Finite Group Databasebeta

← C2×#21457462 #30555156

Subgroups — C2×#21457462 #30555156

Order 15616.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519810C211yesmaximal, characteristic, complemented
2C22×#14519809C211yesmaximal, characteristic, complemented
3C2×#16840425C211yesmaximal, characteristic, complemented
4C2×#16840414C211yesmaximal, characteristic
5#21457462C2116yesmaximal, direct product factor
6C2×#16840140C211yesmaximal, characteristic, complemented
7C2×#16840021C211yesmaximal, characteristic, complemented
8C2×#16839971C211yesmaximal, characteristic, complemented
9C2×#16839966C211yesmaximal, characteristic, complemented
10C2×#16839927C211yesmaximal, characteristic, complemented
11C2×#16839922C211yesmaximal, characteristic, complemented
12C2×#16839919C211yesmaximal, characteristic, complemented
13C2×#16839917C211yesmaximal, characteristic, complemented
14C2×#16839849C211yesmaximal, characteristic, complemented
15C2×#16839838C211yesmaximal, characteristic, complemented
16C2×C61×#470C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758222C2211yescharacteristic
19C23×Dic122C2211yescharacteristic
20C22×Q8×D61C2211yescharacteristic
21C2×#14519810—28no—
22C2×#14519810C2218yescomplemented
23C2×#14519809—28no—
24C2×#14519809C2218yescomplemented
25C22×Dic244C2211yescharacteristic
26C22×Dic244C2211yescharacteristic
27C22×#11758202C2211yescharacteristic
28C22×#11758202C2211yescharacteristic
29C22×#11758202C2211yescharacteristic
30C22×#11758190C2211yescharacteristic
31C22×#11758190C2211yescharacteristic
32C22×#11758201C2211yescharacteristic
33C22×#11758189C2211yescharacteristic
34#16840425—24no—
35#16840425C2218yescomplemented
36#16840414—24no—
37#16840414C2218yes—
38C2×#14519776—21no—
39C2×#14519775C2211yescharacteristic
40C2×#14519775C2211yescharacteristic
41C2×#14519762—21no—
42C2×#14519759—21no—
43C2×#14519757C2211yescharacteristic
44C2×#14519757C2211yescharacteristic
45C2×#14519755—21no—
46C2×#14519754—21no—
47C2×#14519750—21no—
48C2×#14519742C2211yescharacteristic
49C2×#14519739C2211yescharacteristic
50C2×C4×C22⋊D61C2211yescharacteristic
51C2×#14519737—21no—
52C2×C4⋊C4×D61—21no—
53#16840140C2218yescomplemented
54#16840021C2218yescomplemented
55#16839971C2218yescomplemented
56#16839966C2218yescomplemented
57#16839927C2218yescomplemented
58#16839922C2218yescomplemented
59#16839919C2218yescomplemented
60#16839917C2218yescomplemented
61#16839849C2218yescomplemented
62#16839838C2218yescomplemented
63C2×#14519706C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519700C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519697C2211yescharacteristic
68C2×C22⋊#92418C2211yescharacteristic
69C2×#14519689C2211yescharacteristic
70C2×C8×Dic61C2211yescharacteristic
71C22×Q16×C61C2211yescharacteristic
72C22×M16×C61C2211yescharacteristic
73C2×C22⋊Q8×C61C2211yescharacteristic
74C2×C22⋊Q8×C61C2211yescharacteristic
75C61×#470C2218yescomplemented
76C2×#106×C61C2211yescharacteristic
77C2×#103×C61C2211yescharacteristic
78C2×#103×C61C2211yescharacteristic
79C2×#11758226—22no—
80C2×#11758226—24no—
81C2×#11758226—42no—
82C2×#11758226C2314yes—
83C2×#11758222—22no—
84C2×#11758222—24no—
85C2×#11758222—42no—
86C2×#11758222C2314yes—
87C22×Dic122—24no—
88C22×Dic122—21no—
