Finite Group Databasebeta

← #29700247

Subgroups — #29700247

Order 15616.

1266 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839841C211yesmaximal, characteristic, complemented
2C2×#16839839C211yesmaximal, characteristic, complemented
3C2×#16839724C211yesmaximal, characteristic, complemented
4C2×#16839724C211yesmaximal, characteristic, complemented
5C4×#14519747C211yesmaximal, characteristic
6#21446615C211yesmaximal, characteristic, complemented
7#21446427C211yesmaximal, characteristic, complemented
8#21446115C211yesmaximal, characteristic, complemented
9#21446115C211yesmaximal, characteristic, complemented
10#21446113C211yesmaximal, characteristic, complemented
11#21446003C211yesmaximal, characteristic, complemented
12#21446000C211yesmaximal, characteristic, complemented
13#21445602C211yesmaximal, characteristic, complemented
14#21445599C211yesmaximal, characteristic, complemented
15C61×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21C22×#11758189C2211yescharacteristic, complemented
22C2×#14519747C411yescharacteristic
23C2×C4×D244C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×C4×C22⋊D61C2211yescharacteristic
26#16839841—24no—
27#16839839—24no—
28C2×C4⋊#92418C2211yescharacteristic, complemented
29C2×#14519706C2211yescharacteristic, complemented
30#16839724—24no—
31#16839724—24no—
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38C2×#14519689C2211yescharacteristic, complemented
39C2×#14519689C2211yescharacteristic, complemented
40C2×#14519689C2211yescharacteristic, complemented
41C2×#14519687C2211yescharacteristic, complemented
42C2×C4×#92418C2211yescharacteristic, complemented
43#16839640C411yescharacteristic
44#16839640C411yescharacteristic
45#16839639C411yescharacteristic
46#16839637C411yescharacteristic
47#16839636C411yescharacteristic
48#16839636C411yescharacteristic
49#16839617C411yescharacteristic
50C4×#11758198C2211yescharacteristic
51C4×#11758198C2211yescharacteristic
52#16839517C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56C2×C4⋊C8×C61C2211yescharacteristic, complemented
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C4×C8×C61C2211yescharacteristic, complemented
60C4×C22⋊C4×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic, complemented
62C61×#336C2211yescharacteristic, complemented
63C24×D61C2×C411yescharacteristic
64C22×D244C2×C411yescharacteristic
65C22×D244C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic
67C23×Dic61C2×C411yescharacteristic
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61—41no—
73C22×C4×D61—41no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C2×#11758189—22no—
80C2×#11758189—22no—
81C2×#11758189—22no—
82C2×#11758189—22no—
83C2×#11758189—22no—
84C2×#11758189—22no—
85C2×#11758189—22no—
86C2×#11758189—22no—
87C2×#11758189—22no—
88C2×#11758189—22no—
89C2×#11758189—41no—
90C2×#11758189—41no—
91C2×#11758189—41no—
92C2×#11758189—41no—
93C2×#11758189—41no—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98#14519747—24no—
99C4×D244—22no—
100C4×D244—22no—
101C4×D244—22no—
102C4×D244—22no—
103C4×C22⋊D61—41no—
104C4×C22⋊D61—41no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×C4⋊Dic61C2×C411yescharacteristic
107C2×#11758196C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C4⋊#92418—22no—
120#14519706—41no—
121C22⋊#92418—22no—
122C22⋊#92418—22no—
123#14519689—22no—
124#14519689—22no—
125#14519689—22no—
126#14519689—22no—
127#14519689—41no—
128#14519689D414yescomplemented
129#14519689D414yescomplemented
130#14519687—41no—
131C4×#92418—22no—
132#14519684C2×C411yescharacteristic
133#14519684C2×C411yescharacteristic
134#14519684C2×C411yescharacteristic
135#14519684C2×C411yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C42×C61C2311yescharacteristic
144C2×C42×C61C2311yescharacteristic
145C4⋊C8×C61—22no—
