Finite Group Databasebeta

← #29586735

Subgroups — #29586735

Order 15616.

1506 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840308C211yesmaximal, characteristic
2C22×#14519705C211yesmaximal, characteristic, complemented
3C22×#14519704C211yesmaximal, characteristic, complemented
4C22×#14519703C211yesmaximal, characteristic, complemented
5#21445512C211yesmaximal, characteristic, complemented
6C4×#14519684C211yesmaximal, characteristic, complemented
7C22×#104×C61C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10#16840308—22no—
11#16840308—22no—
12#16840308—22no—
13#16840308—22no—
14C2×#14519775C411yescharacteristic, complemented
15C2×#14519773C411yescharacteristic, complemented
16C2×#14519766C411yescharacteristic, complemented
17C2×#14519764C411yescharacteristic, complemented
18C2×#14519749—22no—
19C2×C4×C22⋊D61—22no—
20C22×C4×Dic61C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22C2×#14519705—22no—
23C2×#14519705—22no—
24C2×#14519705—22no—
25C2×#14519704—22no—
26C2×#14519704—22no—
27C2×#14519704—22no—
28C2×#14519703—22no—
29C2×#14519703—22no—
30C2×#14519703—22no—
31C2×#14519684—22no—
32#16839516—22no—
33C22×#41×C61C2211yescharacteristic
34C22×M16×C61C2211yescharacteristic
35C22×C42×C61C2211yescharacteristic
36C2×#104×C61—22no—
37C2×#104×C61—22no—
38C2×#104×C61—22no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222D412yes—
50C2×#11758222D412yes—
51C22×Dic122C2×C411yescharacteristic
52C22×D244C2×C411yescharacteristic
53C22×C22⋊D61—21no—
54C22×C22⋊D61—22no—
55C23×Dic61—21no—
56C23×Dic61D412yes—
57C22×C4×D61—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194—21no—
63C2×#11758194D412yescomplemented
64C22×#92418—21no—
65#14519775—22no—
66#14519775—22no—
67#14519773—22no—
68#14519773—22no—
69#14519766—22no—
70#14519766—22no—
71#14519764—22no—
72#14519764—22no—
73#14519749—28no—
74#14519749—28no—
75C4×C22⋊D61—28no—
76C4×C22⋊D61—28no—
77C2×#11758196—22no—
78C2×C22⋊Dic61—22no—
79C2×#11758198—22no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61D412yes—
92C2×C4×Dic61D412yescomplemented
93#14519705—28no—
94#14519704—28no—
95#14519703—28no—
96#14519684—28no—
97C2×#41×C61—21no—
98C2×#41×C61—21no—
99C2×#41×C61—21no—
100C2×#41×C61—21no—
101C2×#41×C61—21no—
102C2×#41×C61—21no—
103C2×#41×C61—21no—
104C2×#41×C61—21no—
105C2×#41×C61—21no—
106C2×#41×C61—21no—
107C2×#41×C61D412yes—
108C2×#41×C61D412yes—
109C22×Q8×C61C2×C411yescharacteristic
110C22×D4×C61—21no—
111C22×D4×C61C2×C411yescharacteristic
112C23×C4×C61—21no—
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61—21no—
120C2×M16×C61D412yescomplemented
121C22×C8×C61—21no—
122C2×C42×C61—21no—
123C2×C42×C61—21no—
124C2×C42×C61—21no—
125C2×C42×C61—21no—
126C2×C42×C61—21no—
127C2×C42×C61D412yescomplemented
128#104×C61—28no—
129C24×C61—21no—
130C24×C61C2×D411yescharacteristic
131C23×D61—21no—
132#41×C61—22no—
133#41×C61—22no—
134#41×C61—22no—
135#41×C61—22no—
136#41×C61—22no—
137#41×C61—22no—
138#41×C61—22no—
139#41×C61—22no—
140#41×C61—41no—
141#41×C61—41no—
142#41×C61—41no—
143#41×C61—41no—
144#41×C61—41no—
145#41×C61—41no—
146#41×C61—41no—
147#41×C61—41no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61C22⋊C412yes—
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—41no—
162C2×D4×C61—41no—
163C2×D4×C61—41no—
164C2×D4×C61—41no—
165C2×D4×C61C22⋊C412yes—
166C22×C4×C61—24no—
167C22×C4×C61—21no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—42no—
172C22×C4×C61—41no—
173C22×C4×C61—41no—
174C22×C4×C61—41no—
175C22×C4×C61—41no—