89C22×Dic122—22no—
90C22×Dic122—21no—
91C22×Dic122—42no—
92C22×Dic122C2311yescharacteristic
93C22×Dic122C2311yescharacteristic
94C22×Dic122C2314yes—
95C22×Dic122C2311yescharacteristic
96C2×Q8×D61—22no—
97C2×Q8×D61—24no—
98C2×Q8×D61—42no—
99C2×Q8×D61C2314yes—
100C22×D244—21no—
101C22×D244C2311yescharacteristic
102C22×C22⋊D61—21no—
103C22×C22⋊D61D411yescharacteristic
104C23×Dic61—21no—
105C22×C4×D61—21no—
106C22×C4×D61—21no—
107C22×C4×D61—21no—
108C22×C4×D61—21no—
109C22×C4×D61C2311yescharacteristic
110#14519810—232no—
111#14519809—232no—
112C2×Dic244—24no—
113C2×Dic244—24no—
114C2×Dic244C2314yes—
115C2×Dic244C2314yes—
116C2×#11758202—24no—
117C2×#11758202—42no—
118C2×#11758202—42no—
119C2×#11758202C2314yes—
120C2×#11758202C2314yes—
121C2×#11758202C2314yes—
122C2×#11758190—24no—
123C2×#11758190D418yescomplemented
124C2×#11758190C2314yes—
125C2×#11758190C2314yes—
126C2×#11758201—24no—
127C2×#11758201C2314yes—
128C2×#11758189—24no—
129C2×#11758189C2314yes—
130C22×#92418C2311yescharacteristic
131C22×#92418C2311yescharacteristic
132#14519776—28no—
133#14519775—22no—
134#14519775—22no—
135#14519775C2314yes—
136#14519775C2314yes—
137#14519762—28no—
138#14519759—28no—
139#14519757—22no—
140#14519757—22no—
141#14519757C2314yes—
142#14519757C2314yes—
143#14519755—28no—
144#14519754—28no—
145#14519750—28no—
146#14519742—22no—
147#14519742C2314yes—
148#14519739—22no—
149#14519739C2314yes—
150C4×C22⋊D61D414yes—
151C4×C22⋊D61C2314yes—
152#14519737—28no—
153C2×C4⋊Dic61—21no—
154C2×C4⋊Dic61—21no—
155C2×#11758196—21no—
156C2×#11758196—21no—
157C2×#11758196—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C4⋊C4×D61—28no—
162C2×C22⋊Dic61D411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×#11758198D411yescharacteristic
167C2×C4×Dic61—21no—
168C2×C4×Dic61C2311yescharacteristic
169#14519706C2314yes—
170#14519700C2314yes—
171#14519700C2314yes—
172#14519700C2314yes—
173#14519697C2314yes—
174C22⋊#92418C2314yes—
175#14519689C2314yes—
176C8×Dic61C2314yes—
177C22×Q8×C61C2311yescharacteristic
178C22×Q8×C61C2311yescharacteristic
179C23×C4×C61C2311yescharacteristic
180C2×Q16×C61—24no—
181C2×Q16×C61C2314yes—
182C2×M16×C61—24no—
183C2×M16×C61C2314yes—
184C22×C8×C61C2311yescharacteristic
185C22×C8×C61C2311yescharacteristic
186C22⋊Q8×C61—22no—
187C22⋊Q8×C61—22no—
188C22⋊Q8×C61C2314yes—
189C22⋊Q8×C61C2314yes—
190C2×C4⋊C4×C61—21no—
191C2×C4⋊C4×C61—21no—
192C2×C4⋊C4×C61C2311yescharacteristic
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C22⋊C4×C61—21no—
195C2×C22⋊C4×C61—21no—
196#106×C61C2314yes—
197#103×C61C2314yes—
198#103×C61C2314yes—
199C24×C61C2×D411yescharacteristic
200C23×D61—21no—
201C23×D61C2×D411yescharacteristic
202C2×Q8×C61—21no—
203C2×Q8×C61—21no—
204C2×Q8×C61—22no—
205C2×Q8×C61—22no—
206C2×Q8×C61—22no—
207C2×Q8×C61—22no—
208C2×Q8×C61C2412yes—
209C2×Q8×C61C2412yes—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D412yes—
218C22×C4×C61C2412yes—
219C22×C4×C61C2411yescharacteristic
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—44no—
223C2×C22⋊D61C2×D414yes—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—24no—
228C22×Dic61—44no—
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232#11758226—28no—
233#11758226—44no—
234#11758226—48no—
