Finite Group Databasebeta

← #29717769

Subgroups — #29717769

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840001C211yesmaximal, characteristic, complemented
2C2×#16839918C211yesmaximal, characteristic, complemented
3C2×#16839918C211yesmaximal, characteristic, complemented
4C22×#14519701C211yesmaximal, characteristic, complemented
5#21449270C211yesmaximal, characteristic
6#21447062C211yesmaximal, characteristic, complemented
7#21447019C211yesmaximal, characteristic, complemented
8#21446919C211yesmaximal, characteristic, complemented
9#21446827C211yesmaximal, characteristic, complemented
10#21446160C211yesmaximal, characteristic, complemented
11#21446127C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic
13#21446073C211yesmaximal, characteristic, complemented
14#21445754C211yesmaximal, characteristic, complemented
15C2×D4×Q8×C61C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23#16840001—24no—
24#16839918—24no—
25#16839918—24no—
26C2×#14519710C2211yescharacteristic
27C2×#14519701—24no—
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41#16839695—21no—
42#16839685—21no—
43#16839668C2211yescharacteristic
44#16839660C2211yescharacteristic
45#16839642—21no—
46#16839622C2211yescharacteristic
47#16839620—21no—
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C23×Q8×C61C2211yescharacteristic
53C23×Q8×C61C2211yescharacteristic
54D4×Q8×C61—24no—
55D4×Q8×C61—24no—
56C2×C4⋊Q8×C61—21no—
57C2×C4⋊Q8×C61C2211yescharacteristic
58C2×C22⋊Q8×C61—21no—
59C2×C22⋊Q8×C61—21no—
60C2×C22⋊Q8×C61C2211yescharacteristic
61C2×C22⋊Q8×C61C2211yescharacteristic
62C2×C4×Q8×C61C2211yescharacteristic
63C2×C4×D4×C61—21no—
64C2×C4×D4×C61C2211yescharacteristic
65C22×Dic122C2311yescharacteristic
66C23×Dic61—21no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758202—22no—
71C2×#11758202—22no—
72C2×#11758202—22no—
73C2×#11758202—41no—
74C2×#11758202—41no—
75C2×#11758202—41no—
76C22×#92418—22no—
77C22×#92418—22no—
78C22×#92418—41no—
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519756—22no—
84#14519756—22no—
85#14519756—22no—
86#14519756—41no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—41no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99#14519710—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701—22no—
105#14519701—22no—
106#14519701—22no—
107#14519701—41no—
108#14519701D414yescomplemented
109#14519700—22no—
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112C22⋊#92418—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C22×Q8×C61—22no—
118C22×Q8×C61—22no—
119C22×Q8×C61—21no—
120C22×Q8×C61—21no—
121C22×Q8×C61—22no—
122C22×Q8×C61—22no—
123C22×Q8×C61—22no—
124C22×Q8×C61—22no—
125C22×Q8×C61—22no—
126C22×Q8×C61—41no—
127C22×Q8×C61—41no—
128C22×Q8×C61—41no—
129C22×Q8×C61—41no—
130C22×Q8×C61D414yes—
131C22×Q8×C61C2311yescharacteristic
132C22×Q8×C61C2311yescharacteristic
133C22×Q8×C61C2311yescharacteristic
134C22×D4×C61D411yescharacteristic
135C23×C4×C61—21no—
136C23×C4×C61—21no—
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C4⋊Q8×C61—28no—
140C4⋊Q8×C61—22no—
141C4⋊Q8×C61—22no—
142C22⋊Q8×C61—28no—
143C22⋊Q8×C61—28no—
144C22⋊Q8×C61—22no—
145C22⋊Q8×C61—22no—
146C22⋊Q8×C61—22no—
147C22⋊Q8×C61D414yes—
148C4×Q8×C61—22no—
149C4×Q8×C61—22no—
150C4×D4×C61—28no—
151C4×D4×C61—22no—
152C4×D4×C61—22no—
153C2×C4⋊C4×C61—21no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61—21no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61D411yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61D411yescharacteristic
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C42×C61—21no—
