Finite Group Databasebeta

← C2×#21457854 #30556682

Subgroups — C2×#21457854 #30556682

Order 15616.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840486C211yesmaximal, characteristic, complemented
2C2×#16840405C211yesmaximal, characteristic
3#21457854C2116yesmaximal, direct product factor
4C2×#16840102C211yesmaximal, characteristic, complemented
5C2×#16840084C211yesmaximal, characteristic, complemented
6C2×#16840049C211yesmaximal, characteristic, complemented
7C2×#16840019C211yesmaximal, characteristic, complemented
8C2×#16839990C211yesmaximal, characteristic, complemented
9C2×#16839981C211yesmaximal, characteristic, complemented
10C2×#16839927C211yesmaximal, characteristic, complemented
11C2×#16839914C211yesmaximal, characteristic, complemented
12C2×#16839864C211yesmaximal, characteristic, complemented
13C2×#16839835C211yesmaximal, characteristic, complemented
14C2×#16839765C211yesmaximal, characteristic, complemented
15C2×#16839757C211yesmaximal, characteristic, complemented
16C2×C61×#489C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758202C2211yescharacteristic, complemented
20C22×#11758190C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758189C2211yescharacteristic
23C22×C8×D61C2211yescharacteristic, complemented
24#16840486—24no—
25#16840486C2218yescomplemented
26#16840405—24no—
27#16840405C2218yes—
28C2×#14519772—21no—
29C2×#14519772—21no—
30C2×#14519766—21no—
31C2×#14519759—21no—
32C2×#14519757C2211yescharacteristic
33C2×#14519757C2211yescharacteristic, complemented
34C2×#14519753C2211yescharacteristic
35C2×#14519750—21no—
36C2×#14519748C2211yescharacteristic
37C2×#14519747—21no—
38C2×Q8×Dic61—21no—
39C2×C4×Dic122C2211yescharacteristic, complemented
40C2×C4×D244C2211yescharacteristic
41C2×C4×D244C2211yescharacteristic
42C2×#14519735C2211yescharacteristic
43C2×#14519735C2211yescharacteristic, complemented
44C2×C22⋊C4×D61—21no—
45#16840102C2218yescomplemented
46#16840084C2218yescomplemented
47#16840049C2218yescomplemented
48#16840019C2218yescomplemented
49#16839990C2218yescomplemented
50#16839981C2218yescomplemented
51#16839927C2218yescomplemented
52#16839914C2218yescomplemented
53#16839864C2218yescomplemented
54#16839835C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519708C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×C4⋊#92418C2211yescharacteristic, complemented
59#16839765C2218yescomplemented
60#16839757C2218yescomplemented
61C2×#14519702C2211yescharacteristic, complemented
62C2×#14519701C2211yescharacteristic, complemented
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic, complemented
69C2×C4⋊Q8×C61C2211yescharacteristic, complemented
70C2×#124×C61C2211yescharacteristic
71C61×#489C2218yescomplemented
72C2×#103×C61C2211yescharacteristic, complemented
73C2×#103×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758226—22no—
79C2×#11758226—24no—
80C2×#11758226—42no—
81C2×#11758226C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×D244—21no—
84C22×D244D411yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C2×D4×D61—24no—
89C2×D4×D61—22no—
90C2×D4×D61—42no—
91C2×D4×D61C2314yes—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C2×#11758202—42no—
97C2×#11758202C2314yescomplemented
98C2×#11758190—24no—
99C2×#11758190C2314yes—
100C2×#11758200—42no—
101C2×#11758200C2314yes—
102C2×#11758189—42no—
103C2×#11758189C2314yes—
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106C2×C8×D61—42no—
107C2×C8×D61C2314yescomplemented
108#14519772—28no—
109#14519772—28no—
110#14519766—28no—
111#14519759—28no—
112#14519757—22no—
113#14519757—22no—
114#14519757C2314yes—
115#14519757C2314yescomplemented
