Finite Group Databasebeta

← #29702244

Subgroups — #29702244

Order 15616.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839840C211yesmaximal, characteristic, complemented
2C2×#16839837C211yesmaximal, characteristic, complemented
3C2×#16839836C211yesmaximal, characteristic, complemented
4C2×#16839787C211yesmaximal, characteristic, complemented
5#21449057C211yesmaximal, characteristic
6#21446535C211yesmaximal, characteristic, complemented
7#21446429C211yesmaximal, characteristic, complemented
8#21446422C211yesmaximal, characteristic, complemented
9#21446113C211yesmaximal, characteristic, complemented
10#21446108C211yesmaximal, characteristic, complemented
11#21446001C211yesmaximal, characteristic, complemented
12#21446001C211yesmaximal, characteristic, complemented
13#21445691C211yesmaximal, characteristic, complemented
14#21445588C211yesmaximal, characteristic, complemented
15C61×#1955C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22C2×#14519734C2211yescharacteristic
23#16839840—24no—
24#16839837—24no—
25#16839836—24no—
26#16839787—24no—
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519706C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519687C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38C2×C8×Dic61C2211yescharacteristic
39#16839693C411yescharacteristic
40#16839688C411yescharacteristic
41#16839685C411yescharacteristic
42#16839685C411yescharacteristic
43#16839678C411yescharacteristic
44#16839678C411yescharacteristic
45#16839676C411yescharacteristic
46#16839670C411yescharacteristic
47C4×C4⋊Dic61C2211yescharacteristic
48C4×C22⋊Dic61C2211yescharacteristic
49C4×C22⋊Dic61C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758194—22no—
67C2×#11758194—22no—
68C2×#11758194—22no—
69C2×#11758194—22no—
70C2×#11758194—41no—
71C2×#11758194—41no—
72C2×#11758189—22no—
73C2×#11758189—22no—
74C2×#11758189—41no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C2×C8×D61—41no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86#14519734—22no—
87#14519734—22no—
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×C22⋊Dic61C2×C411yescharacteristic
95C2×C22⋊Dic61C2×C411yescharacteristic
96C2×C22⋊Dic61C2×C411yescharacteristic
97C2×C22⋊Dic61C2×C411yescharacteristic
98C2×C22⋊Dic61C2×C411yescharacteristic
99C2×C22⋊Dic61C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107C4⋊#92418D414yescomplemented
108#14519706—22no—
109#14519706—22no—
110#14519706—22no—
111#14519706—22no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114#14519689—22no—
115#14519689D414yescomplemented
116#14519687—22no—
117C4×#92418—22no—
118C8×Dic61—22no—
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C4×D4×C61—22no—
133C4×D4×C61—22no—
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—22no—
139C22⋊C8×C61—22no—
140C22⋊C8×C61—22no—
141C22⋊C8×C61—41no—
142C22⋊C8×C61—41no—
143#97×C61—22no—
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C2×D4×C61—22no—
148C2×D4×C61—41no—
149C2×D4×C61—41no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—41no—
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61C2×D412yes—
185C2×C4×D61#4112yes—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61C2×D412yes—
198C4⋊C4×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C42×C61C2×D412yes—
202C42×C61#4112yes—
203C22⋊Dic61—22no—
204C22⋊Dic61—22no—
205C22⋊Dic61—22no—
206C22⋊Dic61—41no—
207C22⋊Dic61—41no—
208C22⋊Dic61—41no—
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213C4⋊Dic61—22no—
214C4⋊Dic61—41no—
215#11758196—22no—
216#11758196—22no—
217#11758196—22no—
218#11758196—22no—
219C4×Dic61—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225#11758194—44no—
226#11758194—44no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418C2×D412yes—
237C2×#92418C2×D412yes—
238C2×#92418C2×D412yes—
