Finite Group Databasebeta

← C2×#21455656 #30547579

Subgroups — C2×#21455656 #30547579

Order 15616.

2018 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840389C211yesmaximal, characteristic
2C2×#16840238C211yesmaximal, characteristic
3#21455656C2116yesmaximal, direct product factor
4C2×#16840071C211yesmaximal, characteristic, complemented
5C2×#16840070C211yesmaximal, characteristic, complemented
6C2×#16840069C211yesmaximal, characteristic, complemented
7C2×#16840068C211yesmaximal, characteristic, complemented
8C2×#16840056C211yesmaximal, characteristic, complemented
9C2×#16840045C211yesmaximal, characteristic, complemented
10C2×#16840044C211yesmaximal, characteristic, complemented
11C2×#16839803C211yesmaximal, characteristic
12C2×#16839799C211yesmaximal, characteristic
13C2×#16839787C211yesmaximal, characteristic
14C2×#16839769C211yesmaximal, characteristic
15C2×#103×D61C211yesmaximal, characteristic
16C2×C61×#477C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840389—24no—
21#16840389C2218yes—
22C2×#14519776C2211yescharacteristic
23C2×#14519775—21no—
24C2×#14519769C2211yescharacteristic
25C2×#14519768C2211yescharacteristic
26C2×#14519767—21no—
27C2×#14519755—21no—
28C2×#14519753—21no—
29#16840238—24no—
30#16840238C2218yes—
31C2×Q8×Dic61C2211yescharacteristic
32C2×C4×Dic122—21no—
33C2×C4×Dic122C2211yescharacteristic
34C2×#14519742—21no—
35C2×#14519742C2211yescharacteristic
36C2×#14519735—21no—
37C2×#14519735C2211yescharacteristic
38C2×#14519735C2211yescharacteristic
39C2×#14519734—21no—
40C2×#14519734C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840071C2218yescomplemented
43#16840070C2218yescomplemented
44#16840069C2218yescomplemented
45#16840068C2218yescomplemented
46#16840056C2218yescomplemented
47#16840045C2218yescomplemented
48#16840044C2218yescomplemented
49#16839803C2218yes—
50#16839799C2218yes—
51C2×#14519711C2211yescharacteristic
52C2×#14519710C2211yescharacteristic
53C2×#14519709C2211yescharacteristic
54C2×#14519708C2211yescharacteristic
55C2×#14519708C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57#16839787C2218yes—
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61#16839769C2218yes—
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519701C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519700C2211yescharacteristic
68#103×D61C2218yes—
69C2×C4⋊Q8×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C61×#477C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#107×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C2×Q8×D61—22no—
81C2×Q8×D61—24no—
82C2×Q8×D61Q818yescomplemented
83C2×Q8×D61C2314yes—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—24no—
88C2×#11758189C2314yes—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—24no—
92C2×C8×D61C2314yes—
93#14519776—22no—
94#14519776C2314yes—
95#14519775—28no—
96#14519769—22no—
97#14519769C2314yes—
98#14519768—22no—
99#14519768C2314yes—
100#14519767—28no—
101#14519755—28no—
102#14519753—28no—
103Q8×Dic61—22no—
104Q8×Dic61C2314yes—
105C4×Dic122—22no—
106C4×Dic122—28no—
107C4×Dic122C2314yes—
108#14519742—28no—
109#14519742—22no—
110#14519742C2314yes—
111#14519735—22no—
112#14519735—22no—
113#14519735—28no—
114#14519735C2314yes—
115#14519735C2314yes—
116#14519734—28no—
117#14519734D414yes—
118#14519734C2314yes—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196D411yescharacteristic
132C2×#11758196D411yescharacteristic
133C4⋊C4×D61—22no—
134C4⋊C4×D61C2314yes—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198D411yescharacteristic
138C2×#11758198D411yescharacteristic
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61C2311yescharacteristic
