Finite Group Databasebeta

← #30608786

Subgroups — #30608786

Order 15616.

1422 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊#6923C211yesmaximal, characteristic
2C2×#16840698C211yesmaximal, characteristic
3#21461008C212yesmaximal
4#21461006C212yesmaximal
5#21461005C212yesmaximal
6#21461004C212yesmaximal
7C4×(C2×#6923)⋊C4C211yesmaximal, characteristic
8C4×(C2×#6923)⋊C4C211yesmaximal, characteristic
9C4×(C2×#6923)⋊C4C211yesmaximal, characteristic
10C4×(C2×#6923)⋊C4C211yesmaximal, characteristic
11C4×C4⋊C4×D61C211yesmaximal, characteristic
12C22×C4⋊#6923C2212yes—
13C22×C4×#6923C2211yescharacteristic
14C22×C4×#6923C2211yescharacteristic
15C22×C4×#6923C2211yescharacteristic
16C22×C4×#6923C2211yescharacteristic
17C4×C4⋊#6923—24no—
18#16840698—24no—
19C2×(C2×#6923)⋊C4C2212yes—
20C2×(C2×#6923)⋊C4C2212yes—
21C2×(C2×#6923)⋊C4C2212yes—
22C2×(C2×#6923)⋊C4C2212yes—
23C2×(C2×#6923)⋊C4C2212yes—
24C2×(C2×#6923)⋊C4C2212yes—
25C2×(C2×#6923)⋊C4C2212yes—
26C2×(C2×#6923)⋊C4C2212yes—
27C2×(C2×#6923)⋊C4C2212yes—
28C2×(C2×#6923)⋊C4C2212yes—
29C2×(C2×#6923)⋊C4C2212yes—
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32C2×C42×D61C2211yescharacteristic
33C2×C42×D61C2211yescharacteristic
34C2×C42×D61C2211yescharacteristic
35C4⋊C4×Dic61C411yescharacteristic, complemented
36C4⋊C4×Dic61C411yescharacteristic, complemented
37C4×#11758196C411yescharacteristic, complemented
38C4×#11758196C411yescharacteristic, complemented
39C4×C4⋊Dic61C411yescharacteristic, complemented
40#16839613C411yescharacteristic, complemented
41#16839613C411yescharacteristic, complemented
42#95×D61C2211yescharacteristic
43#95×D61C2211yescharacteristic
44C4×C4⋊C4×C61C411yescharacteristic, complemented
45C23×#6923C2312yes—
46C23×#6923C2312yes—
47C23×#6923C2312yes—
48C23×#6923C2312yes—
49C2×C4⋊#6923—24no—
50C2×C4⋊#6923—24no—
51C2×C4⋊#6923—24no—
52C2×C4×#6923—22no—
53C2×C4×#6923—22no—
54C2×C4×#6923—22no—
55C2×C4×#6923—22no—
56C2×C4×#6923—22no—
57C2×C4×#6923—22no—
58C2×C4×#6923—22no—
59C2×C4×#6923—22no—
60C2×C4×#6923—22no—
61C2×C4×#6923—22no—
62C2×C4×#6923D414yes—
63C2×C4×#6923Q814yes—
64(C2×#6923)⋊C4—24no—
65(C2×#6923)⋊C4—24no—
66(C2×#6923)⋊C4—24no—
67(C2×#6923)⋊C4—24no—
68(C2×#6923)⋊C4—24no—
69(C2×#6923)⋊C4—24no—
70(C2×#6923)⋊C4—24no—
71(C2×#6923)⋊C4—24no—
72(C2×#6923)⋊C4—24no—
73(C2×#6923)⋊C4—24no—
74(C2×#6923)⋊C4—24no—
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C22×C4×D61C2311yescharacteristic
80C22×C4×D61C2311yescharacteristic
81C22×C4×D61C2311yescharacteristic
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×#11758196C2×C411yescharacteristic
85C2×#11758196C2×C411yescharacteristic
86C2×#11758196C2×C411yescharacteristic
87C2×#11758196C2×C411yescharacteristic
88C4⋊C4×D61—24no—
89C4⋊C4×D61—24no—
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2×C411yescharacteristic
93C2×C4×Dic61C2×C411yescharacteristic
94C2×C4×Dic61C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2×C411yescharacteristic
99C42×D61—22no—
100C42×D61—22no—
101C42×D61—22no—
102C42×D61—22no—
103C42×D61—22no—
104C42×D61—22no—
105#14519684C2×C411yescharacteristic
106#14519684C2×C411yescharacteristic
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111C2×C4⋊C4×C61C2×C411yescharacteristic
112C2×C4⋊C4×C61C2×C411yescharacteristic
113C2×C42×C61C2×C411yescharacteristic
114C2×C42×C61C2×C411yescharacteristic
115C2×C42×C61C2×C411yescharacteristic
116#95×C61C2×C411yescharacteristic
117#95×C61C2×C411yescharacteristic
118C23×D61C2411yescharacteristic
119C22×#6923—22no—
