Finite Group Databasebeta

← #30609339

Subgroups — #30609339

Order 15616.

1398 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840712C211yesmaximal, characteristic
2C2×#16840706C211yesmaximal, characteristic, complemented
3#21461007C211yesmaximal, characteristic, complemented
4#21461005C211yesmaximal, characteristic, complemented
5#21461003C211yesmaximal, characteristic
6#21461002C211yesmaximal, characteristic
7#21461002C211yesmaximal, characteristic
8#21461002C211yesmaximal, characteristic
9#21461000C211yesmaximal, characteristic
10#21460999C211yesmaximal, characteristic, complemented
11#21460998C211yesmaximal, characteristic, complemented
12#21460996C211yesmaximal, characteristic, complemented
13#21460995C211yesmaximal, characteristic, complemented
14#21460994C211yesmaximal, characteristic, complemented
15#388×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C22⋊#6923C2211yescharacteristic
21C22×C22⋊#6923C2211yescharacteristic
22C22×C22⋊#6923C2211yescharacteristic
23C22×C22⋊#6923C2211yescharacteristic
24C22×C4×#6923C2211yescharacteristic
25C22×C4×#6923C2211yescharacteristic
26#16840712—24no—
27#16840706—24no—
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
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C2×C4⋊C4×D61C2211yescharacteristic
47C2×C22⋊C4×D61C2211yescharacteristic
48C2×C22⋊C4×D61C2211yescharacteristic
49C2×C22⋊C4×D61C2211yescharacteristic
50C2×C42×D61C2211yescharacteristic
51#16839656C411yescharacteristic, complemented
52#16839655C411yescharacteristic, complemented
53#16839654C411yescharacteristic, complemented
54#16839653C411yescharacteristic, complemented
55#16839652C411yescharacteristic, complemented
56#16839651C411yescharacteristic, complemented
57#16839650C411yescharacteristic, complemented
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#388C411yescharacteristic, 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—41no—
72C2×C4⋊#6923—41no—
73C2×C4⋊#6923—41no—
74C2×C4⋊#6923—41no—
75C2×C4⋊#6923—41no—
76C2×C4⋊#6923—41no—
77C2×C4⋊#6923—41no—
78C2×C4⋊#6923—41no—
79C2×C4⋊#6923—41no—
80C2×C4⋊#6923D414yes—
81C2×C22⋊#6923—22no—
82C2×C22⋊#6923—22no—
83C2×C22⋊#6923—22no—
84C2×C22⋊#6923—22no—
85C2×C22⋊#6923—41no—
86C2×C22⋊#6923—41no—
87C2×C22⋊#6923—41no—
88C2×C22⋊#6923—41no—
89C2×C22⋊#6923—41no—
90C2×C22⋊#6923—41no—
91C2×C22⋊#6923—41no—
92C2×C22⋊#6923—41no—
93C2×C4×#6923—22no—
94C2×C4×#6923—22no—
95C2×C4×#6923—22no—
96C2×C4×#6923—41no—
97C2×C4×#6923—41no—
98C2×C4×#6923—41no—
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—41no—
112(C2×#6923)⋊C4—41no—
113(C2×#6923)⋊C4—41no—
114(C2×#6923)⋊C4—41no—
115(C2×#6923)⋊C4—41no—
116(C2×#6923)⋊C4—41no—
117C24×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C2×C4⋊Dic61C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C4⋊C4×D61—41no—
128C4⋊C4×D61—41no—
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
138C22⋊C4×D61—22no—
139C22⋊C4×D61—22no—
140C22⋊C4×D61—22no—
141C22⋊C4×D61—22no—
142C22⋊C4×D61—41no—
143C22⋊C4×D61—41no—
144C2×C4×Dic61C2×C411yescharacteristic
145C2×C4×Dic61C2×C411yescharacteristic
146C2×C4×Dic61C2×C411yescharacteristic
147C42×D61—22no—
148C42×D61—22no—
