Finite Group Databasebeta

← #29712421

Subgroups — #29712421

Order 15616.

1300 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic, complemented
2C2×#16839763C211yesmaximal, characteristic, complemented
3#21449158C211yesmaximal, characteristic
4#21446958C211yesmaximal, characteristic, complemented
5#21446953C211yesmaximal, characteristic, complemented
6#21446826C211yesmaximal, characteristic, complemented
7#21446819C211yesmaximal, characteristic, complemented
8#21446253C211yesmaximal, characteristic, complemented
9#21446176C211yesmaximal, characteristic, complemented
10#21446162C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21446123C211yesmaximal, characteristic, complemented
13#21446114C211yesmaximal, characteristic, complemented
14#21445906C211yesmaximal, characteristic, complemented
15C2×C61×#452C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17#16840470—24no—
18#16840470—24no—
19C2×#14519776C2211yescharacteristic
20C2×#14519767—21no—
21C2×#14519757—21no—
22C2×#14519754—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519753C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737—21no—
29C22×C4⋊Dic61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31#16839763—24no—
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40#16839676—21no—
41#16839670—21no—
42#16839669C2211yescharacteristic
43#16839665C2211yescharacteristic
44#16839641—21no—
45#16839635—21no—
46#16839622C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×#41×C61C2211yescharacteristic
56C22×Q16×C61C2211yescharacteristic
57C22×SD16×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C61×#452—24no—
60C2×#103×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C22×Dic122—21no—
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C22×C4×D61C2311yescharacteristic
69C2×#11758194—22no—
70C2×#11758194—41no—
71C2×#11758194—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519776—22no—
75#14519776—22no—
76#14519767—28no—
77#14519757—28no—
78#14519754—28no—
79#14519753—22no—
80#14519753—22no—
81#14519753—22no—
82#14519753—41no—
83#14519748—22no—
84#14519748—41no—
85Q8×Dic61—22no—
86Q8×Dic61—22no—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—22no—
89#14519737—28no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61D414yescomplemented
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196D411yescharacteristic
103C4⋊C4×D61—22no—
104C4⋊C4×D61—22no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61D411yescharacteristic
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198D411yescharacteristic
113C2×C4×Dic61—21no—
114C2×C4×Dic61C2311yescharacteristic
115#14519701—22no—
116#14519701—22no—
117#14519701—41no—
118#14519701—41no—
119#14519698—22no—
120#14519698—22no—
121#14519689—41no—
122#14519689—41no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126C2×#41×C61—22no—
127C2×#41×C61—22no—
128C2×#41×C61—22no—
129C2×#41×C61—22no—
130C2×#41×C61—41no—
131C2×#41×C61—41no—
132C22×Q8×C61C2311yescharacteristic
133C22×Q8×C61C2311yescharacteristic
134C22×D4×C61—21no—
135C22×D4×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C23×C4×C61C2311yescharacteristic
138C2×Q16×C61—22no—
139C2×Q16×C61—22no—
140C2×Q16×C61—41no—
141C2×SD16×C61—22no—
142C2×SD16×C61—22no—
143C2×SD16×C61—41no—
144C22×C8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C22⋊Q8×C61—22no—
147C22⋊Q8×C61D414yescomplemented
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C22⋊C4×C61—21no—
151#103×C61—22no—
152#102×C61—22no—
153C22⋊C8×C61—22no—
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C23×D61C2×D411yescharacteristic
157#41×C61—28no—
158#41×C61—44no—
159#41×C61—44no—
160#41×C61—44no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61C2×D412yes—
172C2×Q8×C61#4112yes—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—42no—
179C2×D4×C61—42no—
180C2×D4×C61—42no—
181C2×D4×C61#4112yes—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—42no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—42no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—81no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—24no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—81no—
208C22×Dic61—81no—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—24no—
219C2×C4×D61—81no—
220C2×C4×D61—81no—
221C2×Dic122—24no—
222C2×Dic122—81no—
223C2×Dic122—81no—
224Q16×C61—44no—
225SD16×C61—44no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C2×D412yes—
235C22⋊C4×C61—24no—
236C22⋊Dic61—22no—
237C22⋊Dic61—42no—
238C22⋊Dic61—42no—
