Finite Group Databasebeta

← #29727578

Subgroups — #29727578

Order 15616.

1052 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839969C211yesmaximal, characteristic, complemented
2C2×#16839917C211yesmaximal, characteristic
3C2×#16839917C211yesmaximal, characteristic
4C2×C4×#11758202C211yesmaximal, characteristic, complemented
5C22⋊C4×Dic122C211yesmaximal, characteristic
6#21447211C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic
8#21447019C211yesmaximal, characteristic
9#21446919C211yesmaximal, characteristic, complemented
10#21446679C211yesmaximal, characteristic, complemented
11#21446427C211yesmaximal, characteristic
12#21446163C211yesmaximal, characteristic, complemented
13#21446160C211yesmaximal, characteristic, complemented
14#21446072C211yesmaximal, characteristic, complemented
15C61×#2429C211yesmaximal, characteristic
16C23×Dic122C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23#16839969—24no—
24#16839917—24no—
25#16839917—24no—
26C4×#11758202—24no—
27C2×#14519710C2211yescharacteristic
28C2×#14519710C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C4×#92418C2211yescharacteristic
41#16839668C2211yescharacteristic
42#16839668C2211yescharacteristic
43#16839666—21no—
44#16839666—21no—
45#16839622C2211yescharacteristic
46#16839620—21no—
47C22⋊C4×Dic61—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C61×#398—21no—
57C61×#396—21no—
58C61×#391C2211yescharacteristic
59C61×#389—21no—
60C61×#389C2211yescharacteristic
61C61×#388—21no—
62C4×C22⋊C4×C61C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122—22no—
65C22×Dic122—22no—
66C22×Dic122—22no—
67C22×Dic122—22no—
68C22×Dic122—41no—
69C22×Dic122—41no—
70C22×Dic122C2311yescharacteristic
71C22×Dic122C2311yescharacteristic
72C23×Dic61—21no—
73C2×#11758202—22no—
74C2×#11758202—22no—
75C2×#11758202—22no—
76C2×#11758202—22no—
77C2×#11758202—22no—
78C2×#11758202—22no—
79C2×#11758202—22no—
80C2×#11758202—22no—
81C2×#11758202—22no—
82C2×#11758202—41no—
83C2×#11758202—41no—
84C2×#11758202D414yes—
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C4×Dic122—22no—
90C4×Dic122—22no—
91C4×Dic122—41no—
92C4×Dic122—41no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100#14519710—22no—
101#14519710—41no—
102C4⋊#92418—22no—
103#14519701—22no—
104#14519701—22no—
105#14519701—22no—
106#14519701—41no—
107#14519700—22no—
108#14519700—22no—
109#14519700—22no—
110#14519700D414yes—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113C4×#92418—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×Q8×C61C2311yescharacteristic
120C22×Q8×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C4⋊Q8×C61—22no—
123C4⋊Q8×C61—41no—
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—41no—
127C22⋊Q8×C61—41no—
128C4×Q8×C61—22no—
129C4×Q8×C61—41no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61D411yescharacteristic
141C2×C22⋊C4×C61D411yescharacteristic
142C2×C42×C61—21no—
143C2×C42×C61C2311yescharacteristic
144C2×C42×C61C2311yescharacteristic
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61D411yescharacteristic
149#95×C61D411yescharacteristic
150C24×C61C2×D411yescharacteristic
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61C2×D412yes—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2411yescharacteristic
179C22×Dic61—21no—
180C22×Dic61—24no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—42no—
185C22×Dic61—42no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—24no—
194C2×Dic122—21no—
195C2×Dic122—44no—
196C2×Dic122—44no—
197C2×Dic122—44no—
198C2×Dic122—42no—
199C2×Dic122—42no—
200C2×Dic122—44no—
201C2×Dic122C2×D412yes—
202C2×Dic122C2×D412yes—
203C2×Dic122#4112yes—
204C2×Dic122#4112yes—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61—42no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61—42no—
214C4⋊C4×C61C2×D412yes—
215C22⋊C4×C61—41no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61Q1614yescomplemented
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C42×C61—21no—
223C42×C61—42no—
224C22⋊Dic61—42no—
225#11758202—28no—