149#14519684C2×C411yescharacteristic
150#14519684C2×C411yescharacteristic
151#14519684C2×C411yescharacteristic
152#14519684C2×C411yescharacteristic
153#14519684C2×C411yescharacteristic
154#14519684C2×C411yescharacteristic
155C2×C4⋊C4×C61C2×C411yescharacteristic
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C22⋊C4×C61C2×C411yescharacteristic
158C2×C22⋊C4×C61C2×C411yescharacteristic
159C2×C42×C61C2×C411yescharacteristic
160#95×C61C2×C411yescharacteristic
161#95×C61C2×C411yescharacteristic
162C24×C61C22×C411yescharacteristic
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61C22×C411yescharacteristic
178C23×D61C2411yescharacteristic
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×#6923—21no—
200C22×#6923—21no—
201C22×#6923—21no—
202C22×#6923—21no—
203C22×#6923—21no—
204C22×#6923—21no—
205C22×#6923—21no—
206C22×#6923—21no—
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—21no—
219C22×#6923—21no—
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—21no—
227C22×#6923—21no—
228C22×#6923—21no—
229C22×#6923—21no—
230C22×#6923—21no—
231C22×#6923C2×D412yes—
232C22×#6923C2×D412yes—
233C22×#6923#4112yes—
234C22×#6923#4112yes—
235C22×C4×C61C22×C411yescharacteristic
236C22×C4×C61C22×C411yescharacteristic
237C22×C4×C61C22×C411yescharacteristic
238C22×C4×C61C22×C411yescharacteristic
239C22×C4×C61C22×C411yescharacteristic
240C22×C4×C61C22×C411yescharacteristic
241C22×Dic61C22×C411yescharacteristic
242C22×Dic61C22×C411yescharacteristic
243C22×Dic61C22×C411yescharacteristic
244C22×Dic61C22×C411yescharacteristic
245C22×Dic61C22×C411yescharacteristic
246C22×Dic61C22×C411yescharacteristic
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×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61C2×D412yes—
280C2×C4×D61#4112yes—
281C2×C4×D61#4112yes—
282C2×C4×D61#4112yes—
283C22⋊#6923—44no—
284C22⋊#6923—44no—
285C22⋊#6923—44no—
286C22⋊#6923—44no—
287C4⋊#6923—44no—
288C4⋊#6923—44no—
289C4⋊#6923—44no—
290C4⋊#6923—44no—
291C4×#6923—44no—
292C4×#6923—44no—
293C4⋊C4×C61—41no—
294C22⋊C4×C61—22no—
295C22⋊C4×C61—22no—
296C22⋊C4×C61—41no—
297C42×C61—22no—
298C22⋊Dic61—22no—
299C22⋊Dic61—22no—
300C22⋊Dic61—41no—
301#11758198—22no—
302#11758198—22no—
303#11758198—22no—
304#11758198—22no—
305#11758198—41no—
306#11758198—41no—
307C4⋊Dic61—41no—
308#11758196—41no—
309#11758196—41no—
310C4×Dic61—22no—
311C4×Dic61—22no—
312C4×Dic61—22no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61C23×C411yescharacteristic
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61C22×D411yescharacteristic
357C22×D61C2×#4111yescharacteristic
358C22×D61C2×#4111yescharacteristic
359C22×D61C2×#4111yescharacteristic
360C22×D61C2×#4111yescharacteristic
361C22×D61C2×#4111yescharacteristic
362C22×D61H(5,𝔽2)11yescharacteristic
363C22×D61H(5,𝔽2)11yescharacteristic
364C22×D61H(5,𝔽2)11yescharacteristic
365C22×D61H(5,𝔽2)11yescharacteristic
366C22×D61H(5,𝔽2)11yescharacteristic
367C22×D612−1+411yescharacteristic
368C22×D612−1+411yescharacteristic
369C22×D612−1+411yescharacteristic
370C2×#6923—22no—
371C2×#6923—22no—
372C2×#6923—22no—
373C2×#6923—22no—
374C2×#6923—22no—
375C2×#6923—22no—
376C2×#6923—22no—