176C22×C4×C61—41no—
177C22×C4×C61—41no—
178C22×C4×C61C22×C411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61#4111yescharacteristic
189C22×C4×C61#4111yescharacteristic
190C22×C4×C61#4111yescharacteristic
191C22×C4×C61#4111yescharacteristic
192C2×C22⋊D61—28no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61—22no—
195C2×C22⋊D61—44no—
196C2×C22⋊D61—41no—
197C2×C22⋊D61—41no—
198C2×C22⋊D61—41no—
199C2×C22⋊D61—41no—
200C2×C22⋊D61—44no—
201C22×Dic61—24no—
202C22×Dic61—21no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—24no—
207C22×Dic61—42no—
208C22×Dic61—42no—
209C22×Dic61—41no—
210C22×Dic61—41no—
211C22×Dic61C22⋊C412yes—
212C22×Dic61C22⋊C412yes—
213#11758222—22no—
214#11758222—22no—
215#11758222—22no—
216#11758222—22no—
217#11758222—22no—
218#11758222—22no—
219#11758222—22no—
220#11758222—22no—
221#11758222—41no—
222#11758222—41no—
223#11758222—41no—
224#11758222—41no—
225#11758222—41no—
226#11758222—41no—
227#11758222—41no—
228#11758222—41no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244C22⋊C412yes—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—41no—
238C2×C4×D61—41no—
239C2×C4×D61—41no—
240C2×C4×D61—41no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122C22⋊C412yes—
247M16×C61—22no—
248M16×C61—22no—
249M16×C61—41no—
250M16×C61—41no—
251C2×C8×C61—22no—
252C2×C8×C61—41no—
253C2×C8×C61—41no—
254C42×C61—22no—
255C42×C61—22no—
256C42×C61—41no—
257C42×C61—41no—
258C22⋊Dic61—28no—
259#11758198—28no—
260#11758196—28no—
261C4×Dic61—21no—
262C4×Dic61—21no—
263C4×Dic61—21no—
264C4×Dic61—21no—
265C4×Dic61—22no—
266C4×Dic61—22no—
267C4×Dic61—22no—
268C4×Dic61—22no—
269C4×Dic61—41no—
270C4×Dic61—41no—
271#11758194—22no—
272#11758194—22no—
273#11758194—41no—
274#11758194—41no—
275C2×#92418—22no—
276C2×#92418—41no—
277C2×#92418—41no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61C2×C22⋊C411yescharacteristic
286C23×C61#12011yescharacteristic
287C23×C61#12011yescharacteristic
288C23×C61#12111yescharacteristic
289C23×C61#12111yescharacteristic
290C23×C61#12411yescharacteristic
291C23×C61#12711yescharacteristic
292C22×D61—22no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—42no—
296C22×D61—42no—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—41no—
300Q8×C61—41no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—42no—
304D4×C61—42no—
305D4×C61—42no—
306D4×C61—42no—
307D4×C61—41no—
308D4×C61—41no—
309C2×C4×C61—24no—
310C2×C4×C61—22no—
311C2×C4×C61—42no—
312C2×C4×C61—44no—
313C2×C4×C61—44no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C4×D411yescharacteristic
324C2×C4×C61C4×D411yescharacteristic
325C2×C4×C61C4×D411yescharacteristic
326C2×C4×C61C4×D411yescharacteristic
327C2×C4×C61#12011yescharacteristic
328C2×C4×C61#12011yescharacteristic
329C2×C4×C61#12011yescharacteristic
330C2×C4×C61#12011yescharacteristic
331C2×C4×C61#12011yescharacteristic
332C2×C4×C61#12011yescharacteristic
333C2×C4×C61#12111yescharacteristic
334C2×C4×C61#12111yescharacteristic
335C2×C4×C61#12111yescharacteristic
336C2×C4×C61#12111yescharacteristic
337C2×C4×C61#12111yescharacteristic
338C2×C4×C61#12111yescharacteristic
339C2×C4×C61#12111yescharacteristic
340C2×C4×C61#12111yescharacteristic
341C2×C4×C61#12111yescharacteristic
342C2×C4×C61#12111yescharacteristic
343C2×C4×C61#12311yescharacteristic
344C2×C4×C61#12311yescharacteristic
345C2×C4×C61#12311yescharacteristic
346C2×C4×C61#12311yescharacteristic
347C2×C4×C61#12411yescharacteristic
348C2×C4×C61#12711yescharacteristic
