689—41no—
143#14519689—41no—
144#14519689—41no—
145C22×D4×C61C2×C411yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×M16×C61—22no—
149C2×M16×C61—41no—
150C2×M16×C61—41no—
151C22×C8×C61C2311yescharacteristic
152C22×C8×C61C2311yescharacteristic
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155C4×D4×C61—22no—
156C4×D4×C61—22no—
157C2×C4⋊C4×C61C2×C411yescharacteristic
158C2×C22⋊C4×C61C2×C411yescharacteristic
159C2×C22⋊C4×C61C2×C411yescharacteristic
160C2×C42×C61C2311yescharacteristic
161C22⋊C8×C61—22no—
162C22⋊C8×C61—41no—
163C22⋊C8×C61—41no—
164C24×C61C22×C411yescharacteristic
165C24×C61C22×C411yescharacteristic
166C23×D61C22×C411yescharacteristic
167C23×D61C22×C411yescharacteristic
168C23×D61C22×C411yescharacteristic
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—41no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61—22no—
195C2×C22⋊D61—41no—
196C2×C22⋊D61—41no—
197C2×C22⋊D61—41no—
198C2×C22⋊D61—41no—
199C2×C22⋊D61—41no—
200C2×C22⋊D61—41no—
201C2×C22⋊D61—41no—
202C2×C22⋊D61—41no—
203C2×C22⋊D61—41no—
204C2×C22⋊D61—41no—
205C2×C22⋊D61C22⋊C414yes—
206C2×C22⋊D61C22⋊C414yes—
207C22×Dic61C22×C411yescharacteristic
208C22×Dic61C22×C411yescharacteristic
209C22×Dic61C22×C411yescharacteristic
210C22×Dic61C22×C411yescharacteristic
211C22×Dic61C22×C411yescharacteristic
212#11758222—44no—
213#11758222—44no—
214#11758222—44no—
215#11758222—44no—
216#11758222—44no—
217#11758222—44no—
218#11758222—44no—
219#11758222—44no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—41no—
224C2×D244—41no—
225C2×D244—41no—
226C2×D244—41no—
227C2×D244—41no—
228C2×D244C22⋊C414yes—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—22no—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—22no—
247C2×C4×D61—41no—
248C2×C4×D61—41no—
249C2×C4×D61C2×D412yes—
250C2×C4×D61C2×D412yes—
251C2×C4×D61C2×D412yes—
252C2×C4×D61C2×D412yes—
253C2×Dic122—22no—
254C2×Dic122—41no—
255C2×Dic122—41no—
256C2×Dic122—41no—
257C2×Dic122—41no—
258C2×Dic122C22⋊C414yes—
259M16×C61—44no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61—21no—
272C4⋊C4×C61—22no—
273C22⋊C4×C61—22no—
274C22⋊C4×C61—22no—
275C42×C61—21no—
276C42×C61—21no—
277C22⋊Dic61—22no—
278C22⋊Dic61—22no—
279#11758198—22no—
280#11758198—22no—
281#11758198—22no—
282#11758198—22no—
283C4⋊Dic61—22no—
284#11758196—22no—
285#11758196—22no—
286C4×Dic61—21no—
287C4×Dic61—21no—
288C4×Dic61—22no—
289C4×Dic61—22no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—21no—
301C2×#92418—21no—
302C2×#92418—44no—
303#11758189—44no—
304C8×D61—44no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61C2×C22⋊C412yes—
319C23×C61C23×C411yescharacteristic
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—21no—
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—21no—
339C22×D61C2×C22⋊C412yes—
340C22×D61C2×C22⋊C412yes—
341D4×C61—44no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61C2×C22⋊C412yes—
361C2×C4×C61#13112yes—
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61H(5,𝔽2)11yescharacteristic
365C2×C4×C61H(5,𝔽2)11yescharacteristic
366C2×C4×C61H(5,𝔽2)11yescharacteristic
367C2×C4×C61H(5,𝔽2)11yescharacteristic
368C22⋊D61—44no—
369C22⋊D61—44no—
370C22⋊D61—44no—
371C22⋊D61—44no—
372C22⋊D61—44no—
373C22⋊D61—44no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61C2×C22⋊C412yes—