377C2×#6923—22no—
378C2×#6923—22no—
379C2×#6923—22no—
380C2×#6923—22no—
381C2×#6923—22no—
382C2×#6923—41no—
383C2×#6923—41no—
384C2×#6923—41no—
385C2×#6923—41no—
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—41no—
398C2×#6923—41no—
399C2×#6923—41no—
400C2×#6923—41no—
401C2×#6923—41no—
402C2×#6923—41no—
403C2×#6923—41no—
404C2×#6923—41no—
405C2×#6923—41no—
406C2×#6923—41no—
407C2×#6923—41no—
408C2×#6923—41no—
409C2×#6923—41no—
410C2×#6923—41no—
411C2×#6923—41no—
412C2×#6923—41no—
413C2×#6923—41no—
414C2×#6923—41no—
415C2×#6923—41no—
416C2×#6923—41no—
417C2×#6923—41no—
418C2×#6923—41no—
419C2×#6923—41no—
420C2×#6923—41no—
421C2×#6923—41no—
422C2×#6923—41no—
423C2×#6923—41no—
424C2×#6923—41no—
425C2×#6923—41no—
426C2×C4×C61—21no—
427C2×C4×C61—21no—
428C2×C4×C61—21no—
429C2×C4×C61—21no—
430C2×C4×C61—21no—
431C2×C4×C61—21no—
432C2×C4×C61—21no—
433C2×C4×C61—21no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×C4×C61—21no—
442C2×C4×C61#11712yes—
443C2×C4×C61C4×D412yes—
444C2×Dic61—21no—
445C2×Dic61—21no—
446C2×Dic61—21no—
447C2×Dic61—21no—
448C2×Dic61—21no—
449C2×Dic61—21no—
450C2×Dic61—21no—
451C2×Dic61—21no—
452C2×Dic61—21no—
453C2×Dic61—21no—
454C2×Dic61—21no—
455C2×Dic61—21no—
456C2×Dic61—21no—
457C2×Dic61—21no—
458C2×Dic61—21no—
459C2×Dic61—21no—
460C2×Dic61#11712yes—
461C2×Dic61C4×D412yes—
462C4×D61—22no—
463C4×D61—22no—
464C4×D61—22no—
465C4×D61—22no—
466C4×D61—22no—
467C4×D61—22no—
468C4×D61—22no—
469C4×D61—22no—
470C4×D61—41no—
471C4×D61—41no—
472C4×D61—41no—
473C4×D61—41no—
474C4×D61—41no—
475C4×D61—41no—
476C4×D61—41no—
477C4×D61—41no—
478C4×D61—41no—
479C4×D61—41no—
480C4×D61—41no—
481C4×D61—41no—
482C4×D61—41no—
483C4×D61—41no—
484C4×D61—41no—
485C4×D61—41no—
486#14399—611nomaximal, Sylow
487C22×C61—41no—
488C22×C61—41no—
489C22×C61—41no—
490C22×C61—41no—
491C22×C61—41no—
492C22×C61—41no—
493C22×C61—41no—
494C22×C61C2×#11711yescharacteristic
495C22×C61C2×C4×D411yescharacteristic
496C22×C61C4×#4111yescharacteristic
497C22×C61#51811yescharacteristic
498C22×C61#52011yescharacteristic
499C22×C61#52011yescharacteristic
500C22×C61#52011yescharacteristic
501C2×D61—41no—
502C2×D61—41no—
503C2×D61—41no—
504C2×D61—41no—
505C2×D61—41no—
506C2×D61—41no—
507C2×D61—41no—
508C2×D61—81no—
509C2×D61—81no—
510C2×D61—81no—
511C2×D61—81no—
512C2×D61—81no—
513C2×D61—81no—
514C2×D61—81no—
515C2×D61—81no—
516C2×D61#53411yescharacteristic
517C2×D61#53611yescharacteristic
518C2×D61#53811yescharacteristic
519C2×D61#53811yescharacteristic
520C2×D61#53811yescharacteristic
521C2×D61#53911yescharacteristic
522C2×D61#53911yescharacteristic
523C2×D61#53911yescharacteristic
524C2×D61#53911yescharacteristic
525C2×D61#53911yescharacteristic
526C2×D61#54111yescharacteristic
527C2×D61#54211yescharacteristic
528C2×D61#54611yescharacteristic
529C2×D61#54711yescharacteristic
530C2×D61#55011yescharacteristic
531C2×D61#55011yescharacteristic
532C2×D61#55211yescharacteristic
533C2×D61#55211yescharacteristic
534C2×D61#55311yescharacteristic
535C2×D61#55511yescharacteristic
536C2×D61#55511yescharacteristic
537C2×D61#55511yescharacteristic
538C2×D61#55511yescharacteristic