235Q8×D61—28no—
236Q8×D61—44no—
237Q8×D61—48no—
238#11758222—28no—
239#11758222—44no—
240#11758222—48no—
241C2×D244—21no—
242C2×D244—22no—
243C2×D244—24no—
244C2×D244—44no—
245C2×D244C2×D414yes—
246C2×D244C2412yes—
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61—24no—
250C2×C4×D61—24no—
251C2×C4×D61—24no—
252C2×C4×D61—24no—
253C2×C4×D61—44no—
254C2×C4×D61—44no—
255C2×C4×D61—44no—
256C2×C4×D61—44no—
257C2×C4×D61C2×D412yes—
258C2×C4×D61C2412yes—
259C2×Dic122—21no—
260C2×Dic122—22no—
261C2×Dic122—22no—
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122—22no—
265C2×Dic122—28no—
266C2×Dic122—24no—
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122—24no—
270C2×Dic122—44no—
271C2×Dic122—48no—
272C2×Dic122—44no—
273C2×Dic122—44no—
274C2×Dic122C2×D414yes—
275C2×Dic122C2412yes—
276C2×Dic122C2412yes—
277C2×Dic122C2412yes—
278Q16×C61—28no—
279M16×C61—28no—
280C2×C8×C61—22no—
281C2×C8×C61C2×D414yes—
282C2×C8×C61C2412yes—
283C2×C8×C61C2412yes—
284C4⋊C4×C61—24no—
285C4⋊C4×C61—24no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61C2412yes—
289C4⋊C4×C61C2412yes—
290C22⋊C4×C61—24no—
291C22⋊C4×C61—24no—
292C22⋊Dic61C2×D414yes—
293#11758202—28no—
294#11758202—44no—
295#11758202—44no—
296#11758201—28no—
297#11758198—24no—
298#11758198—24no—
299#11758198—24no—
300#11758198C2×D414yes—
301C4⋊Dic61—24no—
302C4⋊Dic61—24no—
303#11758196—24no—
304#11758196—24no—
305#11758196—24no—
306#11758196—24no—
307#11758196—24no—
308#11758196C2×D414yes—
309C4×Dic61—24no—
310C4×Dic61C2×D412yes—
311C4×Dic61C2412yes—
312C2×#92418—22no—
313C2×#92418—22no—
314C2×#92418C2412yes—
315C2×#92418C2412yes—
316Dic244—28no—
317Dic244—28no—
318#11758190—28no—
319#11758190C2×D4116yescomplemented
320#11758189—28no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61C22×D412yes—
325C23×C61C22×D411yescharacteristic
326C22×D61—22no—
327C22×D61—24no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61C22×D412yes—
334Q8×C61—22no—
335Q8×C61—22no—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—42no—
339Q8×C61—42no—
340C2×C4×C61—22no—
341C2×C4×C61—24no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61—42no—
351C2×C4×C61—42no—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D412yes—
355C2×C4×C61H(5,𝔽2)12yes—
356C2×C4×C61C2511yescharacteristic
357C22⋊D61—28no—
358C22⋊D61—48no—
359C2×Dic61—24no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—48no—
366C2×Dic61—42no—
367C2×Dic61—42no—
368C2×Dic61#13714yescomplemented
369C2×Dic61C22×D412yes—
370C2×Dic61C22×D412yes—
371C2×Dic61C22×D412yes—
372D244—24no—
373D244—22no—
374D244—48no—
375D244C22×D414yes—
376C4×D61—24no—
377C4×D61—22no—
378C4×D61—22no—
379C4×D61—48no—
380C4×D61—48no—
381C4×D61—48no—
382C4×D61—48no—
383Dic122—24no—
384Dic122—22no—
385Dic122—22no—
386Dic122—22no—
387Dic122—22no—
388Dic122—22no—
389Dic122—48no—
390Dic122—48no—
391Dic122—42no—
392Dic122—42no—
393Dic122C22×D414yes—
394C8×C61—22no—
395C8×C61C22×D414yes—
396#92418—22no—
397#92418—22no—
398C2×#3276—611nomaximal, Sylow
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—44no—
403C22×C61D4212yes—
404C22×C61C2×#13712yes—
405C22×C61#57812yes—
406C22×C61C23×D411yescharacteristic
407C2×D61—22no—
408C2×D61—24no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—44no—
