Finite Group Databasebeta

← C2×#21457811 #30556588

Subgroups — C2×#21457811 #30556588

Order 15616.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840419C211yesmaximal, characteristic, complemented
2C2×#16840413C211yesmaximal, characteristic, complemented
3#21457811C2116yesmaximal, direct product factor
4C2×#16840120C211yesmaximal, characteristic, complemented
5C2×#16840097C211yesmaximal, characteristic, complemented
6C2×#16840074C211yesmaximal, characteristic, complemented
7C2×#16840055C211yesmaximal, characteristic, complemented
8C2×#16840008C211yesmaximal, characteristic, complemented
9C2×#16839997C211yesmaximal, characteristic, complemented
10C2×#16839976C211yesmaximal, characteristic, complemented
11C2×#16839907C211yesmaximal, characteristic, complemented
12C2×#16839902C211yesmaximal, characteristic, complemented
13C2×#16839865C211yesmaximal, characteristic, complemented
14C2×#16839831C211yesmaximal, characteristic, complemented
15C2×#103×D61C211yesmaximal, characteristic, complemented
16C2×C61×#417C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×Q8×D61C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840419—24no—
24#16840419C2218yescomplemented
25#16840413—24no—
26#16840413C2218yescomplemented
27C2×#14519776C2211yescharacteristic
28C2×#14519764—21no—
29C2×#14519764C2211yescharacteristic
30C2×#14519762—21no—
31C2×#14519760—21no—
32C2×#14519756—21no—
33C2×#14519756C2211yescharacteristic
34C2×#14519755—21no—
35C2×#14519752C2211yescharacteristic
36C2×#14519751C2211yescharacteristic
37C2×#14519748—21no—
38C2×#14519748C2211yescharacteristic
39C2×Q8×Dic61C2211yescharacteristic
40C2×#14519739C2211yescharacteristic
41C2×C4×C22⋊D61—21no—
42C2×C4×C22⋊D61C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840120C2218yescomplemented
45#16840097C2218yescomplemented
46#16840074C2218yescomplemented
47#16840055C2218yescomplemented
48#16840008C2218yescomplemented
49#16839997C2218yescomplemented
50#16839976C2218yescomplemented
51#16839907C2218yescomplemented
52#16839902C2218yescomplemented
53#16839865C2218yescomplemented
54#16839831C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63#103×D61C2218yescomplemented
64C2×#14519699C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic
71C22×C4⋊C4×C61C2211yescharacteristic
72C61×#417C2218yescomplemented
73C2×#103×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122—21no—
80C22×Dic122—21no—
81C22×Dic122C2311yescharacteristic
82C2×Q8×D61—22no—
83C2×Q8×D61—24no—
84C2×Q8×D61—42no—
85C2×Q8×D61C2314yes—
86C22×D244—21no—
87C22×D244C2311yescharacteristic
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61D411yescharacteristic
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C2×#11758190—42no—
96C2×#11758190C2314yes—
97C2×#11758201—24no—
98C2×#11758201C2314yes—
99C2×#11758199—42no—
100C2×#11758199C2314yes—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—42no—
104C2×C8×D61C2314yes—
105#14519776—22no—
106#14519776C2314yes—
107#14519764—28no—
108#14519764—22no—
109#14519764C2314yes—
110#14519762—28no—
111#14519760—28no—
112#14519756—22no—
113#14519756—28no—
114#14519756C2314yes—
115#14519755—28no—
116#14519752—22no—
117#14519752C2314yes—
118#14519751—22no—
119#14519751C2314yes—
120#14519748—28no—
121#14519748—22no—
122#14519748C2314yes—
123Q8×Dic61—22no—
124Q8×Dic61C2314yes—
125#14519739—22no—
126#14519739C2314yes—
127C4×C22⋊D61—28no—
128C4×C22⋊D61D414yes—