539C2×D61#55611yescharacteristic
540C2×D61H(3,𝔽4)11yescharacteristic
541C2×D61#56211yescharacteristic
542C2×D61#56211yescharacteristic
543C2×D61#56311yescharacteristic
544#6923—42no—
545#6923—42no—
546#6923—42no—
547#6923—42no—
548#6923—81no—
549#6923—81no—
550#6923—81no—
551#6923—81no—
552C4×C61—22no—
553C4×C61—22no—
554C4×C61—41no—
555C4×C61—41no—
556C4×C61—41no—
557C4×C61—41no—
558Dic61—22no—
559Dic61—22no—
560Dic61—41no—
561Dic61—41no—
562Dic61—41no—
563Dic61—41no—
564C2×#388—611no—
565C2×#388—611no—
566C2×#382—611no—
567#1444—611no—
568#1442—611no—
569#1440—611no—
570#1439—611no—
571#1439—611no—
572#1439—611no—
573#1437—611no—
574#1436—611no—
575#1436—611no—
576C4⋊#95—611no—
577#1434—611no—
578#1434—611no—
579C2×C61—81no—
580C2×C61#231811yescharacteristic
581C2×C61#232211yescharacteristic
582C2×C61#233411yescharacteristic
583C2×C61#234611yescharacteristic
584C2×C61#235411yescharacteristic
585C2×C61#236311yescharacteristic
586C2×C61#237911yescharacteristic
587D61—81no—
588D61#268611yescharacteristic
589D61#269411yescharacteristic
590D61#272111yescharacteristic
591D61#273311yescharacteristic
592D61#277511yescharacteristic
593D61#278111yescharacteristic
594D61#278311yescharacteristic
595D61#278511yescharacteristic
596C22×C4⋊C4—611no—
597C22×C4⋊C4—611no—
598C22×C4⋊C4—611no—
599C22×C4⋊C4—611no—
600C22×C4⋊C4—611no—
601C22×C22⋊C4—611no—
602C22×C22⋊C4—611no—
603C22×C22⋊C4—611no—
604C22×C22⋊C4—611no—
605C22×C22⋊C4—611no—
606C22×C22⋊C4—611no—
607C22×C22⋊C4—611no—
608C22×C42—611no—
609C22×C42—611no—
610C22×C42—611no—
611#388—611no—
612#388—611no—
613#388—611no—
614#388—611no—
615#388—611no—
616#388—611no—
617#388—611no—
618#388—1224no—
619#388#692311yescharacteristic, complemented
620#382—1224no—
621C2×#95—611no—
622C2×#95—611no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C61#1439911yescharacteristic, complemented, Sylow
642C25—611no—
643C23×C4—611no—
644C23×C4—611no—
645C23×C4—611no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—611no—
651C23×C4—611no—
652C23×C4—611no—
653C23×C4—611no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C2×C4⋊C4—614no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—611no—
660C2×C4⋊C4—611no—
661C2×C4⋊C4—1222no—
662C2×C4⋊C4—1222no—
663C2×C4⋊C4—2441no—
664C2×C4⋊C4—2441no—
665C2×C4⋊C4—2441no—
666C2×C4⋊C4—2441no—
667C2×C4⋊C4—2441no—
668C2×C4⋊C4—2441no—
669C2×C4⋊C4—2441no—
670C2×C4⋊C4—2441no—
671C2×C4⋊C4—2441no—
672C2×C4⋊C4—2441no—
673C2×C4⋊C4—2441no—
674C2×C4⋊C4C2×#692311yescharacteristic
675C2×C22⋊C4—611no—
676C2×C22⋊C4—611no—
677C2×C22⋊C4—611no—
678C2×C22⋊C4—611no—
679C2×C22⋊C4—611no—
680C2×C22⋊C4—611no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—611no—
683C2×C22⋊C4—611no—
684C2×C22⋊C4—1222no—
685C2×C22⋊C4—1222no—
686C2×C22⋊C4—1222no—
687C2×C22⋊C4—1222no—
688C2×C22⋊C4—1222no—
689C2×C22⋊C4—1222no—
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—2441no—
693C2×C22⋊C4—2441no—
694C2×C22⋊C4—2441no—
695C2×C22⋊C4—2441no—
696C2×C22⋊C4—2441no—
697C2×C22⋊C4—2441no—
698C2×C22⋊C4—2441no—
699C2×C22⋊C4—2441no—
700C2×C22⋊C4—2441no—
701C2×C22⋊C4—2441no—
702C2×C22⋊C4C2×#692311yescharacteristic
703C2×C22⋊C4C2×#692311yescharacteristic
