Finite Group Databasebeta

← C2×#21457952 #30556738

Subgroups — C2×#21457952 #30556738

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840453C211yesmaximal, characteristic, complemented
2C2×#16840432C211yesmaximal, characteristic
3#21457952C2116yesmaximal, direct product factor
4C2×#16840126C211yesmaximal, characteristic, complemented
5C2×#16840079C211yesmaximal, characteristic, complemented
6C2×#16840084C211yesmaximal, characteristic, complemented
7C2×#16840070C211yesmaximal, characteristic, complemented
8C2×#16840005C211yesmaximal, characteristic, complemented
9C2×#16839988C211yesmaximal, characteristic, complemented
10C2×#16839921C211yesmaximal, characteristic, complemented
11C2×#16839921C211yesmaximal, characteristic, complemented
12C2×#16839867C211yesmaximal, characteristic, complemented
13C2×#16839832C211yesmaximal, characteristic, complemented
14C2×#16839760C211yesmaximal, characteristic, complemented
15C2×#16839755C211yesmaximal, characteristic, complemented
16C2×C61×#460C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758189C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840453—24no—
23#16840453C2218yescomplemented
24#16840432—24no—
25#16840432C2218yes—
26C2×#14519773—21no—
27C2×#14519771—21no—
28C2×#14519769C2211yescharacteristic
29C2×#14519767—21no—
30C2×#14519762—21no—
31C2×#14519753C2211yescharacteristic
32C2×#14519753C2211yescharacteristic
33C2×#14519749—21no—
34C2×#14519749—21no—
35C2×#14519748C2211yescharacteristic
36C2×#14519748C2211yescharacteristic
37C2×C4×Dic122C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C2×D4×Dic61—21no—
40C2×#14519735C2211yescharacteristic
41C2×#14519734—21no—
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840126C2218yescomplemented
44#16840084C2218yescomplemented
45#16840079C2218yescomplemented
46#16840070C2218yescomplemented
47#16840005C2218yescomplemented
48#16839988C2218yescomplemented
49#16839921C2218yescomplemented
50#16839921C2218yescomplemented
51#16839867C2218yescomplemented
52#16839832C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519709C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56#16839760C2218yescomplemented
57#16839755C2218yescomplemented
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#127×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#460C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—22no—
78C2×#11758224—22no—
79C2×#11758224—24no—
80C2×#11758224—24no—
81C2×#11758224—42no—
82C2×#11758224—42no—
83C2×#11758224C2314yes—
84C2×#11758224C2314yes—
85C22×Dic122C2311yescharacteristic
86C22×D244D411yescharacteristic
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C23×Dic61—21no—
92C23×Dic61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C2×#11758202—24no—
97C2×#11758202C2314yes—
98C2×#11758189—42no—
99C2×#11758189C2314yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C2×C8×D61—42no—
103C2×C8×D61C2314yes—
104#14519773—28no—
105#14519771—28no—
106#14519769—22no—
107#14519769C2314yes—
108#14519767—28no—
109#14519762—28no—
110#14519753—22no—
111#14519753—22no—
112#14519753C2314yes—
113#14519753C2314yes—
114#14519749—28no—
115#14519749—28no—
116#14519748—22no—
117#14519748—22no—
118#14519748C2314yes—
119#14519748C2314yes—
120C4×Dic122—22no—
121C4×Dic122C2314yes—
122C4×D244D414yes—
123C4×D244C2314yes—
124D4×Dic61—28no—
125#14519735—22no—
126#14519735C2314yes—
127#14519734—28no—
128C2×C4⋊Dic61D411yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C4⋊C4×D61—22no—
139C4⋊C4×D61C2314yes—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198D411yescharacteristic
146C2×#11758198D411yescharacteristic
147C2×C4×Dic61—21no—
148C2×C4×Dic61—21no—
149#14519711C2314yes—
150#14519709C2314yes—
151#14519708C2314yes—
152#14519702C2314yes—
153#14519702C2314yes—
154#14519701C2314yes—
155#14519700C2314yes—
156#14519698C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160#14519689C2314yes—
161#14519689C2314yes—
162#14519688C2314yes—
163C22×Q8×C61C2311yescharacteristic