412C2×D61—48no—
413C2×D61—42no—
414C2×D61—42no—
415C4×C61—22no—
416C4×C61—42no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61—42no—
420C4×C61D4212yes—
421C4×C61C23×D411yescharacteristic
422C4×C61C2×H(5,𝔽2)11yescharacteristic
423Dic61—24no—
424Dic61—22no—
425Dic61—22no—
426Dic61—42no—
427Dic61—42no—
428Dic61C2×#13714yescomplemented
429C22×#137—611no—
430C22×#137—611no—
431C2×D4×Q8—611no—
432C2×#547—611no—
433#3276—6116no—
434C2×#494—611no—
435C2×#470—611no—
436C2×#470D6111yescharacteristic, complemented
437C2×#462—611no—
438C2×#461—611no—
439C2×#452—611no—
440C2×#452—611no—
441C2×#451—611no—
442C2×#451—611no—
443C2×C4×SD16—611no—
444C2×#436—611no—
445C2×C61—42no—
446C2×C61#327614yescomplemented
447C2×C61C2×D4211yescharacteristic
448C2×C61C22×#13711yescharacteristic
449C2×C61C2×#57811yescharacteristic
450D61—42no—
451D61—44no—
452C22×#41—611no—
453C22×#41—611no—
454C23×Q8—611no—
455C23×Q8—611no—
456C2×#137—618no—
457C2×#137—618no—
458C2×#137—1228no—
459C2×#137—1228no—
460C22×Q16—611no—
461C22×Q16—611no—
462C22×Q16—611no—
463C22×Q16—611no—
464C22×Q16—611no—
465C22×Q16C2×D6111yescharacteristic
466C22×SD16—611no—
467C22×SD16—611no—
468C22×SD16—611no—
469C22×M16—611no—
470C22×M16C2×D6111yescharacteristic
471D4×Q8—618no—
472D4×Q8—1224no—
473#547—618no—
474#547—1224no—
475C2×C4⋊Q8—611no—
476C2×C4⋊Q8—611no—
477C2×C4⋊Q8—1221no—
478C2×#123—1221no—
479C2×#123—1221no—
480C2×C22⋊Q8—611no—
481C2×C22⋊Q8—611no—
482C2×C22⋊Q8—1221no—
483C2×C22⋊Q8—1221no—
484C2×C22⋊Q8C2×D6111yescharacteristic
485C2×C22⋊Q8C2×D6111yescharacteristic
486C2×#121—1221no—
487C2×C4×Q8—611no—
488C2×C4×D4—611no—
489C2×C4×D4—611no—
490C2×C4×D4—1221no—
491C22×C4⋊C4—1221no—
492#494—618no—
493#470—618no—
494#470C2×D6118yescomplemented
495#462—618no—
496#461—618no—
497#452—618no—
498#452—618no—
499#451—618no—
500#451—618no—
501C4×SD16—618no—
502#436—618no—
503C2×#106C2×D6111yescharacteristic
504C2×C4⋊C8—611no—
505C2×#103—611no—
506C2×#103—611no—
507C2×#103—611no—
508C2×#103C2×D6111yescharacteristic
509C2×#103C2×D6111yescharacteristic
510C2×#102—611no—
511C2×C22⋊C8—611no—
512C2×C22⋊C8—611no—
513C2×C4×C8—611no—
514C61C2×#327611yescharacteristic, complemented, Sylow
515C2×#41—614no—
516C2×#41—614no—
517C2×#41—1224no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—1224no—
521C2×#41—2442no—
522C2×#41—2442no—
523C22×Q8—614no—
524C22×Q8—611no—
525C22×Q8—611no—
526C22×Q8—611no—
527C22×Q8—614no—
528C22×Q8—1221no—
529C22×Q8—1224no—
530C22×Q8—1222no—
531C22×Q8—1221no—
532C22×Q8—1222no—
533C22×Q8—1224no—
534C22×Q8—2442no—
535C22×Q8—2442no—
536C22×Q8C22×D6111yescharacteristic
537C22×Q8C22×D6111yescharacteristic
538C22×D4—611no—
539C22×D4—611no—
540C22×D4—1221no—
541C22×D4—1221no—
542C23×C4—611no—
543C23×C4—1221no—
544C23×C4—1221no—
545C23×C4—1221no—
546C23×C4—1221no—
547C23×C4—1221no—
548C23×C4C22×D6111yescharacteristic
549#137—12232no—
550#137—12232no—
551C2×Q16—24no—
552C2×Q16—614no—
553C2×Q16—614no—
554C2×Q16—614no—
555C2×Q16—614no—
556C2×Q16—614no—
557C2×Q16—1224no—
558C2×Q16—1224no—
559C2×Q16—1224no—
560C2×Q16—2442no—
561C2×Q16—2442no—
562C2×Q16C22×D6114yes—
563C2×SD16—614no—
564C2×SD16—618no—
565C2×SD16—614no—
566C2×SD16—614no—
567C2×SD16—1224no—
568C2×SD16—1224no—
569C2×M16—24no—
570C2×M16—614no—