239C22⋊Dic61—81no—
240C22⋊Dic61—81no—
241#11758198—24no—
242#11758198—22no—
243#11758198—42no—
244C4⋊Dic61—24no—
245C4⋊Dic61—24no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61C2×D412yes—
253C4⋊Dic61C2×D412yes—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257#11758196—22no—
258#11758196—42no—
259C4×Dic61—24no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262#11758194—44no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—22no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61#12012yes—
283C23×C61C22×D411yescharacteristic
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61#13712yes—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—41no—
296Q8×C61—41no—
297Q8×C61—41no—
298Q8×C61—41no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—48no—
302D4×C61—41no—
303D4×C61—41no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—48no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61#12012yes—
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61C2×#4111yescharacteristic
325C2×C4×C61H(5,𝔽2)11yescharacteristic
326C2×C4×C61H(5,𝔽2)11yescharacteristic
327C22⋊D61—28no—
328C22⋊D61—84no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—22no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—22no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—84no—
350C2×Dic61#13712yes—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—84no—
356Dic122—84no—
357C8×C61—41no—
358C8×C61—41no—
359#92418—41no—
360#92418—41no—
361#23981—611nomaximal, Sylow
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61C2×#12011yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61#54611yescharacteristic
379C22×C61C2×#13711yescharacteristic
380C22×C61C2×#13711yescharacteristic
381C22×C61#57611yescharacteristic
382C22×C61#57711yescharacteristic
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C4×C61—22no—
391C4×C61—42no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61#52511yescharacteristic
395C4×C61#53511yescharacteristic
396C4×C61#54611yescharacteristic
397C4×C61#54611yescharacteristic
398Dic61—22no—
399Dic61—41no—
400Dic61—41no—
401Dic61—42no—
402Dic61—42no—
403Dic61—81no—
404Dic61—81no—
405C2×#554—611no—
406C2×#452D6111yescharacteristic, complemented
407C2×#417—611no—
408#2407—611no—
409#2024—611no—
410#2023—611no—
411#2001—611no—
412#2000—611no—
413#1894—611no—
414#1880—611no—
415#1878—611no—
416#1874—611no—
417#1872—611no—
418#1870—611no—
419#1823—611no—
420C2×C61—42no—
421C2×C61—82no—
422C2×C61#240411yescharacteristic
423C2×C61#300411yescharacteristic
424C2×C61#301211yescharacteristic
425C2×C61#331411yescharacteristic
426C2×C61#331611yescharacteristic
427C2×C61#333111yescharacteristic
428C2×C61#333311yescharacteristic
429D61—42no—
430C22×#41C2×D6111yescharacteristic
431C22×Q16C2×D6111yescharacteristic
432C22×SD16C2×D6111yescharacteristic
433C22×M16—611no—
434#554—1224no—
435#554—1224no—
436C2×C4⋊Q8—611no—
437C2×#125—1221no—
438C2×C22⋊Q8—611no—
439C2×C22⋊Q8—611no—
440C2×C22⋊Q8—1221no—
441C2×C22⋊Q8—1221no—
442C2×C22⋊Q8C2×D6111yescharacteristic
443C2×#121—611no—
444C2×C4×Q8—611no—
445C2×C4×D4—611no—
446C2×C4×D4—1221no—
447C22×C4⋊C4—611no—
448C22×C4⋊C4—611no—
449#452—24no—
450#417—1224no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103C2×D6111yescharacteristic
456C2×#102—611no—
457C2×#102—611no—
458C2×#102C2×D6111yescharacteristic
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×C22⋊C8C2×D6111yescharacteristic
462#394—1221no—
463#392—1221no—
464#391—611no—
465#390—611no—
466#386—1221no—
467#385—1221no—
468#380—611no—
469#340—611no—
470#340—611no—
471#340—611no—
472#340—611no—
473#340—611no—
474#340—611no—
475#336—611no—
476#336—611no—
477C61#2398111yescharacteristic, complemented, Sylow
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C22×Q8—1221no—
485C22×Q8C22×D6111yescharacteristic
486C22×Q8C22×D6111yescharacteristic
487C22×D4—21no—
488C22×D4—611no—
489C22×D4—1221no—
490C22×D4C22×D6111yescharacteristic
491C23×C4—21no—
492C23×C4—611no—
493C23×C4—1221no—
494C23×C4—1221no—
495C23×C4C22×D6111yescharacteristic
496C2×Q16—22no—
497C2×Q16—22no—
498C2×Q16—41no—
499C2×SD16—22no—
500C2×SD16—22no—
501C2×SD16—41no—
502C2×M16—1222no—
503C2×M16—2441no—
504C2×M16—2441no—
505C22×C8—611no—
506C22×C8—611no—
507C22×C8C22×D6111yescharacteristic
508C22×C8C22×D6111yescharacteristic
509C4⋊Q8—1222no—
510C4⋊Q8—1222no—
511#125—1228no—
512C22⋊Q8—22no—
513C22⋊Q8—1228no—
514C22⋊Q8—1228no—
515C22⋊Q8—1222no—
516C22⋊Q8—1222no—
517C22⋊Q8—1222no—
518C22⋊Q8—2441no—