164C22×D4×C61—21no—
165C22×D4×C61—21no—
166C22×D4×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C2×SD16×C61—42no—
169C2×SD16×C61—42no—
170C2×SD16×C61C2314yes—
171C2×SD16×C61C2314yes—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174#127×C61—22no—
175#127×C61C2314yes—
176C4×Q8×C61—22no—
177C4×Q8×C61C2314yes—
178C2×C4⋊C4×C61—21no—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C42×C61—21no—
181C2×C42×C61C2311yescharacteristic
182C4⋊C8×C61C2314yes—
183#102×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C24×C61—21no—
187C23×D61C2×D411yescharacteristic
188C23×D61C2×D411yescharacteristic
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61C2412yes—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—24no—
196C2×D4×C61—24no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—44no—
202C2×D4×C61—82no—
203C2×D4×C61C2412yes—
204C2×D4×C61C2412yes—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2411yescharacteristic
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—24no—
214C2×C22⋊D61—44no—
215C2×C22⋊D61—44no—
216C2×C22⋊D61—82no—
217C2×C22⋊D61—82no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—24no—
223C22×Dic61—24no—
224C22×Dic61—44no—
225C22×Dic61—44no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228#11758224—28no—
229#11758224—28no—
230#11758224—44no—
231#11758224—44no—
232#11758224—48no—
233#11758224—48no—
234C2×D244—42no—
235C2×D244C2×D414yes—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—24no—
241C2×C4×D61—44no—
242C2×C4×D61C2×D412yes—
243C2×C4×D61C2×D412yes—
244C2×C4×D61C2412yes—
245C2×C4×D61C2412yes—
246C2×Dic122—21no—
247C2×Dic122—22no—
248C2×Dic122#4114yes—
249C2×Dic122C2412yes—
250SD16×C61—44no—
251SD16×C61—44no—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61C2412yes—
255C2×C8×C61C2412yes—
256C4⋊C4×C61—24no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C2412yes—
259C42×C61—24no—
260C42×C61C2×D412yes—
261C42×C61C2412yes—
262C22⋊Dic61—24no—
263C22⋊Dic61—24no—
264#11758202—28no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198C2×D414yes—
269#11758198C2×D414yes—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61C2×D414yes—
274C4⋊Dic61C2412yes—
275C4⋊Dic61C2412yes—
276C4⋊Dic61C2412yes—
277#11758196—24no—
278#11758196—24no—
279#11758196—24no—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283C4×Dic61—24no—
284C4×Dic61—24no—
285C2×#92418—22no—
286C2×#92418—22no—
287C2×#92418C2412yes—
288C2×#92418C2412yes—
289#11758189—44no—
290C8×D61—44no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61C22×D411yescharacteristic
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61C22×D412yes—
307C22×D61C22×D412yes—
308Q8×C61—22no—
309Q8×C61—22no—
310Q8×C61—42no—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—48no—
316D4×C61—42no—
317D4×C61—42no—
318D4×C61—84no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61C22×D412yes—
326C2×C4×C61C22×D412yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C2×#4112yes—
329C2×C4×C61H(5,𝔽2)12yes—
330C2×C4×C61C2511yescharacteristic
331C22⋊D61—48no—
332C22⋊D61—48no—
333C22⋊D61—84no—
334C22⋊D61—84no—
335C2×Dic61—24no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—48no—
343C2×Dic61—48no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61C22×D412yes—
348C2×Dic61C22×D412yes—
349D244—44no—
350C4×D61—24no—
351C4×D61—24no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—48no—
357Dic122—24no—
358Dic122—22no—
359Dic122C2×#4114yes—
360C8×C61—22no—
361C8×C61—22no—
362#92418—22no—
363#92418—22no—
364C2×#3317—611nomaximal, Sylow
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—84no—
372C22×C61—84no—
373C22×C61#54612yes—
374C22×C61#57512yes—
375C22×C61#57712yes—
376C22×C61C23×D411yescharacteristic
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—44no—
384C2×D61—44no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61#54612yes—
390C4×C61C22×#4111yescharacteristic
391C4×C61C2×H(5,𝔽2)11yescharacteristic
392Dic61—24no—
393Dic61—22no—
394Dic61—22no—