571C2×M16—1224no—
572C2×M16C22×D6114yes—
573C22×C8—611no—
574C22×C8—611no—
575C22×C8C22×D6111yescharacteristic
576C22×C8C22×D6111yescharacteristic
577C4⋊Q8—614no—
578C4⋊Q8—614no—
579C4⋊Q8—1222no—
580C4⋊Q8—1222no—
581C4⋊Q8—1228no—
582#123—1228no—
583#123—1228no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—614no—
587C22⋊Q8—614no—
588C22⋊Q8—1228no—
589C22⋊Q8—1228no—
590C22⋊Q8—1222no—
591C22⋊Q8—1222no—
592C22⋊Q8C22×D6114yes—
593C22⋊Q8C22×D6114yes—
594#121—1228no—
595C4×Q8—614no—
596C4×Q8—1222no—
597C4×D4—614no—
598C4×D4—614no—
599C4×D4—614no—
600C4×D4—1222no—
601C4×D4—1228no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—1228no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4—1221no—
613C2×C4⋊C4C22×D6111yescharacteristic
614C2×C4⋊C4C22×D6111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—611no—
618C2×C22⋊C4—611no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C42—611no—
623C2×C42—1221no—
624#106C22×D6114yes—
625C4⋊C8—614no—
626#103—614no—
627#103—614no—
628#103—614no—
629#103C22×D6114yes—
630#103C22×D6114yes—
631#102—614no—
632C22⋊C8—614no—
633C22⋊C8—614no—
634C4×C8—614no—
635C24—611no—
636C24—1221no—
637C24D4×D6111yescharacteristic
638#41—1228no—
639#41—1228no—
640#41—2444no—
641#41—2448no—
642#41—2444no—
643#41—2448no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—22no—
650C2×Q8—614no—
651C2×Q8—612no—
652C2×Q8—612no—
653C2×Q8—612no—
654C2×Q8—1224no—
655C2×Q8—1228no—
656C2×Q8—1221no—
657C2×Q8—1224no—
658C2×Q8—1221no—
659C2×Q8—1221no—
660C2×Q8—1222no—
661C2×Q8—1228no—
662C2×Q8—1222no—
663C2×Q8—1222no—
664C2×Q8—1222no—
665C2×Q8—1222no—
666C2×Q8—2444no—
667C2×Q8—2444no—
668C2×Q8—2448no—
669C2×Q8—2444no—
670C2×Q8—2444no—
671C2×Q8—2448no—
672C2×Q8C23×D6112yes—
673C2×Q8C23×D6112yes—
674C2×D4—614no—
675C2×D4—614no—
676C2×D4—612no—
677C2×D4—1224no—
678C2×D4—1224no—
679C2×D4—1224no—
680C2×D4—1221no—
681C2×D4—1222no—
682C2×D4—2444no—
683C2×D4—2444no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—612no—
694C22×C4—612no—
695C22×C4—1224no—
696C22×C4—1224no—
697C22×C4—1224no—
698C22×C4—1221no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1224no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1224no—
705C22×C4—2444no—
706C22×C4—2444no—
707C22×C4—2444no—
708C22×C4—2444no—
709C22×C4—2444no—
710C22×C4D4×D6112yes—
711C22×C4D4×D6111yescharacteristic
712C22×C4C23×D6112yes—
713C22×C4C23×D6111yescharacteristic
714Q16—28no—
715Q16—1228no—
716Q16—1228no—
717Q16—1228no—
718Q16—2444no—
719Q16—2444no—
720SD16—6116no—
721SD16—1228no—
722SD16—1228no—
723M16—28no—
724M16—1228no—
725C2×C8—22no—
726C2×C8—612no—
727C2×C8—612no—
728C2×C8—1222no—
729C2×C8—1222no—
730C2×C8D4×D6114yes—
731C2×C8C23×D6112yes—
732C2×C8C23×D6112yes—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—614no—
738C4⋊C4—1224no—
739C4⋊C4—1224no—
740C4⋊C4—1224no—
741C4⋊C4—1224no—
742C4⋊C4—1224no—
743C4⋊C4—1224no—
744C4⋊C4—1224no—
745C4⋊C4C23×D6112yes—
746C4⋊C4C23×D6112yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—614no—
750C22⋊C4—614no—
751C22⋊C4—1224no—
752C22⋊C4—1224no—
753C22⋊C4—1224no—
754C42—612no—
755C42—612no—
756C42—1224no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—612no—
761C23—1222no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1224no—
