Finite Group Databasebeta

← C2×#21456687 #30550684

Subgroups — C2×#21456687 #30550684

Order 15616.

2314 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840335C211yesmaximal, characteristic, complemented
2C2×#16840328C211yesmaximal, characteristic
3#21456687C2116yesmaximal, direct product factor
4C2×#16840105C211yesmaximal, characteristic, complemented
5C2×#16840102C211yesmaximal, characteristic, complemented
6C2×#16840089C211yesmaximal, characteristic, complemented
7C2×#16840084C211yesmaximal, characteristic, complemented
8C2×#16840008C211yesmaximal, characteristic, complemented
9C2×#16839993C211yesmaximal, characteristic, complemented
10C2×#16839989C211yesmaximal, characteristic, complemented
11C2×#16839902C211yesmaximal, characteristic, complemented
12C2×#16839899C211yesmaximal, characteristic, complemented
13C2×#16839914C211yesmaximal, characteristic, complemented
14C2×#16839911C211yesmaximal, characteristic, complemented
15C2×#16839730C211yesmaximal, characteristic, complemented
16C2×C61×#468C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic, complemented
19C22×D4×D61C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C23×#92418C2211yescharacteristic, complemented
24#16840335—24no—
25#16840335C2218yescomplemented
26#16840328—24no—
27#16840328C2218yes—
28C2×#14519776—21no—
29C2×#14519773—21no—
30C2×#14519763—21no—
31C2×#14519763—21no—
32C2×#14519762—21no—
33C2×#14519759—21no—
34C2×#14519757C2211yescharacteristic
35C2×#14519756C2211yescharacteristic, complemented
36C2×#14519753C2211yescharacteristic
37C2×#14519752C2211yescharacteristic
38C2×#14519751C2211yescharacteristic
39C2×#14519748C2211yescharacteristic
40C2×#14519747—21no—
41C2×#14519745—21no—
42C2×#14519735C2211yescharacteristic
43C2×#14519735C2211yescharacteristic, complemented
44#16840105C2218yescomplemented
45#16840102C2218yescomplemented
46#16840089C2218yescomplemented
47#16840084C2218yescomplemented
48#16840008C2218yescomplemented
49#16839993C2218yescomplemented
50#16839989C2218yescomplemented
51#16839914C2218yescomplemented
52#16839911C2218yescomplemented
53#16839902C2218yescomplemented
54#16839899C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519708C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519702C2211yescharacteristic, complemented
59C2×#14519701C2211yescharacteristic, complemented
60C2×#14519700C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64#16839730C2218yescomplemented
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic, complemented
69C22×SD16×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic, complemented
71C2×C22⋊Q8×C61C2211yescharacteristic, complemented
72C2×#121×C61C2211yescharacteristic
73C61×#468C2218yescomplemented
74C2×#107×C61C2211yescharacteristic, complemented
75C2×#103×C61C2211yescharacteristic, complemented
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222D414yes—
81C2×#11758222C2314yes—
82C22×Dic122—21no—
83C22×Dic122D411yescharacteristic
84C22×Dic122C2311yescharacteristic
85C2×Q8×D61—22no—
86C2×Q8×D61—42no—
87C2×Q8×D61—42no—
88C2×Q8×D61C2314yescomplemented
89C22×D244—21no—
90C22×D244D411yescharacteristic
91C22×D244C2311yescharacteristic
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C22×C22⋊D61D411yescharacteristic
96C22×C22⋊D61D411yescharacteristic
97C2×D4×D61—22no—
98C2×D4×D61—42no—
99C2×D4×D61—42no—
100C2×D4×D61C2314yes—
101C22×C4×D61—21no—
102C22×C4×D61C2311yescharacteristic
103C22×C4×D61C2311yescharacteristic
104C2×#11758190—42no—
105C2×#11758190C2314yes—
106C2×#11758200—42no—
107C2×#11758200C2314yes—
108C2×#11758201—42no—
109C2×#11758201C2314yes—
110C22×#92418—42no—
111C22×#92418C2311yescharacteristic
112C22×#92418C2311yescharacteristic
113C22×#92418C2314yescomplemented
114#14519776—28no—
115#14519773—28no—
116#14519763—28no—
117#14519763—28no—
118#14519762—28no—
119#14519759—28no—
120#14519757—22no—
121#14519757C2314yes—
122#14519756—22no—