146C22⋊C8×C61—22no—
147C22⋊C8×C61—22no—
148C4×C8×C61—22no—
149#95×C61C2×C411yescharacteristic
150#95×C61C2×C411yescharacteristic
151C24×C61C22×C411yescharacteristic
152C23×D61—22no—
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—41no—
156C23×D61—41no—
157C23×D61—41no—
158C23×D61—41no—
159C23×D61C22×C411yescharacteristic
160C23×D61C22×C411yescharacteristic
161C23×D61C22×C411yescharacteristic
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—41no—
176C2×C22⋊D61—41no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—41no—
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—41no—
190C2×D244—41no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—44no—
210C2×C4×D61—44no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C2×C4×D61—41no—
214C2×C4×D61—41no—
215C2×C4×D61C2×D412yes—
216C2×C4×D61C2×D412yes—
217C2×C4×D61#4112yes—
218C2×C4×D61#4112yes—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61C2×D412yes—
230C2×C8×C61C2×D412yes—
231C22⋊C4×C61—41no—
232C22⋊C4×C61M1614yescomplemented
233C42×C61—21no—
234C42×C61—21no—
235C42×C61—21no—
236C42×C61—21no—
237C22⋊Dic61—41no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—41no—
245#11758198—41no—
246#11758198—41no—
247C4⋊Dic61—22no—
248C4⋊Dic61—22no—
249#11758196—41no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418C2×D412yes—
263C2×#92418C2×D412yes—
264#11758189—44no—
265#11758189—44no—
266#11758189—44no—
267#11758189—44no—
268#11758189—44no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61C2×M1612yes—
276C23×C61C23×C411yescharacteristic
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—44no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61—44no—
302C22×D61—44no—
303C22×D61C4×D412yes—
304C22×D61C4×D412yes—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61C2×M1612yes—
323C2×C4×C61C2×M1612yes—
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C2×#4111yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61H(5,𝔽2)11yescharacteristic
329C2×C4×C61H(5,𝔽2)11yescharacteristic
330C22⋊D61—44no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—44no—
345C2×Dic61C4×D412yes—
346C2×Dic61C4×D412yes—
347D244—44no—
348D244—44no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—44no—
358C4×D61—44no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—41no—
363C8×C61—22no—
364C8×C61—22no—
365C8×C61—41no—
366C8×C61—41no—
367#92418—22no—
368#92418—22no—
369#92418—41no—
370#92418—41no—
371#22852—611nomaximal, Sylow
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61C2×C4×D411yescharacteristic
380C22×C61C2×C4×D411yescharacteristic
381C22×C61#51811yescharacteristic
382C22×C61C22×M1611yescharacteristic
383C22×C61#56811yescharacteristic
384C22×C61#56811yescharacteristic
385C22×C61#56811yescharacteristic
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—416no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C4×C61—22no—
409C4×C61—22no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61D4211yescharacteristic
414C4×C61#54611yescharacteristic
415C4×C61#54611yescharacteristic
416C4×C61#55111yescharacteristic
417Dic61—22no—
418Dic61—22no—
419Dic61—41no—
420Dic61—41no—
421Dic61—41no—
422C2×#436—611no—
423C2×#436—611no—
424C2×#407—611no—
425C2×#407—611no—
426C4×#120—611no—
427#1955—611no—
428#1923—611no—
429#1923D6111yescharacteristic, complemented
430#1870—611no—
431#1870—611no—
432#1870—611no—
433#1851—611no—
434#1851—611no—
435#1753—611no—
436#1753—611no—
437C2×C61—42no—
438C2×C61#235811yescharacteristic
439C2×C61#293011yescharacteristic
440C2×C61#293011yescharacteristic
441C2×C61D4×M1611yescharacteristic
442C2×C61D4×M1611yescharacteristic
443C2×C61#297511yescharacteristic
444C2×C61#297811yescharacteristic
445D61—42no—
446D61—42no—
447D61—81no—
448C24×C4—611no—
449C22×M16—611no—
450C22×M16—611no—