116#14519753—22no—
117#14519753C2314yes—
118#14519750—28no—
119#14519748—22no—
120#14519748C2314yes—
121#14519747—28no—
122Q8×Dic61—28no—
123C4×Dic122—22no—
124C4×Dic122C2314yescomplemented
125C4×D244—22no—
126C4×D244D414yes—
127C4×D244C2314yes—
128C4×D244C2314yes—
129#14519735—22no—
130#14519735—22no—
131#14519735C2314yes—
132#14519735C2314yescomplemented
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61D411yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×C22⋊Dic61—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198D411yescharacteristic
148C2×#11758198D411yescharacteristic
149C22⋊C4×D61—28no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61—21no—
152C2×C4×Dic61—21no—
153#14519711C2314yescomplemented
154#14519708C2314yescomplemented
155#14519708C2314yescomplemented
156C4⋊#92418C2314yescomplemented
157#14519702C2314yescomplemented
158#14519701C2314yescomplemented
159#14519699C2314yes—
160#14519698C2314yes—
161#14519697C2314yes—
162#14519697C2314yes—
163#14519689C2314yes—
164#14519689C2314yescomplemented
165C22×Q8×C61—21no—
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170C4⋊Q8×C61—22no—
171C4⋊Q8×C61C2314yescomplemented
172#124×C61—22no—
173#124×C61C2314yes—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C42×C61C2311yescharacteristic
180#103×C61C2314yescomplemented
181#103×C61C2314yescomplemented
182#102×C61C2314yes—
183#102×C61C2314yes—
184#97×C61C2314yescomplemented
185C24×C61—21no—
186C23×D61—21no—
187C23×D61—24no—
188C23×D61—44no—
189C23×D61—44no—
190C23×D61—82no—
191C23×D61C2×D411yescharacteristic
192C23×D61C2×D411yescharacteristic
193C2×Q8×C61—21no—
194C2×Q8×C61—24no—
195C2×Q8×C61—22no—
196C2×Q8×C61—22no—
197C2×Q8×C61—44no—
198C2×Q8×C61C2412yes—
199C2×D4×C61—21no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61C2412yes—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2411yescharacteristic
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—44no—
212C2×C22⋊D61—82no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218#11758226—28no—
219#11758226—44no—
220#11758226—48no—
221D4×D61—28no—
222D4×D61—44no—
223D4×D61—48no—
224C2×D244—21no—
225C2×D244—22no—
226C2×D244—24no—
227C2×D244—42no—
228C2×D244—44no—
229C2×D244C2×D414yes—
230C2×D244#4114yes—
231C2×D244C2412yes—
232C2×C4×D61—22no—
233C2×C4×D61—22no—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—44no—
239C2×C4×D61—82no—
240C2×C4×D61C2×D412yes—
241C2×C4×D61C2×D412yes—
242C2×C4×D61C2412yes—
243C2×C4×D61C2412yes—
244C2×Dic122—22no—
245C2×Dic122—22no—
246C2×Dic122—21no—
247C2×Dic122C2412yes—
248C2×C8×C61—22no—
249C2×C8×C61—22no—
250C2×C8×C61C2412yes—
251C2×C8×C61C2412yes—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C2412yes—
256C4⋊C4×C61C2412yes—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—24no—
259C42×C61C2×D412yes—
260C42×C61C2412yes—
261C22⋊Dic61—24no—
262#11758202—44no—
263#11758200—44no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198C2×D414yes—
271#11758198C2×D414yes—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—24no—
275C4⋊Dic61—24no—
276C4⋊Dic61C2×D414yes—
277C4⋊Dic61C2412yes—
278C4⋊Dic61C2412yes—
279#11758196—24no—
280#11758196—24no—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61—24no—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418C2412yes—
287C2×#92418C2412yes—
288#11758190—28no—
289#11758189—44no—
290C8×D61—44no—
291C23×C61—22no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61C22×D411yescharacteristic
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—24no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—48no—
305C22×D61—48no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—84no—