226#11758202—44no—
227#11758202—44no—
228#11758202—44no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233#11758196—42no—
234#11758196—42no—
235C4×Dic61—42no—
236C4×Dic61—42no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418C2×D412yes—
248C2×#92418C2×D412yes—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61C2×Q1612yes—
256C23×C61C22×D411yescharacteristic
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61—41no—
260Q8×C61—41no—
261Q8×C61—41no—
262Q8×C61—41no—
263Q8×C61—41no—
264Q8×C61—41no—
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—21no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61C2×Q1612yes—
295C2×C4×C61C2×Q1612yes—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61H(5,𝔽2)11yescharacteristic
301C2×C4×C61H(5,𝔽2)11yescharacteristic
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—48no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315Dic122—22no—
316Dic122—22no—
317Dic122—22no—
318Dic122—22no—
319Dic122—22no—
320Dic122—48no—
321Dic122—41no—
322Dic122—41no—
323Dic122#12114yes—
324#92418—22no—
325#92418—22no—
326#92418—41no—
327#92418—41no—
328#25161—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61#52511yescharacteristic
337C22×C61D4211yescharacteristic
338C22×C61D4211yescharacteristic
339C22×C61C22×Q1611yescharacteristic
340C22×C61#57511yescharacteristic
341C22×C61#57811yescharacteristic
342C22×C61#57811yescharacteristic
343C4×C61—22no—
344C4×C61—22no—
345C4×C61—41no—
346C4×C61—42no—
347C4×C61—41no—
348C4×C61—42no—
349C4×C61—41no—
350C4×C61—81no—
351C4×C61—81no—
352C4×C61C2×#12111yescharacteristic
353C4×C61#53811yescharacteristic
354C4×C61#54611yescharacteristic
355C4×C61#54611yescharacteristic
356Dic61—24no—
357Dic61—42no—
358Dic61—81no—
359Dic61—81no—
360C2×#462—611no—
361C2×#451—611no—
362C2×#451—611no—
363C2×C4×Q16—611no—
364#2429D6111yescharacteristic
365Q8×C22⋊C4—611no—
366#2068—611no—
367#2036—611no—
368#2036—611no—
369#2016—611no—
370#1969—611no—
371#1923—611no—
372#1878—611no—
373#1878—611no—
374#1863—611no—
375C2×C61—42no—
376C2×C61#242411yescharacteristic
377C2×C61#310411yescharacteristic
378C2×C61#312711yescharacteristic
379C2×C61#326911yescharacteristic
380C2×C61#327711yescharacteristic
381C2×C61D4×Q1611yescharacteristic
382C2×C61D4×Q1611yescharacteristic
383C23×Q8—611no—
384C22×Q16—611no—
385C22×Q16—611no—
386C22×Q16—611no—
387C22×Q16—611no—
388C2×C4⋊Q8C2×D6111yescharacteristic
389C2×C22⋊Q8C2×D6111yescharacteristic
390C2×C22⋊Q8C2×D6111yescharacteristic
391C2×C4×Q8—611no—
392C2×C4×Q8—611no—
393C2×C4×Q8C2×D6111yescharacteristic
394#462—1224no—
395#451—1224no—
396#451—1224no—
397C4×Q16—1224no—
398C2×#107—611no—
399C2×#107—611no—
400C2×C4⋊C8—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103—611no—
407C2×#103—611no—
408C2×#103—611no—
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×C4×C8—611no—
412#398—21no—
413#396—21no—
414#391—611no—
415#391—611no—
416#391—1221no—
417#391—1221no—
418#391C2×D6111yescharacteristic
419#389—21no—
420#389C2×D6111yescharacteristic
421#388—21no—
422#380—611no—
423#380—1221no—
424C4×C22⋊C4—1221no—
425C4×C22⋊C4C2×D6111yescharacteristic
426#340—611no—
427#340—611no—
428#336—611no—
429#336—611no—
430C61#2516111yescharacteristic, complemented, Sylow
431C22×Q8—611no—
432C22×Q8—611no—
433C22×Q8—1222no—
434C22×Q8—1222no—
435C22×Q8—1222no—
436C22×Q8—1222no—
437C22×Q8—1221no—
438C22×Q8—2441no—
439C22×Q8—2441no—
440C22×Q8C22×D6111yescharacteristic
441C22×Q8C22×D6111yescharacteristic
442C23×C4—1221no—
443C23×C4C22×D6111yescharacteristic
444C2×Q16—614no—
445C2×Q16—1222no—
446C2×Q16—1222no—
447C2×Q16—1222no—
448C2×Q16—1222no—
449C2×Q16—1222no—
450C2×Q16—1222no—
451C2×Q16—1222no—
452C2×Q16—1222no—
453C2×Q16—1222no—
454C2×Q16—2441no—
455C2×Q16—2441no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C4⋊Q8—22no—
461C4⋊Q8—41no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—41no—
465C22⋊Q8—41no—
466C4×Q8—22no—
467C4×Q8—41no—
468C4×Q8—1222no—
469C4×Q8—1222no—
470C4×Q8—2441no—
