Finite Group Databasebeta

← #30616860

Subgroups — #30616860

Order 15616.

1456 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×#16840797C211yesmaximal, characteristic, complemented
3C2×#16840795C211yesmaximal, characteristic, complemented
4C2×#16840793C211yesmaximal, characteristic, complemented
5#21461796C211yesmaximal, characteristic, complemented
6#21461793C211yesmaximal, characteristic, complemented
7#21461792C211yesmaximal, 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
14C22⋊C4×#92420C211yesmaximal, characteristic, complemented
15#21449031C211yesmaximal, characteristic
16C2×#14519864—24no—
17C2×#14519864—24no—
18C2×#14519864—24no—
19C22×#11758213C2211yescharacteristic
20C22×#11758217C2211yescharacteristic
21C22×#11758217C2211yescharacteristic
22C22×#11758217C2211yescharacteristic
23C22×D61⋊C8C2211yescharacteristic
24C23×#92420C2211yescharacteristic
25C23×#92420C2211yescharacteristic
26#16840797—24no—
27#16840795—24no—
28#16840793—24no—
29C2×#14519844C2211yescharacteristic
30C2×#14519844C2211yescharacteristic
31C2×C4⋊#92420C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×C22⋊#92420C2211yescharacteristic
35C2×C22⋊#92420C2211yescharacteristic
36C2×C22⋊#92420C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×C22⋊#92420C2211yescharacteristic
39C2×C22⋊#92420C2211yescharacteristic
40C2×C22⋊#92420C2211yescharacteristic
41C2×#14519832C2211yescharacteristic
42C2×C4×#92420C2211yescharacteristic
43C2×C4×#92420C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48#16840628C2211yescharacteristic
49#16840628C2211yescharacteristic
50C22×#11758224C2211yescharacteristic
51C2×D4×Dic61C2211yescharacteristic
52C2×D4×Dic61C2211yescharacteristic
53C2×#14519737C2211yescharacteristic
54#16839683C411yescharacteristic
55#16839678C411yescharacteristic
56#16839678C411yescharacteristic
57#16839676C411yescharacteristic
58#16839674C411yescharacteristic
59#16839670C411yescharacteristic
60#16839670C411yescharacteristic
61C22⋊C4×Dic61C2211yescharacteristic
62C22⋊C4×Dic61C2211yescharacteristic
63#16839609C2211yescharacteristic
64C61×#392C411yescharacteristic
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×#11758217—22no—
75C2×#11758217—22no—
76C2×#11758217—22no—
77C2×#11758217D414yescomplemented
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—
100C22⋊#92420—22no—
101C22⋊#92420—22no—
102C22⋊#92420—22no—
103C22⋊#92420—22no—
104C22⋊#92420—22no—
105C22⋊#92420—22no—
106C22⋊#92420—22no—
107#14519832—22no—
108C4×#92420—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×C22⋊D61C2×C411yescharacteristic
118C22×C22⋊D61C2×C411yescharacteristic
119C22×C22⋊D61C2×C411yescharacteristic
120C23×Dic61C2311yescharacteristic
121C23×Dic61C2311yescharacteristic
122C23×Dic61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124D4×Dic61—22no—
125D4×Dic61—22no—
126D4×Dic61—22no—
127D4×Dic61—22no—
128#14519737—22no—
129#14519737—22no—
130C2×C4⋊Dic61C2×C411yescharacteristic
131C2×C4⋊Dic61C2×C411yescharacteristic
132C2×#11758196C2×C411yescharacteristic
133C2×C22⋊Dic61C2×C411yescharacteristic
134C2×C22⋊Dic61C2×C411yescharacteristic
135C2×C22⋊Dic61C2×C411yescharacteristic
136C2×C22⋊Dic61C2×C411yescharacteristic
137C2×C22⋊Dic61C2×C411yescharacteristic
138C2×C22⋊Dic61C2×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
151C22×D4×C61C2×C411yescharacteristic
152C22×D4×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
159C24×C61C22×C411yescharacteristic
160C23×D61C22×C411yescharacteristic
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—41no—
168C2×D4×C61—41no—
169C2×D4×C61—41no—
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C411yescharacteristic
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—22no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61—41no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61C22×C411yescharacteristic
198C22×Dic61C22×C411yescharacteristic
199C22×Dic61C22×C411yescharacteristic
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202C22×Dic61C22×C411yescharacteristic
203C22×Dic61C2×D412yes—
204C22×Dic61C2×D412yes—