120C22×#6923—22no—
121C22×#6923—22no—
122C22×#6923—22no—
123C22×#6923—22no—
124C22×#6923—22no—
125C22×#6923—22no—
126C22×#6923—22no—
127C22×#6923—22no—
128C22×#6923—22no—
129C22×#6923—22no—
130C22×#6923—22no—
131C22×#6923—22no—
132C22×#6923—22no—
133C22×#6923—22no—
134C22×#6923—22no—
135C22×#6923—22no—
136C22×#6923—22no—
137C22×#6923—22no—
138C22×#6923—22no—
139C22×#6923—22no—
140C22×#6923—22no—
141C22×#6923—22no—
142C22×#6923—22no—
143C22×#6923C2×D414yes—
144C22×#6923C2×Q814yes—
145C22×#6923#4114yes—
146C22×#6923#4114yes—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—22no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—22no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61C2×D412yes—
184C2×C4×D61C2×Q812yes—
185C2×C4×D61#4114yes—
186C2×C4×D61#4114yes—
187C2×C4×D61#4112yes—
188C2×C4×D61#4112yes—
189C2×C4×D61#4112yes—
190C2×C4×D61#4112yes—
191C4⋊#6923—216no—
192C4×#6923—28no—
193C4×#6923—28no—
194C4×#6923—44no—
195C4×#6923—44no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C42×C61—22no—
199C42×C61—22no—
200C42×C61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C23×C61C23×C411yescharacteristic
217C22×D61C22×D411yescharacteristic
218C22×D61C22×Q811yescharacteristic
219C22×D61C2×#4111yescharacteristic
220C22×D61C2×#4111yescharacteristic
221C22×D61C2×#4111yescharacteristic
222C22×D61C2×#4112yes—
223C22×D61C2×#4112yes—
224C22×D61C2×#4111yescharacteristic
225C22×D61C2×#4112yes—
226C22×D61C2×#4112yes—
227C2×#6923—24no—
228C2×#6923—24no—
229C2×#6923—24no—
230C2×#6923—24no—
231C2×#6923—24no—
232C2×#6923—24no—
233C2×#6923—24no—
234C2×#6923—24no—
235C2×#6923—24no—
236C2×#6923—24no—
237C2×#6923—24no—
238C2×#6923—24no—
239C2×#6923—42no—
240C2×#6923—42no—
241C2×#6923—42no—
242C2×#6923—42no—
243C2×#6923—42no—
244C2×#6923—42no—
245C2×#6923—42no—
246C2×#6923—42no—
247C2×#6923—42no—
248C2×#6923—42no—
249C2×#6923—42no—
250C2×#6923—42no—
251C2×#6923—42no—
252C2×#6923—42no—
253C2×#6923—42no—
254C2×#6923—42no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61#11712yes—
272C2×C4×C61#11712yes—
273C2×C4×C61#11712yes—
274C2×C4×C61C4×D412yes—
275C2×C4×C61C4×Q812yes—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61#11712yes—
293C2×Dic61#11712yes—
294C2×Dic61#11712yes—
295C2×Dic61C4×D412yes—
296C2×Dic61C4×Q812yes—
297C4×D61—24no—
298C4×D61—24no—
299C4×D61—24no—
300C4×D61—24no—
301C4×D61—42no—
302C4×D61—42no—
303C4×D61—42no—
304C4×D61—42no—
305C4×D61—42no—
306C4×D61—42no—
307C4×D61—42no—
308C4×D61—42no—
309C4×D61C22⋊Q814yes—
310C4×D61#12314yes—
311C4×D61#12514yes—
312C4×D61#12614yes—
313#13846—611nomaximal, Sylow
314C22×C61C2×#11711yescharacteristic
315C22×C61C2×#11711yescharacteristic
316C22×C61C2×#11711yescharacteristic
317C22×C61C2×C4×D411yescharacteristic
318C22×C61C2×C4×Q811yescharacteristic
319C22×C61C4×#4111yescharacteristic
320C22×C61C4×#4111yescharacteristic
321C2×D61C2×C22⋊Q811yescharacteristic
322C2×D61C2×#12311yescharacteristic
323C2×D61#52512yes—
324C2×D61C2×#12511yescharacteristic
325C2×D61C2×#12611yescharacteristic
326C2×D61#52912yes—
327C2×D61#52912yes—
328C2×D61#52912yes—
329C2×D61#52912yes—
330C2×D61#52912yes—
331C2×D61#52912yes—
332C2×D61#52912yes—
333C2×D61#52912yes—
334C2×D61#53212yes—
335C2×D61#53312yes—
336C2×D61#53312yes—
337#6923—44no—
338#6923—44no—
339#6923—44no—
340#6923—44no—
341C4×C61—22no—
342C4×C61—22no—
343C4×C61—41no—
344C4×C61—41no—
345C4×C61—41no—
346C4×C61—41no—
347C4×C61#38714yes—
348Dic61—22no—
349Dic61—22no—
350Dic61—41no—
351Dic61—41no—