129C4×C22⋊D61C2314yes—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C4⋊C4×D61—22no—
138C4⋊C4×D61C2314yes—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61D411yescharacteristic
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198D411yescharacteristic
148C2×C4×Dic61—21no—
149C2×C4×Dic61C2311yescharacteristic
150#14519711C2314yes—
151#14519710C2314yes—
152#14519710C2314yes—
153#14519706C2314yes—
154#14519702C2314yes—
155#14519701C2314yes—
156#14519700C2314yes—
157#14519700C2314yes—
158#14519699C2314yes—
159#14519698C2314yes—
160C22⋊#92418C2314yes—
161#14519689C2314yes—
162#14519687C2314yes—
163C2×#41×C61—22no—
164C2×#41×C61—24no—
165C2×#41×C61—42no—
166C2×#41×C61C2314yes—
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61—21no—
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61—21no—
171C23×C4×C61—21no—
172C23×C4×C61C2311yescharacteristic
173C2×M16×C61—42no—
174C2×M16×C61C2314yes—
175C22×C8×C61C2311yescharacteristic
176C22×C8×C61C2311yescharacteristic
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61—22no—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C4⋊C4×C61C2314yes—
182#103×C61C2314yes—
183#103×C61C2314yes—
184#102×C61C2314yes—
185#102×C61C2314yes—
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C23×D61—21no—
189C23×D61C2×D411yescharacteristic
190#41×C61—28no—
191#41×C61—44no—
192#41×C61—48no—
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61#4114yescomplemented
196C2×Q8×C61C2412yes—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—44no—
202C2×D4×C61C2412yes—
203C22×C4×C61—21no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—24no—
209C22×C4×C61—24no—
210C22×C4×C61—44no—
211C22×C4×C61—44no—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2412yes—
215C22×C4×C61C2411yescharacteristic
216C2×C22⋊D61—24no—
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61C2×D414yes—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228Q8×D61—28no—
229Q8×D61—44no—
230Q8×D61—48no—
231#11758222—432no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—24no—
235C2×D244—21no—
236C2×D244—44no—
237C2×D244C2412yes—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—24no—
241C2×C4×D61—24no—
242C2×C4×D61—24no—
243C2×C4×D61—44no—
244C2×C4×D61—44no—
245C2×C4×D61—44no—
246C2×C4×D61C2×D412yes—
247C2×C4×D61C2412yes—
248C2×Dic122—22no—
249C2×Dic122—22no—
250C2×Dic122—21no—
251C2×Dic122—24no—
252C2×Dic122—24no—
253C2×Dic122—44no—
254C2×Dic122—44no—
255C2×Dic122C2412yes—
256M16×C61—44no—
257C2×C8×C61—22no—
258C2×C8×C61—22no—
259C2×C8×C61C2412yes—
260C2×C8×C61C2412yes—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—24no—
264C4⋊C4×C61C2412yes—
265C4⋊C4×C61C2412yes—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61—24no—
269C22⋊Dic61—24no—
270C22⋊Dic61C2×D414yes—
271#11758201—28no—
272#11758199—44no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198C2×D414yes—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—24no—
280C4⋊Dic61C2412yes—
281C4⋊Dic61C2412yes—
282#11758196—24no—
283#11758196—24no—
284#11758196—24no—
285#11758196C2×D414yes—
286C4×Dic61—24no—
287C4×Dic61C2×D412yes—
288C4×Dic61C2412yes—
289C2×#92418—22no—
290C2×#92418—22no—
291C2×#92418C2412yes—
292C2×#92418C2412yes—
293#11758190—44no—
294C8×D61—44no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61C22×D412yes—
303C23×C61C22×D411yescharacteristic
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—42no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61AGL(1,ℤ/8)14yes—