387C2×Dic61C2×C22⋊C412yes—
388C2×Dic61#13112yes—
389D244—44no—
390D244—44no—
391D244—44no—
392C4×D61—22no—
393C4×D61—22no—
394C4×D61—22no—
395C4×D61—22no—
396C4×D61—22no—
397C4×D61—22no—
398C4×D61—22no—
399C4×D61—22no—
400C4×D61—44no—
401C4×D61—44no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406Dic122—44no—
407Dic122—44no—
408C8×C61—41no—
409C8×C61—41no—
410C8×C61—41no—
411C8×C61—41no—
412#92418—41no—
413#92418—41no—
414#92418—41no—
415#92418—41no—
416#21745—611nomaximal, Sylow
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61C22×C22⋊C411yescharacteristic
432C22×C61#51811yescharacteristic
433C22×C61#51811yescharacteristic
434C22×C61C2×#13111yescharacteristic
435C22×C61C2×#13111yescharacteristic
436C22×C61#56811yescharacteristic
437C22×C61#56811yescharacteristic
438C2×D61—22no—
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—41no—
458C2×D61—41no—
459C4×C61—22no—
460C4×C61—22no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61#53411yescharacteristic
464C4×C61#53411yescharacteristic
465C4×C61#53411yescharacteristic
466C4×C61#53411yescharacteristic
467Dic61—22no—
468Dic61—22no—
469Dic61—22no—
470Dic61—41no—
471Dic61—41no—
472C2×#532—611no—
473C2×#408—611no—
474C2×#408—611no—
475#1870—611no—
476#1870—611no—
477#1870—611no—
478#1870D6111yescharacteristic, complemented
479#1869—611no—
480#1869—611no—
481#1869—611no—
482#1869—611no—
483#1817—611no—
484#1817—611no—
485#1780—611no—
486#1780—611no—
487C2×C61—42no—
488C2×C61—81no—
489C2×C61#230811yescharacteristic
490C2×C61#288011yescharacteristic
491C2×C61#288011yescharacteristic
492C2×C61#297911yescharacteristic
493C2×C61#298011yescharacteristic
494C2×C61#298111yescharacteristic
495C2×C61#298111yescharacteristic
496D61—42no—
497D61—42no—
498D61—81no—
499C22×#41—611no—
500C22×#41—611no—
501C22×M16—611no—
502C22×M16C2×D6111yescharacteristic
503C23×C8—611no—
504C23×C8—611no—
505#532—1224no—
506#532—1224no—
507C2×C4⋊Q8—611no—
508C2×#127—611no—
509C2×#124—611no—
510C2×#124—611no—
511C2×#121—611no—
512C2×#121—611no—
513C2×#121—611no—
514C2×#121—611no—
515C2×C4×D4—611no—
516C2×C4×D4—611no—
517C2×C4×D4—611no—
518C2×C4×D4C2×D6111yescharacteristic
519C22×C42—611no—
520#408—1224no—
521#408—1224no—
522C2×C22⋊C8—611no—
523C2×C22⋊C8—611no—
524C2×C22⋊C8—611no—
525C2×C22⋊C8—611no—
526C2×C22⋊C8—611no—
527C2×C22⋊C8—611no—
528C2×C22⋊C8—611no—
529C2×C22⋊C8—611no—
530C2×C22⋊C8—611no—
531C2×C22⋊C8—611no—
532C2×C22⋊C8—611no—
533C2×C22⋊C8—611no—
534C2×C22⋊C8—611no—
535C2×C22⋊C8C2×D6111yescharacteristic
536C2×C22⋊C8C2×D6111yescharacteristic
537C2×C22⋊C8C2×D6111yescharacteristic
538#336—611no—
539#336—611no—
540#336—611no—
541#336—611no—
542#336—611no—
543#336—611no—
544#336C2×D6111yescharacteristic
545#336C2×D6111yescharacteristic
546C61#2174511yescharacteristic, complemented, Sylow
547C2×#41—614no—
548C2×#41—614no—
549C2×#41—1222no—
550C2×#41—1222no—
551C2×#41—2441no—
552C2×#41—2441no—
553C2×#41—2441no—
554C2×#41—2441no—
555C2×#41—2441no—
556C2×#41—2441no—
557C2×#41—2441no—
558C2×#41—2441no—
559C22×Q8—611no—
560C22×Q8—611no—
561C22×D4—611no—
562C22×D4—611no—
563C22×D4—611no—
564C22×D4—611no—
565C22×D4—611no—
566C22×D4—611no—
567C22×D4—611no—
568C22×D4—611no—
569C22×D4—611no—
570C22×D4C4×D6111yescharacteristic