165C2×C42×C61C2311yescharacteristic
166C24×C61C2×D411yescharacteristic
167C24×C61C2×D411yescharacteristic
168C2×Q8×C61—24no—
169C2×Q8×C61—24no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—28no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—42no—
185C2×Q8×C61—42no—
186C2×Q8×C61—42no—
187C2×Q8×C61—42no—
188C2×Q8×C61—44no—
189C2×Q8×C61—44no—
190C2×Q8×C61—44no—
191C2×Q8×C61—44no—
192C2×Q8×C61—44no—
193C2×Q8×C61—44no—
194C2×Q8×C61—44no—
195C2×Q8×C61C2×D412yes—
196C2×Q8×C61C2×D412yes—
197C2×Q8×C61C2×D412yes—
198C2×Q8×C61C2×D412yes—
199C2×Q8×C61#4112yes—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61Q1614yescomplemented
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—24no—
209C22×C4×C61—24no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—42no—
220C22×C4×C61—42no—
221C22×C4×C61—42no—
222C22×C4×C61—42no—
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—42no—
235C22×Dic61—42no—
236C22×Dic61—81no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C4⋊C4×C61—24no—
244C4⋊C4×C61—24no—
245C4⋊C4×C61—24no—
246C4⋊C4×C61—24no—
247C4⋊C4×C61—24no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C2×D412yes—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—22no—
255C42×C61—24no—
256C42×C61—21no—
257C42×C61—21no—
258C22⋊Dic61—42no—
259C22⋊Dic61—42no—
260C22⋊Dic61—81no—
261#11758202—44no—
262#11758202—44no—
263#11758202—44no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—42no—
270C4⋊Dic61C2×D412yes—
271#11758196—42no—
272#11758196—42no—
273#11758196—81no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—44no—
286C2×#92418C2×D412yes—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61#12012yes—
298C23×C61C2×Q1612yes—
299C23×C61C2×Q1612yes—
300C23×C61#13712yes—
301C23×C61C22×D411yescharacteristic
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—22no—
308Q8×C61—22no—
309Q8×C61—48no—
310Q8×C61—48no—
311Q8×C61—41no—
312Q8×C61—41no—
313Q8×C61—41no—
314Q8×C61—41no—
315Q8×C61#12114yes—
316D4×C61—28no—
317C2×C4×C61—21no—
318C2×C4×C61—22no—
319C2×C4×C61—21no—
320C2×C4×C61—22no—
321C2×C4×C61—21no—
322C2×C4×C61—22no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—21no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—48no—
338C2×C4×C61—48no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61#12012yes—
350C2×C4×C61C2×Q1612yes—
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C2×#4111yescharacteristic
355C2×C4×C61H(5,𝔽2)11yescharacteristic
356C2×C4×C61H(5,𝔽2)11yescharacteristic
357C2×Dic61—22no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—84no—
370Dic122—41no—
371Dic122—41no—
372Dic122—41no—
373Dic122—41no—
374#92418—22no—
375#92418—41no—
376#92418—41no—
377#92418—41no—
378#24437—611nomaximal, Sylow
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61#45114yescomplemented
393C22×C61C2×#12011yescharacteristic
394C22×C61D4211yescharacteristic
395C22×C61#54611yescharacteristic
396C22×C61C22×Q1611yescharacteristic
397C22×C61C2×#13711yescharacteristic
398C22×C61#57711yescharacteristic
399C22×C61#57811yescharacteristic
400C4×C61—22no—
401C4×C61—24no—
402C4×C61—22no—
403C4×C61—41no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—41no—
407C4×C61—42no—
408C4×C61C2×#12111yescharacteristic
409C4×C61#53411yescharacteristic
410C4×C61D4211yescharacteristic
411C4×C61#54611yescharacteristic
412Dic61—42no—
413Dic61—81no—
414Dic61—81no—
415Dic61—81no—
416C2×D4×Q8D6111yescharacteristic
417C2×#467—611no—
418C2×#451—611no—
419C2×#451—611no—
420C22×#103—611no—
421#2417—611no—
422#2043—611no—
423#2036—611no—
424#2016—611no—
