Finite Group Databasebeta

← #30616850

Subgroups — #30616850

Order 15616.

1470 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519864C211yesmaximal, characteristic, complemented
2C2×#16840794C211yesmaximal, characteristic, complemented
3C2×#16840792C211yesmaximal, characteristic, complemented
4C2×#16840789C211yesmaximal, characteristic, complemented
5#21461798C211yesmaximal, characteristic, complemented
6#21461795C211yesmaximal, characteristic, complemented
7#21461794C211yesmaximal, characteristic, complemented
8#21461766C211yesmaximal, characteristic, complemented
9#21461764C211yesmaximal, characteristic, complemented
10#21461763C211yesmaximal, characteristic, complemented
11#21461643C211yesmaximal, characteristic, complemented
12#21461561C211yesmaximal, characteristic, complemented
13#21461560C211yesmaximal, characteristic, complemented
14#21461556C211yesmaximal, characteristic, complemented
15#21449033C211yesmaximal, characteristic
16C2×#14519864—24no—
17C2×#14519864—24no—
18C2×#14519864—24no—
19C22×#11758213C2211yescharacteristic
20C22×#11758217C2211yescharacteristic
21C22×#11758217C2211yescharacteristic
22C22×D61⋊C8C2211yescharacteristic
23C22×D61⋊C8C2211yescharacteristic
24C23×#92420C2211yescharacteristic
25C23×#92420C2211yescharacteristic
26#16840794—24no—
27#16840792—24no—
28#16840789—24no—
29C2×#14519844C2211yescharacteristic
30C2×#14519844C2211yescharacteristic
31C2×C4⋊#92420C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×#14519834C2211yescharacteristic
35C2×#14519834C2211yescharacteristic
36C2×#14519834C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×C22⋊#92420C2211yescharacteristic
39C2×C22⋊#92420C2211yescharacteristic
40C2×C22⋊#92420C2211yescharacteristic
41C2×#14519832C2211yescharacteristic
42C2×#14519832C2211yescharacteristic
43C2×C4×#92420C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48#16840628C2211yescharacteristic
49#16840628C2211yescharacteristic
50C22×#11758224C2211yescharacteristic
51C2×#14519739C2211yescharacteristic
52C2×#14519737C2211yescharacteristic
53C2×#14519737C2211yescharacteristic
54#16839682C411yescharacteristic
55#16839677C411yescharacteristic
56#16839677C411yescharacteristic
57#16839675C411yescharacteristic
58#16839671C411yescharacteristic
59#16839671C411yescharacteristic
60#16839670C411yescharacteristic
61C22⋊C4×Dic61C2211yescharacteristic
62C22⋊C4×Dic61C2211yescharacteristic
63#16839609C2211yescharacteristic
64C61×#394C411yescharacteristic
65#14519864—232no—
66C2×#11758213—22no—
67C2×#11758213—22no—
68C2×#11758213D414yescomplemented
69C2×#11758217—22no—
70C2×#11758217—22no—
71C2×#11758217—22no—
72C2×#11758217—22no—
73C2×#11758217—22no—
74C2×#11758217D414yescomplemented
75C2×D61⋊C8—22no—
76C2×D61⋊C8—22no—
77C2×D61⋊C8—22no—
78C2×D61⋊C8—22no—
79C2×D61⋊C8—22no—
80C2×D61⋊C8—22no—
81C22×#92420—22no—
82C22×#92420—22no—
83C22×#92420—22no—
84C22×#92420—22no—
85C22×#92420—22no—
86C22×#92420D414yescomplemented
87C22×#92420C2311yescharacteristic
88C22×#92420C2311yescharacteristic
89C22×#92420C2311yescharacteristic
90C22×#92420C2311yescharacteristic
91C22×#92420C2311yescharacteristic
92C22×#92420C2311yescharacteristic
93C22×#92420C2311yescharacteristic
94C22×#92420C2311yescharacteristic
95#14519844—22no—
96#14519844—22no—
97C4⋊#92420—22no—
98#14519834—22no—
99#14519834—22no—
100#14519834—22no—
101#14519834—22no—
102#14519834—22no—
103C22⋊#92420—22no—
104C22⋊#92420—22no—
105C22⋊#92420—22no—
106C22⋊#92420—22no—
107#14519832—22no—
108#14519832—22no—
109C4×#92420—22no—
110C2×#11758224—22no—
111C2×#11758224—22no—
112C2×#11758224—22no—
113C2×#11758224—22no—
114C2×#11758224—22no—
115C2×#11758224—22no—
116C22×Dic122C2×C411yescharacteristic
117C22×D244C2×C411yescharacteristic
118C22×C22⋊D61C2×C411yescharacteristic
119C22×C22⋊D61C2×C411yescharacteristic
120C22×C22⋊D61C2×C411yescharacteristic
