Finite Group Databasebeta

← C2×#21456671 #30550666

Subgroups — C2×#21456671 #30550666

Order 15616.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840340C211yesmaximal, characteristic, complemented
2#21456671C2116yesmaximal, direct product factor
3C2×#16840078C211yesmaximal, characteristic, complemented
4C2×#16840103C211yesmaximal, characteristic, complemented
5C2×#16840086C211yesmaximal, characteristic, complemented
6C2×#16840073C211yesmaximal, characteristic, complemented
7C2×#16840013C211yesmaximal, characteristic, complemented
8C2×#16840006C211yesmaximal, characteristic, complemented
9C2×#16839996C211yesmaximal, characteristic, complemented
10C2×#16839989C211yesmaximal, characteristic, complemented
11C2×#16839905C211yesmaximal, characteristic, complemented
12C2×#16839905C211yesmaximal, characteristic, complemented
13C2×#16839913C211yesmaximal, characteristic, complemented
14C2×#16839896C211yesmaximal, characteristic, complemented
15C2×#16839729C211yesmaximal, characteristic, complemented
16C2×C61×#535C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic, complemented
18C22×#11758200C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C22×#11758194C2211yescharacteristic, complemented
23C23×#92418C2211yescharacteristic, complemented
24#16840340—24no—
25#16840340C2218yescomplemented
26C2×#14519756C2211yescharacteristic
27C2×#14519756C2211yescharacteristic, complemented
28C2×#14519753—21no—
29C2×#14519751C2211yescharacteristic
30C2×#14519751C2211yescharacteristic, complemented
31C2×#14519749—21no—
32C2×#14519749—21no—
33C2×#14519748—21no—
34C22×C4⋊Dic61C2211yescharacteristic, complemented
35#16840103C2218yescomplemented
36#16840086C2218yescomplemented
37#16840078C2218yescomplemented
38#16840073C2218yescomplemented
39#16840013C2218yescomplemented
40#16840006C2218yescomplemented
41#16839996C2218yescomplemented
42#16839989C2218yescomplemented
43#16839913C2218yescomplemented
44#16839905C2218yescomplemented
45#16839905C2218yescomplemented
46#16839896C2218yescomplemented
47C2×#14519710C2211yescharacteristic, complemented
48C2×#14519710C2211yescharacteristic, complemented
49C2×#14519708C2211yescharacteristic, complemented
50C2×#14519708C2211yescharacteristic, complemented
51C2×#14519700C2211yescharacteristic, complemented
52C2×#14519700C2211yescharacteristic, complemented
53C2×#14519698C2211yescharacteristic
54C2×#14519698C2211yescharacteristic
55C2×#14519698C2211yescharacteristic
56C2×#14519698C2211yescharacteristic
57C2×#14519697C2211yescharacteristic, complemented
58C2×#14519697C2211yescharacteristic, complemented
59#16839729C2218yescomplemented
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic, complemented
63C2×C22⋊#92418C2211yescharacteristic, complemented
64C22×#41×C61C2211yescharacteristic
65C23×D4×C61C2211yescharacteristic
66C61×#535—24no—
67C61×#535C2218yescomplemented
68C2×#127×C61—21no—
69C2×#124×C61—21no—
70C2×#121×C61C2211yescharacteristic
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C2×#121×C61C2211yescharacteristic
74C2×#120×C61—21no—
75C2×#120×C61—21no—
76C2×#117×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222C2314yescomplemented
81C22×Dic122C2311yescharacteristic
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C2×#11758200—42no—
