Finite Group Databasebeta

← #30609644

Subgroups — #30609644

Order 15616.

1422 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840711C211yesmaximal, characteristic
2C2×C42×#6923C211yesmaximal, characteristic
3#21460999C211yesmaximal, characteristic
4#21460999C211yesmaximal, characteristic
5#21460999C211yesmaximal, characteristic
6#21460999C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic
8#21460998C211yesmaximal, characteristic
9#21460998C211yesmaximal, characteristic
10#21460998C211yesmaximal, characteristic
11#21460995C211yesmaximal, characteristic
12#21460994C211yesmaximal, characteristic
13#21460994C211yesmaximal, characteristic
14#21460994C211yesmaximal, characteristic
15#387×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4×#6923C2211yescharacteristic
19C22×C4×#6923C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22C22×C4×#6923C2211yescharacteristic
23C22×C4×#6923C2211yescharacteristic
24#16840711—24no—
25C2×(C2×#6923)⋊C4C2211yescharacteristic
26C2×(C2×#6923)⋊C4C2211yescharacteristic
27C2×(C2×#6923)⋊C4C2211yescharacteristic
28C2×(C2×#6923)⋊C4C2211yescharacteristic
29C2×(C2×#6923)⋊C4C2211yescharacteristic
30C2×(C2×#6923)⋊C4C2211yescharacteristic
31C2×(C2×#6923)⋊C4C2211yescharacteristic
32C2×(C2×#6923)⋊C4C2211yescharacteristic
33C2×(C2×#6923)⋊C4C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36C2×(C2×#6923)⋊C4C2211yescharacteristic
37C2×(C2×#6923)⋊C4C2211yescharacteristic
38C2×(C2×#6923)⋊C4C2211yescharacteristic
39C2×(C2×#6923)⋊C4C2211yescharacteristic
40C2×(C2×#6923)⋊C4C2211yescharacteristic
41C2×(C2×#6923)⋊C4C2211yescharacteristic
42C2×(C2×#6923)⋊C4C2211yescharacteristic
43C2×(C2×#6923)⋊C4C2211yescharacteristic
44C2×(C2×#6923)⋊C4C2211yescharacteristic
45C42×#6923—24no—
46C2×C4⋊C4×D61C2211yescharacteristic
47C2×C4⋊C4×D61C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839649C411yescharacteristic, complemented
50#16839648C411yescharacteristic, complemented
51#16839647C411yescharacteristic, complemented
52#16839646C411yescharacteristic, complemented
53#16839645C411yescharacteristic, complemented
54#16839644C411yescharacteristic, complemented
55#16839643C411yescharacteristic, complemented
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#387C411yescharacteristic, complemented
61C23×#6923C2311yescharacteristic
62C23×#6923C2311yescharacteristic
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C2×C4⋊#6923—22no—
70C2×C4⋊#6923—22no—
71C2×C4⋊#6923—22no—
72C2×C4⋊#6923—22no—
73C2×C4⋊#6923—22no—
74C2×C4⋊#6923—22no—
75C2×C4×#6923—22no—
76C2×C4×#6923—22no—
77C2×C4×#6923—22no—
78C2×C4×#6923—22no—
79C2×C4×#6923—22no—
80C2×C4×#6923—22no—
81C2×C4×#6923—22no—
82C2×C4×#6923—22no—
83C2×C4×#6923—22no—
84C2×C4×#6923—22no—
85C2×C4×#6923—22no—
86C2×C4×#6923—22no—
87C2×C4×#6923—22no—
88C2×C4×#6923—22no—
89C2×C4×#6923—22no—
90C2×C4×#6923—22no—
91C2×C4×#6923D414yes—
92C2×C4×#6923Q814yes—
93(C2×#6923)⋊C4—22no—
94(C2×#6923)⋊C4—22no—
95(C2×#6923)⋊C4—22no—
96(C2×#6923)⋊C4—22no—
97(C2×#6923)⋊C4—22no—
98(C2×#6923)⋊C4—22no—
99(C2×#6923)⋊C4—22no—
100(C2×#6923)⋊C4—22no—
101(C2×#6923)⋊C4—22no—