121C22×C22⋊D61C2×C411yescharacteristic
122C23×Dic61C2311yescharacteristic
123C23×Dic61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126#14519739—22no—
127#14519739—22no—
128#14519737—22no—
129#14519737—22no—
130#14519737—22no—
131#14519737—22no—
132C2×#11758196C2×C411yescharacteristic
133C2×#11758196C2×C411yescharacteristic
134C2×C22⋊Dic61C2×C411yescharacteristic
135C2×C22⋊Dic61C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×#11758198C2×C411yescharacteristic
138C2×#11758198C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C2×C4×Dic61C2311yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144C2×C4×Dic61C2311yescharacteristic
145#14519684C2×C411yescharacteristic
146#14519684C2×C411yescharacteristic
147#14519684C2×C411yescharacteristic
148#14519684C2×C411yescharacteristic
149#14519684C2×C411yescharacteristic
150C22×D4×C61C2×C411yescharacteristic
151C2×C4⋊C4×C61C2×C411yescharacteristic
152C2×C22⋊C4×C61C2×C411yescharacteristic
153C2×C22⋊C4×C61C2×C411yescharacteristic
154C2×C22⋊C4×C61C2×C411yescharacteristic
155C2×C22⋊C4×C61C2×C411yescharacteristic
156#95×C61C2×C411yescharacteristic
157C24×C61C22×C411yescharacteristic
158C24×C61C22×C411yescharacteristic
159C23×D61C22×C411yescharacteristic
160C23×D61C22×C411yescharacteristic
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—22no—
180C2×C22⋊D61—41no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C22×C411yescharacteristic
194C22×Dic61C2×D412yes—
195C22×Dic61C2×D412yes—
196C22×Dic61#4112yes—
197C22×Dic61#4112yes—
198C22×Dic61C2411yescharacteristic
199#11758224—28no—
200#11758224—28no—
201#11758224—28no—
202#11758224—28no—
203C2×D244—22no—
204C2×D244—22no—
205C2×D244—41no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61C2×D412yes—
217C2×C4×D61#4112yes—
218C2×Dic122—22no—
219C2×Dic122—22no—
220C2×Dic122—22no—
221#11758217—28no—
222#11758217—28no—
223C2×#92420—28no—
224C2×#92420—21no—
225C2×#92420—21no—
226C2×#92420—21no—
227C2×#92420—21no—
228C2×#92420—21no—
229C2×#92420—21no—
230C2×#92420—28no—
231C2×#92420—21no—
232C2×#92420—21no—
233C2×#92420—21no—
234C2×#92420—21no—
235C2×#92420—21no—
236C2×#92420—21no—
237C2×#92420—21no—
238C2×#92420—21no—
239C2×#92420—21no—
240C2×#92420—21no—
241C2×#92420—21no—
242C2×#92420—21no—
243C2×#92420C2×D412yes—
244C2×#92420C2×D412yes—
245C2×#92420C2×D412yes—
246C2×#92420C2×D412yes—
247C2×#92420C2×D412yes—
248C2×#92420C2×D412yes—
249#11758213—28no—
250D61⋊C8—28no—
251D61⋊C8—44no—
252C4⋊C4×C61—22no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—22no—
255C22⋊C4×C61—41no—
256C22⋊C4×C61—41no—
257C22⋊Dic61—22no—
258C22⋊Dic61—41no—
259#11758198—22no—
260#11758198—22no—
261#11758198—22no—
262#11758198—22no—
263#11758198—22no—
264#11758198—41no—
265#11758196—22no—
266#11758196—22no—
267C4×Dic61—21no—
268C4×Dic61—21no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271C4×Dic61—21no—
272C4×Dic61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61C4×D412yes—
286C23×C61C4×D412yes—
287C23×C61C23×C411yescharacteristic
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61C4×D412yes—
301C22×D61#13112yescomplemented
302D4×C61—28no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61C4×D412yes—
318C22⋊D61—28no—
319C22⋊D61—28no—
320C22⋊D61—28no—
321C22⋊D61—44no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61C4×D412yes—
343C2×Dic61C4×D412yes—
344C2×Dic61#13112yescomplemented
345C2×Dic61C22×D411yescharacteristic
346C2×Dic61C22×D411yescharacteristic
347C2×Dic61C22×D411yescharacteristic
348C2×Dic61C2×#4111yescharacteristic
349C2×Dic61C2×#4111yescharacteristic
350C2×Dic61C2×#4111yescharacteristic
351D244—44no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360Dic122—28no—
361#92420—22no—
362#92420—22no—
363#92420—22no—
364#92420—41no—
365#92420—41no—
366#92420—41no—
367#92420—41no—
368#92420#12014yes—
369#21443—611nomaximal, Sylow