239#11758189—44no—
240C8×D61—44no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61C23×C411yescharacteristic
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61C4×D412yes—
263D4×C61—44no—
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—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61C4×D412yes—
283C2×C4×C61C4×D412yes—
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C2×C4×C612−1+411yescharacteristic
290C22⋊D61—44no—
291C22⋊D61—44no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61C4×D412yes—
312C2×Dic61#13112yes—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C8×C61—22no—
318C8×C61—41no—
319C8×C61—41no—
320C8×C61—41no—
321#92418—22no—
322#92418—22no—
323#92418—22no—
324#92418—41no—
325#22994—611nomaximal, Sylow
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61C2×C4×D411yescharacteristic
341C22×C61C2×C4×D411yescharacteristic
342C22×C61#52011yescharacteristic
343C22×C61C2×#13111yescharacteristic
344C22×C61#56811yescharacteristic
345C22×C61#56811yescharacteristic
346C22×C61#56811yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61D4211yescharacteristic
359C4×C61#54711yescharacteristic
360C4×C61#54811yescharacteristic
361C4×C61#55311yescharacteristic
362Dic61—22no—
363Dic61—22no—
364Dic61—41no—
365Dic61—41no—
366Dic61—41no—
367Dic61—41no—
368Dic61—41no—
369C2×#436—611no—
370C2×#436—611no—
371C2×#435—611no—
372C2×#424—611no—
373#2392—611no—
374#1955D6111yescharacteristic, complemented
375#1939—611no—
376#1924—611no—
377#1923—611no—
378#1870—611no—
379#1869—611no—
380#1851—611no—
381#1851—611no—
382#1771—611no—
383#1750—611no—
384C2×C61—81no—
385C2×C61—81no—
386C2×C61#236111yescharacteristic
387C2×C61#293011yescharacteristic
388C2×C61#293011yescharacteristic
389C2×C61#293311yescharacteristic
390C2×C61#293511yescharacteristic
391C2×C61#299311yescharacteristic
392C2×C61#299511yescharacteristic
393D61—42no—
394C22×M16—611no—
395C22×M16—611no—
396C22×M16—611no—
397C23×C8—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4C2×D6111yescharacteristic
401C2×#117—611no—
402#436—1224no—
403#436—1224no—
404#435—1224no—
405#424—1224no—
406C2×C4⋊C8—611no—
407C2×C4⋊C8—611no—
408C2×C4⋊C8—611no—
409C2×C4⋊C8—611no—
410C2×C4⋊C8—611no—
411C2×C4⋊C8C2×D6111yescharacteristic
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8C2×D6111yescharacteristic
417C2×C22⋊C8C2×D6111yescharacteristic
418C2×C22⋊C8C2×D6111yescharacteristic
419C2×C22⋊C8C2×D6111yescharacteristic
420C2×#97—611no—
421C2×#97C2×D6111yescharacteristic
422C2×C4×C8—611no—
423C2×C4×C8—611no—
424#398—611no—
425#397—611no—
426#396—611no—
427#396—611no—
428#394—611no—
429#394—611no—
430#394—611no—
431#392—611no—
432C4×C4⋊C4—611no—
433C4×C22⋊C4—611no—
434C4×C22⋊C4—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336—611no—
440#336—611no—
441C61#2299411yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—611no—
444C22×D4C4×D6111yescharacteristic
445C23×C4—611no—
446C23×C4C22×D6111yescharacteristic
447C23×C4C22×D6111yescharacteristic
448C2×M16—1222no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C2×M16—2441no—
455C2×M16—2441no—
456C2×M16—2441no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—2441no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474#117—1222no—
475#117—1222no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4C4×D6111yescharacteristic
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4C4×D6111yescharacteristic
494C2×C22⋊C4C4×D6111yescharacteristic
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42C22×D6111yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—614no—
501C4⋊C8—1222no—
502C4⋊C8—1222no—
503C4⋊C8—1222no—
504C4⋊C8—1222no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—41no—
508C22⋊C8—41no—
509C22⋊C8—614no—
510C22⋊C8—1222no—
511C22⋊C8—1222no—
512C22⋊C8—1222no—