349C22⋊D61—416no—
350C22⋊D61—42no—
351C22⋊D61—42no—
352C22⋊D61—42no—
353C22⋊D61—42no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—24no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—44no—
362C2×Dic61—44no—
363C2×Dic61—42no—
364C2×Dic61—44no—
365C2×Dic61—44no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—42no—
369C2×Dic61#10414yescomplemented
370D244—22no—
371D244—22no—
372D244—41no—
373D244—41no—
374C4×D61—42no—
375C4×D61—42no—
376C4×D61—42no—
377C4×D61—42no—
378Dic122—22no—
379Dic122—22no—
380Dic122—41no—
381Dic122—41no—
382C8×C61—42no—
383#92418—42no—
384#11011—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—42no—
394C22×C61—44no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—82no—
398C22×C61#37911yescharacteristic
399C22×C61#39011yescharacteristic
400C22×C61#39011yescharacteristic
401C22×C61#39211yescharacteristic
402C22×C61#39211yescharacteristic
403C22×C61#39411yescharacteristic
404C22×C61#39411yescharacteristic
405C22×C61C2×#10412yes—
406C22×C61#42112yes—
407C2×D61—42no—
408C2×D61—44no—
409C2×D61—81no—
410C2×D61—81no—
411C2×D61—82no—
412C4×C61—44no—
413C4×C61—42no—
414C4×C61#38611yescharacteristic
415C4×C61#38611yescharacteristic
416C4×C61#38611yescharacteristic
417C4×C61#38611yescharacteristic
418C4×C61#39211yescharacteristic
419C4×C61#39211yescharacteristic
420C4×C61#39411yescharacteristic
421C4×C61#39411yescharacteristic
422Dic61—24no—
423Dic61—44no—
424Dic61—42no—
425Dic61—42no—
426C2×#532—611no—
427C22×#104—611no—
428C22×#104—611no—
429C22×#104—611no—
430C22×#104D6111yescharacteristic, complemented
431#1728—611no—
432C4×#95—611no—
433C2×C61—21no—
434C2×C61—21no—
435C2×C61—21no—
436C2×C61—21no—
437C2×C61—82no—
438C2×C61#143811yescharacteristic
439C2×C61#178912yes—
440C2×C61#196211yescharacteristic
441C2×C61#196311yescharacteristic
442C2×C61#198012yes—
443D61—82no—
444C22×#41—611no—
445C22×#41C2×D6111yescharacteristic
446C22×M16—611no—
447C22×M16C2×D6111yescharacteristic
448#532—1222no—
449#532—1222no—
450#532—1222no—
451#532—1222no—
452C2×C4⋊Q8—611no—
453C2×#127—611no—
454C2×#124—611no—
455C2×#124—611no—
456C2×#121—1222no—
457C2×C4×D4—1222no—
458C22×C42—611no—
459C22×C42—611no—
460C22×C42C2×D6111yescharacteristic
461C2×#104—22no—
462C2×#104—22no—
463C2×#104—22no—
464C2×#104—1222no—
465C2×#104—1222no—
466C2×#104—1222no—
467C2×#104—1222no—
468C2×#104—1222no—
469C2×#104—1222no—
470C2×#104—1222no—
471C2×#104—1222no—
472C2×#104—1222no—
473C2×#95—1222no—
474#336—1222no—
475C61#1101111yescharacteristic, complemented, Sylow
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—612no—
487C2×#41—612no—
488C2×#41—1221no—
489C2×#41—1221no—
490C2×#41—1221no—
491C2×#41—1221no—
492C2×#41—1221no—
493C2×#41—1221no—
494C2×#41—1221no—
495C2×#41—1221no—
496C2×#41—1221no—
497C2×#41—1221no—
498C2×#41D24412yes—
499C2×#41C22⋊D6112yes—
500C22×Q8—611no—
501C22×Q8C4×D6111yescharacteristic
502C22×D4—21no—
503C22×D4—611no—
504C22×D4—1222no—
505C22×D4—1221no—
506C22×D4C4×D6111yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—612no—
510C23×C4—1221no—
511C23×C4—1221no—
512C23×C4C22×D6111yescharacteristic
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—612no—
519C2×M16—1221no—
520C2×M16—1221no—
521C2×M16—1221no—
522C2×M16—1221no—
523C2×M16—1221no—
524C2×M16C22⋊D6112yescomplemented
525C22×C8—21no—
526C22×C8—1221no—
527C4⋊Q8—1222no—
528C4⋊Q8—1222no—
529#127—1222no—
530#127—1222no—
531#124—1222no—
532#124—1222no—
533#124—1222no—
534#124—1222no—
535#121—1228no—
536#121—1228no—