205C22×Dic61#4112yes—
206C22×Dic61#4112yes—
207C22×Dic61C2411yescharacteristic
208#11758224—28no—
209#11758224—28no—
210#11758224—28no—
211#11758224—28no—
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—
223#11758217—44no—
224C2×#92420—28no—
225C2×#92420—21no—
226C2×#92420—21no—
227C2×#92420—21no—
228C2×#92420—21no—
229C2×#92420—21no—
230C2×#92420—21no—
231C2×#92420—28no—
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×#92420—21no—
244C2×#92420C2×D412yes—
245C2×#92420C2×D412yes—
246C2×#92420C2×D412yes—
247C2×#92420C2×D412yes—
248C2×#92420C2×D412yes—
249C2×#92420C2×D412yes—
250#11758213—28no—
251D61⋊C8—28no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—41no—
255C22⋊Dic61—22no—
256C22⋊Dic61—22no—
257C22⋊Dic61—22no—
258C22⋊Dic61—22no—
259C22⋊Dic61—22no—
260C22⋊Dic61—22no—
261#11758198—22no—
262#11758198—22no—
263#11758198—41no—
264C4⋊Dic61—22no—
265C4⋊Dic61—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×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61C4×D412yes—
293C23×C61C4×D412yes—
294C23×C61C23×C411yescharacteristic
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61C4×D412yes—
302D4×C61—28no—
303D4×C61—44no—
304D4×C61—44no—
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×C61C4×D412yes—
316C2×C4×C61#13112yescomplemented
317C22⋊D61—28no—
318C22⋊D61—28no—
319C22⋊D61—44no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61C4×D412yes—
348C2×Dic61C4×D412yes—
349C2×Dic61#13112yescomplemented
350C2×Dic61C22×D411yescharacteristic
351C2×Dic61C22×D411yescharacteristic
352C2×Dic61C22×D411yescharacteristic
353C2×Dic61C2×#4111yescharacteristic
354C2×Dic61C2×#4111yescharacteristic
355C2×Dic61C2×#4111yescharacteristic
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
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#21445—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×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61C2×C4×D411yescharacteristic
392C22×C61C2×C4×D411yescharacteristic
393C22×C61C2×C4×D411yescharacteristic
394C22×C61C2×#13111yescharacteristic
395C22×C61C2×#13111yescharacteristic
396C22×C61#56811yescharacteristic
397C22×C61#56811yescharacteristic
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C4×C61—22no—
406C4×C61—22no—
407C4×C61—41no—
408C4×C61—41no—
409Dic61—22no—
410Dic61—22no—
411Dic61—22no—
412Dic61—41no—
413Dic61—41no—
414Dic61—41no—
415Dic61C2×#12011yescharacteristic
416Dic61#52511yescharacteristic
417Dic61#52511yescharacteristic
418Dic61#52511yescharacteristic
419C22×#131—611no—
420C2×#436—611no—
421C2×#436—611no—
422C2×#435—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—
433C8×C22⋊C4—611no—
434C2×C61—42no—
435C2×C61—42no—
436C2×C61—81no—
437C2×C61C4×#12011yescharacteristic
438C2×C61#293011yescharacteristic
439C2×C61#293111yescharacteristic
440C2×C61#293311yescharacteristic
441C2×C61#293311yescharacteristic
442C2×C61#293511yescharacteristic
443C2×C61#293511yescharacteristic
444D61—42no—
445C22×#41—611no—
446C2×#131—1224no—
447C2×#131—1224no—
448C2×#131—1224no—
449C22×M16—611no—
450C22×M16—611no—
451C22×M16—611no—
452C22×M16—611no—
453C23×C8—611no—
454C23×C8—611no—
455C23×C8—611no—
456C2×C4×D4—611no—
457C2×C4×D4—611no—
458C2×C4×D4—611no—
459#436—1224no—
460#436—1224no—
461#435—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×C4×C8—611no—
476C2×C4×C8—611no—
477#395—611no—
478#394—611no—
479#394—611no—
480#394—611no—
481#393—611no—
482#392—611no—
483#392—611no—
484#392#692311yescharacteristic
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#2144511yescharacteristic, 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×D4C2×#692311yescharacteristic
506C22×D4C2×#692311yescharacteristic
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—
522C2×M16—1222no—
523C2×M16—1222no—
524C2×M16—1222no—
525C22×C8—611no—
526C22×C8—614no—
527C22×C8—611no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—611no—
531C22×C8—611no—
532C22×C8—611no—
533C22×C8—611no—
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⋊C4—611no—
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⋊C4—611no—