425#2001—611no—
426#1878—611no—
427#1872—611no—
428#1869—611no—
429#1863—611no—
430#1787—611no—
431C2×C61—24no—
432C2×C61—42no—
433C2×C61#241011yescharacteristic
434C2×C61C2×#45111yescharacteristic
435C2×C61#301311yescharacteristic
436C2×C61#326611yescharacteristic
437C2×C61D4×Q1611yescharacteristic
438C2×C61#329911yescharacteristic
439C2×C61#331211yescharacteristic
440C23×Q8C2×D6111yescharacteristic
441C23×Q8C2×D6111yescharacteristic
442C22×Q16—611no—
443C22×Q16—611no—
444C22×Q16—611no—
445C23×C8—611no—
446D4×Q8—24no—
447D4×Q8—24no—
448C2×C4⋊Q8—21no—
449C2×C4⋊Q8C2×D6111yescharacteristic
450C2×C22⋊Q8—21no—
451C2×C22⋊Q8—21no—
452C2×C22⋊Q8—611no—
453C2×C22⋊Q8—611no—
454C2×C22⋊Q8C2×D6111yescharacteristic
455C2×C22⋊Q8C2×D6111yescharacteristic
456C2×C4×Q8C2×D6111yescharacteristic
457C2×C4×D4—21no—
458C2×C4×D4C2×D6111yescharacteristic
459C22×C4⋊C4—611no—
460#467—1224no—
461#451—1224no—
462#451—1224no—
463C2×#107—611no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—1224no—
475C2×C22⋊C8—611no—
476C2×C22⋊C8—611no—
477C2×C22⋊C8—611no—
478#398—1221no—
479#396—1221no—
480#391—611no—
481#389—611no—
482#386—1221no—
483#380—611no—
484#380—1221no—
485#340—611no—
486#340—611no—
487#336—611no—
488#336—611no—
489C61#2443711yescharacteristic, complemented, Sylow
490C22×Q8—22no—
491C22×Q8—22no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—22no—
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—22no—
498C22×Q8—22no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—611no—
504C22×Q8C22⋊D6114yes—
505C22×Q8C22×D6111yescharacteristic
506C22×Q8C22×D6111yescharacteristic
507C22×Q8C22×D6111yescharacteristic
508C22×D4C22⋊D6111yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—1221no—
512C23×C4C22×D6111yescharacteristic
513C23×C4C22×D6111yescharacteristic
514C2×Q16—1222no—
515C2×Q16—1222no—
516C2×Q16—1222no—
517C2×Q16—1222no—
518C2×Q16—1222no—
519C2×Q16—1222no—
520C2×Q16—2441no—
521C2×Q16—2441no—
522C2×Q16—2441no—
523C22×C8—611no—
524C22×C8—611no—
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—1222no—
528C22×C8—1222no—
529C22×C8—2441no—
530C4⋊Q8—28no—
531C4⋊Q8—22no—
532C4⋊Q8—22no—
533C22⋊Q8—28no—
534C22⋊Q8—28no—
535C22⋊Q8—22no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8—1222no—
539C22⋊Q8—1222no—
540C22⋊Q8—1222no—
541C22⋊Q8—2441no—
542C22⋊Q8C22⋊D6114yes—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×D4—28no—
546C4×D4—22no—
547C4×D4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—1222no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—2441no—
562C2×C4⋊C4C22⋊D6111yescharacteristic
563C2×C4⋊C4C22×D6111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4C22⋊D6111yescharacteristic
570C2×C22⋊C4C22⋊D6111yescharacteristic
571C2×C42—21no—
572C2×C42C22×D6111yescharacteristic
573#107—1222no—
574#103—614no—
575#103—1222no—
576#103—1222no—
577#103—1222no—
578#103—1222no—
579#103—1222no—
580#103—1222no—
581#103—1222no—
582#103—1222no—
583#103—2441no—
584C22⋊C8—1222no—
585C22⋊C8—1222no—
586C22⋊C8—2441no—
587#95—1221no—
588#95—1221no—
589#95—1221no—
590#95—1221no—
591C24C2×C22⋊D6111yescharacteristic
592C24C2×C22⋊D6111yescharacteristic
593C2×Q8—24no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—28no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8—42no—
612C2×Q8—42no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—44no—
616C2×Q8—44no—
617C2×Q8—44no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8D4×D6112yes—
627C2×Q8#1175822412yes—
628C2×Q8C2×C22⋊D6112yes—
629C2×Q8C2×C22⋊D6112yes—
630C2×Q8C2×C22⋊D6112yes—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4#1175820214yescomplemented