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#552—611no—
399C2×#550—611no—
400#3317—6116no—
401C2×#490—611no—
402C2×#481—611no—
403C2×#482—611no—
404C2×#479—611no—
405C2×#468—611no—
406C2×#465—611no—
407C2×#460D6111yescharacteristic, complemented
408C2×#452—611no—
409C2×#452—611no—
410C2×#441—611no—
411C2×#435—611no—
412C2×#417—611no—
413C2×#416—611no—
414C2×C61—82no—
415C2×C61—82no—
416C2×C61#331714yescomplemented
417C2×C61C2×#54611yescharacteristic
418C2×C61C2×#57511yescharacteristic
419C2×C61C2×#57711yescharacteristic
420D61—42no—
421D61—42no—
422C22×#41—611no—
423C22×#41—611no—
424C22×Q16—611no—
425C22×SD16C2×D6111yescharacteristic
426C22×SD16C2×D6111yescharacteristic
427C22×M16—611no—
428C23×C8—611no—
429#552—618no—
430#552—1224no—
431#550—618no—
432#550—1224no—
433C2×#127—1221no—
434C2×#127C2×D6111yescharacteristic
435C2×#126—1221no—
436C2×#125—611no—
437C2×#125—1221no—
438C2×#123—1221no—
439C2×C22⋊Q8—611no—
440C2×C22⋊Q8—611no—
441C2×#121—611no—
442C2×#121—611no—
443C2×#121—1221no—
444C2×#121—1221no—
445C2×C4×Q8—611no—
446C2×C4×Q8C2×D6111yescharacteristic
447C2×C4×D4—611no—
448C2×C4×D4—1221no—
449C2×#117—611no—
450C2×#117—1221no—
451C22×C4⋊C4—611no—
452#490—618no—
453#482—618no—
454#481—618no—
455#479—618no—
456#468—618no—
457#465—618no—
458#460C2×D6118yescomplemented
459#452—618no—
460#452—618no—
461#441—618no—
462#435—618no—
463C2×#107—611no—
464C2×#106—611no—
465C2×#106—611no—
466C2×C4⋊C8C2×D6111yescharacteristic
467#417—618no—
468#416—618no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102C2×D6111yescharacteristic
478C2×#102C2×D6111yescharacteristic
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×#97—611no—
482C61C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—614no—
484C2×#41—614no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1224no—
488C2×#41—1224no—
489C2×#41—2442no—
490C2×#41—2442no—
491C22×Q8—611no—
492C22×Q8C22×D6111yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—611no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4C22×D6111yescharacteristic
501C22×D4C22×D6111yescharacteristic
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4—1221no—
507C2×Q16—614no—
508C2×Q16—1224no—
509C2×SD16—42no—
510C2×SD16—42no—
511C2×SD16C22×D6114yes—
512C2×SD16C22×D6114yes—
513C2×M16—614no—
514C2×M16—2442no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—614no—
518C22×C8—2442no—
519C22×C8C22×D6111yescharacteristic
520C22×C8C22×D6111yescharacteristic
521#127—22no—
522#127—1228no—
523#127C22×D6114yes—
524#126—1228no—
525#125—614no—
526#125—1228no—
527#125—1222no—
528#123—1228no—
529C22⋊Q8—614no—
530C22⋊Q8—614no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533#121—614no—
534#121—614no—
535#121—1228no—
536#121—1228no—
537#121—1222no—
538#121—1222no—
539C4×Q8—22no—
540C4×Q8—614no—
541C4×Q8—1222no—
542C4×Q8C22×D6114yes—
543C4×D4—614no—
544C4×D4—614no—
545C4×D4—1228no—
546#117—614no—
547#117—1228no—
548#117—1222no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—614no—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4—611no—
564C2×C22⋊C4—611no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C42—21no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574#107—614no—
575#106—614no—
576#106—614no—
577C4⋊C8C22×D6114yes—
578#103—614no—
579#103—614no—
580#103—614no—
581#103—614no—
582#102—614no—
583#102—614no—
584#102—614no—
585#102—614no—
586#102C22×D6114yes—
587#102C22×D6114yes—
588C22⋊C8—614no—
589C22⋊C8—614no—
590#97—614no—
591C24—21no—
592C24—21no—
593C24—611no—
594C24—611no—
595#41—1228no—
596#41—1228no—
597#41—2444no—
598#41—2444no—
599#41—2448no—
600#41—2448no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—614no—
605C2×Q8—612no—
606C2×Q8—1221no—
607C2×Q8—1222no—
608C2×Q8C23×D6112yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—82no—
619C2×D4—614no—
620C2×D4—1224no—
621C2×D4—1224no—
622C2×D4—1224no—
623C2×D4—1224no—
624C2×D4—4882no—
625C2×D4—4882no—
626C2×D4—2442no—
627C2×D4—2444no—
628C2×D4—2444no—