309C22×D61—816no—
310C22×D61C22×D412yes—
311C22×D61C22×D412yes—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—48no—
315Q8×C61—42no—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—42no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61C22×D412yes—
328C2×C4×C61C22×D412yes—
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C2×#4112yes—
331C2×C4×C61H(5,𝔽2)12yes—
332C2×C4×C61C2511yescharacteristic
333C22⋊D61—48no—
334C22⋊D61—84no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61C22×D412yes—
344C2×Dic61C22×D412yes—
345D244—24no—
346D244—22no—
347D244—44no—
348D244—48no—
349D244C2×#4114yes—
350C4×D61—24no—
351C4×D61—24no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—48no—
357C4×D61—84no—
358Dic122—22no—
359Dic122—22no—
360Dic122—42no—
361C8×C61—22no—
362C8×C61—22no—
363#92418—22no—
364#92418—22no—
365C2×#3311—611nomaximal, Sylow
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—84no—
370C22×C61#54612yes—
371C22×C61#57512yes—
372C22×C61#57712yes—
373C22×C61C23×D411yescharacteristic
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—24no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—44no—
382C2×D61—44no—
383C2×D61—48no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—816no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61#54612yes—
393C4×C61C22×#4111yescharacteristic
394C4×C61C2×H(5,𝔽2)11yescharacteristic
395Dic61—22no—
396Dic61—22no—
397Dic61—42no—
398Dic61—42no—
399Dic61—42no—
400C2×#556—611no—
401C2×#546—611no—
402#3311—6116no—
403C2×#489D6111yescharacteristic, complemented
404C2×#485—611no—
405C2×#482—611no—
406C2×#476—611no—
407C2×#470—611no—
408C2×#465—611no—
409C2×#464—611no—
410C2×#452—611no—
411C2×#450—611no—
412C2×#440—611no—
413C2×#435—611no—
414C2×#418—611no—
415C2×#416—611no—
416C2×C61—82no—
417C2×C61#331114yescomplemented
418C2×C61C2×#54611yescharacteristic
419C2×C61C2×#57511yescharacteristic
420C2×C61C2×#57711yescharacteristic
421D61—42no—
422D61—42no—
423D61—44no—
424C22×#41—611no—
425C23×D4—611no—
426C22×Q16—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C22×M16—611no—
430C23×C8—611no—
431#556—618no—
432#556—1224no—
433#546—618no—
434#546—1224no—
435C2×C4⋊Q8C2×D6111yescharacteristic, complemented
436C2×#126—1221no—
437C2×#126—1221no—
438C2×#124—1221no—
439C2×#124C2×D6111yescharacteristic
440C2×#123—1221no—
441C2×C22⋊Q8—611no—
442C2×C22⋊Q8—611no—
443C2×C22⋊Q8—611no—
444C2×#121—611no—
445C2×#121—1221no—
446C2×#120—1221no—
447C2×C4×Q8—611no—
448C2×C4×Q8—1221no—
449C2×C4×D4—611no—
450C2×C4×D4—611no—
451C2×#117—611no—
452C2×#117—611no—
453C22×C22⋊C4—1221no—
454#489C2×D6118yescomplemented
455#485—618no—
456#482—618no—
457#476—618no—
458#470—618no—
459#465—618no—
460#464—618no—
461#452—618no—
462#450—618no—
463#440—618no—
464#435—618no—
465C2×#107—611no—
466C2×#106—611no—
467C2×#106—611no—
468C2×C4⋊C8—611no—
469#418—618no—
470#416—618no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103C2×D6111yescharacteristic, complemented
474C2×#103C2×D6111yescharacteristic, complemented
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×#102C2×D6111yescharacteristic
480C2×#102C2×D6111yescharacteristic
481C2×C22⋊C8—611no—
482C2×C22⋊C8—611no—
483C2×#97C2×D6111yescharacteristic, complemented
484C61C2×#331111yescharacteristic, complemented, Sylow
485C25—1221no—
486C2×#41—614no—
487C2×#41—1222no—
488C2×#41—1224no—
489C2×#41—2442no—
490C22×Q8—21no—
491C22×Q8—611no—
492C22×Q8C22×D6111yescharacteristic
493C22×D4—614no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4—1221no—
497C22×D4—1222no—
498C22×D4—1221no—
499C22×D4—1224no—
500C22×D4—1221no—
501C22×D4—2442no—
502C22×D4C22×D6111yescharacteristic