311C22×D61C22×D412yes—
312Q8×C61—24no—
313Q8×C61—22no—
314Q8×C61C2×#4114yescomplemented
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—48no—
318D4×C61—42no—
319C2×C4×C61—24no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—24no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—48no—
328C2×C4×C61—48no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61C22×D412yes—
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C2×#4112yes—
334C2×C4×C61H(5,𝔽2)12yes—
335C2×C4×C61C2511yescharacteristic
336C22⋊D61—28no—
337C22⋊D61—48no—
338C22⋊D61—48no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61C22×D412yes—
349C2×Dic61C22×D412yes—
350C2×Dic61C22×D412yes—
351D244—22no—
352D244—22no—
353D244—48no—
354D244—42no—
355C4×D61—24no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—48no—
359C4×D61—48no—
360C4×D61—48no—
361Dic122—22no—
362Dic122—22no—
363Dic122—48no—
364Dic122—48no—
365Dic122—42no—
366C8×C61—22no—
367C8×C61—22no—
368#92418—22no—
369#92418—22no—
370C2×#3308—611nomaximal, Sylow
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—44no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—84no—
379C22×C61#54612yes—
380C22×C61C2×AGL(1,ℤ/8)12yes—
381C22×C61#57812yes—
382C22×C61C23×D411yescharacteristic
383C2×D61—22no—
384C2×D61—28no—
385C2×D61—22no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—84no—
390C2×D61C2×AGL(1,ℤ/8)14yes—
391C4×C61—24no—
392C4×C61—22no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61#54612yes—
396C4×C61C22×#4111yescharacteristic
397C4×C61C2×H(5,𝔽2)11yescharacteristic
398Dic61—22no—
399Dic61—22no—
400Dic61—22no—
401Dic61—42no—
402Dic61—42no—
403Dic61—42no—
404C2×#548—611no—
405C2×#547—611no—
406#3308—6116no—
407C2×#489—611no—
408C2×#484—611no—
409C2×#480—611no—
410C2×#477—611no—
411C2×#468—611no—
412C2×#466—611no—
413C2×#463—611no—
414C2×#449—611no—
415C2×#448—611no—
416C2×#440—611no—
417C2×#435—611no—
418C2×#417D6111yescharacteristic, complemented
419C22×#103—611no—
420C2×C61—42no—
421C2×C61—82no—
422C2×C61#330814yescomplemented
423C2×C61C2×#54611yescharacteristic
424C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
425C2×C61C2×#57811yescharacteristic
426D61—24no—
427D61—82no—
428C22×#41—1221no—
429C22×#41C2×D6111yescharacteristic
430C23×Q8—611no—
431C22×SD16—611no—
432C22×SD16—611no—
433C22×D8—611no—
434C22×M16C2×D6111yescharacteristic
435C23×C8—611no—
436#548—618no—
437#548—1224no—
438#547—618no—
439#547—1224no—
440C2×C4⋊Q8—611no—
441C2×#124—611no—
442C2×#124—1221no—
443C2×#123—1221no—
444C2×#123—1221no—
445C2×C22⋊Q8—611no—
446C2×C22⋊Q8—1221no—
447C2×C22⋊Q8—1221no—
448C2×#121—611no—
449C2×#121—611no—
450C2×#121—611no—
451C2×#121—1221no—
452C2×C4×Q8—611no—
453C2×C4×D4—611no—
454C2×C4×D4—611no—
455C2×C4×D4—1221no—
456C22×C4⋊C4—611no—
457C22×C4⋊C4C2×D6111yescharacteristic
458#489—618no—
459#484—618no—
460#480—618no—
461#477—618no—
462#468—618no—
463#466—618no—
464#463—618no—
465#449—618no—
466#448—618no—
467#440—618no—
468#435—618no—
469C2×#107—611no—
470C2×#107—611no—
471C2×#107—611no—
472C2×C4⋊C8—611no—
473#417C2×D6118yescomplemented
474C2×#103—611no—
475C2×#103—611no—
476C2×#103—611no—
477C2×#103—611no—
478C2×#103—618no—
479C2×#103C2×D6111yescharacteristic
480C2×#103C2×D6111yescharacteristic
481C2×#102—611no—
482C2×#102—611no—
483C2×#102C2×D6111yescharacteristic
484C2×#102C2×D6111yescharacteristic
485C2×C22⋊C8—611no—
486C2×C22⋊C8—611no—