352Dic61—41no—
353Dic61—41no—
354Dic61#38714yes—
355C2×C4×C4⋊C4—611no—
356C2×C4×C4⋊C4—611no—
357C2×#376—611no—
358#1445—612no—
359#1443—612no—
360#1442—612no—
361#1441—612no—
362C4×#95—611no—
363C4×#95—611no—
364C4×#95—611no—
365C4×#95—611no—
366C2×C61#228311yescharacteristic
367C2×C61C2×#38711yescharacteristic
368C2×C61#229011yescharacteristic
369C2×C61#229311yescharacteristic
370C2×C61#229511yescharacteristic
371C2×C61#229511yescharacteristic
372C2×C61#229811yescharacteristic
373D61#239512yes—
374D61#239612yes—
375D61#240112yes—
376D61#240212yes—
377C22×C4⋊C4—611no—
378C22×C4⋊C4—611no—
379C22×C4⋊C4—612no—
380C22×C42—611no—
381C22×C42—611no—
382C22×C42—611no—
383C22×C42—611no—
384C22×C42—611no—
385C22×C42—611no—
386C22×C42—611no—
387C4×C4⋊C4—611no—
388C4×C4⋊C4—611no—
389C4×C4⋊C4—611no—
390C4×C4⋊C4—611no—
391C4×C4⋊C4—611no—
392C4×C4⋊C4—611no—
393C4×C4⋊C4—611no—
394C4×C4⋊C4—1224no—
395C4×C4⋊C4#692311yescharacteristic, complemented
396#376—1224no—
397C2×#95—611no—
398C2×#95—611no—
399C2×#95—612no—
400C2×#95—612no—
401C2×#95—612no—
402C2×#95—612no—
403C2×#95—612no—
404C2×#95—612no—
405C2×#95—612no—
406C2×#95—612no—
407C2×#95—612no—
408C2×#95—612no—
409C2×#95—612no—
410C61#1384611yescharacteristic, complemented, Sylow
411C23×C4—611no—
412C23×C4—611no—
413C23×C4—611no—
414C23×C4—612no—
415C23×C4—612no—
416C23×C4—612no—
417C23×C4—612no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4—611no—
421C23×C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—1224no—
429C2×C4⋊C4—1224no—
430C2×C4⋊C4—1224no—
431C2×C4⋊C4—1224no—
432C2×C4⋊C4—1224no—
433C2×C4⋊C4C2×#692311yescharacteristic
434C2×C4⋊C4C2×#692311yescharacteristic
435C2×C42—614no—
436C2×C42—614no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—1222no—
447C2×C42—1222no—
448C2×C42—1222no—
449C2×C42—1222no—
450C2×C42—1222no—
451C2×C42—1222no—
452C2×C42—1222no—
453C2×C42—1222no—
454C2×C42—1222no—
455C2×C42—1222no—
456C2×C42—1222no—
457C2×C42—1222no—
458C2×C42—1222no—
459C2×C42—1222no—
460C2×C42—1222no—
461C2×C42—1222no—
462C2×C42C2×#692311yescharacteristic
463C2×C42C2×#692311yescharacteristic
464C2×C42C2×#692311yescharacteristic
465#95—611no—
466#95—611no—
467#95—611no—
468#95—611no—
469#95—611no—
470#95—611no—
471#95—1224no—
472#95—1224no—
473#95—1224no—
474#95—1224no—
475#95—1224no—
476#95—1224no—
477#95—1224no—
478#95—1224no—
479#95—1224no—
480#95—1224no—
481#95—1224no—
482#95C2×#692311yescharacteristic
483#95C2×#692311yescharacteristic
484C24—611no—
485C22×C4—611no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—612no—
489C22×C4—612no—
490C22×C4—612no—
491C22×C4—612no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—614no—
495C22×C4—614no—
496C22×C4—614no—
497C22×C4—614no—
498C22×C4—614no—
499C22×C4—614no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—1221no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1222no—
514C22×C4—1222no—
515C22×C4—1222no—
516C22×C4—1222no—
517C22×C4—1222no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1222no—
524C22×C4—1222no—
525C22×C4—1222no—
526C22×C4—1222no—
527C22×C4—1222no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4—1222no—
531C22×C4—1222no—
532C22×C4—1222no—
533C22×C4—1222no—
534C22×C4—1222no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—1222no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1222no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4C22×#692311yescharacteristic
551C22×C4C22×#692311yescharacteristic
552C22×C4C22×#692311yescharacteristic