519C22⋊Q8C22⋊D6114yescomplemented
520#121—1222no—
521#121—2441no—
522C4×Q8—1222no—
523C4×Q8—1222no—
524C4×D4—1228no—
525C4×D4—1222no—
526C4×D4—1222no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—614no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—1222no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1222no—
541C2×C4⋊C4—1222no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C42—611no—
554C2×C42—1221no—
555#103—22no—
556#103—1222no—
557#103—1222no—
558#103—2441no—
559#103—2441no—
560#102—22no—
561#102—1222no—
562#102—1222no—
563C22⋊C8—22no—
564C22⋊C8—2441no—
565C22⋊C8—2441no—
566#95—1221no—
567#95—1221no—
568#95—1221no—
569C24—21no—
570C24—611no—
571C24D4×D6111yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—1224no—
587C2×Q8—4881no—
588C2×Q8—4881no—
589C2×Q8#1175822412yes—
590C2×Q8C2×C22⋊D6112yes—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—4881no—
603C2×D4—2442no—
604C2×D4—2442no—
605C2×D4#1175822412yes—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—1224no—
620C22×C4—1224no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—4881no—
632C22×C4—4881no—
633C22×C4—4881no—
634C22×C4—4881no—
635C22×C4D4×D6112yes—
636C22×C4D4×D6111yescharacteristic
637C22×C4C2×C22⋊D6112yes—
638C22×C4C23×D6111yescharacteristic
639Q16—44no—
640SD16—44no—
641M16—2444no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C4⋊C4—21no—
655C4⋊C4—24no—
656C4⋊C4—612no—
657C4⋊C4—612no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1224no—
665C4⋊C4—1222no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—2442no—
671C4⋊C4C2×C22⋊D6112yes—
672C22⋊C4—24no—
673C22⋊C4—1224no—
674C22⋊C4—1222no—
675C22⋊C4—1222no—
676C22⋊C4—4881no—
677C22⋊C4—4881no—
678C22⋊C4—2442no—
679C22⋊C4—2442no—
680C22⋊C4—2442no—
681C42—1224no—
682C42—1221no—
683C42—1221no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—612no—
698C23—1221no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23#1451974512yes—
705C23C2×D4×D6111yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8—41no—
714Q8—4884no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—1228no—
721D4—4884no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—612no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1221no—
745C2×C4—1221no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—4884no—
750C2×C4—4884no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4#1451974512yes—
766C2×C4C2×D4×D6111yescharacteristic
767C2×C4C22×C22⋊D6111yescharacteristic
768C2×C4C2×#1175822411yescharacteristic
769C2×C4C2×#1175822411yescharacteristic
770C2×C4#1451982211yescharacteristic
771C2×C4#1451982211yescharacteristic
772C8—41no—
773C8—41no—
774C8—2441no—
775C8—2441no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—1222no—
791C22—1222no—
792C22—1222no—
793C22—2441no—
794C22—2441no—
795C22—2441no—
796C22—2441no—
797C22C2×#1451974511yescharacteristic
798C22#1684039911yescharacteristic
799C22#1684039911yescharacteristic
800C22#137×D6111yescharacteristic
801C22#137×D6111yescharacteristic
802C22#1684056411yescharacteristic
803C22#1684056911yescharacteristic
804C4—22no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—1222no—
809C4—4881no—
810C4—4881no—
811C4—2441no—
812C4—2442no—
813C4—2442no—
814C4—2441no—
815C4#1684026811yescharacteristic
816C4#1684032711yescharacteristic
817C4#1684040611yescharacteristic
818C4#1684040611yescharacteristic
819C2—42no—
820C2—82no—
821C2—2442no—
822C2#2144913511yescharacteristic
823C2#2145505111yescharacteristic
824C2#2145511911yescharacteristic
825C2#2145789311yescharacteristic
826C2#2145792311yescharacteristic
827C2#2145812811yescharacteristic
828C2#2145815011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radical#21449158C2
hypercenterC2×#452D61
hypocenterC61#23981
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16840470C2semidirect
2. C2×#16839763C2semidirect
4. #21446958C2semidirect
5. #21446953C2semidirect
6. #21446826C2semidirect
7. #21446819C2semidirect
8. #21446253C2semidirect
9. #21446176C2semidirect
10. #21446162C2semidirect
11. #21446133C2semidirect
12. #21446123C2semidirect
13. #21446114C2semidirect
14. #21445906C2semidirect
15. C2×C61×#452C2semidirect
93. C2×C4⋊Dic61D4semidirect
147. C22⋊Q8×C61D4semidirect
406. C2×#452D61semidirect
477. C61#23981semidirect
519. C22⋊Q8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168397632
#214491582
#214469582
#214469532
#214468262
#214468192
#214462532
#214461762
#214461622
#214461332
#214461232
#214461142
#214459062
C2×C61×#4522
#2398161