89C2×#11758200—42no—
90C2×#11758200C2314yes—
91C2×#11758200C2314yes—
92C2×#11758199—42no—
93C2×#11758199—42no—
94C2×#11758199C2314yes—
95C2×#11758199C2314yes—
96C2×#11758194—42no—
97C2×#11758194C2314yescomplemented
98C22×#92418—42no—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C22×#92418C2314yescomplemented
104#14519756—22no—
105#14519756—22no—
106#14519756C2314yes—
107#14519756C2314yescomplemented
108#14519753—28no—
109#14519751—22no—
110#14519751—22no—
111#14519751C2314yes—
112#14519751C2314yescomplemented
113#14519749—28no—
114#14519749—28no—
115#14519748—28no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—22no—
118C2×C4⋊Dic61C2311yescharacteristic
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2314yescomplemented
121C2×#11758196—21no—
122C2×#11758196—21no—
123C2×C22⋊Dic61—21no—
124C2×C22⋊Dic61—21no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127#14519710C2314yescomplemented
128#14519710C2314yescomplemented
129#14519708C2314yescomplemented
130#14519708C2314yescomplemented
131#14519700C2314yescomplemented
132#14519700C2314yescomplemented
133#14519698C2314yes—
134#14519698C2314yes—
135#14519698C2314yes—
136#14519698C2314yes—
137#14519697C2314yescomplemented
138#14519697C2314yescomplemented
139C22⋊#92418C2314yes—
140C22⋊#92418C2314yes—
141C22⋊#92418C2314yescomplemented
142C22⋊#92418C2314yescomplemented
143C25×C61—21no—
144C2×#41×C61—42no—
145C2×#41×C61—42no—
146C2×#41×C61D414yes—
147C2×#41×C61C2314yes—
148C22×Q8×C61D411yescharacteristic
149C22×D4×C61—21no—
150C22×D4×C61—21no—
151C22×D4×C61—21no—
152C22×D4×C61—21no—
153C22×D4×C61—21no—
154C22×D4×C61—22no—
155C22×D4×C61—42no—
156C22×D4×C61—42no—
157C22×D4×C61D411yescharacteristic
158C22×D4×C61D411yescharacteristic
159C22×D4×C61D411yescharacteristic
160C22×D4×C61C2311yescharacteristic
161C22×D4×C61C2311yescharacteristic
162C22×D4×C61C2314yes—
163C23×C4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166#127×C61—28no—
167#124×C61—28no—
168#121×C61—22no—
169#121×C61—22no—
170#121×C61—22no—
171#121×C61—22no—
172#121×C61C2314yes—
173#121×C61C2314yes—
174#121×C61C2314yes—
175#121×C61C2314yes—
176#120×C61—28no—
177#120×C61—28no—
178#117×C61—22no—
179#117×C61C2314yes—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C4⋊C4×C61C2311yescharacteristic
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61—21no—
184C2×C22⋊C4×C61—21no—
185C2×C22⋊C4×C61—21no—
186C2×C22⋊C4×C61—21no—
187C2×C42×C61—21no—
188C24×C61—21no—
189C24×C61—21no—
190C24×C61—24no—
191C24×C61—44no—
192C24×C61—82no—
193C24×C61—82no—
194C24×C61C2×D411yescharacteristic
195C24×C61C2×D411yescharacteristic
196C24×C61C2×D411yescharacteristic
197C23×D61—21no—
198#41×C61—48no—
199#41×C61—44no—
200#41×C61—44no—
201C2×Q8×C61—42no—
202C2×Q8×C61C2×D414yes—
203C2×D4×C61—24no—
204C2×D4×C61—24no—
205C2×D4×C61—24no—
206C2×D4×C61—24no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—24no—
210C2×D4×C61—22no—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61—22no—
214C2×D4×C61—44no—
215C2×D4×C61—44no—
216C2×D4×C61—42no—
217C2×D4×C61—42no—
218C2×D4×C61—42no—
219C2×D4×C61—44no—
220C2×D4×C61—48no—
221C2×D4×C61—82no—
222C2×D4×C61—82no—
223C2×D4×C61—82no—
224C2×D4×C61—82no—
225C2×D4×C61C2×D414yes—