102(C2×#6923)⋊C4—22no—
103(C2×#6923)⋊C4—22no—
104(C2×#6923)⋊C4—22no—
105(C2×#6923)⋊C4—22no—
106(C2×#6923)⋊C4—22no—
107(C2×#6923)⋊C4—22no—
108(C2×#6923)⋊C4—22no—
109(C2×#6923)⋊C4—22no—
110(C2×#6923)⋊C4—22no—
111(C2×#6923)⋊C4—22no—
112(C2×#6923)⋊C4—22no—
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C2×C4⋊Dic61C2×C411yescharacteristic
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C4⋊C4×D61—22no—
127C4⋊C4×D61—22no—
128C4⋊C4×D61—22no—
129C4⋊C4×D61—22no—
130C2×C4×Dic61C2×C411yescharacteristic
131C2×C4×Dic61C2×C411yescharacteristic
132C2×C4×Dic61C2×C411yescharacteristic
133C42×D61—22no—
134C42×D61—22no—
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137#14519684C2×C411yescharacteristic
138#14519684C2×C411yescharacteristic
139#14519684C2×C411yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143#14519684C2×C411yescharacteristic
144#14519684C2×C411yescharacteristic
145#14519684C2×C411yescharacteristic
146#14519684C2×C411yescharacteristic
147C2×C4⋊C4×C61C2×C411yescharacteristic
148C2×C4⋊C4×C61C2×C411yescharacteristic
149C2×C42×C61C2×C411yescharacteristic
150#95×C61C2×C411yescharacteristic
151#95×C61C2×C411yescharacteristic
152#95×C61C2×C411yescharacteristic
153#95×C61C2×C411yescharacteristic
154C23×D61C2411yescharacteristic
155C22×#6923—21no—
156C22×#6923—21no—
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—21no—
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—21no—
182C22×#6923—21no—
183C22×#6923—21no—
184C22×#6923—21no—
185C22×#6923—21no—
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—21no—
192C22×#6923—21no—
193C22×#6923—21no—
194C22×#6923—21no—
195C22×#6923—21no—
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923C2×D412yes—
200C22×#6923C2×D412yes—
201C22×#6923C2×Q812yes—
202C22×#6923C2×Q812yes—
203C22×#6923#4112yes—
204C22×#6923#4112yes—
205C22×#6923#4112yes—
206C22×#6923#4112yes—
207C22×#6923#4112yes—
208C22×#6923#4112yes—
209C22×#6923#4112yes—
210C22×#6923#4112yes—
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
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—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
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—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61C2×D412yes—
262C2×C4×D61C2×Q812yes—
263C2×C4×D61#4112yes—
264C2×C4×D61#4112yes—
265C2×C4×D61#4112yes—
266C2×C4×D61#4112yes—
267C4⋊#6923—44no—
268C4⋊#6923—44no—
269C4×#6923—28no—
270C4×#6923—28no—
271C4×#6923—28no—
272C4×#6923—28no—
273C4×#6923—28no—
274C4×#6923—28no—
275C4⋊C4×C61—22no—
276C4⋊C4×C61—22no—
277C42×C61—22no—
278C4⋊Dic61—22no—
279C4⋊Dic61—22no—
280#11758196—22no—
281#11758196—22no—
282#11758196—22no—
283#11758196—22no—
284C4×Dic61—22no—
285C4×Dic61—22no—
286C4×Dic61—22no—
287C23×C61C23×C411yescharacteristic
288C22×D61C22×D411yescharacteristic
289C22×D61C22×Q811yescharacteristic
290C22×D61C2×#4111yescharacteristic
291C22×D61C2×#4111yescharacteristic
292C22×D61C2×#4111yescharacteristic
293C22×D61C2×#4111yescharacteristic
294C22×D61C2×#4111yescharacteristic
295C22×D61C2×#4111yescharacteristic
296C22×D61C2×#4111yescharacteristic
