Finite Group Databasebeta

← #29587067

Subgroups — #29587067

Order 15616.

1282 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519697C211yesmaximal, characteristic
2C22×#14519697C211yesmaximal, characteristic
3C2×#16839664C211yesmaximal, characteristic
4C2×#16839524C211yesmaximal, characteristic, complemented
5C2×#16839524C211yesmaximal, characteristic, complemented
6C2×#16839517C211yesmaximal, characteristic, complemented
7C2×C61×#389C211yesmaximal, characteristic, complemented
8C23×D244C2211yescharacteristic
9C23×#92418C2211yescharacteristic
10C23×#92418C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×#11758198—21no—
13C22×#11758198—21no—
14C2×#14519697—22no—
15C2×#14519697—22no—
16C2×#14519697—22no—
17C2×#14519697—22no—
18C2×#14519697—22no—
19C2×#14519697C414yescomplemented
20#16839664—22no—
21#16839664—22no—
22#16839524—22no—
23#16839524—22no—
24#16839517—22no—
25C22×C4⋊C4×C61—21no—
26C22×C4⋊C4×C61C2211yescharacteristic
27C22×C4⋊C4×C61C2211yescharacteristic
28C22×C42×C61C2211yescharacteristic
29C61×#389—22no—
30C61×#389—22no—
31C2×#95×C61—21no—
32C24×D61—21no—
33C22×D244—21no—
34C22×D244—21no—
35C22×D244—21no—
36C22×D244—21no—
37C22×D244—21no—
38C22×D244—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244C2×C412yes—
45C22×D244D412yes—
46C22×D244Q812yes—
47C23×Dic61—21no—
48C22×#92418—21no—
49C22×#92418—21no—
50C22×#92418—21no—
51C22×#92418—21no—
52C22×#92418—21no—
53C22×#92418—21no—
54C22×#92418—21no—
55C22×#92418—21no—
56C22×#92418—21no—
57C22×#92418—21no—
58C22×#92418—21no—
59C22×#92418—21no—
60C22×#92418C2×C412yes—
61C22×#92418D412yes—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61D412yes—
68C2×#11758198—24no—
69C2×#11758198—24no—
70C2×#11758198—42no—
71C2×#11758198—42no—
72C2×#11758198—42no—
73C2×#11758198—42no—
74#14519697—28no—
75#14519697—28no—
76C23×C4×C61—21no—
77C23×C4×C61—21no—
78C23×C4×C61D411yescharacteristic
79C23×C4×C61D411yescharacteristic
80C23×C4×C61C2311yescharacteristic
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—24no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—42no—
91C2×C4⋊C4×C61—42no—
92C2×C4⋊C4×C61C2×C412yes—
93C2×C4⋊C4×C61D412yes—
94C2×C4⋊C4×C61D412yes—
95C2×C4⋊C4×C61D412yes—
96C2×C42×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61—21no—
99C2×C42×C61—21no—
100C2×C42×C61—21no—
101C2×C42×C61—21no—
102#95×C61—24no—
103C24×C61C2×D411yescharacteristic
104C23×D61—22no—
105C23×D61—22no—
106C23×D61—22no—
107C23×D61—41no—
108C23×D61—41no—
109C23×D61—41no—
110C23×D61—41no—
111C23×D61—41no—
112C23×D61—41no—
113C23×D61—41no—
114C23×D61—41no—
115C23×D61—41no—
116C23×D61—41no—
117C23×D61—41no—
118C23×D61—41no—
119C22×C4×C61—22no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—22no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—41no—
136C22×C4×C61—41no—
137C22×C4×C61—41no—
138C22×C4×C61—41no—
139C22×C4×C61—41no—
140C22×C4×C61—41no—
141C22×C4×C61—41no—
142C22×C4×C61—41no—
143C22×C4×C61—41no—
144C22×C4×C61—41no—
145C22×C4×C61D812yes—
146C22×C4×C61SD1612yes—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×Q811yescharacteristic