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61C2×C4×D411yescharacteristic
385C22×C61C2×C4×D411yescharacteristic
386C22×C61C2×C4×D411yescharacteristic
387C22×C61C2×#13111yescharacteristic
388C22×C61C2×#13111yescharacteristic
389C22×C61#56811yescharacteristic
390C22×C61#56811yescharacteristic
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—22no—
396C2×D61—22no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C4×C61—22no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—41no—
409C4×C61—41no—
410Dic61—22no—
411Dic61—22no—
412Dic61—22no—
413Dic61—41no—
414Dic61—41no—
415Dic61C2×#12011yescharacteristic
416Dic61#52511yescharacteristic
417Dic61#52511yescharacteristic
418Dic61#52511yescharacteristic
419C22×#131—611no—
420C2×#435—611no—
421C2×#435—611no—
422C2×C8×D4—611no—
423#2388—611no—
424#1870—611no—
425#1869—611no—
426#1869—611no—
427#1851—611no—
428#1850—611no—
429#1850—611no—
430#1780—611no—
431#1753—611no—
432#1753—611no—
433#1752—611no—
434C2×C61—42no—
435C2×C61—42no—
436C2×C61C4×#12011yescharacteristic
437C2×C61#292911yescharacteristic
438C2×C61#293211yescharacteristic
439C2×C61#293311yescharacteristic
440C2×C61#293311yescharacteristic
441C2×C61#293511yescharacteristic
442C2×C61#293511yescharacteristic
443D61—42no—
444D61—42no—
445C22×#41—611no—
446C2×#131—1224no—
447C2×#131—1224no—
448C2×#131—1224no—
449C22×M16—611no—
450C22×M16—611no—
451C22×M16—611no—
452C23×C8—611no—
453C23×C8—611no—
454C23×C8—611no—
455C23×C8—611no—
456C2×C4×D4—611no—
457C2×C4×D4—611no—
458C2×C4×D4—611no—
459#435—1224no—
460#435—1224no—
461C8×D4—1224no—
462C2×C4⋊C8—611no—
463C2×C4⋊C8—611no—
464C2×C4⋊C8—611no—
465C2×C22⋊C8—611no—
466C2×C22⋊C8—611no—
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×C22⋊C8—611no—
474C2×#97—611no—
475C2×#97—611no—
476C2×C4×C8—611no—
477#395—611no—
478#394—611no—
479#394—611no—
480#394#692311yescharacteristic
481#393—611no—
482#392—611no—
483#392—611no—
484#392—611no—
485C4×C22⋊C4—611no—
486C4×C22⋊C4—611no—
487C4×C22⋊C4—611no—
488#336—611no—
489#336—611no—
490#336—611no—
491#336—611no—
492#336—611no—
493#336—611no—
494C61#2144311yescharacteristic, complemented, Sylow
495C2×#41—1222no—
496C2×#41—1222no—
497C2×#41—1222no—
498C2×#41—1222no—
499C2×#41—1222no—
500C2×#41—1222no—
501C22×Q8—611no—
502C22×D4—611no—
503C22×D4—611no—
504C22×D4—611no—
505C22×D4—611no—
506C22×D4—611no—
507C22×D4C2×#692311yescharacteristic
508C23×C4—611no—
509C23×C4—611no—
510C23×C4—611no—
511C23×C4—611no—
512#131—12232no—
513C2×M16—614no—
514C2×M16—614no—
515C2×M16—1222no—
516C2×M16—1222no—
517C2×M16—1222no—
518C2×M16—1222no—
519C2×M16—1222no—
520C2×M16—1222no—
521C2×M16—1222no—
522C22×C8—611no—
523C22×C8—614no—
524C22×C8—611no—
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—611no—
531C22×C8—1222no—
532C22×C8—1222no—
533C22×C8—1222no—
534C22×C8—1222no—
535C22×C8—1222no—
536C22×C8—1222no—
537C22×C8—1222no—
538C22×C8—1222no—
539C22×C8—1222no—
540C22×C8—1222no—
541C22×C8—1222no—
542C4×D4—1222no—
543C4×D4—1222no—
544C4×D4—1222no—
545C4×D4—1222no—
546C4×D4—1222no—
547C4×D4—1222no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4C2×#692311yescharacteristic
551C2×C22⋊C4—611no—
552C2×C22⋊C4—611no—
553C2×C22⋊C4—611no—
554C2×C22⋊C4—611no—
555C2×C22⋊C4—611no—
556C2×C22⋊C4—611no—
557C2×C22⋊C4—611no—
558C2×C22⋊C4—611no—
559C2×C22⋊C4C2×#692311yescharacteristic
560C2×C22⋊C4C2×#692311yescharacteristic
561C2×C22⋊C4C2×#692311yescharacteristic
562C2×C22⋊C4C2×#692311yescharacteristic
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C4⋊C8—1222no—
567C4⋊C8—1222no—
568C4⋊C8—1222no—
569C22⋊C8—1222no—
570C22⋊C8—1222no—
571C22⋊C8—1222no—
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574C22⋊C8—1222no—
575C22⋊C8—1222no—
576C22⋊C8—1222no—
577C22⋊C8—1222no—
578#97—1222no—
579#97—1222no—
580C4×C8—1222no—
581#95—611no—
582#95—611no—
583#95—611no—
584#95—611no—