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—
579C4×C8—1222no—
580C4×C8—1222no—
581#95—611no—
582#95—611no—
583#95—611no—
584#95—611no—
585#95—611no—
586#95C2×#692311yescharacteristic
587C24—611no—
588C24C22×#692311yescharacteristic
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—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—1222no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—1222no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—1222no—
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—611no—
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×C4—1221no—
647C22×C4C22×#692311yescharacteristic
648C22×C4C22×#692311yescharacteristic
649C22×C4C22×#692311yescharacteristic
650C22×C4C22×#692311yescharacteristic
651M16—1228no—
652M16—1228no—
653M16—1228no—
654M16—2444no—
655C2×C8—612no—
656C2×C8—612no—
657C2×C8—612no—
658C2×C8—612no—
659C2×C8—612no—
660C2×C8—612no—
661C2×C8—1228no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1228no—
669C2×C8—1228no—
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—1221no—
682C4⋊C4—1222no—
683C4⋊C4—1222no—
684C4⋊C4—1222no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—41no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4—1222no—
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—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—612no—
723C23—1221no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23D4×#692312yes—
730C23D4×#692312yes—
731C23C23×#692311yescharacteristic
732Q8—1228no—
733D4—28no—
734D4—44no—
735D4—44no—
736D4—1228no—
737D4—1228no—
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—611no—
750C2×C4—611no—
751C2×C4—611no—
752C2×C4—611no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—612no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
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—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
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—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4D4×#692312yes—
790C2×C4#1451986412yescomplemented
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—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—1222no—
821C22—1222no—
822C22—1222no—
823C22—2441no—
824C22—2441no—
825C22—2441no—
826C22—2441no—
827C22C2×D4×#692311yescharacteristic
828C22C2×D4×#692311yescharacteristic
829C22C2×D4×#692311yescharacteristic
830C22C2×#1451986411yescharacteristic
831C22D61⋊#13111yescharacteristic
832C22#1684084011yescharacteristic
833C22#1684084011yescharacteristic
834C4—22no—
835C4—22no—
836C4—41no—
837C4—41no—
838C4—611no—
839C4—611no—
840C4—611no—
841C4—611no—
842C4—1222no—
843C4—1222no—
844C4—1222no—
845C4—2441no—
846C4—2441no—
847C4—2441no—
848C2—42no—
849C2—42no—
850C2—81no—
851C2—2442no—
852C2#120×#692311yescharacteristic
853C2#2146253811yescharacteristic
854C2#2146254211yescharacteristic
855C2#2146255011yescharacteristic
856C2#2146255111yescharacteristic
857C2#2146256211yescharacteristic
858C2#2146256311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#392C4
prime radical#21449031C2
cosocleC22×Dic61C24
hypercenter#392#6923
hypocenterC61#21445
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#14519864C2semidirect
2. C2×#16840797C2semidirect
3. C2×#16840795C2semidirect
4. C2×#16840793C2semidirect
5. #21461796C2semidirect
6. #21461793C2semidirect
7. #21461792C2semidirect
8. #21461766C2semidirect
9. #21461764C2semidirect
10. #21461763C2semidirect
11. #21461643C2semidirect
12. #21461561C2semidirect
13. #21461560C2semidirect
14. C22⋊C4×#92420C2semidirect
68. C2×#11758213D4semidirect
77. C2×#11758217D4semidirect
86. C22×#92420D4semidirect
316. C2×C4×C61#131semidirect
349. C2×Dic61#131semidirect
494. C61#21445semidirect
790. C2×C4#14519864semidirect

Maximal subgroups

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

subgroupindex
C22×#145198642
C2×#168407972
C2×#168407952
C2×#168407932
#214617962
#214617932
#214617922
#214617662
#214617642
#214617632
#214616432
#214615612
#214615602
C22⋊C4×#924202
#214490312
#2144561