155C22×C4×C61#4111yescharacteristic
156C22×C4×C61#4111yescharacteristic
157C22×C4×C61#4111yescharacteristic
158C22×C4×C61#4111yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C22×C4×C61#4111yescharacteristic
161C22×Dic61—22no—
162C22×Dic61—41no—
163C22×Dic61—41no—
164C22×Dic61—41no—
165C22×Dic61—41no—
166C22×Dic61—41no—
167C22×Dic61—41no—
168C2×D244—22no—
169C2×D244—22no—
170C2×D244—22no—
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—22no—
180C2×D244—22no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—41no—
184C2×D244—41no—
185C2×D244—41no—
186C2×D244—41no—
187C2×D244—41no—
188C2×D244—41no—
189C2×D244—41no—
190C2×D244—41no—
191C2×D244—41no—
192C2×D244—41no—
193C2×D244—41no—
194C2×D244—41no—
195C2×D244C4⋊C414yescomplemented
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C4⋊C4×C61—22no—
199C4⋊C4×C61—22no—
200C4⋊C4×C61—22no—
201C4⋊C4×C61—48no—
202C4⋊C4×C61—41no—
203C4⋊C4×C61—41no—
204C4⋊C4×C61C22⋊C414yescomplemented
205C42×C61—41no—
206C42×C61—41no—
207C42×C61—41no—
208C42×C61—41no—
209#11758198—48no—
210#11758198—48no—
211C4⋊Dic61—22no—
212C4⋊Dic61—22no—
213C4⋊Dic61—41no—
214C4⋊Dic61—41no—
215C2×#92418—22no—
216C2×#92418—22no—
217C2×#92418—22no—
218C2×#92418—22no—
219C2×#92418—22no—
220C2×#92418—22no—
221C2×#92418—41no—
222C2×#92418—41no—
223C2×#92418—41no—
224C2×#92418—41no—
225C2×#92418—41no—
226C2×#92418—41no—
227C2×#92418—41no—
228C2×#92418—41no—
229C23×C61C4×D411yescharacteristic
230C23×C61#12011yescharacteristic
231C23×C61#12011yescharacteristic
232C23×C61#12111yescharacteristic
233C23×C61#12111yescharacteristic
234C23×C61C22⋊Q811yescharacteristic
235C23×C61#12411yescharacteristic
236C23×C61C2×D811yescharacteristic
237C23×C61C2×SD1611yescharacteristic
238C23×C61#13511yescharacteristic
239C23×C61#13511yescharacteristic
240C23×C61AGL(1,ℤ/8)11yescharacteristic
241C23×C61AGL(1,ℤ/8)11yescharacteristic
242C23×C61AGL(1,ℤ/8)11yescharacteristic
243C23×C61#13711yescharacteristic
244C22×D61—24no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—42no—
250C22×D61—42no—
251C22×D61—42no—
252C22×D61—42no—
253C22×D61—42no—
254C22×D61—42no—
255C22×D61—42no—
256C22×D61—42no—
257C22×D61—42no—
258C22×D61—42no—
259C22×D61—42no—
260C22×D61—42no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—81no—
264C22×D61—81no—
265C22×D61—81no—
266C22×D61—81no—
267C22×D61—81no—
268C22×D61—81no—
269C22×D61—81no—
270C22×D61—81no—
271C22×D61—81no—
272C22×D61—81no—
273C22×D61—81no—
274C22×D61—81no—
275C22×D61—81no—
276C22×D61—81no—
277C22×D61—81no—
278C22×D61—81no—
279C2×C4×C61—24no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—42no—
295C2×C4×C61—41no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—81no—
304C2×C4×C61—81no—
305C2×C4×C61—81no—
306C2×C4×C61—81no—
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C4⋊C411yescharacteristic
309C2×C4×C61#11711yescharacteristic
310C2×C4×C61C4×D411yescharacteristic
311C2×C4×C61C4×D411yescharacteristic
312C2×C4×C61C4×D411yescharacteristic
313C2×C4×C61#12011yescharacteristic