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—1221no—
506C23×C4—1221no—
507C2×Q16—614no—
508C2×Q16—2442no—
509C2×SD16—614no—
510C2×SD16—614no—
511C2×SD16—1224no—
512C2×SD16—2442no—
513C2×M16—614no—
514C2×M16—2442no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—614no—
518C22×C8—2442no—
519C22×C8C22×D6111yescharacteristic
520C22×C8C22×D6111yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8C22×D6114yescomplemented
523#126—1228no—
524#126—1228no—
525#124—22no—
526#124—1228no—
527#124C22×D6114yes—
528#123—1228no—
529C22⋊Q8—614no—
530C22⋊Q8—614no—
531C22⋊Q8—614no—
532C22⋊Q8—1222no—
533C22⋊Q8—1222no—
534C22⋊Q8—1222no—
535#121—614no—
536#121—1228no—
537#121—1222no—
538#120—1228no—
539C4×Q8—614no—
540C4×Q8—1228no—
541C4×Q8—1222no—
542C4×D4—614no—
543C4×D4—614no—
544C4×D4—614no—
545C4×D4—1222no—
546#117—614no—
547#117—614no—
548#117—1222no—
549#117—1222no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4C22×D6111yescharacteristic
559C2×C4⋊C4C22×D6111yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—611no—
563C2×C22⋊C4—611no—
564C2×C22⋊C4—1228no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C42—1221no—
573C2×C42—1221no—
574C2×C42—1221no—
575C2×C42C22×D6111yescharacteristic
576#107—614no—
577#106—614no—
578#106—614no—
579C4⋊C8—614no—
580#103—614no—
581#103—614no—
582#103C22×D6114yescomplemented
583#103C22×D6114yescomplemented
584#102—614no—
585#102—614no—
586#102—614no—
587#102—614no—
588#102C22×D6114yes—
589#102C22×D6114yes—
590C22⋊C8—614no—
591C22⋊C8—614no—
592#97C22×D6114yescomplemented
593C24—21no—
594C24—611no—
595C24—611no—
596C24—1224no—
597C24—1221no—
598C24—4882no—
599C24—2444no—
600C24—2444no—
601#41—1228no—
602#41—2444no—
603#41—2448no—
604C2×Q8—24no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—44no—
609C2×Q8—612no—
610C2×Q8—1221no—
611C2×Q8—1222no—
612C2×Q8—1222no—
613C2×Q8C23×D6112yes—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—614no—
618C2×D4—614no—
619C2×D4—612no—
620C2×D4—1224no—
621C2×D4—1224no—
622C2×D4—1228no—
623C2×D4—1224no—
624C2×D4—1221no—
625C2×D4—1222no—
626C2×D4—4882no—
627C2×D4—2442no—
628C2×D4—2444no—
629C2×D4—2444no—
630C2×D4—2448no—
631C2×D4—2444no—
632C2×D4C23×D6112yes—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—612no—
639C22×C4—612no—
640C22×C4—612no—
641C22×C4—612no—
642C22×C4—1224no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1224no—
651C22×C4—4882no—
652C22×C4—2444no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656Q16—2444no—
657SD16—1228no—
658SD16—2444no—
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—21no—
672C4⋊C4—614no—
673C4⋊C4—612no—
674C4⋊C4—612no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1224no—
681C4⋊C4C23×D6112yes—
682C4⋊C4C23×D6112yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—614no—
686C22⋊C4—614no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C42—1224no—
695C42—1224no—
696C42—1224no—
697C42D4×D6112yes—
698C42C23×D6112yes—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—612no—
704C23—612no—
705C23—1222no—
706C23—1222no—
707C23—1222no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—1222no—
712C23—1224no—
713C23—4884no—
714C23—48816no—
715C23—2448no—
716C23—2448no—
717C23—2442no—
718C23—2442no—
719C23C2×D4×D6111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—48no—
723Q8—42no—
724Q8—1222no—
725Q8—1222no—
726Q8—2442no—
727D4—22no—
728D4—22no—
729D4—42no—
730D4—614no—
731D4—1222no—
732D4—1224no—
733D4—4884no—
734D4—2444no—
735D4—2448no—
736D4—2448no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—612no—
746C2×C4—612no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1224no—