704C2×C22⋊C4C2×#692311yescharacteristic
705C2×C42—611no—
706C2×C42—611no—
707C2×C42—611no—
708C2×C42—1222no—
709C2×C42—1222no—
710C2×C42—1222no—
711C2×C42—1222no—
712C2×C42—1222no—
713C2×C42—2441no—
714C2×C42—2441no—
715C2×C42—2441no—
716C2×C42C2×#692311yescharacteristic
717#95—611no—
718#95—611no—
719#95—611no—
720#95—611no—
721#95—611no—
722#95—611no—
723#95—1222no—
724#95—1222no—
725#95—1222no—
726#95—1222no—
727#95—1222no—
728#95—1222no—
729#95—1222no—
730#95—1222no—
731#95—1222no—
732#95—1222no—
733#95—1222no—
734#95—1222no—
735#95—2441no—
736#95—2441no—
737#95—2441no—
738#95—2441no—
739#95—2441no—
740#95—2441no—
741#95C2×#692311yescharacteristic
742#95C2×#692311yescharacteristic
743C24—611no—
744C24—611no—
745C24—1221no—
746C24—1221no—
747C24—1221no—
748C24—1221no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24C22×#692311yescharacteristic
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—612no—
763C22×C4—612no—
764C22×C4—612no—
765C22×C4—612no—
766C22×C4—612no—
767C22×C4—612no—
768C22×C4—612no—
769C22×C4—612no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4C22×#692311yescharacteristic
859C22×C4C22×#692311yescharacteristic
860C22×C4C22×#692311yescharacteristic
861C22×C4C22×#692311yescharacteristic
862C22×C4C22×#692311yescharacteristic
863C22×C4C22×#692311yescharacteristic
864C4⋊C4—41no—
865C4⋊C4—2441no—
866C4⋊C4—2441no—
867C4⋊C4—2441no—
868C4⋊C4—2444no—
869C4⋊C4—2444no—
870C4⋊C4—2444no—
871C4⋊C4—2444no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—41no—
875C22⋊C4—1222no—
876C22⋊C4—1222no—
877C22⋊C4—1222no—
878C22⋊C4—1222no—
879C22⋊C4—1222no—
880C22⋊C4—1222no—
881C22⋊C4—2441no—
882C22⋊C4—2441no—
883C22⋊C4—2441no—
884C22⋊C4—2444no—
885C22⋊C4—2444no—
886C22⋊C4—2444no—
887C22⋊C4—2444no—
888C42—22no—
889C42—1222no—
890C42—1222no—
891C42—1222no—
892C42—2444no—
893C42—2444no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—611no—
902C23—611no—
903C23—611no—
904C23—611no—
905C23—611no—
906C23—611no—
907C23—611no—
908C23—611no—
909C23—611no—
910C23—611no—
911C23—611no—
912C23—611no—
913C23—611no—
914C23—611no—
915C23—1221no—
916C23—1221no—
917C23—1221no—
918C23—1221no—
919C23—1221no—
920C23—1221no—
921C23—1221no—
922C23—2441no—
923C23—2441no—
924C23—2441no—
925C23—2441no—
926C23—2441no—
927C23—2441no—
928C23—2441no—
929C23—2441no—
930C23—2441no—
931C23—2441no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23—2441no—
948C23—2441no—
949C23—2441no—
950C23C23×#692311yescharacteristic
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—612no—
968C2×C4—612no—
969C2×C4—1222no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—1221no—
978C2×C4—1221no—
979C2×C4—1221no—
980C2×C4—1221no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—1222no—
984C2×C4—1222no—
985C2×C4—1222no—
986C2×C4—1222no—
987C2×C4—1222no—
988C2×C4—1222no—
989C2×C4—1222no—
990C2×C4—1222no—
991C2×C4—1222no—
992C2×C4—1222no—
993C2×C4—1221no—
994C2×C4—1221no—
995C2×C4—1221no—
996C2×C4—1221no—
997C2×C4—1221no—
998C2×C4—1221no—
999C2×C4—1221no—
1000C2×C4—1221no—
1001C2×C4—1221no—
1002C2×C4—1221no—
1003C2×C4—1221no—
1004C2×C4—1221no—
1005C2×C4—2441no—
1006C2×C4—2441no—