487C2×#97—611no—
488C61C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—22no—
490C2×#41—24no—
491C2×#41—42no—
492C2×#41—1228no—
493C2×#41—2448no—
494C2×#41C22×D6114yes—
495C22×Q8—614no—
496C22×Q8—611no—
497C22×Q8—1221no—
498C22×Q8—1221no—
499C22×Q8—1222no—
500C22×Q8—1224no—
501C22×Q8—2442no—
502C22×Q8C22×D6111yescharacteristic
503C22×D4—21no—
504C22×D4—611no—
505C22×D4—611no—
506C22×D4—1221no—
507C22×D4—1221no—
508C22×D4—1221no—
509C22×D4C22×D6111yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—611no—
513C23×C4—1221no—
514C23×C4—1221no—
515C23×C4—1221no—
516C23×C4C22×D6111yescharacteristic
517C2×SD16—614no—
518C2×SD16—614no—
519C2×SD16—1224no—
520C2×SD16—2442no—
521C2×D8—614no—
522C2×D8—2442no—
523C2×M16—42no—
524C2×M16C22×D6114yes—
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—614no—
528C22×C8—2442no—
529C22×C8C22×D6111yescharacteristic
530C22×C8C22×D6111yescharacteristic
531C4⋊Q8—614no—
532C4⋊Q8—1222no—
533#124—614no—
534#124—1222no—
535#124—1228no—
536#123—1228no—
537#123—1228no—
538C22⋊Q8—614no—
539C22⋊Q8—1228no—
540C22⋊Q8—1228no—
541C22⋊Q8—1222no—
542#121—614no—
543#121—614no—
544#121—614no—
545#121—1222no—
546#121—1222no—
547#121—1228no—
548#121—1222no—
549C4×Q8—614no—
550C4×Q8—1222no—
551C4×D4—614no—
552C4×D4—614no—
553C4×D4—614no—
554C4×D4—1222no—
555C4×D4—1228no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—614no—
562C2×C4⋊C4—1222no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C4⋊C4C22×D6114yes—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C42—611no—
580C2×C42—1221no—
581#107—614no—
582#107—614no—
583#107—614no—
584C4⋊C8—614no—
585#103—614no—
586#103—614no—
587#103—614no—
588#103—614no—
589#103C22×D6114yes—
590#103C22×D6114yes—
591#102—614no—
592#102—614no—
593#102C22×D6114yes—
594#102C22×D6114yes—
595C22⋊C8—614no—
596C22⋊C8—614no—
597#97—614no—
598C24—21no—
599C24—611no—
600C24—1221no—
601C24D4×D6111yescharacteristic
602#41—28no—
603#41—44no—
604#41—48no—
605#41—24432no—
606C2×Q8—21no—
607C2×Q8—22no—
608C2×Q8—612no—
609C2×Q8—1224no—
610C2×Q8—1224no—
611C2×Q8—1221no—
612C2×Q8—1228no—
613C2×Q8—1222no—
614C2×Q8—1222no—
615C2×Q8—2444no—
616C2×Q8—2444no—
617C2×Q8—2444no—
618C2×Q8—2448no—
619C2×Q8#1175822214yescomplemented
620C2×Q8C23×D6112yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—44no—
626C2×D4—614no—
627C2×D4—612no—
628C2×D4—1224no—
629C2×D4—1224no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1221no—
633C2×D4—1222no—
634C2×D4—1222no—
635C2×D4—2444no—
636C2×D4—2444no—
637C2×D4—2444no—
638C2×D4C23×D6112yes—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—612no—
652C22×C4—612no—
653C22×C4—1224no—
654C22×C4—1224no—
655C22×C4—1224no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—2444no—
662C22×C4—2444no—
663C22×C4—2444no—
664C22×C4D4×D6112yes—
665C22×C4D4×D6111yescharacteristic
666C22×C4C23×D6112yes—
667C22×C4C23×D6111yescharacteristic
668SD16—1228no—
669SD16—2444no—
670D8—2444no—
671M16—44no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—612no—
675C2×C8—612no—
676C2×C8—1222no—
677C2×C8—1222no—
678C2×C8—2444no—
679C2×C8C23×D6112yes—
680C2×C8C23×D6112yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—614no—
685C4⋊C4—612no—
686C4⋊C4—612no—
687C4⋊C4—1224no—
688C4⋊C4—1224no—
689C4⋊C4—1224no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1224no—
693C4⋊C4C23×D6112yes—
694C4⋊C4C23×D6112yes—
695C22⋊C4—614no—
696C22⋊C4—614no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C22⋊C4—1224no—