585#95—611no—
586#95C2×#692311yescharacteristic
587C24—611no—
588C24—611no—
589C24C22×#692311yescharacteristic
590C24C22×#692311yescharacteristic
591#41—1228no—
592#41—1228no—
593#41—1228no—
594#41—1228no—
595C2×Q8—1222no—
596C2×Q8—1222no—
597C2×Q8—1222no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—1222no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—1222no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—2441no—
615C2×D4—2441no—
616C22×C4—611no—
617C22×C4—612no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4C22×#692311yescharacteristic
647C22×C4C22×#692311yescharacteristic
648C22×C4C22×#692311yescharacteristic
649C22×C4C22×#692311yescharacteristic
650C22×C4C22×#692311yescharacteristic
651M16—1228no—
652M16—1228no—
653M16—1228no—
654C2×C8—612no—
655C2×C8—612no—
656C2×C8—612no—
657C2×C8—612no—
658C2×C8—612no—
659C2×C8—612no—
660C2×C8—1228no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1228no—
668C2×C8—1228no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—2444no—
682C4⋊C4—22no—
683C4⋊C4—1222no—
684C4⋊C4—1222no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4—2441no—
696C22⋊C4—2441no—
697C42—1221no—
698C42—1221no—
699C42—1221no—
700C42—1221no—
701C42—1221no—
702C42—1221no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—612no—
716C23—612no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23—1221no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23D4×#692312yes—
730C23D4×#692312yes—
731C23C23×#692311yescharacteristic
732Q8—1228no—
733D4—28no—
734D4—1228no—
735D4—1228no—
736D4—1228no—
737D4—2444no—
738D4—2444no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—612no—
760C2×C4—612no—
761C2×C4—612no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4D4×#692312yes—
791C8—614no—
792C8—1222no—
793C8—1222no—
794C8—1222no—
795C8—2441no—
796C8—2441no—
797C8—2441no—
798C8—2441no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—1222no—
814C22—1222no—
815C22—1222no—
816C22—1222no—
817C22—1222no—
818C22—1222no—
819C22—2441no—
820C22—2441no—
821C22—2441no—
822C22—2441no—
823C22—2441no—
824C22—2441no—
825C22—2441no—
826C22—2441no—
827C22C2×D4×#692311yescharacteristic
828C22C2×D4×#692311yescharacteristic
829C22C2×D4×#692311yescharacteristic
830C22D61⋊#13111yescharacteristic
831C22D61⋊#13111yescharacteristic
832C22#1684084011yescharacteristic
833C22#1684084111yescharacteristic
834C4—22no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—611no—
840C4—611no—
841C4—611no—
842C4—611no—
843C4—1222no—
844C4—1222no—
845C4—1222no—
846C4—2441no—
847C4—2441no—
848C2—42no—
849C2—42no—
850C2—2442no—
851C2—2442no—
852C2#120×#692311yescharacteristic
853C2#2146253611yescharacteristic
854C2#2146254711yescharacteristic
855C2#2146255011yescharacteristic
856C2#2146255311yescharacteristic
857C2#2146256311yescharacteristic
858C2#2146256411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#394C4
prime radical#21449033C2
cosocleC22×Dic61C24
hypercenter#394#6923
hypocenterC61#21443
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×#14519864C2semidirect
2. C2×#16840794C2semidirect
3. C2×#16840792C2semidirect
4. C2×#16840789C2semidirect
5. #21461798C2semidirect
6. #21461795C2semidirect
7. #21461794C2semidirect
8. #21461766C2semidirect
9. #21461764C2semidirect
10. #21461763C2semidirect
11. #21461643C2semidirect
12. #21461561C2semidirect
13. #21461560C2semidirect
14. #21461556C2semidirect
68. C2×#11758213D4semidirect
74. C2×#11758217D4semidirect
86. C22×#92420D4semidirect
301. C22×D61#131semidirect
344. C2×Dic61#131semidirect
494. C61#21443semidirect

Maximal subgroups

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

subgroupindex
C22×#145198642
C2×#168407942
C2×#168407922
C2×#168407892
#214617982
#214617952
#214617942
#214617662
#214617642
#214617632
#214616432
#214615612
#214615602
#214615562
#214490332
#2144361