297C22×D61C2×#4111yescharacteristic
298C22×D61C2×#4111yescharacteristic
299C22×D61C2×#4111yescharacteristic
300C22×D61C2×#4111yescharacteristic
301C22×D61C2×#4111yescharacteristic
302C2×#6923—22no—
303C2×#6923—22no—
304C2×#6923—22no—
305C2×#6923—22no—
306C2×#6923—22no—
307C2×#6923—22no—
308C2×#6923—22no—
309C2×#6923—22no—
310C2×#6923—22no—
311C2×#6923—22no—
312C2×#6923—22no—
313C2×#6923—22no—
314C2×#6923—22no—
315C2×#6923—22no—
316C2×#6923—22no—
317C2×#6923—22no—
318C2×#6923—22no—
319C2×#6923—22no—
320C2×#6923—22no—
321C2×#6923—22no—
322C2×#6923—22no—
323C2×#6923—22no—
324C2×#6923—22no—
325C2×#6923—22no—
326C2×#6923—41no—
327C2×#6923—41no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—41no—
337C2×#6923—41no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—41no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923C22⋊Q814yes—
355C2×#6923#12314yes—
356C2×#6923#12514yes—
357C2×#6923#12614yes—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61#11712yes—
377C2×C4×C61C4×D412yes—
378C2×C4×C61C4×Q812yes—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61#11712yes—
398C2×Dic61C4×D412yes—
399C2×Dic61C4×Q812yes—
400C4×D61—22no—
401C4×D61—22no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—22no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428#14704—611nomaximal, Sylow
429C22×C61C2×#11711yescharacteristic
430C22×C61C2×C4×D411yescharacteristic
431C22×C61C2×C4×Q811yescharacteristic
432C22×C61C4×#4111yescharacteristic
433C22×C61C4×#4111yescharacteristic
434C22×C61C4×#4111yescharacteristic
435C22×C61C4×#4111yescharacteristic
436C2×D61C2×C22⋊Q811yescharacteristic
437C2×D61C2×#12311yescharacteristic
438C2×D61#52511yescharacteristic
439C2×D61#52511yescharacteristic
440C2×D61#52511yescharacteristic
441C2×D61#52511yescharacteristic
442C2×D61C2×#12511yescharacteristic
443C2×D61C2×#12611yescharacteristic
444C2×D61#52911yescharacteristic
445C2×D61#52911yescharacteristic
446C2×D61#52911yescharacteristic
447C2×D61#52911yescharacteristic
448C2×D61#52911yescharacteristic
449C2×D61#52911yescharacteristic
450C2×D61#52911yescharacteristic
451C2×D61#52911yescharacteristic
452C2×D61#52911yescharacteristic
453C2×D61#52911yescharacteristic
454C2×D61#52911yescharacteristic
455C2×D61#52911yescharacteristic
456C2×D61#52911yescharacteristic
457C2×D61#52911yescharacteristic
458C2×D61#52911yescharacteristic
459C2×D61#52911yescharacteristic
460C2×D61#53311yescharacteristic
461C2×D61#53311yescharacteristic
462C2×D61#53311yescharacteristic
463C2×D61#53311yescharacteristic
464#6923—24no—
465#6923—24no—
466#6923—24no—
467#6923—24no—
468#6923—81no—
469#6923—81no—
470#6923—81no—
471#6923—81no—
472C4×C61—22no—
473C4×C61—22no—
474C4×C61—22no—
475C4×C61—41no—
476C4×C61—41no—
477C4×C61—41no—
478C4×C61—41no—
479Dic61—22no—
480Dic61—22no—
481Dic61—22no—
482Dic61—41no—
483Dic61—41no—
484Dic61—41no—
485Dic61—41no—
486C2×#387—611no—
487C2×#387—611no—
488C2×C43—611no—
489#1436—611no—
490#1436—611no—
491#1436—611no—
492#1436—611no—
493#1436—611no—
494#1436—611no—
495#1436—611no—
496#1436—611no—
497#1434—611no—