703C22⋊C4—1224no—
704C42—612no—
705C42—612no—
706C42—1224no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—614no—
715C23—612no—
716C23—1222no—
717C23—1222no—
718C23—1222no—
719C23—2442no—
720C23—2442no—
721C23—2442no—
722C23C2×D4×D6112yes—
723C23C2×D4×D6111yescharacteristic
724Q8—22no—
725Q8—24no—
726Q8—1222no—
727Q8—1222no—
728Q8—2448no—
729Q8—2448no—
730Q8—2442no—
731Q8C2×#1175822214yescomplemented
732D4—22no—
733D4—22no—
734D4—48no—
735D4—42no—
736D4—1228no—
737D4—1222no—
738D4—1222no—
739D4—2448no—
740D4—2448no—
741D4—2448no—
742D4—2442no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—48no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—612no—
756C2×C4—612no—
757C2×C4—612no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1224no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—2448no—
768C2×C4—2448no—
769C2×C4—2448no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4C2×D4×D6112yes—
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4C2×#1175822212yes—
776C2×C4#1451982212yes—
777C2×C4C24×D6111yescharacteristic
778C8—22no—
779C8—22no—
780C8—1222no—
781C8—1222no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—44no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—84no—
790C22—614no—
791C22—1222no—
792C22—1222no—
793C22—1228no—
794C22—4884no—
795C22—2442no—
796C22—2442no—
797C22—2442no—
798C22#1684040212yes—
799C22AGL(1,ℤ/8)×D6112yes—
800C22#1684057812yes—
801C22C22×D4×D6111yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—1222no—
807C4—1222no—
808C4—1222no—
809C4—2442no—
810C4—2442no—
811C4—2442no—
812C4#1684040212yes—
813C4C22×#1175822211yescharacteristic
814C4C2×#1451982211yescharacteristic
815C2—42no—
816C2—82no—
817C2—1224no—
818C2—4882no—
819C2#2145781114yesdirect product factor
820C2C2×#1684040211yescharacteristic
821C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
822C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
hypercenterC2×#417D61
hypocenterC61C2×#3308
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#16840419C2semidirect
2. C2×#16840413C2semidirect
3. #21457811C2direct (N × H)
4. C2×#16840120C2semidirect
5. C2×#16840097C2semidirect
6. C2×#16840074C2semidirect
7. C2×#16840055C2semidirect
8. C2×#16840008C2semidirect
9. C2×#16839997C2semidirect
10. C2×#16839976C2semidirect
11. C2×#16839907C2semidirect
12. C2×#16839902C2semidirect
13. C2×#16839865C2semidirect
14. C2×#16839831C2semidirect
15. C2×#103×D61C2semidirect
16. C2×C61×#417C2semidirect
24. #16840419C22semidirect
26. #16840413C22semidirect
44. #16840120C22semidirect
45. #16840097C22semidirect
46. #16840074C22semidirect
47. #16840055C22semidirect
48. #16840008C22semidirect
49. #16839997C22semidirect
50. #16839976C22semidirect
51. #16839907C22semidirect
52. #16839902C22semidirect
53. #16839865C22semidirect
54. #16839831C22semidirect
63. #103×D61C22semidirect
72. C61×#417C22semidirect
195. C2×Q8×C61#41semidirect
314. Q8×C61C2×#41semidirect
418. C2×#417D61semidirect
422. C2×C61#3308semidirect
473. #417C2×D61semidirect
488. C61C2×#3308semidirect
619. C2×Q8#11758222semidirect
731. Q8C2×#11758222semidirect
819. C2#21457811direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404192
C2×#168404132
#214578112
C2×#168401202
C2×#168400972
C2×#168400742
C2×#168400552
C2×#168400082
C2×#168399972
C2×#168399762
C2×#168399072
C2×#168399022
C2×#168398652
C2×#168398312
C2×#103×D612
C2×C61×#4172
C2×#330861