754C2×C4—1224no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—4884no—
759C2×C4—2448no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2442no—
763C2×C4C2×D4×D6112yes—
764C2×C4C2×D4×D6112yes—
765C2×C4C2×D4×D6111yescharacteristic
766C2×C4#41×D6112yes—
767C2×C4#1451982312yes—
768C2×C4C24×D6111yescharacteristic
769C8—22no—
770C8—22no—
771C8—1222no—
772C8—1222no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—1222no—
778C22—1222no—
779C22—1224no—
780C22—1222no—
781C22—1222no—
782C22—1222no—
783C22—1222no—
784C22—48816no—
785C22—2442no—
786C22—2442no—
787C22—2444no—
788C22—2444no—
789C22—2448no—
790C22#1684040512yes—
791C22#1684055812yes—
792C22#1684057112yes—
793C22C22×D4×D6111yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—1222no—
800C4—1222no—
801C4—2442no—
802C4—2442no—
803C4—2442no—
804C4#1684040512yes—
805C4C2×#41×D6111yescharacteristic
806C4C2×#1451982311yescharacteristic
807C2—82no—
808C2—2442no—
809C2—2442no—
810C2—2444no—
811C2#2145785414yesdirect product factor
812C2C2×#1684040511yescharacteristic
813C2C2×#1684055811yescharacteristic
814C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#489C2
socleC23×C61C22×D4
prime radicalC2×#16840405C2
hypercenterC2×#489D61
hypocenterC61C2×#3311
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#16840486C2semidirect
3. #21457854C2direct (N × H)
4. C2×#16840102C2semidirect
5. C2×#16840084C2semidirect
6. C2×#16840049C2semidirect
7. C2×#16840019C2semidirect
8. C2×#16839990C2semidirect
9. C2×#16839981C2semidirect
10. C2×#16839927C2semidirect
11. C2×#16839914C2semidirect
12. C2×#16839864C2semidirect
13. C2×#16839835C2semidirect
14. C2×#16839765C2semidirect
15. C2×#16839757C2semidirect
16. C2×C61×#489C2semidirect
19. C22×#11758202C22semidirect
23. C22×C8×D61C22semidirect
25. #16840486C22semidirect
33. C2×#14519757C22semidirect
39. C2×C4×Dic122C22semidirect
43. C2×#14519735C22semidirect
45. #16840102C22semidirect
46. #16840084C22semidirect
47. #16840049C22semidirect
48. #16840019C22semidirect
49. #16839990C22semidirect
50. #16839981C22semidirect
51. #16839927C22semidirect
52. #16839914C22semidirect
53. #16839864C22semidirect
54. #16839835C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519708C22semidirect
57. C2×#14519708C22semidirect
58. C2×C4⋊#92418C22semidirect
59. #16839765C22semidirect
60. #16839757C22semidirect
61. C2×#14519702C22semidirect
62. C2×#14519701C22semidirect
68. C2×#14519689C22semidirect
69. C2×C4⋊Q8×C61C22semidirect
71. C61×#489C22semidirect
72. C2×#103×C61C22semidirect
73. C2×#103×C61C22semidirect
76. C2×#97×C61C22semidirect
97. C2×#11758202C23semidirect
107. C2×C8×D61C23semidirect
115. #14519757C23semidirect
124. C4×Dic122C23semidirect
132. #14519735C23semidirect
153. #14519711C23semidirect
154. #14519708C23semidirect
155. #14519708C23semidirect
156. C4⋊#92418C23semidirect
157. #14519702C23semidirect
158. #14519701C23semidirect
164. #14519689C23semidirect
171. C4⋊Q8×C61C23semidirect
180. #103×C61C23semidirect
181. #103×C61C23semidirect
184. #97×C61C23semidirect
403. C2×#489D61semidirect
417. C2×C61#3311semidirect
435. C2×C4⋊Q8C2×D61semidirect
454. #489C2×D61semidirect
473. C2×#103C2×D61semidirect
474. C2×#103C2×D61semidirect
483. C2×#97C2×D61semidirect
484. C61C2×#3311semidirect
522. C4⋊Q8C22×D61semidirect
582. #103C22×D61semidirect
583. #103C22×D61semidirect
592. #97C22×D61semidirect
811. C2#21457854direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404862
C2×#168404052
#214578542
C2×#168401022
C2×#168400842
C2×#168400492
C2×#168400192
C2×#168399902
C2×#168399812
C2×#168399272
C2×#168399142
C2×#168398642
C2×#168398352
C2×#168397652
C2×#168397572
C2×C61×#4892
C2×#331161