451C22×M16—611no—
452C22×M16—611no—
453C22×M16—611no—
454C2×#120—611no—
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C2×C4×D4—611no—
458#436—1224no—
459#436—1224no—
460C2×C4⋊C8—611no—
461C2×C4⋊C8—611no—
462C2×C4⋊C8C2×D6111yescharacteristic, complemented
463#407—1224no—
464#407—1224no—
465C2×C22⋊C8—611no—
466C2×C22⋊C8—611no—
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×C22⋊C8—611no—
474C2×C22⋊C8C2×D6111yescharacteristic
475C2×C22⋊C8C2×D6111yescharacteristic
476C2×#97—611no—
477C2×C4×C8—611no—
478C2×C4×C8C2×D6111yescharacteristic, complemented
479#386—611no—
480#386—611no—
481#386—611no—
482#385—611no—
483#385—611no—
484#385—611no—
485#379—611no—
486C4×C22⋊C4—611no—
487C4×C22⋊C4—611no—
488C4×C22⋊C4C2×D6111yescharacteristic
489#336—611no—
490#336—611no—
491#336—611no—
492#336—611no—
493#336C2×D6111yescharacteristic, complemented
494#336C2×D6111yescharacteristic, complemented
495C61#2285211yescharacteristic, complemented, Sylow
496C25—611no—
497C22×D4—611no—
498C22×D4—611no—
499C22×D4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—1222no—
507C23×C4—1222no—
508C23×C4—1222no—
509C23×C4—1222no—
510C23×C4—2441no—
511C23×C4—2441no—
512C23×C4C22×D6111yescharacteristic
513C2×M16—1222no—
514C2×M16—1222no—
515C2×M16—1222no—
516C2×M16—1222no—
517C2×M16—1222no—
518C2×M16—1222no—
519C2×M16—1222no—
520C2×M16—1222no—
521C2×M16—1222no—
522C2×M16—1222no—
523C2×M16—2441no—
524C2×M16—2441no—
525C2×M16—2441no—
526C2×M16—2441no—
527C2×M16—2441no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—611no—
531C22×C8—611no—
532C22×C8C22×D6111yescharacteristic
533C22×C8C22×D6111yescharacteristic
534C22×C8C22×D6111yescharacteristic
535C22×C8C22×D6111yescharacteristic
536#120—1224no—
537C4×D4—1222no—
538C4×D4—1222no—
539C4×D4—1222no—
540C4×D4—1222no—
541C4×D4—2441no—
542C4×D4—2441no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—611no—
553C2×C22⋊C4—611no—
554C2×C22⋊C4—611no—
555C2×C22⋊C4—611no—
556C2×C22⋊C4C4×D6111yescharacteristic
557C2×C22⋊C4C4×D6111yescharacteristic
558C2×C42—611no—
559C2×C42C22×D6111yescharacteristic
560C2×C42C22×D6111yescharacteristic
561C4⋊C8—22no—
562C4⋊C8—1222no—
563C4⋊C8—2441no—
564C22⋊C8—22no—
565C22⋊C8—22no—
566C22⋊C8—614no—
567C22⋊C8—614no—
568C22⋊C8—1222no—
569C22⋊C8—1222no—
570C22⋊C8—1222no—
571C22⋊C8—1222no—
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574C22⋊C8—2441no—
575#97—2441no—
576C4×C8—22no—
577C4×C8—1222no—
578#95—611no—
579#95—611no—
580#95—611no—
581#95—611no—
582#95C4×D6111yescharacteristic
583#95C4×D6111yescharacteristic
584C24—611no—
585C24—611no—
586C24—611no—
587C24—1222no—
588C24—1222no—
589C24—1222no—
590C24—2441no—
591C24—2441no—
592C24—2441no—
593C24—2441no—
594C24C2×C4×D6111yescharacteristic
595C2×D4—1222no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—2441no—
601C2×D4—2441no—
602C2×D4—2441no—
603C2×D4—2441no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—612no—
613C22×C4—612no—
614C22×C4—612no—
615C22×C4—612no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—2441no—
640C22×C4—2441no—
641C22×C4—2444no—
642C22×C4—2444no—
643C22×C4—2444no—
644C22×C4—2444no—
645C22×C4—2441no—
646C22×C4C2×C4×D6111yescharacteristic
647C22×C4C2×C4×D6111yescharacteristic
648C22×C4C2×C4×D6111yescharacteristic
649C22×C4C2×C4×D6111yescharacteristic
650C22×C4C2×C4×D6111yescharacteristic
651C22×C4C23×D6111yescharacteristic
652M16—2444no—
653M16—2444no—
654M16—2444no—
655M16—2444no—
656M16—2444no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—612no—
668C2×C8—612no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8D4×D6112yes—
680C2×C8D4×D6112yes—
681C4⋊C4—1222no—
682C4⋊C4—1222no—
683C4⋊C4—2441no—
684C22⋊C4—41no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—2441no—
692C22⋊C4—2441no—
693C22⋊C4—2441no—
694C22⋊C4—2441no—
695C22⋊C4#1175818914yescomplemented