226C2×D4×C61C2×D414yes—
227C2×D4×C61C2×D414yes—
228C2×D4×C61C2412yes—
229C2×D4×C61C2412yes—
230C22×C4×C61—22no—
231C22×C4×C61—22no—
232C22×C4×C61—22no—
233C22×C4×C61—22no—
234C22×C4×C61—22no—
235C22×C4×C61—22no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2412yes—
245C22×C4×C61C2412yes—
246C22×C4×C61C2412yes—
247C22×C4×C61C2411yescharacteristic
248C2×C22⋊D61—24no—
249C2×C22⋊D61—24no—
250C2×C22⋊D61—24no—
251C2×C22⋊D61—44no—
252C2×C22⋊D61—82no—
253C2×C22⋊D61—82no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—24no—
258C22×Dic61—82no—
259#11758222—44no—
260#11758222—44no—
261#11758222—48no—
262C2×D244—22no—
263C2×D244—22no—
264C2×D244—21no—
265C2×D244C2412yes—
266C2×C4×D61—24no—
267C2×C4×D61—44no—
268C2×Dic122—22no—
269C2×Dic122—22no—
270C2×Dic122—21no—
271C2×Dic122C2412yes—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61C2412yes—
275C4⋊C4×C61C2412yes—
276C22⋊C4×C61—24no—
277C22⋊C4×C61—24no—
278C22⋊C4×C61—24no—
279C22⋊C4×C61—24no—
280C22⋊C4×C61—24no—
281C42×C61—24no—
282C22⋊Dic61—24no—
283C22⋊Dic61—24no—
284#11758200—44no—
285#11758200—44no—
286#11758199—44no—
287#11758199—44no—
288#11758198—24no—
289#11758198—24no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—24no—
293C4⋊Dic61C2412yes—
294C4⋊Dic61C2412yes—
295#11758196—24no—
296#11758196—24no—
297#11758194—44no—
298C2×#92418—22no—
299C2×#92418—22no—
300C2×#92418—22no—
301C2×#92418—22no—
302C2×#92418—44no—
303C2×#92418C2412yes—
304C2×#92418C2412yes—
305C2×#92418C2412yes—
306C2×#92418C2412yes—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—48no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—42no—
322C23×C61—42no—
323C23×C61—42no—
324C23×C61—42no—
325C23×C61—84no—
326C23×C61—84no—
327C23×C61—816no—
328C23×C61C22×D412yes—
329C23×C61C22×D412yes—
330C23×C61C22×D412yes—
331C23×C61C22×D411yescharacteristic
332C22×D61—22no—
333C22×D61—42no—
334C22×D61—42no—
335C22×D61—42no—
336Q8×C61—44no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—44no—
342D4×C61—44no—
343D4×C61—44no—
344D4×C61—48no—
345D4×C61—42no—
346D4×C61—42no—
347D4×C61—84no—
348D4×C61—84no—
349D4×C61—84no—
350D4×C61—84no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—24no—
355C2×C4×C61—24no—
356C2×C4×C61—24no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—42no—
366C2×C4×C61—42no—
367C2×C4×C61C22×D412yes—
368C2×C4×C61C22×D412yes—
369C2×C4×C61C22×D412yes—
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61H(5,𝔽2)12yes—
372C2×C4×C61H(5,𝔽2)12yes—
373C2×C4×C61C2511yescharacteristic
374C22⋊D61—48no—
375C22⋊D61—84no—
376C22⋊D61—84no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—42no—
381C2×Dic61—42no—
382C2×Dic61—42no—
383C2×Dic61—84no—
384D244—22no—
385D244—22no—
386D244—42no—
387C4×D61—48no—
388Dic122—22no—
389Dic122—22no—
390Dic122—42no—
391#92418—22no—
392#92418—22no—
393#92418—22no—
394#92418—22no—
395C2×#3198—611nomaximal, Sylow
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—44no—
406C22×C61—44no—
407C22×C61—44no—
408C22×C61—42no—
409C22×C61—42no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—816no—
415C22×C61—84no—
416C22×C61—84no—
417C22×C61#53412yes—
418C22×C61#57612yes—
419C22×C61#57712yes—
420C22×C61C23×D411yescharacteristic
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—22no—