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4C22×D6111yescharacteristic
577C23×C4C22×D6111yescharacteristic
578C2×M16—22no—
579C2×M16—41no—
580C2×M16—41no—
581C2×M16—1222no—
582C2×M16—2441no—
583C2×M16—2441no—
584C22×C8—611no—
585C22×C8—611no—
586C22×C8—611no—
587C22×C8—611no—
588C22×C8—1222no—
589C22×C8—1222no—
590C22×C8—2441no—
591C22×C8—2441no—
592C22×C8—2441no—
593C22×C8—2441no—
594C22×C8C22×D6111yescharacteristic
595C22×C8C22×D6111yescharacteristic
596C22×C8C22×D6111yescharacteristic
597C22×C8C22×D6111yescharacteristic
598C4⋊Q8—1224no—
599#127—1224no—
600#124—1224no—
601#124—1224no—
602#121—1224no—
603#121—1224no—
604#121—1224no—
605#121—1224no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—1222no—
609C4×D4—1222no—
610C4×D4—1222no—
611C4×D4—1222no—
612C4×D4—1222no—
613C4×D4—1222no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—611no—
616C2×C4⋊C4—611no—
617C2×C4⋊C4C4×D6111yescharacteristic
618C2×C22⋊C4—611no—
619C2×C22⋊C4—611no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—611no—
624C2×C22⋊C4C4×D6111yescharacteristic
625C2×C22⋊C4C4×D6111yescharacteristic
626C2×C42—611no—
627C2×C42—611no—
628C2×C42—611no—
629C2×C42—1222no—
630C2×C42—1222no—
631C2×C42C22×D6111yescharacteristic
632C22⋊C8—22no—
633C22⋊C8—41no—
634C22⋊C8—41no—
635C22⋊C8—1222no—
636C22⋊C8—1222no—
637C22⋊C8—1222no—
638C22⋊C8—1222no—
639C22⋊C8—1222no—
640C22⋊C8—1222no—
641C22⋊C8—1222no—
642C22⋊C8—2441no—
643C22⋊C8—2441no—
644C22⋊C8—2441no—
645C22⋊C8—2441no—
646C22⋊C8—2441no—
647C22⋊C8—2441no—
648C24—611no—
649C24—611no—
650C24—611no—
651C24C2×C4×D6111yescharacteristic
652C24C2×C4×D6111yescharacteristic
653#41—2444no—
654#41—2444no—
655#41—2444no—
656#41—2444no—
657#41—2444no—
658#41—2444no—
659#41—2444no—
660#41—2444no—
661C2×Q8—614no—
662C2×Q8—1222no—
663C2×Q8—2441no—
664C2×Q8—2441no—
665C2×Q8—2441no—
666C2×Q8—2441no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—41no—
670C2×D4—614no—
671C2×D4—614no—
672C2×D4—614no—
673C2×D4—1222no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—1222no—
677C2×D4—1222no—
678C2×D4—1222no—
679C2×D4—1222no—
680C2×D4—1222no—
681C2×D4—1222no—
682C2×D4—2441no—
683C2×D4—2441no—
684C2×D4—2441no—
685C2×D4—2441no—
686C2×D4—2441no—
687C2×D4—2441no—
688C2×D4—2441no—
689C2×D4—2441no—
690C2×D4—2441no—
691C2×D4—2441no—
692C2×D4—2441no—
693C2×D4—2441no—
694C2×D4—2441no—
695C2×D4—2441no—
696C2×D4—2441no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—612no—
711C22×C4—612no—
712C22×C4—612no—
713C22×C4—612no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—1222no—
717C22×C4—1222no—
718C22×C4—1222no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1222no—
734C22×C4—2441no—
735C22×C4—2441no—
736C22×C4C2×C4×D6111yescharacteristic
737C22×C4C2×C4×D6111yescharacteristic
738C22×C4C2×C4×D6111yescharacteristic
739C22×C4C2×C4×D6111yescharacteristic
740C22×C4D4×D6112yes—
741C22×C4D4×D6112yes—
742C22×C4C23×D6111yescharacteristic
743M16—44no—
744M16—2444no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—1221no—
758C2×C8—1221no—
759C2×C8—1221no—
760C2×C8—1221no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—1221no—
769C2×C8—2444no—
770C2×C8—2444no—
771C4⋊C4—22no—
772C4⋊C4—1222no—
773C4⋊C4—1222no—
774C4⋊C4—1222no—
775C22⋊C4—22no—
776C22⋊C4—22no—
777C22⋊C4—1222no—
778C22⋊C4—1222no—
779C22⋊C4—1222no—
780C22⋊C4—1222no—