314C2×C4×C61#12111yescharacteristic
315C2×C4×C61#12111yescharacteristic
316C2×C4×C61#12111yescharacteristic
317C2×C4×C61#12111yescharacteristic
318C2×C4×C61#12111yescharacteristic
319C2×C4×C61#12111yescharacteristic
320C2×C4×C61C22⋊Q811yescharacteristic
321C2×C4×C61C22⋊Q811yescharacteristic
322C2×C4×C61C22⋊Q811yescharacteristic
323C2×C4×C61C22⋊Q811yescharacteristic
324C2×C4×C61C22⋊Q811yescharacteristic
325C2×C4×C61#12311yescharacteristic
326C2×C4×C61#12311yescharacteristic
327C2×C4×C61#12311yescharacteristic
328C2×C4×C61#12311yescharacteristic
329C2×C4×C61#12311yescharacteristic
330C2×C4×C61#12411yescharacteristic
331C2×C4×C61#12411yescharacteristic
332C2×C4×C61#12611yescharacteristic
333C2×C4×C61#12611yescharacteristic
334C2×C4×C61#12711yescharacteristic
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—81no—
339C2×Dic61—81no—
340C2×Dic61—81no—
341C2×Dic61—81no—
342D244—24no—
343D244—24no—
344D244—42no—
345D244—42no—
346D244—42no—
347D244—42no—
348D244—42no—
349D244—42no—
350#92418—42no—
351#92418—42no—
352#11066—611nomaximal, Sylow
353C22×C61#38511yescharacteristic
354C22×C61#38611yescharacteristic
355C22×C61#38811yescharacteristic
356C22×C61#39211yescharacteristic
357C22×C61#39311yescharacteristic
358C22×C61#39411yescharacteristic
359C22×C61#39611yescharacteristic
360C22×C61C4×D811yescharacteristic
361C22×C61C4×SD1611yescharacteristic
362C22×C61#44011yescharacteristic
363C22×C61#44211yescharacteristic
364C22×C61#44711yescharacteristic
365C22×C61#44711yescharacteristic
366C22×C61#44811yescharacteristic
367C22×C61#44911yescharacteristic
368C22×C61#44911yescharacteristic
369C22×C61#44911yescharacteristic
370C22×C61#45011yescharacteristic
371C22×C61#45211yescharacteristic
372C22×C61#45911yescharacteristic
373C22×C61#46011yescharacteristic
374C22×C61#46311yescharacteristic
375C22×C61#46411yescharacteristic
376C22×C61#46511yescharacteristic
377C22×C61#46611yescharacteristic
378C22×C61#46811yescharacteristic
379C22×C61#46911yescharacteristic
380C22×C61#47411yescharacteristic
381C22×C61#47611yescharacteristic
382C22×C61#47811yescharacteristic
383C22×C61#47811yescharacteristic
384C22×C61#48611yescharacteristic
385C22×C61#48811yescharacteristic
386C22×C61#48911yescharacteristic
387C22×C61#49011yescharacteristic
388C2×D61—44no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61—82no—
392C2×D61—82no—
393C2×D61—82no—
394C2×D61—82no—
395C2×D61—82no—
396C2×D61—82no—
397C2×D61—82no—
398C2×D61—82no—
399C2×D61—82no—
400C2×D61—82no—
401C2×D61—82no—
402C2×D61—82no—
403C4×C61—44no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—82no—
407C4×C61#38011yescharacteristic
408C4×C61#38511yescharacteristic
409C4×C61#38811yescharacteristic
410C4×C61#39011yescharacteristic
411C4×C61#39411yescharacteristic
412C4×C61#39611yescharacteristic
413C4×C61#39711yescharacteristic
414C4×C61#39911yescharacteristic
415Dic61—82no—
416C22×#102—611no—
417C22×#102—611no—
418C2×#390—611no—
419C2×#389D6111yescharacteristic, complemented
420C2×#340—611no—
421C2×#340—611no—
422C2×#336—611no—
423C2×C61#143911yescharacteristic