513#97—22no—
514#97—1222no—
515C4×C8—1222no—
516C4×C8—1222no—
517#95—611no—
518#95—611no—
519#95—611no—
520#95—611no—
521#95—611no—
522#95—611no—
523C24—611no—
524C24C2×C4×D6111yescharacteristic
525C24C2×C4×D6111yescharacteristic
526C2×D4—22no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—1222no—
530C2×D4—1222no—
531C2×D4—1222no—
532C2×D4—2441no—
533C2×D4—2441no—
534C2×D4—2441no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4C2×C4×D6111yescharacteristic
561C22×C4C2×C4×D6111yescharacteristic
562C22×C4C2×C4×D6111yescharacteristic
563C22×C4C2×C4×D6111yescharacteristic
564C22×C4C23×D6111yescharacteristic
565M16—2444no—
566M16—2444no—
567M16—2444no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—612no—
580C2×C8—612no—
581C2×C8—612no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—2444no—
592C2×C8D4×D6112yes—
593C4⋊C4—22no—
594C4⋊C4—1222no—
595C4⋊C4—1222no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—2441no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—1222no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—2441no—
610C22⋊C4—2441no—
611C22⋊C4—2441no—
612C42—1221no—
613C42—1221no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42D4×D6112yes—
619C42#1175822412yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—612no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23C22×C4×D6111yescharacteristic
642D4—44no—
643D4—2444no—
644D4—2444no—
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—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4#1451973712yes—
689C2×C4#1451973712yes—
690C2×C4C2×D4×D6111yescharacteristic
691C2×C4C2×D4×D6111yescharacteristic
692C2×C4#41×D6111yescharacteristic
693C2×C4C2×#1175822411yescharacteristic
694C2×C4#1451982211yescharacteristic
695C2×C4#1451982411yescharacteristic
696C8—22no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—1222no—
701C8—1222no—
702C8—1222no—
703C8—2441no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—1222no—
719C22—1222no—
720C22—1222no—
721C22—2441no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22C4×D4×D6111yescharacteristic
726C22C2×#1451973711yescharacteristic
727C22#1684024111yescharacteristic
728C22#131×D6111yescharacteristic
729C22#1684052711yescharacteristic
730C22#1684052811yescharacteristic
731C22#1684052811yescharacteristic
732C4—22no—
733C4—22no—
734C4—41no—
735C4—41no—
736C4—1222no—
737C4—1222no—
738C4—2441no—
739C4—2441no—
740C4—2441no—
741C4—2441no—
742C4—2441no—
743C4#1684039711yescharacteristic
744C4#1684041211yescharacteristic
745C4#1684042011yescharacteristic
746C4#1684045911yescharacteristic
747C2—81no—
748C2—81no—
749C2—2442no—
750C2#2144884011yescharacteristic
751C2#2145451711yescharacteristic
752C2#2145451811yescharacteristic
753C2#2145454211yescharacteristic
754C2#2145455911yescharacteristic
755C2#2145496111yescharacteristic
756C2#2145499011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1955C2
prime radical#16839670C4
cosocleC22×C4×C61C24
hypercenter#1955D61
hypocenterC61#22994
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. C2×#16839840C2semidirect
2. C2×#16839837C2semidirect
3. C2×#16839836C2semidirect
4. C2×#16839787C2semidirect
6. #21446535C2semidirect
7. #21446429C2semidirect
8. #21446422C2semidirect
9. #21446113C2semidirect
10. #21446108C2semidirect
11. #21446001C2semidirect
12. #21446001C2semidirect
13. #21445691C2semidirect
14. #21445588C2semidirect
15. C61×#1955C2semidirect
107. C4⋊#92418D4semidirect
115. #14519689D4semidirect
374. #1955D61semidirect
441. C61#22994semidirect

Maximal subgroups

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

subgroupindex
C2×#168398402
C2×#168398372
C2×#168398362
C2×#168397872
#214490572
#214465352
#214464292
#214464222
#214461132
#214461082
#214460012
#214456912
#214455882
C61×#19552
#2299461