123#14519756C2314yescomplemented
124#14519753—22no—
125#14519753C2314yes—
126#14519752—22no—
127#14519752C2314yes—
128#14519751—22no—
129#14519751C2314yes—
130#14519748—22no—
131#14519748C2314yes—
132#14519747—28no—
133#14519745—28no—
134#14519735—22no—
135#14519735—22no—
136#14519735C2314yes—
137#14519735C2314yescomplemented
138C2×C4⋊Dic61—21no—
139C2×C4⋊Dic61C2311yescharacteristic
140C2×C4⋊Dic61C2311yescharacteristic
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×C4×Dic61—21no—
152C2×C4×Dic61—21no—
153#14519711C2314yescomplemented
154#14519708C2314yescomplemented
155#14519708C2314yescomplemented
156#14519702C2314yescomplemented
157#14519701C2314yescomplemented
158#14519700C2314yescomplemented
159#14519699C2314yes—
160#14519698C2314yes—
161#14519697C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164#14519689C2314yescomplemented
165#14519689C2314yescomplemented
166C22×Q8×C61C2311yescharacteristic
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61C2311yescharacteristic
170C2×SD16×C61—42no—
171C2×SD16×C61C2314yes—
172C2×M16×C61—42no—
173C2×M16×C61C2314yescomplemented
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2311yescharacteristic
176C22⋊Q8×C61—22no—
177C22⋊Q8×C61C2314yescomplemented
178#121×C61—22no—
179#121×C61C2314yes—
180C2×C4⋊C4×C61—21no—
181C2×C4⋊C4×C61C2311yescharacteristic
182C2×C4⋊C4×C61C2311yescharacteristic
183C2×C22⋊C4×C61—21no—
184C2×C22⋊C4×C61—21no—
185#107×C61C2314yescomplemented
186#103×C61C2314yescomplemented
187#102×C61C2314yes—
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C23×D61—21no—
191C23×D61—24no—
192C23×D61—44no—
193C23×D61—82no—
194C23×D61—82no—
195C23×D61C2×D411yescharacteristic
196C23×D61C2×D411yescharacteristic
197C2×Q8×C61—21no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61C2412yes—
201C2×D4×C61—24no—
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—82no—
206C2×D4×C61C2412yes—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
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—42no—
220C2×C22⋊D61—42no—
221C2×C22⋊D61—44no—
222C2×C22⋊D61—82no—
223C2×C22⋊D61—82no—
224C2×C22⋊D61C2×D414yes—
225C2×C22⋊D61C2×D414yes—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231Q8×D61—44no—
232Q8×D61—44no—
233Q8×D61—48no—
234D4×D61—44no—
235D4×D61—44no—
236D4×D61—48no—
237#11758222—48no—
238#11758222—44no—
239#11758222—44no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—21no—
243C2×D244—24no—
244C2×D244—42no—
245C2×D244—82no—
246C2×D244C2×D414yes—
247C2×D244C2412yes—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×C4×D61—24no—
253C2×C4×D61—44no—
254C2×C4×D61C2×D412yes—
255C2×C4×D61C2×D412yes—
256C2×C4×D61C2412yes—
257C2×C4×D61C2412yes—
258C2×Dic122—22no—
259C2×Dic122—22no—
260C2×Dic122—21no—
261C2×Dic122—24no—
262C2×Dic122—42no—
263C2×Dic122—44no—
264C2×Dic122C2×D414yes—
265C2×Dic122C2412yes—
266SD16×C61—44no—
267M16×C61—44no—
268C2×C8×C61—22no—
269C2×C8×C61—22no—
270C2×C8×C61C2412yes—
271C2×C8×C61C2412yes—
272C4⋊C4×C61—24no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61C2412yes—
276C4⋊C4×C61C2412yes—
277C22⋊C4×C61—24no—
278C22⋊C4×C61—24no—
279C22⋊Dic61—24no—
280C22⋊Dic61—24no—
281#11758201—44no—
282#11758200—44no—
283#11758198—24no—
284#11758198—24no—
285#11758198—24no—
286#11758198—24no—
287#11758198—24no—
288#11758198—24no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—24no—
292C4⋊Dic61C2412yes—
293C4⋊Dic61C2412yes—
294#11758196—24no—
295#11758196—24no—
296C4×Dic61—24no—
297C4×Dic61—24no—
298C2×#92418—22no—
299C2×#92418—22no—
300C2×#92418—44no—
301C2×#92418C2412yes—
302C2×#92418C2412yes—
303#11758190—44no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61C22×D412yes—
312C23×C61C22×D411yescharacteristic
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—48no—
321C22×D61—42no—
322C22×D61—42no—
323C22×D61—42no—
324C22×D61—84no—
325C22×D61—84no—
326C22×D61—816no—
327C22×D61C22×D412yes—
328C22×D61C22×D412yes—