498#1434—611no—
499#1434—611no—
500#1434—611no—
501C2×C61#229011yescharacteristic
502C2×C61#229511yescharacteristic
503C2×C61#229811yescharacteristic
504C2×C61C4×#12311yescharacteristic
505C2×C61C4×C22⋊Q811yescharacteristic
506C2×C61C4×#12611yescharacteristic
507C2×C61C4×#12511yescharacteristic
508D61#285111yescharacteristic
509D61#285211yescharacteristic
510D61#285311yescharacteristic
511D61#285511yescharacteristic
512D61#286311yescharacteristic
513D61#286411yescharacteristic
514D61#286511yescharacteristic
515D61#286611yescharacteristic
516C22×C4⋊C4—611no—
517C22×C4⋊C4—611no—
518C22×C4⋊C4—611no—
519C22×C4⋊C4—611no—
520C22×C42—611no—
521C22×C42—611no—
522C22×C42—611no—
523C22×C42—611no—
524C22×C42—611no—
525C22×C42—611no—
526C22×C42—611no—
527#387—611no—
528#387—611no—
529#387—611no—
530#387—611no—
531#387—611no—
532#387—611no—
533#387—611no—
534#387—1224no—
535#387#692311yescharacteristic, complemented
536C2×#95—611no—
537C2×#95—611no—
538C2×#95—611no—
539C2×#95—611no—
540C2×#95—611no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95—611no—
544C2×#95—611no—
545C2×#95—611no—
546C2×#95—611no—
547C2×#95—611no—
548C2×#95—611no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C43—1224no—
561C61#1470411yescharacteristic, complemented, Sylow
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—611no—
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C2×C4⋊C4—611no—
578C2×C4⋊C4—611no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—611no—
582C2×C4⋊C4—611no—
583C2×C4⋊C4—1222no—
584C2×C4⋊C4—1222no—
585C2×C4⋊C4—1222no—
586C2×C4⋊C4—1222no—
587C2×C4⋊C4—1222no—
588C2×C4⋊C4—1222no—
589C2×C4⋊C4—1222no—
590C2×C4⋊C4—1222no—
591C2×C4⋊C4—1222no—
592C2×C4⋊C4—1222no—
593C2×C4⋊C4C2×#692311yescharacteristic
594C2×C4⋊C4C2×#692311yescharacteristic
595C2×C42—614no—
596C2×C42—614no—
597C2×C42—611no—
598C2×C42—611no—
599C2×C42—611no—
600C2×C42—1222no—
601C2×C42—1222no—
602C2×C42—1222no—
603C2×C42—1222no—
604C2×C42—1222no—
605C2×C42—1222no—
606C2×C42—1222no—
607C2×C42—1222no—
608C2×C42—1222no—
609C2×C42—1222no—
610C2×C42—1222no—
611C2×C42—1222no—
612C2×C42—1222no—
613C2×C42—1222no—
614C2×C42—1222no—
615C2×C42—1222no—
616C2×C42—1222no—
617C2×C42—1222no—
618C2×C42C2×#692311yescharacteristic
619#95—611no—
620#95—611no—
621#95—611no—
622#95—611no—
623#95—611no—
624#95—611no—
625#95—611no—
626#95—611no—
627#95—611no—
628#95—611no—
629#95—611no—
630#95—611no—
631#95—1222no—
632#95—1222no—
633#95—1222no—
634#95—1222no—
635#95—1222no—
636#95—1222no—
637#95—1222no—
638#95—1222no—
639#95—1222no—
640#95—1222no—
641#95—1222no—
642#95—1222no—
643#95—1222no—
644#95—1222no—
645#95—1222no—
646#95—1222no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650#95—1222no—
651#95C2×#692311yescharacteristic
652#95C2×#692311yescharacteristic
653#95C2×#692311yescharacteristic
654#95C2×#692311yescharacteristic
655C24—611no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—612no—
676C22×C4—612no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
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—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4C22×#692311yescharacteristic