145#14519711C2314yes—
146#14519710C2314yes—
147#14519709C2314yes—
148#14519708C2314yes—
149#14519708C2314yes—
150#14519708C2314yes—
151C4⋊#92418C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519701C2314yes—
157#14519701C2314yes—
158#14519700C2314yes—
159#14519700C2314yes—
160C22×Q8×C61—21no—
161C22×Q8×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164C4⋊Q8×C61—22no—
165C4⋊Q8×C61C2314yes—
166C4×Q8×C61—22no—
167C4×Q8×C61C2314yes—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C42×C61—21no—
174C2×C42×C61C2311yescharacteristic
175#107×C61C2314yes—
176#107×C61C2314yes—
177C4⋊C8×C61C2314yes—
178#103×C61C2314yes—
179#103×C61C2314yes—
180C23×D61C2×D411yescharacteristic
181C2×Q8×C61—21no—
182C2×Q8×C61—24no—
183C2×Q8×C61—22no—
184C2×Q8×C61—82no—
185C2×Q8×C61C2×Q814yes—
186C2×Q8×C61C2412yes—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201Q8×D61—216no—
202Q8×D61—28no—
203Q8×D61C2×Q8116yescomplemented
204C2×C4×D61—28no—
205C2×C4×D61—24no—
206C2×C4×D61—24no—
207C2×C4×D61—82no—
208C2×C4×D61C2×D412yes—
209C2×C4×D61C2×Q814yes—
210C2×C4×D61#4114yes—
211C2×C4×D61C2412yes—
212C2×Dic122—21no—
213C2×Dic122—22no—
214C2×Dic122—28no—
215C2×Dic122—24no—
216C2×Dic122—24no—
217C2×Dic122—82no—
218C2×Dic122C2×Q814yes—
219C2×Dic122C2412yes—
220C2×C8×C61—22no—
221C2×C8×C61—22no—
222C2×C8×C61C2412yes—
223C2×C8×C61C2412yes—
224C4⋊C4×C61—24no—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61C2412yes—
230C4⋊C4×C61C2412yes—
231C4⋊C4×C61C2412yes—
232C42×C61—24no—
233C42×C61C2×D412yes—
234C42×C61C2412yes—
235#11758198—24no—
236#11758198—24no—
237#11758198C2×D414yes—
238#11758198C2×D414yes—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—24no—
243C4⋊Dic61—24no—
244C4⋊Dic61C2412yes—
245C4⋊Dic61C2412yes—
246C4⋊Dic61C2412yes—
247#11758196—24no—
248#11758196—24no—
249#11758196—24no—
250#11758196—24no—
251#11758196—24no—
252#11758196—24no—
253#11758196—24no—
254#11758196C2×D414yes—
255#11758196C2×D414yes—
256C4×Dic61—24no—
257C4×Dic61—24no—
258C4×Dic61—24no—
259C4×Dic61—24no—
260C4×Dic61—24no—
261C4×Dic61C2×D412yes—
262C4×Dic61C2412yes—
263C2×#92418—22no—
264C2×#92418—22no—
265C2×#92418C2412yes—
266C2×#92418C2412yes—
267#11758189—28no—
268C8×D61—28no—
269C23×C61C22×D411yescharacteristic
270C22×D61—22no—
271C22×D61—22no—
272C22×D61C22⋊Q814yes—
273C22×D61C22×D412yes—
274Q8×C61—24no—
275Q8×C61—22no—
276Q8×C61—84no—
277Q8×C61C22×Q814yes—
278C2×C4×C61—24no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61C22×D412yes—
289C2×C4×C61C22×D412yes—
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C22×Q812yes—
292C2×C4×C61C2×#4112yes—
293C2×C4×C61C2511yescharacteristic
294C2×Dic61—24no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61C22⋊Q814yes—
305C2×Dic61C22×D412yes—
306C2×Dic61C22×D412yes—
307C2×Dic61C22×D412yes—
308C4×D61—216no—
309C4×D61—84no—
310C4×D61C22⋊Q818yes—
311C4×D61C22×Q814yes—
312C4×D61C2×#4114yes—
313Dic122—24no—
314Dic122—22no—
315Dic122—216no—
316Dic122—84no—
317Dic122C22×Q814yes—
318C8×C61—22no—
319C8×C61—22no—
320#92418—22no—
321#92418—22no—
322C2×#3082—611nomaximal, Sylow
323C22×C61C2×C22⋊Q812yes—
324C22×C61#57712yes—
325C22×C61#57812yes—
326C22×C61C23×D411yescharacteristic
327C2×D61—28no—
328C2×D61—22no—
329C2×D61—22no—
330C2×D61C2×C22⋊Q814yes—
331C4×C61—24no—
332C4×C61—22no—
333C4×C61—22no—
334C4×C61—42no—
335C4×C61—42no—
336C4×C61—42no—
337C4×C61C2×C22⋊Q812yes—
338C4×C61C23×Q811yescharacteristic
339C4×C61C22×#4111yescharacteristic
340Dic61—24no—
341Dic61—22no—
342Dic61—22no—
343Dic61—42no—
344Dic61—42no—
345Dic61—42no—
346Dic61C2×C22⋊Q814yes—
347C2×#544—611no—
348C2×#519—611no—