537C4×D4—1228no—
538C4×D4—1228no—
539C2×C4⋊C4—1222no—
540C2×C22⋊C4—1222no—
541C2×C22⋊C4—1222no—
542C2×C42—21no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—21no—
546C2×C42—21no—
547C2×C42—611no—
548C2×C42—611no—
549C2×C42—612no—
550C2×C42—612no—
551C2×C42—1221no—
552C2×C42—1221no—
553C2×C42—1221no—
554C2×C42—1221no—
555C2×C42—1221no—
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42—1221no—
559C2×C42—1221no—
560C2×C42C22⋊D6112yescomplemented
561#104—28no—
562#104—1228no—
563#104—1228no—
564#104—1228no—
565#95—1228no—
566C24—21no—
567C24—1221no—
568C24D4×D6111yescharacteristic
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—41no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41—1222no—
586#41—1222no—
587#41—1222no—
588#41—1222no—
589#41—1222no—
590#41—1222no—
591#41—1222no—
592#41—1222no—
593#41—2441no—
594#41—2441no—
595#41—2441no—
596#41—2441no—
597#41—2441no—
598#41—2441no—
599#41—2441no—
600#41—2441no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—612no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8—1221no—
611C2×Q8—1221no—
612C2×Q8#1175819812yes—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—612no—
625C2×D4—1228no—
626C2×D4—1222no—
627C2×D4—1222no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—2444no—
634C2×D4—2444no—
635C2×D4—2441no—
636C2×D4—2441no—
637C2×D4—2441no—
638C2×D4—2441no—
639C2×D4#1175819812yes—
640C22×C4—24no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—42no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—612no—
653C22×C4—612no—
654C22×C4—1224no—
655C22×C4—1224no—
656C22×C4—1221no—
657C22×C4—1222no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1222no—
662C22×C4—2442no—
663C22×C4—2442no—
664C22×C4—2441no—
665C22×C4—2441no—
666C22×C4—2441no—
667C22×C4—2441no—
668C22×C4—2441no—
669C22×C4—2441no—
670C22×C4C2×C4×D6111yescharacteristic
671C22×C4C2×D24411yescharacteristic
672C22×C4#1175822211yescharacteristic
673C22×C4#1175822211yescharacteristic
674C22×C4D4×D6111yescharacteristic
675C22×C4D4×D6111yescharacteristic
676C22×C4D4×D6111yescharacteristic
677C22×C4D4×D6111yescharacteristic
678C22×C4D4×D6111yescharacteristic
679C22×C4#1175822411yescharacteristic
680C22×C4#1175822411yescharacteristic
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C2×C22⋊D6111yescharacteristic
683C22×C4C2×C22⋊D6111yescharacteristic
684M16—22no—
685M16—22no—
686M16—41no—
687M16—41no—
688M16—1222no—
689M16—1222no—
690M16—2441no—
691M16—2441no—
692C2×C8—22no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—1222no—
696C2×C8—2441no—
697C2×C8—2441no—
698C4⋊C4—1228no—
699C22⋊C4—1228no—
700C22⋊C4—1228no—
701C42—22no—
702C42—22no—
703C42—41no—
704C42—41no—
705C42—1221no—
706C42—1221no—
707C42—1221no—
708C42—1221no—
709C42—1222no—
710C42—1222no—
711C42—1222no—
712C42—1222no—
713C42—2441no—
714C42—2441no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—42no—
719C23—42no—
720C23—41no—
721C23—41no—
722C23—1222no—
723C23—2442no—
724C23—2442no—
725C23—2441no—
726C23—2441no—
727C23C22⋊C4×D6111yescharacteristic
728C23#1451974511yescharacteristic
729C23#1451974711yescharacteristic
730C23#1451974911yescharacteristic
731C23#1451975011yescharacteristic
732C23#1451976311yescharacteristic
733C23#1451977311yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—41no—
737Q8—41no—
738Q8—1222no—
739Q8—1222no—
740Q8—2441no—
741Q8—2441no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—42no—
746D4—42no—
747D4—42no—
748D4—41no—
749D4—41no—
750D4—1222no—
751D4—1222no—