766C23—2442no—
767C23—2442no—
768C23C2×D4×D6112yes—
769C23C2×D4×D6111yescharacteristic
770Q8—22no—
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—42no—
775Q8—42no—
776Q8—614no—
777Q8—1222no—
778Q8—1224no—
779Q8—1222no—
780Q8—1222no—
781Q8—1222no—
782Q8—1222no—
783Q8—2448no—
784Q8—2448no—
785Q8—2442no—
786Q8—2442no—
787D4—614no—
788D4—1228no—
789D4—1222no—
790D4—1224no—
791D4—2448no—
792D4—2448no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—614no—
806C2×C4—612no—
807C2×C4—612no—
808C2×C4—612no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1224no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1224no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—2448no—
819C2×C4—2448no—
820C2×C4—2448no—
821C2×C4—2448no—
822C2×C4—2448no—
823C2×C4—2442no—
824C2×C4—2442no—
825C2×C4C2×D4×D6112yes—
826C2×C4C2×D4×D6112yes—
827C2×C4C2×D4×D6111yescharacteristic
828C2×C4#1451982312yes—
829C2×C4C24×D6111yescharacteristic
830C8—22no—
831C8—1222no—
832C8—1222no—
833C8C2×D4×D6114yes—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—44no—
838C22—1222no—
839C22—1224no—
840C22—1222no—
841C22—1222no—
842C22—2444no—
843C22—2448no—
844C22—2442no—
845C22—2442no—
846C22#1684039612yes—
847C22#137×D6112yes—
848C22#1684057812yes—
849C22C22×D4×D6111yescharacteristic
850C4—22no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—614no—
856C4—1222no—
857C4—1224no—
858C4—1222no—
859C4—2442no—
860C4—2442no—
861C4#1684039612yes—
862C4C22×D4×D6111yescharacteristic
863C4C2×#1451982311yescharacteristic
864C2—42no—
865C2—2442no—
866C2—2444no—
867C2#2145746214yesdirect product factor
868C2C2×#1684039611yescharacteristic
869C2C2×#137×D6111yescharacteristic
870C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#470C2
socleC23×C61C22×D4
prime radicalC2×#16840414C2
hypercenterC2×#470D61
hypocenterC61C2×#3276
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C22×#14519810C2semidirect
2. C22×#14519809C2semidirect
3. C2×#16840425C2semidirect
5. #21457462C2direct (N × H)
6. C2×#16840140C2semidirect
7. C2×#16840021C2semidirect
8. C2×#16839971C2semidirect
9. C2×#16839966C2semidirect
10. C2×#16839927C2semidirect
11. C2×#16839922C2semidirect
12. C2×#16839919C2semidirect
13. C2×#16839917C2semidirect
14. C2×#16839849C2semidirect
15. C2×#16839838C2semidirect
16. C2×C61×#470C2semidirect
22. C2×#14519810C22semidirect
24. C2×#14519809C22semidirect
35. #16840425C22semidirect
53. #16840140C22semidirect
54. #16840021C22semidirect
55. #16839971C22semidirect
56. #16839966C22semidirect
57. #16839927C22semidirect
58. #16839922C22semidirect
59. #16839919C22semidirect
60. #16839917C22semidirect
61. #16839849C22semidirect
62. #16839838C22semidirect
75. C61×#470C22semidirect
123. C2×#11758190D4semidirect
319. #11758190C2×D4semidirect
368. C2×Dic61#137semidirect
428. Dic61C2×#137semidirect
436. C2×#470D61semidirect
446. C2×C61#3276semidirect
494. #470C2×D61semidirect
514. C61C2×#3276semidirect
867. C2#21457462direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198102
C22×#145198092
C2×#168404252
C2×#168404142
#214574622
C2×#168401402
C2×#168400212
C2×#168399712
C2×#168399662
C2×#168399272
C2×#168399222
C2×#168399192
C2×#168399172
C2×#168398492
C2×#168398382
C2×C61×#4702
C2×#327661