349#3082—6116no—
350C2×#479—611no—
351C2×#479—611no—
352C2×#479—611no—
353C2×#479—611no—
354C2×#477—611no—
355C2×#477D6111yescharacteristic, complemented
356C2×#475—611no—
357C2×#475—611no—
358C2×#428—611no—
359C2×#427—611no—
360C2×#424—611no—
361C2×#419—611no—
362C22×#103—611no—
363C2×C61#308214yescomplemented
364C2×C61C22×C22⋊Q811yescharacteristic
365C2×C61C2×#57711yescharacteristic
366C2×C61C2×#57811yescharacteristic
367D61—24no—
368C23×Q8—611no—
369C22×M16—611no—
370C23×C8—611no—
371#544—618no—
372#544—1224no—
373C2×C4⋊Q8—611no—
374C2×C4⋊Q8—1221no—
375C2×C4⋊Q8C2×D6111yescharacteristic
376C2×#125—611no—
377C2×#125—611no—
378C2×#125—1221no—
379C2×C22⋊Q8—1221no—
380C2×C22⋊Q8—1221no—
381#519—618no—
382#519—1224no—
383C2×C4×Q8—611no—
384C2×C4×Q8—611no—
385C2×C4×Q8—611no—
386C2×C4×Q8—1221no—
387C2×C4×Q8—1221no—
388C2×C4×Q8C2×D6111yescharacteristic
389C2×#117—611no—
390C2×#117—611no—
391C2×#117—611no—
392C2×#117—1221no—
393C2×#117—1221no—
394C22×C4⋊C4—611no—
395#479—618no—
396#479—618no—
397#479—618no—
398#479—618no—
399#477—618no—
400#477C2×D6118yescomplemented
401#475—618no—
402#475—618no—
403#428—618no—
404#427—618no—
405C2×#107—611no—
406C2×#107—611no—
407C2×#107C2×D6111yescharacteristic
408C2×#107C2×D6111yescharacteristic
409C2×#106—611no—
410C2×#106—611no—
411C2×#106—611no—
412C2×#106—611no—
413#424—618no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×C4⋊C8—611no—
417C2×C4⋊C8C2×D6111yescharacteristic
418#419—618no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#103—611no—
423C2×#103—611no—
424C2×#103—611no—
425C2×#103—618no—
426C2×#103C2×D6111yescharacteristic
427C2×#103C2×D6111yescharacteristic
428C61C2×#308211yescharacteristic, complemented, Sylow
429C22×Q8—21no—
430C22×Q8—618no—
431C22×Q8—614no—
432C22×Q8—611no—
433C22×Q8—1221no—
434C22×Q8—1221no—
435C22×Q8—1222no—
436C22×Q8—1224no—
437C22×Q8C22×D6111yescharacteristic
438C23×C4—611no—
439C23×C4—1221no—
440C23×C4—1221no—
441C2×M16—614no—
442C2×M16—1224no—
443C22×C8—611no—
444C22×C8—611no—
445C22×C8—614no—
446C22×C8—1224no—
447C22×C8C22×D6111yescharacteristic
448C22×C8C22×D6111yescharacteristic
449C4⋊Q8—22no—
450C4⋊Q8—614no—
451C4⋊Q8—1222no—
452C4⋊Q8—1228no—
453C4⋊Q8C22×D6114yes—
454#125—614no—
455#125—614no—
456#125—1222no—
457#125—1228no—
458#125—1222no—
459C22⋊Q8—1228no—
460C22⋊Q8—1228no—
461C4×Q8—22no—
462C4×Q8—614no—
463C4×Q8—614no—
464C4×Q8—614no—
465C4×Q8—1228no—
466C4×Q8—1222no—
467C4×Q8—1222no—
468C4×Q8—1228no—
469C4×Q8—1222no—
470C4×Q8C22×D6114yes—
471#117—614no—
472#117—614no—
473#117—614no—
474#117—614no—
475#117—1228no—
476#117—1228no—
477#117—1222no—
478#117—1222no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—614no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C4⋊C4C22×D6111yescharacteristic
500C2×C22⋊C4—611no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—21no—
505C2×C42—611no—
506C2×C42—1221no—
507C2×C42—1221no—
508C2×C42—1221no—
509C2×C42—1221no—
510C2×C42—1221no—
511C2×C42C22×D6111yescharacteristic
512#107—614no—
513#107—614no—
514#107C22×D6114yes—
515#107C22×D6114yes—
516#106—614no—
517#106—614no—
518#106—614no—
519#106—614no—
520C4⋊C8—614no—
521C4⋊C8—614no—
522C4⋊C8—614no—
523C4⋊C8C22×D6114yes—
524#103—614no—
525#103—614no—
526#103—614no—
527#103—614no—
528#103—614no—
529#103—614no—
530#103C22×D6114yes—
531#103C22×D6114yes—
532C24—611no—
533C2×Q8—21no—
534C2×Q8—24no—
535C2×Q8—22no—
536C2×Q8—82no—
537C2×Q8—6116no—
538C2×Q8—614no—
539C2×Q8—612no—
540C2×Q8—1224no—
541C2×Q8—1228no—
542C2×Q8—1224no—
543C2×Q8—12216no—
544C2×Q8—1228no—
545C2×Q8—1221no—
546C2×Q8—1222no—
547C2×Q8—4882no—
548C2×Q8Q8×D6114yes—