427C4×C61—22no—
428C4×C61—42no—
429C4×C61—42no—
430C4×C61#53412yes—
431C4×C61C2×H(5,𝔽2)11yescharacteristic
432C4×C61C2×H(5,𝔽2)11yescharacteristic
433Dic61—42no—
434Dic61—42no—
435Dic61—42no—
436C2×#537—611no—
437C2×#535D6111yescharacteristic, complemented
438#3198—6116no—
439C2×#481—611no—
440C2×#485—611no—
441C2×#482—611no—
442C2×#480—611no—
443C2×#469—611no—
444C2×#468—611no—
445C2×#466—611no—
446C2×#465—611no—
447C2×#449—611no—
448C2×#449—611no—
449C2×#450—611no—
450C2×#447—611no—
451C2×#408—611no—
452C2×C61—42no—
453C2×C61—42no—
454C2×C61—42no—
455C2×C61—82no—
456C2×C61—82no—
457C2×C61#319814yescomplemented
458C2×C61C2×#53411yescharacteristic
459C2×C61C2×#57611yescharacteristic
460C2×C61C2×#57711yescharacteristic
461D61—82no—
462C22×#41—611no—
463C22×#41C2×D6111yescharacteristic
464C23×D4C2×D6111yescharacteristic
465C22×SD16—611no—
466C22×SD16—611no—
467C22×D8—611no—
468C22×D8—611no—
469C22×M16—611no—
470C23×C8—611no—
471#537—618no—
472#537—1224no—
473#535—24no—
474#535C2×D6118yescomplemented
475C2×#127—21no—
476C2×#124—21no—
477C2×C22⋊Q8—611no—
478C2×C22⋊Q8—611no—
479C2×C22⋊Q8—1221no—
480C2×#121—611no—
481C2×#121—611no—
482C2×#121—1221no—
483C2×#121—1221no—
484C2×#121—1221no—
485C2×#121C2×D6111yescharacteristic
486C2×#121C2×D6111yescharacteristic
487C2×#121C2×D6111yescharacteristic
488C2×#121C2×D6111yescharacteristic
489C2×#120—21no—
490C2×#120—21no—
491C2×#117C2×D6111yescharacteristic
492C22×C4⋊C4—611no—
493#485—618no—
494#482—618no—
495#481—618no—
496#480—618no—
497#469—618no—
498#468—618no—
499#466—618no—
500#465—618no—
501#450—618no—
502#449—618no—
503#449—618no—
504#447—618no—
505C2×#107—611no—
506C2×#107—611no—
507C2×#106—611no—
508C2×#106—611no—
509C2×#103—611no—
510C2×#103—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102—611no—
515C2×#102—611no—
516C2×#102—611no—
517#408—618no—
518C2×C22⋊C8—611no—
519C2×C22⋊C8—611no—
520C2×C22⋊C8—611no—
521C2×C22⋊C8—611no—
522C61C2×#319811yescharacteristic, complemented, Sylow
523C25—21no—
524C2×#41—42no—
525C2×#41—42no—
526C2×#41—614no—
527C2×#41—1222no—
528C2×#41—2442no—
529C2×#41—2442no—
530C2×#41C22⋊D6114yes—
531C2×#41C22×D6114yes—
532C22×Q8—611no—
533C22×Q8C22⋊D6111yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—22no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4—611no—
543C22×D4—1221no—
544C22×D4—1221no—
545C22×D4—1221no—
546C22×D4C22⋊D6111yescharacteristic
547C22×D4C22⋊D6111yescharacteristic
548C22×D4C22⋊D6111yescharacteristic
549C22×D4C22×D6111yescharacteristic
550C22×D4C22×D6111yescharacteristic
551C22×D4C22×D6114yes—
552C23×C4—1221no—
553C23×C4—1221no—
554C23×C4C22×D6111yescharacteristic
555C23×C4C22×D6111yescharacteristic
556C23×C4C22×D6111yescharacteristic
557C2×SD16—614no—
558C2×SD16—614no—
559C2×SD16—2442no—
560C2×SD16—2442no—
561C2×D8—614no—
562C2×D8—614no—
563C2×D8—2442no—
564C2×D8—2442no—
565C2×M16—614no—
566C2×M16—2442no—
567C22×C8—611no—
568C22×C8—611no—
569C22×C8—611no—
570C22×C8—611no—
571C22×C8—614no—
572C22×C8—2442no—
573#127—28no—
574#124—28no—
575C22⋊Q8—614no—
576C22⋊Q8—614no—
577C22⋊Q8—1228no—
578C22⋊Q8—1222no—
579C22⋊Q8—1222no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—614no—
585#121—614no—
586#121—1228no—
587#121—1228no—