471C4×Q8—2441no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4C22⋊D6111yescharacteristic
488C2×C22⋊C4C22⋊D6111yescharacteristic
489C2×C42—21no—
490C2×C42—1221no—
491C2×C42—1221no—
492C2×C42C22×D6111yescharacteristic
493C2×C42C22×D6111yescharacteristic
494#107—1222no—
495#107—2441no—
496C4⋊C8—1222no—
497#103—614no—
498#103—1222no—
499#103—1222no—
500#103—1222no—
501#103—1222no—
502#103—1222no—
503#103—1222no—
504#103—2441no—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507C4×C8—1222no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95C22⋊D6111yescharacteristic
517#95C22⋊D6111yescharacteristic
518C24C2×C22⋊D6111yescharacteristic
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—612no—
531C2×Q8—612no—
532C2×Q8—612no—
533C2×Q8—612no—
534C2×Q8—1224no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—2442no—
544C2×Q8—2442no—
545C2×Q8—2444no—
546C2×Q8—2444no—
547C2×Q8—2444no—
548C2×Q8—2444no—
549C2×Q8D4×D6112yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—1221no—
561C22×C4—1224no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4C2×C22⋊D6111yescharacteristic
568C22×C4C2×C22⋊D6111yescharacteristic
569C22×C4C2×C22⋊D6111yescharacteristic
570C22×C4C2×C22⋊D6111yescharacteristic
571C22×C4C2×C22⋊D6111yescharacteristic
572C22×C4C23×D6111yescharacteristic
573Q16—1228no—
574Q16—2444no—
575Q16—2444no—
576Q16—2444no—
577C2×C8—612no—
578C2×C8—612no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—2442no—
603C4⋊C4—2442no—
604C4⋊C4D4×D6112yes—
605C22⋊C4—41no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—2442no—
609C22⋊C4#1175820214yescomplemented
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—42no—
615C42—2442no—
616C42—2442no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×#1175820212yes—
624C23C22×C22⋊D6111yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—614no—
634Q8—1222no—
635Q8—1222no—
636Q8—1222no—
637Q8—1222no—
638Q8—1222no—
639Q8—2448no—
640Q8—2441no—
641Q8—2441no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—2448no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4C2×#1175820212yes—
685C2×C4C2×#1175820212yes—
686C2×C4C2×D4×D6111yescharacteristic
687C2×C4C2×D4×D6111yescharacteristic
688C2×C4#41×D6111yescharacteristic
689C2×C4#41×D6111yescharacteristic
690C2×C4#1451982211yescharacteristic
691C2×C4#1451982211yescharacteristic
692C8—1222no—
693C8—1222no—
694C8—2441no—
695C8—2441no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22#1684026911yescharacteristic
704C22D4×C22⋊D6111yescharacteristic
705C22D4×C22⋊D6111yescharacteristic
706C22C22×#1175820211yescharacteristic
707C22#1684056011yescharacteristic
708C22#1684057711yescharacteristic
709C22#1684057711yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—42no—
715C4—41no—
716C4—42no—
717C4—81no—
718C4—81no—
719C4—1224no—
720C4—4881no—
721C4—4881no—
722C4—2442no—
723C4#121×D6111yescharacteristic
724C4#1684034411yescharacteristic
725C4#1684040111yescharacteristic
726C4#1684040911yescharacteristic
727C2—42no—
728C2#2144935211yescharacteristic
729C2#2145585411yescharacteristic
730C2#2145611411yescharacteristic
731C2#2145737011yescharacteristic
732C2#2145747211yescharacteristic
733C2D4×#1175820211yescharacteristic
734C2D4×#1175820211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2429C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#2429D61
hypocenterC61#25161
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2429

Complements

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

NH ≅ G/Ntype
1. C2×#16839969C2semidirect
4. C2×C4×#11758202C2semidirect
6. #21447211C2semidirect
9. #21446919C2semidirect
10. #21446679C2semidirect
12. #21446163C2semidirect
13. #21446160C2semidirect
14. #21446072C2semidirect
218. C22⋊C4×C61Q16semidirect
430. C61#25161semidirect
609. C22⋊C4#11758202semidirect

Maximal subgroups

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

subgroupindex
C2×#168399692
C2×#168399172
C2×C4×#117582022
C22⋊C4×Dic1222
#214472112
#214470192
#214469192
#214466792
#214464272
#214461632
#214461602
#214460722
C61×#24292
#2516161