752D4—24416no—
753D4—2442no—
754D4—2442no—
755D4—2442no—
756D4—2442no—
757D4—2441no—
758D4—2441no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—614no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1224no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—2444no—
780C2×C4—2444no—
781C2×C4—2444no—
782C2×C4—2444no—
783C2×C4—2442no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4—2442no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4C22⋊C4×D6111yescharacteristic
792C2×C4C2×#1175819811yescharacteristic
793C2×C4#1451973711yescharacteristic
794C2×C4#1451973711yescharacteristic
795C2×C4C4×C22⋊D6111yescharacteristic
796C2×C4C4×C22⋊D6111yescharacteristic
797C2×C4#1451974511yescharacteristic
798C2×C4#1451974511yescharacteristic
799C2×C4#1451974511yescharacteristic
800C2×C4#1451974611yescharacteristic
801C2×C4#1451974711yescharacteristic
802C2×C4#1451974711yescharacteristic
803C2×C4#1451974811yescharacteristic
804C2×C4#1451974811yescharacteristic
805C2×C4#1451974911yescharacteristic
806C2×C4#1451974911yescharacteristic
807C2×C4#1451974911yescharacteristic
808C2×C4#1451975011yescharacteristic
809C2×C4#1451975011yescharacteristic
810C2×C4#1451975011yescharacteristic
811C2×C4#1451975111yescharacteristic
812C2×C4#1451975111yescharacteristic
813C2×C4#1451975911yescharacteristic
814C2×C4#1451975911yescharacteristic
815C2×C4#1451976011yescharacteristic
816C2×C4#1451976111yescharacteristic
817C2×C4#1451976311yescharacteristic
818C2×C4#1451977311yescharacteristic
819C8—42no—
820C8—2442no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—44no—
830C22—42no—
831C22—82no—
832C22—81no—
833C22—81no—
834C22—4882no—
835C22—4881no—
836C22—4881no—
837C22—2444no—
838C22—2442no—
839C22#1683961711yescharacteristic
840C22#1683966211yescharacteristic
841C22#1683966211yescharacteristic
842C22#1683967011yescharacteristic
843C22#1683967111yescharacteristic
844C22#1683967711yescharacteristic
845C22#1683967811yescharacteristic
846C22#104×D6112yes—
847C22#1683977712yes—
848C4—44no—
849C4—42no—
850C4—1224no—
851C4—2444no—
852C4—2442no—
853C4—2442no—
854C4#1683963811yescharacteristic
855C4#1683963811yescharacteristic
856C4#1683963911yescharacteristic
857C4#1683964111yescharacteristic
858C4#1683967011yescharacteristic
859C4#1683967111yescharacteristic
860C4#1683967711yescharacteristic
861C4#1683967811yescharacteristic
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—82no—
867C2—4882no—
868C2#2144405811yescharacteristic
869C2#2144576112yes—
870C2#2144664511yescharacteristic
871C2#2144664911yescharacteristic
872C2#2144673612yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC22×#104×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840308C2
cosocleC23×C4×C61C23
hypercenterC22×#104D61
hypocenterC61#11011
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#14519705C2semidirect
3. C22×#14519704C2semidirect
4. C22×#14519703C2semidirect
5. #21445512C2semidirect
6. C4×#14519684C2semidirect
7. C22×#104×C61C2semidirect
14. C2×#14519775C4semidirect
15. C2×#14519773C4semidirect
16. C2×#14519766C4semidirect
17. C2×#14519764C4semidirect
63. C2×#11758194D4semidirect
92. C2×C4×Dic61D4semidirect
120. C2×M16×C61D4semidirect
127. C2×C42×C61D4semidirect
369. C2×Dic61#104semidirect
430. C22×#104D61semidirect
475. C61#11011semidirect
524. C2×M16C22⋊D61semidirect
560. C2×C42C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403082
C22×#145197052
C22×#145197042
C22×#145197032
#214455122
C4×#145196842
C22×#104×C612
#1101161