588#121—1228no—
589#121—1222no—
590#121—1222no—
591#121C22×D6114yes—
592#121C22×D6114yes—
593#121C22×D6114yes—
594#121C22×D6114yes—
595#120—28no—
596#120—28no—
597#117—22no—
598#117C22×D6114yes—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—614no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4C22×D6111yescharacteristic
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C42—21no—
618#107—614no—
619#107—614no—
620#106—614no—
621#106—614no—
622#103—614no—
623#103—614no—
624#102—614no—
625#102—614no—
626#102—614no—
627#102—614no—
628#102—614no—
629#102—614no—
630C22⋊C8—614no—
631C22⋊C8—614no—
632C22⋊C8—614no—
633C22⋊C8—614no—
634C24—21no—
635C24—21no—
636C24—24no—
637C24—44no—
638C24—82no—
639C24—82no—
640C24—1221no—
641C24C2×C22⋊D6111yescharacteristic
642C24C2×C22⋊D6111yescharacteristic
643C24C2×C22⋊D6111yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—2444no—
648#41—2444no—
649#41—2448no—
650C2×Q8—42no—
651C2×Q8—612no—
652C2×Q8—1221no—
653C2×Q8—1222no—
654C2×Q8—1222no—
655C2×Q8C2×C22⋊D6114yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—24no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—44no—
673C2×D4—48no—
674C2×D4—82no—
675C2×D4—82no—
676C2×D4—82no—
677C2×D4—82no—
678C2×D4—612no—
679C2×D4—1224no—
680C2×D4—1224no—
681C2×D4—1224no—
682C2×D4—1221no—
683C2×D4—1222no—
684C2×D4—1222no—
685C2×D4—4882no—
686C2×D4—4882no—
687C2×D4—2444no—
688C2×D4C2×C22⋊D6114yes—
689C2×D4C2×C22⋊D6114yes—
690C2×D4C2×C22⋊D6114yes—
691C2×D4C23×D6112yes—
692C2×D4C23×D6112yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—1224no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1224no—
706C22×C4—4882no—
707C22×C4—2444no—
708C22×C4C2×C22⋊D6112yes—
709C22×C4C2×C22⋊D6112yes—
710C22×C4C2×C22⋊D6112yes—
711C22×C4C2×C22⋊D6111yescharacteristic
712C22×C4C2×C22⋊D6111yescharacteristic
713C22×C4C2×C22⋊D6111yescharacteristic
714C22×C4C23×D6112yes—
715C22×C4C23×D6112yes—
716C22×C4C23×D6112yes—
717C22×C4C23×D6111yescharacteristic
718SD16—2444no—
719SD16—2444no—
720D8—2444no—
721D8—2444no—
722M16—2444no—
723C2×C8—612no—
724C2×C8—612no—
725C2×C8—612no—
726C2×C8—612no—
727C2×C8—1222no—
728C2×C8—1222no—
729C2×C8—1222no—
730C2×C8—1222no—
731C2×C8—2444no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—612no—
735C4⋊C4—612no—
736C4⋊C4—1224no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1224no—
740C4⋊C4—1224no—
741C4⋊C4C23×D6112yes—
742C4⋊C4C23×D6112yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4—1224no—
752C42—24no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—48no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—84no—
772C23—84no—
773C23—816no—
774C23—1222no—
775C23—2442no—
776C23—2442no—
777C23—2442no—
778C23C22×C22⋊D6112yes—
779C23C22×C22⋊D6112yes—
780C23C22×C22⋊D6112yes—
781C23C22×C22⋊D6111yescharacteristic
782Q8—44no—
783Q8—1222no—
784Q8—1222no—
785Q8—2442no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—44no—
792D4—44no—
793D4—48no—
794D4—42no—
795D4—42no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800D4—1222no—
801D4—1222no—
802D4—4884no—
803D4—4884no—
804D4—2448no—
805D4—2442no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—4884no—
826C2×C4—2448no—
827C2×C4—2442no—
828C2×C4—2442no—
829C2×C4—2442no—