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—4881no—
659C22×C4—2442no—
660C22×C4—2442no—
661C22×C4C2×C22⋊D6111yescharacteristic
662C22×C4C2×C22⋊D6111yescharacteristic
663C22×C4C2×C22⋊D6112yes—
664C22×C4C2×C22⋊D6112yes—
665C22×C4C2×C22⋊D6111yescharacteristic
666C22×C4C2×C22⋊D6111yescharacteristic
667C22×C4C23×D6111yescharacteristic
668Q16—2444no—
669Q16—2444no—
670Q16—2444no—
671C2×C8—612no—
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—
682C2×C8—1221no—
683C2×C8—2444no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—22no—
691C4⋊C4—612no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—4881no—
698C4⋊C4—2442no—
699C4⋊C4—2442no—
700C4⋊C4—2442no—
701C4⋊C4C2×C22⋊D6112yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—4881no—
707C22⋊C4—2442no—
708C22⋊C4—2442no—
709C42—24no—
710C42—21no—
711C42—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23#1451974612yes—
723C23C2×#1175820212yes—
724C23C2×#1175820212yes—
725C23#1451980812yes—
726C23C22×C22⋊D6111yescharacteristic
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—48no—
735Q8—48no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—2441no—
741Q8—2441no—
742Q8—2441no—
743Q8—2441no—
744Q8#1451974914yes—
745D4—28no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—1222no—
779C2×C4—4884no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4#1451974612yes—
792C2×C4C2×#1175820212yes—
793C2×C4C2×D4×D6111yescharacteristic
794C2×C4C22×C22⋊D6111yescharacteristic
795C2×C4C22×C22⋊D6111yescharacteristic
796C2×C4C2×#1175822411yescharacteristic
797C2×C4#1451982211yescharacteristic
798C2×C4#1451982211yescharacteristic
799C8—1222no—
800C8—2441no—
801C8—2441no—
802C8—2441no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22#1683991814yescomplemented
817C22C2×#1451974611yescharacteristic
818C22D4×C22⋊D6111yescharacteristic
819C22#1684040611yescharacteristic
820C22C22×#1175820211yescharacteristic
821C22C2×#1451980811yescharacteristic
822C22#1684057011yescharacteristic
823C22#1684057711yescharacteristic
824C4—22no—
825C4—22no—
826C4—24no—
827C4—41no—
828C4—42no—
829C4—41no—
830C4—42no—
831C4—42no—
832C4—4881no—
833C4—4881no—
834C4—4881no—
835C4—2442no—
836C4C2×#1451974911yescharacteristic
837C4#1684032111yescharacteristic
838C4D4×C22⋊D6111yescharacteristic
839C4#1684040611yescharacteristic
840C2—24no—
841C2—42no—
842C2#2144919311yescharacteristic
843C2C2×#1683991811yescharacteristic
844C2#2145513411yescharacteristic
845C2#2145733011yescharacteristic
846C2D4×#1175820211yescharacteristic
847C2#2145769511yescharacteristic
848C2#2145787011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×D4×Q8×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenterC2×D4×Q8D61
hypocenterC61#24437
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840001C2semidirect
2. C2×#16839918C2semidirect
3. C2×#16839918C2semidirect
4. C22×#14519701C2semidirect
6. #21447062C2semidirect
7. #21447019C2semidirect
8. #21446919C2semidirect
9. #21446827C2semidirect
10. #21446160C2semidirect
11. #21446127C2semidirect
13. #21446073C2semidirect
14. #21445754C2semidirect
108. #14519701D4semidirect
202. C2×D4×C61Q16semidirect
392. C22×C61#451semidirect
489. C61#24437semidirect
633. C2×D4#11758202semidirect
816. C22#16839918semidirect

Maximal subgroups

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

subgroupindex
C2×#168400012
C2×#168399182
C22×#145197012
#214492702
#214470622
#214470192
#214469192
#214468272
#214461602
#214461272
#214461122
#214460732
#214457542
C2×D4×Q8×C612
#2443761