553C22×C4C22×#692311yescharacteristic
554C22×C4C22×#692311yescharacteristic
555C22×C4C22×#692311yescharacteristic
556C22×C4C22×#692311yescharacteristic
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—1222no—
560C4⋊C4—1222no—
561C4⋊C4—1222no—
562C4⋊C4—1222no—
563C4⋊C4—12216no—
564C4⋊C4—1222no—
565C4⋊C4—1222no—
566C42—22no—
567C42—22no—
568C42—22no—
569C42—1222no—
570C42—1222no—
571C42—1222no—
572C42—1222no—
573C42—1222no—
574C42—1222no—
575C42—1228no—
576C42—1228no—
577C42—1222no—
578C42—1222no—
579C42—1222no—
580C42—2444no—
581C42—2444no—
582C23—612no—
583C23—612no—
584C23—611no—
585C23—611no—
586C23—611no—
587C23—611no—
588C23—611no—
589C23—611no—
590C23—612no—
591C23—612no—
592C23C23×#692311yescharacteristic
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—612no—
610C2×C4—612no—
611C2×C4—612no—
612C2×C4—614no—
613C2×C4—614no—
614C2×C4—614no—
615C2×C4—614no—
616C2×C4—612no—
617C2×C4—612no—
618C2×C4—1224no—
619C2×C4—1224no—
620C2×C4—1224no—
621C2×C4—1224no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1224no—
627C2×C4—1224no—
628C2×C4—1224no—
629C2×C4—1224no—
630C2×C4—1224no—
631C2×C4—1224no—
632C2×C4—1224no—
633C2×C4—1224no—
634C2×C4—1224no—
635C2×C4—1224no—
636C2×C4—1224no—
637C2×C4—1224no—
638C2×C4—1221no—
639C2×C4—1221no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—2442no—
651C2×C4—2442no—
652C2×C4—2442no—
653C2×C4—2442no—
654C2×C4—2442no—
655C2×C4—2442no—
656C2×C4—2442no—
657C2×C4—2442no—
658C2×C4—2442no—
659C2×C4—2442no—
660C2×C4—2442no—
661C2×C4—2442no—
662C2×C4—2442no—
663C2×C4—2442no—
664C2×C4—2442no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4—2442no—
669C2×C4—2442no—
670C2×C4—2442no—
671C2×C4—2442no—
672C2×C4—2442no—
673C2×C4—2442no—
674C2×C4#1451985612yes—
675C2×C4#1451985612yes—
676C2×C4#1451985612yes—
677C2×C4D4×#692312yes—
678C2×C4Q8×#692312yes—
679C22—612no—
680C22—612no—
681C22—612no—
682C22—612no—
683C22—612no—
684C22—612no—
685C22—612no—
686C22—612no—
687C22—612no—
688C22—612no—
689C22—612no—
690C22—612no—
691C22—611no—
692C22—611no—
693C22—611no—
694C22—611no—
695C22C2×#1451985611yescharacteristic
696C22C2×#1451985611yescharacteristic
697C22C2×#1451985611yescharacteristic
698C22C2×D4×#692311yescharacteristic
699C22C2×Q8×#692311yescharacteristic
700C22#41×#692311yescharacteristic
701C22#41×#692311yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—614no—
709C4—1222no—
710C4—1222no—
711C4—2444no—
712C4—2444no—
713C4—2444no—
714C4—2444no—
715C4—2441no—
716C4—2441no—
717C4—2441no—
718C4—2441no—
719C4#1684071114yes—
720C2—612no—
721C2—612no—
722C2—612no—
723C2—612no—
724C2#2146226611yescharacteristic
725C2C2×#1684071111yescharacteristic
726C2#2146227311yescharacteristic
727C2#2146227611yescharacteristic
728C2#2146227811yescharacteristic
729C2#2146227811yescharacteristic
730C2#2146228111yescharacteristic
subgroupG/H
centerC22×C4C22×#6923
commutator, socleC23×C61C23×C4
FrattiniC23C23×#6923
FittingC4×C4⋊C4×C61C4
prime radical, cosocleC23×D61C24
hypercenterC4×C4⋊C4#6923
hypocenterC61#13846
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
35. C4⋊C4×Dic61C4semidirect
36. C4⋊C4×Dic61C4semidirect
37. C4×#11758196C4semidirect
38. C4×#11758196C4semidirect
39. C4×C4⋊Dic61C4semidirect
40. #16839613C4semidirect
41. #16839613C4semidirect
44. C4×C4⋊C4×C61C4semidirect
395. C4×C4⋊C4#6923semidirect
410. C61#13846semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊#69232
C2×#168406982
#214610082
#214610062
#214610052
#214610042
C4×(C2×#6923)⋊C42
C4×C4⋊C4×D612
#1384661