1007C2×C4—2441no—
1008C2×C4—2441no—
1009C2×C4—2441no—
1010C2×C4—2441no—
1011C2×C4—2441no—
1012C2×C4—2441no—
1013C2×C4—2441no—
1014C2×C4—2441no—
1015C2×C4—2441no—
1016C2×C4—2441no—
1017C2×C4—2441no—
1018C2×C4—2441no—
1019C2×C4—2441no—
1020C2×C4—2441no—
1021C2×C4—2441no—
1022C2×C4—2441no—
1023C2×C4—2441no—
1024C2×C4—2441no—
1025C2×C4—2441no—
1026C2×C4—2441no—
1027C2×C4—2441no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4—2441no—
1031C2×C4—2441no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4#1451985612yes—
1066C2×C4D4×#692312yes—
1067C22—41no—
1068C22—41no—
1069C22—41no—
1070C22—41no—
1071C22—41no—
1072C22—41no—
1073C22—41no—
1074C22—611no—
1075C22—611no—
1076C22—611no—
1077C22—611no—
1078C22—611no—
1079C22—611no—
1080C22—611no—
1081C22—611no—
1082C22—611no—
1083C22—611no—
1084C22—611no—
1085C22—611no—
1086C22—611no—
1087C22—611no—
1088C22—611no—
1089C22—611no—
1090C22—611no—
1091C22—611no—
1092C22—611no—
1093C22—611no—
1094C22—611no—
1095C22—611no—
1096C22—611no—
1097C22—611no—
1098C22—611no—
1099C22—611no—
1100C22—611no—
1101C22—611no—
1102C22—4881no—
1103C22—4881no—
1104C22—4881no—
1105C22—4881no—
1106C22—4881no—
1107C22—4881no—
1108C22—4881no—
1109C22—4881no—
1110C22—2441no—
1111C22—2441no—
1112C22—2441no—
1113C22—2441no—
1114C22—2441no—
1115C22—2441no—
1116C22—2441no—
1117C22C2×#1451985611yescharacteristic
1118C22C2×D4×#692311yescharacteristic
1119C22#41×#692311yescharacteristic
1120C22#1684082911yescharacteristic
1121C22#1684083111yescharacteristic
1122C22#1684083111yescharacteristic
1123C22#1684083111yescharacteristic
1124C4—22no—
1125C4—22no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—1222no—
1131C4—1222no—
1132C4—4881no—
1133C4—4881no—
1134C4—4881no—
1135C4—4881no—
1136C4—2442no—
1137C4—2442no—
1138C4—2442no—
1139C4—2442no—
1140C4—2441no—
1141C4—2441no—
1142C4—2441no—
1143C4—2441no—
1144C2—81no—
1145C2—611no—
1146C2—611no—
1147C2—611no—
1148C2—611no—
1149C2—611no—
1150C2—611no—
1151C2—611no—
1152C2—611no—
1153C2—4881no—
1154C2#2146230111yescharacteristic
1155C2#2146230511yescharacteristic
1156C2#2146231711yescharacteristic
1157C2#2146232911yescharacteristic
1158C2#2146233711yescharacteristic
1159C2#2146234611yescharacteristic
1160C2#2146236211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#388C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenter#388#6923
hypocenterC61#14399
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#16840706C2semidirect
3. #21461007C2semidirect
4. #21461005C2semidirect
10. #21460999C2semidirect
11. #21460998C2semidirect
12. #21460996C2semidirect
13. #21460995C2semidirect
14. #21460994C2semidirect
51. #16839656C4semidirect
52. #16839655C4semidirect
53. #16839654C4semidirect
54. #16839653C4semidirect
55. #16839652C4semidirect
56. #16839651C4semidirect
57. #16839650C4semidirect
60. C61×#388C4semidirect
619. #388#6923semidirect
641. C61#14399semidirect

Maximal subgroups

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

subgroupindex
C2×#168407122
C2×#168407062
#214610072
#214610052
#214610032
#214610022
#214610002
#214609992
#214609982
#214609962
#214609952
#214609942
#388×D612
#1439961