549C2×Q8C23×D6112yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—611no—
555C22×C4—612no—
556C22×C4—614no—
557C22×C4—614no—
558C22×C4—612no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—1224no—
562C22×C4—1228no—
563C22×C4—1224no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—4882no—
569C22×C4D4×D6111yescharacteristic
570C22×C4D4×D6111yescharacteristic
571C22×C4C23×D6111yescharacteristic
572M16—1228no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—612no—
576C2×C8—612no—
577C2×C8—1228no—
578C2×C8—1222no—
579C2×C8—1222no—
580C2×C8C23×D6112yes—
581C2×C8C23×D6112yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—614no—
588C4⋊C4—614no—
589C4⋊C4—612no—
590C4⋊C4—612no—
591C4⋊C4—612no—
592C4⋊C4—1224no—
593C4⋊C4—1224no—
594C4⋊C4—1224no—
595C4⋊C4—1224no—
596C4⋊C4—1224no—
597C4⋊C4—1224no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1224no—
602C4⋊C4—1224no—
603C4⋊C4—1224no—
604C4⋊C4C23×D6112yes—
605C4⋊C4C23×D6112yes—
606C4⋊C4C23×D6112yes—
607C22⋊C4—614no—
608C22⋊C4—614no—
609C22⋊C4—1224no—
610C22⋊C4—1224no—
611C42—24no—
612C42—612no—
613C42—612no—
614C42—1224no—
615C42—1224no—
616C42—1224no—
617C42—1224no—
618C42—1224no—
619C42D4×D6112yes—
620C42C23×D6112yes—
621C23—614no—
622C23—612no—
623C23—1222no—
624C23—1222no—
625C23C2×D4×D6111yescharacteristic
626Q8—24no—
627Q8—22no—
628Q8—84no—
629Q8—614no—
630Q8—12216no—
631Q8—1224no—
632Q8—1222no—
633Q8—4884no—
634Q8C2×Q8×D6114yes—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—614no—
646C2×C4—612no—
647C2×C4—618no—
648C2×C4—614no—
649C2×C4—614no—
650C2×C4—612no—
651C2×C4—612no—
652C2×C4—12216no—
653C2×C4—1224no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—4884no—
661C2×C4—2442no—
662C2×C4—2442no—
663C2×C4—2442no—
664C2×C4C2×D4×D6112yes—
665C2×C4C2×D4×D6112yes—
666C2×C4C2×D4×D6111yescharacteristic
667C2×C4C2×Q8×D6112yes—
668C2×C4#41×D6112yes—
669C2×C4C24×D6111yescharacteristic
670C8—22no—
671C8—22no—
672C8—1222no—
673C8—1222no—
674C22—614no—
675C22—1228no—
676C22—1222no—
677C22—1222no—
678C22C22⋊Q8×D6112yes—
679C22#1684057212yes—
680C22#1684057512yes—
681C22C22×D4×D6111yescharacteristic
682C4—22no—
683C4—24no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—614no—
689C4—1222no—
690C4—1224no—
691C4—1222no—
692C4—2442no—
693C4—2442no—
694C4—2442no—
695C4C22⋊Q8×D6112yes—
696C4C22×Q8×D6111yescharacteristic
697C4C2×#41×D6111yescharacteristic
698C2—1224no—
699C2#2145565614yesdirect product factor
700C2C2×C22⋊Q8×D6111yescharacteristic
701C2C2×#1684057211yescharacteristic
702C2C2×#1684057511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#477C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenterC2×#477D61
hypocenterC61C2×#3082
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #21455656C2direct (N × H)
4. C2×#16840071C2semidirect
5. C2×#16840070C2semidirect
6. C2×#16840069C2semidirect
7. C2×#16840068C2semidirect
8. C2×#16840056C2semidirect
9. C2×#16840045C2semidirect
10. C2×#16840044C2semidirect
16. C2×C61×#477C2semidirect
42. #16840071C22semidirect
43. #16840070C22semidirect
44. #16840069C22semidirect
45. #16840068C22semidirect
46. #16840056C22semidirect
47. #16840045C22semidirect
48. #16840044C22semidirect
71. C61×#477C22semidirect
82. C2×Q8×D61Q8semidirect
203. Q8×D61C2×Q8semidirect
355. C2×#477D61semidirect
363. C2×C61#3082semidirect
400. #477C2×D61semidirect
428. C61C2×#3082semidirect
699. C2#21455656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403892
C2×#168402382
#214556562
C2×#168400712
C2×#168400702
C2×#168400692
C2×#168400682
C2×#168400562
C2×#168400452
C2×#168400442
C2×#168398032
C2×#168397992
C2×#168397872
C2×#168397692
C2×#103×D612
C2×C61×#4772
C2×#308261