830C2×C4C22×C22⋊D6112yes—
831C2×C4C22×C22⋊D6112yes—
832C2×C4C22×C22⋊D6112yes—
833C2×C4C22×C22⋊D6111yescharacteristic
834C2×C4#1451982212yes—
835C2×C4#1451982212yes—
836C2×C4C24×D6111yescharacteristic
837C8—1222no—
838C8—1222no—
839C8—1222no—
840C8—1222no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—816no—
860C22—84no—
861C22—84no—
862C22—4884no—
863C22—2442no—
864C22—2442no—
865C22—2442no—
866C22#1684032112yes—
867C22#1684056512yes—
868C22#1684057312yes—
869C22C23×C22⋊D6111yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—2442no—
876C4—2442no—
877C4—2442no—
878C4#1684032112yes—
879C4C2×#1451982211yescharacteristic
880C4C2×#1451982211yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—82no—
886C2—4882no—
887C2#2145667114yesdirect product factor
888C2C2×#1684032111yescharacteristic
889C2C2×#1684056511yescharacteristic
890C2C2×#1684057311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#535C2
socleC23×C61C22×D4
hypercenterC2×#535D61
hypocenterC61C2×#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#16840340C2semidirect
2. #21456671C2direct (N × H)
3. C2×#16840078C2semidirect
4. C2×#16840103C2semidirect
5. C2×#16840086C2semidirect
6. C2×#16840073C2semidirect
7. C2×#16840013C2semidirect
8. C2×#16840006C2semidirect
9. C2×#16839996C2semidirect
10. C2×#16839989C2semidirect
11. C2×#16839905C2semidirect
12. C2×#16839905C2semidirect
13. C2×#16839913C2semidirect
14. C2×#16839896C2semidirect
15. C2×#16839729C2semidirect
16. C2×C61×#535C2semidirect
17. C22×#11758222C22semidirect
22. C22×#11758194C22semidirect
23. C23×#92418C22semidirect
25. #16840340C22semidirect
27. C2×#14519756C22semidirect
30. C2×#14519751C22semidirect
34. C22×C4⋊Dic61C22semidirect
35. #16840103C22semidirect
36. #16840086C22semidirect
37. #16840078C22semidirect
38. #16840073C22semidirect
39. #16840013C22semidirect
40. #16840006C22semidirect
41. #16839996C22semidirect
42. #16839989C22semidirect
43. #16839913C22semidirect
44. #16839905C22semidirect
45. #16839905C22semidirect
46. #16839896C22semidirect
47. C2×#14519710C22semidirect
48. C2×#14519710C22semidirect
49. C2×#14519708C22semidirect
50. C2×#14519708C22semidirect
51. C2×#14519700C22semidirect
52. C2×#14519700C22semidirect
57. C2×#14519697C22semidirect
58. C2×#14519697C22semidirect
59. #16839729C22semidirect
62. C2×C22⋊#92418C22semidirect
63. C2×C22⋊#92418C22semidirect
67. C61×#535C22semidirect
80. C2×#11758222C23semidirect
97. C2×#11758194C23semidirect
103. C22×#92418C23semidirect
107. #14519756C23semidirect
112. #14519751C23semidirect
120. C2×C4⋊Dic61C23semidirect
127. #14519710C23semidirect
128. #14519710C23semidirect
129. #14519708C23semidirect
130. #14519708C23semidirect
131. #14519700C23semidirect
132. #14519700C23semidirect
137. #14519697C23semidirect
138. #14519697C23semidirect
141. C22⋊#92418C23semidirect
142. C22⋊#92418C23semidirect
437. C2×#535D61semidirect
457. C2×C61#3198semidirect
474. #535C2×D61semidirect
522. C61C2×#3198semidirect
887. C2#21456671direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403402
#214566712
C2×#168400782
C2×#168401032
C2×#168400862
C2×#168400732
C2×#168400132
C2×#168400062
C2×#168399962
C2×#168399892
C2×#168399052
C2×#168399132
C2×#168398962
C2×#168397292
C2×C61×#5352
C2×#319861