424C2×C61#186211yescharacteristic
425C2×C61#186411yescharacteristic
426C2×C61#187911yescharacteristic
427C2×C61#188011yescharacteristic
428C2×C61#193411yescharacteristic
429C2×C61#193611yescharacteristic
430C2×C61#199911yescharacteristic
431C2×C61#200011yescharacteristic
432C2×C61#202311yescharacteristic
433C2×C61#202511yescharacteristic
434C2×C61#204111yescharacteristic
435C2×C61#204211yescharacteristic
436C2×C61#206511yescharacteristic
437C2×C61#206711yescharacteristic
438D61—84no—
439C23×D4—611no—
440C23×C8—611no—
441C23×C8—611no—
442C22×C4⋊C4—21no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4C2×D6111yescharacteristic
445C22×C4⋊C4C2×D6111yescharacteristic
446C22×C22⋊C4—1221no—
447C22×C22⋊C4—1221no—
448C22×C42C2×D6111yescharacteristic
449C2×#102—614no—
450C2×#102—1222no—
451C2×#102—1222no—
452C2×#102—1222no—
453C2×#102—1222no—
454C2×#102—1222no—
455#390—1222no—
456#390—1222no—
457#389—22no—
458#389—22no—
459C2×#95—21no—
460#340—1222no—
461#340—1222no—
462#336—1222no—
463C61#1106611yescharacteristic, complemented, Sylow
464C25—1221no—
465C22×D4—612no—
466C22×D4—612no—
467C22×D4—612no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4—1221no—
477C22×D4—1221no—
478C22×D4—1221no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—1221no—
482C23×C4C22⋊D6111yescharacteristic
483C23×C4C22⋊D6111yescharacteristic
484C23×C4C22×D6111yescharacteristic
485C22×C8—612no—
486C22×C8—612no—
487C22×C8—1221no—
488C22×C8—1221no—
489C22×C8—1221no—
490C22×C8—1221no—
491C22×C8—1221no—
492C22×C8—1221no—
493C22×C8—1221no—
494C22×C8—1221no—
495C22×C8—1221no—
496C22×C8—1221no—
497C22×C8—1221no—
498C22×C8—1221no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4C4×D6112yes—
517C2×C4⋊C4D24412yes—
518C2×C4⋊C4C22⋊D6112yes—
519C2×C4⋊C4C22⋊D6112yes—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4—1224no—
522C2×C22⋊C4—2442no—
523C2×C22⋊C4—2442no—
524C2×C22⋊C4—2442no—
525C2×C22⋊C4—2442no—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532#102—1228no—
533#102—1228no—
534#95—24no—
535C24—1222no—
536C24—1222no—
537C24—1222no—
538C24—2441no—
539C24—2441no—
540C24—2441no—
541C24—2441no—
542C24—2441no—
543C24—2441no—
544C24—2441no—
545C24—2441no—
546C24—2441no—
547C24—2441no—
548C24—2441no—
549C24—2441no—
550C24C2×C22⋊D6111yescharacteristic
551C2×D4—614no—
552C2×D4—1222no—
553C2×D4—1222no—
554C2×D4—1222no—
555C2×D4—1222no—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—2441no—
568C2×D4—2441no—
569C2×D4—2441no—
570C2×D4—2441no—
571C2×D4—2441no—
572C2×D4—2441no—
573C2×D4—2441no—
574C2×D4—2441no—
575C2×D4—2441no—
576C2×D4—2441no—
577C2×D4—2441no—
578C2×D4—2441no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—1222no—
606C22×C4—2441no—
607C22×C4—2441no—
608C22×C4—2441no—
609C22×C4—2441no—
610C22×C4—2441no—
611C22×C4—2441no—
612C22×C4#1175819912yes—
613C22×C4#1175820112yes—
614C22×C4C2×C4×D6111yescharacteristic
615C22×C4C2×D24411yescharacteristic
616C22×C4#1175822211yescharacteristic
617C22×C4#1175822211yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4D4×D6111yescharacteristic