762C22×C4C22×#692311yescharacteristic
763C22×C4C22×#692311yescharacteristic
764C22×C4C22×#692311yescharacteristic
765C22×C4C22×#692311yescharacteristic
766C22×C4C22×#692311yescharacteristic
767C22×C4C22×#692311yescharacteristic
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—1222no—
771C4⋊C4—1222no—
772C4⋊C4—1222no—
773C4⋊C4—1222no—
774C4⋊C4—1222no—
775C4⋊C4—1222no—
776C4⋊C4—2444no—
777C4⋊C4—2444no—
778C42—22no—
779C42—1222no—
780C42—1222no—
781C42—1228no—
782C42—1228no—
783C42—1228no—
784C42—1228no—
785C42—1228no—
786C42—1228no—
787C42—1222no—
788C23—611no—
789C23—611no—
790C23—611no—
791C23—611no—
792C23—611no—
793C23—611no—
794C23—611no—
795C23—611no—
796C23—611no—
797C23—611no—
798C23—611no—
799C23—611no—
800C23—611no—
801C23—611no—
802C23C23×#692311yescharacteristic
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—614no—
822C2×C4—614no—
823C2×C4—614no—
824C2×C4—614no—
825C2×C4—612no—
826C2×C4—612no—
827C2×C4—612no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—1222no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4#1451985612yes—
927C2×C4D4×#692312yes—
928C2×C4Q8×#692312yes—
929C22—611no—
930C22—611no—
931C22—611no—
932C22—611no—
933C22—611no—
934C22—611no—
935C22—611no—
936C22—611no—
937C22—611no—
938C22—611no—
939C22—611no—
940C22—611no—
941C22—611no—
942C22—611no—
943C22—611no—
944C22—611no—
945C22—611no—
946C22—611no—
947C22—611no—
948C22—611no—
949C22—611no—
950C22—611no—
951C22—611no—
952C22—611no—
953C22—611no—
954C22—611no—
955C22—611no—
956C22—611no—
957C22C2×#1451985611yescharacteristic
958C22C2×D4×#692311yescharacteristic
959C22C2×Q8×#692311yescharacteristic
960C22#41×#692311yescharacteristic
961C22#41×#692311yescharacteristic
962C22#41×#692311yescharacteristic
963C22#41×#692311yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—41no—
968C4—41no—
969C4—41no—
970C4—41no—
971C4—1224no—
972C4—1224no—
973C4—1224no—
974C4—1224no—
975C4—1222no—
976C4—1222no—
977C4—1222no—
978C4—4881no—
979C4—4881no—
980C4—4881no—
981C4—4881no—
982C4—2441no—
983C4—2441no—
984C4—2441no—
985C4—2441no—
986C2—611no—
987C2—611no—
988C2—611no—
989C2—611no—
990C2—611no—
991C2—611no—
992C2—611no—
993C2—611no—
994C2#2146227311yescharacteristic
995C2#2146227811yescharacteristic
996C2#2146228111yescharacteristic
997C2#123×#692311yescharacteristic
998C2C22⋊Q8×#692311yescharacteristic
999C2#126×#692311yescharacteristic
1000C2#125×#692311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#387C4
prime radical, cosocleC23×D61C24
hypercenter#387#6923
hypocenterC61#14704
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
49. #16839649C4semidirect
50. #16839648C4semidirect
51. #16839647C4semidirect
52. #16839646C4semidirect
53. #16839645C4semidirect
54. #16839644C4semidirect
55. #16839643C4semidirect
60. C61×#387C4semidirect
535. #387#6923semidirect
561. C61#14704semidirect

Maximal subgroups

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

subgroupindex
C2×#168407112
C2×C42×#69232
#214609992
#214609982
#214609952
#214609942
#387×D612
#1470461