629C2×D4C23×D6112yes—
630C2×D4C23×D6112yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—612no—
636C22×C4—612no—
637C22×C4—612no—
638C22×C4—612no—
639C22×C4—1224no—
640C22×C4—1224no—
641C22×C4—1224no—
642C22×C4—1221no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656Q16—1228no—
657SD16—44no—
658SD16—44no—
659M16—2444no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—612no—
663C2×C8—612no—
664C2×C8—1222no—
665C2×C8—1222no—
666C2×C8—2444no—
667C2×C8C23×D6112yes—
668C2×C8C23×D6112yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—614no—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—612no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4—1224no—
684C4⋊C4C23×D6112yes—
685C22⋊C4—614no—
686C22⋊C4—614no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C42—24no—
693C42—1224no—
694C42—1224no—
695C42D4×D6112yes—
696C42C23×D6112yes—
697C23—22no—
698C23—22no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—612no—
706C23—612no—
707C23—1222no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—1222no—
712C23—1222no—
713C23C2×D4×D6111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—614no—
718Q8—1222no—
719Q8—1224no—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—48no—
725D4—42no—
726D4—42no—
727D4—84no—
728D4—4884no—
729D4—4884no—
730D4—2444no—
731D4—2448no—
732D4—2448no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—612no—
740C2×C4—612no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1224no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1224no—
750C2×C4—1224no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—2448no—
755C2×C4—2448no—
756C2×C4—2448no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4C2×D4×D6112yes—
761C2×C4C2×D4×D6112yes—
762C2×C4C2×D4×D6111yescharacteristic
763C2×C4#41×D6112yes—
764C2×C4#1451982212yes—
765C2×C4C24×D6111yescharacteristic
766C8—22no—
767C8—22no—
768C8—1222no—
769C8—1222no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—84no—
778C22—1222no—
779C22—1222no—
780C22—1222no—
781C22—1222no—
782C22—1222no—
783C22—1222no—
784C22—2444no—
785C22—2444no—
786C22#1684040912yes—
787C22#1684055812yes—
788C22#1684056812yes—
789C22C22×D4×D6111yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—42no—
794C4—1222no—
795C4—1222no—
796C4—1224no—
797C4—2442no—
798C4—2442no—
799C4—2442no—
800C4#1684040912yes—
801C4C2×#41×D6111yescharacteristic
802C4C2×#1451982211yescharacteristic
803C2—82no—
804C2—82no—
805C2—2442no—
806C2—2442no—
807C2#2145795214yesdirect product factor
808C2C2×#1684040911yescharacteristic
809C2C2×#1684055811yescharacteristic
810C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#460C2
socleC23×C61C22×D4
prime radicalC2×#16840432C2
hypercenterC2×#460D61
hypocenterC61C2×#3317
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#16840453C2semidirect
3. #21457952C2direct (N × H)
4. C2×#16840126C2semidirect
5. C2×#16840079C2semidirect
6. C2×#16840084C2semidirect
7. C2×#16840070C2semidirect
8. C2×#16840005C2semidirect
9. C2×#16839988C2semidirect
10. C2×#16839921C2semidirect
11. C2×#16839921C2semidirect
12. C2×#16839867C2semidirect
13. C2×#16839832C2semidirect
14. C2×#16839760C2semidirect
15. C2×#16839755C2semidirect
16. C2×C61×#460C2semidirect
23. #16840453C22semidirect
43. #16840126C22semidirect
44. #16840084C22semidirect
45. #16840079C22semidirect
46. #16840070C22semidirect
47. #16840005C22semidirect
48. #16839988C22semidirect
49. #16839921C22semidirect
50. #16839921C22semidirect
51. #16839867C22semidirect
52. #16839832C22semidirect
56. #16839760C22semidirect
57. #16839755C22semidirect
73. C61×#460C22semidirect
407. C2×#460D61semidirect
416. C2×C61#3317semidirect
458. #460C2×D61semidirect
482. C61C2×#3317semidirect
807. C2#21457952direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404532
C2×#168404322
#214579522
C2×#168401262
C2×#168400792
C2×#168400842
C2×#168400702
C2×#168400052
C2×#168399882
C2×#168399212
C2×#168398672
C2×#168398322
C2×#168397602
C2×#168397552
C2×C61×#4602
C2×#331761