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42—1221no—
701C42—1221no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—612no—
709C23—612no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23—1221no—
716C23—1221no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23—1221no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23—2444no—
730C23—2444no—
731C23—2444no—
732C23—2444no—
733C23—2444no—
734C23—2444no—
735C23—2444no—
736C23C2×#1175818912yes—
737C23C22×C4×D6111yescharacteristic
738D4—2444no—
739D4—2444no—
740D4—2444no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—2444no—
782C2×C4—2444no—
783C2×C4—2444no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4C2×#1175818912yes—
789C2×C4C2×#1175818912yes—
790C2×C4C2×D4×D6111yescharacteristic
791C2×C4C2×D4×D6111yescharacteristic
792C2×C4#41×D6111yescharacteristic
793C2×C4#41×D6111yescharacteristic
794C2×C4#1451982311yescharacteristic
795C2×C4#1451982311yescharacteristic
796C8—22no—
797C8—22no—
798C8—41no—
799C8—41no—
800C8—1222no—
801C8—1222no—
802C8—2441no—
803C8—2441no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—1222no—
812C22—1222no—
813C22—1222no—
814C22—1222no—
815C22—1222no—
816C22—1222no—
817C22—24416no—
818C22—2441no—
819C22—2441no—
820C22—2441no—
821C22—2441no—
822C22—2441no—
823C22—2441no—
824C22—2441no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22—2441no—
832C22—2441no—
833C22C4×D4×D6111yescharacteristic
834C22C4×D4×D6111yescharacteristic
835C22#1684023611yescharacteristic
836C22C22×#1175818911yescharacteristic
837C22#1684052711yescharacteristic
838C22#1684052711yescharacteristic
839C22#1684052811yescharacteristic
840C4—22no—
841C4—22no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—1222no—
846C4—1222no—
847C4—2441no—
848C4—2441no—
849C4—2441no—
850C4#1684039611yescharacteristic
851C4#1684040411yescharacteristic
852C4#1684040511yescharacteristic
853C4#1684043711yescharacteristic
854C2—42no—
855C2—4881no—
856C2—2442no—
857C2—2442no—
858C2#2144879711yescharacteristic
859C2#2145451711yescharacteristic
860C2#2145451911yescharacteristic
861C2D4×#1175818911yescharacteristic
862C2D4×#1175818911yescharacteristic
863C2#2145485911yescharacteristic
864C2#2145488011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1923C2
prime radicalC2×#14519747C4
cosocleC22×C4×C61C24
hypercenter#1923D61
hypocenterC61#22852
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#16839841C2semidirect
2. C2×#16839839C2semidirect
3. C2×#16839724C2semidirect
4. C2×#16839724C2semidirect
6. #21446615C2semidirect
7. #21446427C2semidirect
8. #21446115C2semidirect
9. #21446115C2semidirect
10. #21446113C2semidirect
11. #21446003C2semidirect
12. #21446000C2semidirect
13. #21445602C2semidirect
14. #21445599C2semidirect
15. C61×#1923C2semidirect
21. C22×#11758189C22semidirect
28. C2×C4⋊#92418C22semidirect
29. C2×#14519706C22semidirect
38. C2×#14519689C22semidirect
39. C2×#14519689C22semidirect
40. C2×#14519689C22semidirect
41. C2×#14519687C22semidirect
42. C2×C4×#92418C22semidirect
52. #16839517C22semidirect
53. #16839517C22semidirect
54. #16839516C22semidirect
55. #16839516C22semidirect
56. C2×C4⋊C8×C61C22semidirect
59. C2×C4×C8×C61C22semidirect
61. C61×#336C22semidirect
62. C61×#336C22semidirect
128. #14519689D4semidirect
129. #14519689D4semidirect
232. C22⋊C4×C61M16semidirect
429. #1923D61semidirect
462. C2×C4⋊C8C2×D61semidirect
478. C2×C4×C8C2×D61semidirect
493. #336C2×D61semidirect
494. #336C2×D61semidirect
495. C61#22852semidirect
695. C22⋊C4#11758189semidirect

Maximal subgroups

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

subgroupindex
C2×#168398412
C2×#168398392
C2×#168397242
C4×#145197472
#214466152
#214464272
#214461152
#214461132
#214460032
#214460002
#214456022
#214455992
C61×#19232
#2285261