620C22×C4D4×D6111yescharacteristic
621C22×C4#1175822411yescharacteristic
622C22×C4Q8×D6111yescharacteristic
623C22×C4#1175822611yescharacteristic
624C22×C4#1175822611yescharacteristic
625C22×C4#1175822611yescharacteristic
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8—1222no—
631C2×C8—1222no—
632C2×C8—1222no—
633C2×C8—1222no—
634C2×C8—2441no—
635C2×C8—2441no—
636C2×C8—2441no—
637C2×C8—2441no—
638C2×C8—2441no—
639C2×C8—2441no—
640C2×C8—2441no—
641C2×C8—2441no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—48no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—1222no—
651C4⋊C4—1222no—
652C4⋊C4—2441no—
653C4⋊C4—2441no—
654C4⋊C4#1175819814yescomplemented
655C22⋊C4—2448no—
656C22⋊C4—2448no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—41no—
661C23—1224no—
662C23—4881no—
663C23—4881no—
664C23—4881no—
665C23—4881no—
666C23—4881no—
667C23—4881no—
668C23—4881no—
669C23—4881no—
670C23—4881no—
671C23—4881no—
672C23—4881no—
673C23—4881no—
674C23—4881no—
675C23—4881no—
676C23—4881no—
677C23—4881no—
678C23—2442no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23—2442no—
688C23—2442no—
689C23—2442no—
690C23—2442no—
691C23—2442no—
692C23—2442no—
693C23—2442no—
694C23—2442no—
695C23—2442no—
696C23C4×C22⋊D6111yescharacteristic
697C23#1451974511yescharacteristic
698C23#1451974611yescharacteristic
699C23#1451974911yescharacteristic
700C23#1451975111yescharacteristic
701C23#1451975311yescharacteristic
702C23#1451976611yescharacteristic
703C23C2×#1175819911yescharacteristic
704C23C2×#1175820111yescharacteristic
705C23#1451979711yescharacteristic
706C23#1451979711yescharacteristic
707C23#1451980211yescharacteristic
708C23#1451980211yescharacteristic
709C23#1451980311yescharacteristic
710C23#1451980811yescharacteristic
711D4—1224no—
712D4—1224no—
713D4—2442no—
714D4—2442no—
715D4—2442no—
716D4—2442no—
717D4—2442no—
718D4—2442no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—4881no—
748C2×C4—4881no—
749C2×C4—4881no—
750C2×C4—4881no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4C2×#1175819811yescharacteristic
755C2×C4C4⋊C4×D6111yescharacteristic
756C2×C4#1451973511yescharacteristic
757C2×C4C4×C22⋊D6111yescharacteristic
758C2×C4#1451973911yescharacteristic
759C2×C4#1451973911yescharacteristic
760C2×C4#1451974511yescharacteristic
761C2×C4#1451974811yescharacteristic
762C2×C4#1451974911yescharacteristic
763C2×C4#1451975111yescharacteristic
764C2×C4#1451975211yescharacteristic
765C2×C4#1451975211yescharacteristic
766C2×C4#1451975211yescharacteristic
767C2×C4#1451975311yescharacteristic
768C2×C4#1451975311yescharacteristic
769C2×C4#1451975511yescharacteristic
770C2×C4#1451975511yescharacteristic
771C2×C4#1451975711yescharacteristic
772C2×C4#1451976011yescharacteristic
773C2×C4#1451976211yescharacteristic
774C2×C4#1451976211yescharacteristic
775C2×C4#1451976211yescharacteristic
776C2×C4#1451976211yescharacteristic
777C2×C4#1451976611yescharacteristic
778C2×C4#1451976611yescharacteristic
779C2×C4#1451977211yescharacteristic
780C2×C4#1451977211yescharacteristic