781C22⋊C4—1222no—
782C22⋊C4—1222no—
783C42—21no—
784C42—21no—
785C42—1222no—
786C42—1222no—
787C42—1221no—
788C42—1221no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—612no—
803C23—612no—
804C23—1221no—
805C23—1221no—
806C23—1221no—
807C23—1221no—
808C23—1221no—
809C23—1221no—
810C23—1221no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—1221no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1221no—
821C23—1221no—
822C23—1221no—
823C23C22⋊C4×D6112yes—
824C23C22×C4×D6111yescharacteristic
825Q8—2444no—
826Q8—2444no—
827D4—44no—
828D4—2444no—
829D4—2444no—
830D4—2444no—
831D4—2444no—
832D4—2444no—
833D4—2444no—
834D4—2444no—
835D4—2444no—
836D4—2444no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—612no—
856C2×C4—612no—
857C2×C4—612no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—2444no—
879C2×C4—2444no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4C22⋊C4×D6112yes—
885C2×C4#1451978512yes—
886C2×C4C2×D4×D6111yescharacteristic
887C2×C4C2×D4×D6111yescharacteristic
888C2×C4#1451982211yescharacteristic
889C2×C4#1451982211yescharacteristic
890C2×C4#1451982311yescharacteristic
891C2×C4#1451982311yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C8—2441no—
897C8—2441no—
898C8—2441no—
899C8—2441no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—1222no—
915C22—1222no—
916C22—1222no—
917C22—1222no—
918C22—1222no—
919C22—1222no—
920C22—2441no—
921C22—2441no—
922C22—2441no—
923C22—2441no—
924C22—2441no—
925C22—2441no—
926C22—2441no—
927C22—2441no—
928C22—2441no—
929C22—2441no—
930C22—2441no—
931C22—2441no—
932C22—2441no—
933C22—2441no—
934C22—2441no—
935C22C2×C22⋊C4×D6111yescharacteristic
936C22#1684023411yescharacteristic
937C22#1684023411yescharacteristic
938C22#131×D6111yescharacteristic
939C22C2×#1451978511yescharacteristic
940C22#1684052711yescharacteristic
941C22#1684052811yescharacteristic
942C4—22no—
943C4—22no—
944C4—41no—
945C4—41no—
946C4—1222no—
947C4—1222no—
948C4—1222no—
949C4—2441no—
950C4—2441no—
951C4#1684032011yescharacteristic
952C4#1684032011yescharacteristic
953C4#1684032211yescharacteristic
954C4#1684032311yescharacteristic
955C2—42no—
956C2—81no—
957C2—4881no—
958C2—2442no—
959C2—2442no—
960C2#2144839311yescharacteristic
961C2#2145426711yescharacteristic
962C2#2145426911yescharacteristic
963C2#2145488411yescharacteristic
964C2#2145488711yescharacteristic
965C2#2145489111yescharacteristic
966C2#2145489611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1870C2
prime radicalC2×#16840309C2
cosocleC22×C4×C61C24
hypercenter#1870D61
hypocenterC61#21745
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#16839730C2semidirect
3. C2×#16839727C2semidirect
4. #21446116C2semidirect
5. #21446115C2semidirect
6. #21446113C2semidirect
7. #21446112C2semidirect
8. #21446110C2semidirect
9. #21446109C2semidirect
10. #21446108C2semidirect
11. #21445886C2semidirect
12. #21445886C2semidirect
13. #21445730C2semidirect
14. #21445730C2semidirect
15. C61×#1870C2semidirect
478. #1870D61semidirect
546. C61#21745semidirect

Maximal subgroups

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

subgroupindex
C2×#168403092
C2×#168397302
C2×#168397272
#214461162
#214461152
#214461132
#214461122
#214461102
#214461092
#214461082
#214458862
#214457302
C61×#18702
#2174561