781C2×C4#1451977311yescharacteristic
782C8—2442no—
783C8—2442no—
784C22—4882no—
785C22—4882no—
786C22—4882no—
787C22—4882no—
788C22—4882no—
789C22—4882no—
790C22—4882no—
791C22—4882no—
792C22—4882no—
793C22—4882no—
794C22—4882no—
795C22—4882no—
796C22—2444no—
797C22—2444no—
798C22—2444no—
799C22#1683963311yescharacteristic
800C22#1683964111yescharacteristic
801C22#1683965211yescharacteristic
802C22#1683967011yescharacteristic
803C22#1683967311yescharacteristic
804C22#1683967911yescharacteristic
805C22#1683968411yescharacteristic
806C22C4×#1175819911yescharacteristic
807C22C4×#1175820111yescharacteristic
808C22#1683986011yescharacteristic
809C22#1683987211yescharacteristic
810C22#1683989511yescharacteristic
811C22#1683989611yescharacteristic
812C22#1683990111yescharacteristic
813C22#1683990511yescharacteristic
814C22#1683990711yescharacteristic
815C22#1683990711yescharacteristic
816C22#1683991211yescharacteristic
817C22#1683992211yescharacteristic
818C22#1683995711yescharacteristic
819C22#1683996211yescharacteristic
820C22#1683997711yescharacteristic
821C22#1683998411yescharacteristic
822C22#1683999311yescharacteristic
823C22#1683999611yescharacteristic
824C22#1684001011yescharacteristic
825C22#1684001311yescharacteristic
826C22#1684003911yescharacteristic
827C22#1684004911yescharacteristic
828C22#1684005911yescharacteristic
829C22#1684005911yescharacteristic
830C22#1684011011yescharacteristic
831C22#1684011911yescharacteristic
832C22#1684012411yescharacteristic
833C22#1684012811yescharacteristic
834C4—44no—
835C4—42no—
836C4—42no—
837C4—82no—
838C4—4882no—
839C4#1683961911yescharacteristic
840C4#1683963311yescharacteristic
841C4#1683965211yescharacteristic
842C4#1683966311yescharacteristic
843C4#1683967911yescharacteristic
844C4#1683968411yescharacteristic
845C4#1683968811yescharacteristic
846C4#1683969711yescharacteristic
847C2—4884no—
848C2#2144406111yescharacteristic
849C2#2144606511yescharacteristic
850C2#2144607911yescharacteristic
851C2#2144616711yescharacteristic
852C2#2144617411yescharacteristic
853C2#2144650111yescharacteristic
854C2#2144651511yescharacteristic
855C2#2144681511yescharacteristic
856C2#2144682011yescharacteristic
857C2#2144695211yescharacteristic
858C2#2144696211yescharacteristic
859C2#2144705311yescharacteristic
860C2#2144706011yescharacteristic
861C2#2144719011yescharacteristic
862C2#2144720411yescharacteristic
subgroupG/H
centerC24C2×C22⋊D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#389C2
socleC24×C61C2×D4
prime radicalC23×D244C22
cosocleC23×C4×C61C23
hypercenterC2×#389D61
hypocenterC61#11066
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×#16839524C2semidirect
5. C2×#16839524C2semidirect
6. C2×#16839517C2semidirect
7. C2×C61×#389C2semidirect
19. C2×#14519697C4semidirect
195. C2×D244C4⋊C4semidirect
204. C4⋊C4×C61C22⋊C4semidirect
419. C2×#389D61semidirect
463. C61#11066semidirect
654. C4⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145196972
C2×#168396642
C2×#168395242
C2×#168395172
C2×C61×#3892
#1106661