329Q8×C61—22no—
330Q8×C61—22no—
331Q8×C61—42no—
332D4×C61—22no—
333D4×C61—22no—
334D4×C61—42no—
335D4×C61—84no—
336C2×C4×C61—22no—
337C2×C4×C61—24no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61C22×D412yes—
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61H(5,𝔽2)12yes—
349C2×C4×C61H(5,𝔽2)12yes—
350C2×C4×C61C2511yescharacteristic
351C22⋊D61—44no—
352C22⋊D61—44no—
353C22⋊D61—48no—
354C22⋊D61—84no—
355C22⋊D61—84no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61—42no—
364C2×Dic61C22×D412yes—
365C2×Dic61C22×D412yes—
366D244—22no—
367D244—22no—
368D244—44no—
369D244—42no—
370D244—84no—
371C4×D61—24no—
372C4×D61—24no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—48no—
378Dic122—22no—
379Dic122—22no—
380Dic122—44no—
381Dic122—48no—
382Dic122—42no—
383C8×C61—22no—
384C8×C61—22no—
385#92418—22no—
386#92418—22no—
387C2×#3200—611nomaximal, Sylow
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—44no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—84no—
396C22×C61#53412yes—
397C22×C61#57712yes—
398C22×C61#57712yes—
399C22×C61C23×D411yescharacteristic
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—44no—
407C2×D61—44no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—816no—
412C2×D61—84no—
413C4×C61—22no—
414C4×C61—42no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61#53412yes—
418C4×C61C2×H(5,𝔽2)11yescharacteristic
419C4×C61C2×H(5,𝔽2)11yescharacteristic
420Dic61—22no—
421Dic61—22no—
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425C2×#536—611no—
426C2×#535—611no—
427#3200—6116no—
428C2×#485—611no—
429C2×#485—611no—
430C2×#482—611no—
431C2×#482—611no—
432C2×#468—611no—
433C2×#468D6111yescharacteristic, complemented
434C2×#465—611no—
435C2×#465—611no—
436C2×#448—611no—
437C2×#448—611no—
438C2×#450—611no—
439C2×#450—611no—
440C2×#408—611no—
441C2×C61—42no—
442C2×C61—82no—
443C2×C61#320014yescomplemented
444C2×C61C2×#53411yescharacteristic
445C2×C61C2×#57711yescharacteristic
446C2×C61C2×#57711yescharacteristic
447D61—42no—
448D61—42no—
449D61—82no—
450C22×#41—611no—
451C23×Q8—611no—
452C23×D4—611no—
453C22×SD16—611no—
454C22×SD16—611no—
455C22×SD16—611no—
456C22×SD16C2×D6111yescharacteristic
457C22×M16C2×D6111yescharacteristic, complemented
458C23×C8—611no—
459#536—618no—
460#536—1224no—
461#535—618no—
462#535—1224no—
463C2×C4⋊Q8—1221no—
464C2×#127—1221no—
465C2×#124—1221no—
466C2×#124—1221no—
467C2×#123—1221no—
468C2×#123—1221no—
469C2×C22⋊Q8—611no—
470C2×C22⋊Q8—611no—
471C2×C22⋊Q8—611no—
472C2×C22⋊Q8C2×D6111yescharacteristic, complemented
473C2×#121—611no—
474C2×#121—611no—
475C2×#121—611no—
476C2×#121C2×D6111yescharacteristic
477C2×#120—1221no—
478C2×#120—1221no—
479C2×#117—611no—
480C2×#117—611no—
481#485—618no—
482#485—618no—
483#482—618no—
484#482—618no—
485#468—618no—
486#468C2×D6118yescomplemented
487#465—618no—
488#465—618no—
489#450—618no—
490#450—618no—
491#448—618no—
492#448—618no—
493C2×#107—611no—
494C2×#107C2×D6111yescharacteristic, complemented
495C2×#106—611no—
496C2×#106—611no—
497C2×#103—611no—
498C2×#103—611no—
499C2×#103—611no—
500C2×#103C2×D6111yescharacteristic, complemented
501C2×#102—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102C2×D6111yescharacteristic
505#408—618no—
506C2×C22⋊C8—611no—
507C2×C22⋊C8—611no—
508C2×C22⋊C8—611no—
509C2×C22⋊C8—611no—
510C61C2×#320011yescharacteristic, complemented, Sylow
511C25—1221no—
512C2×#41—614no—
513C2×#41—614no—
514C2×#41—2442no—
515C2×#41—2442no—
516C22×Q8—611no—
517C22×Q8—614no—
518C22×Q8—611no—
519C22×Q8—1221no—
520C22×Q8—1222no—
521C22×Q8—2442no—
522C22×Q8—2442no—
523C22×Q8C22×D6111yescharacteristic
524C22×D4—21no—
525C22×D4—611no—
526C22×D4—611no—
527C22×D4—614no—
528C22×D4—611no—
529C22×D4—611no—
530C22×D4—1221no—
531C22×D4—1222no—
532C22×D4—1221no—
533C22×D4—1221no—
534C22×D4—1221no—
535C22×D4—2442no—
536C22×D4—2442no—
537C22×D4C22×D6111yescharacteristic
538C23×C4—611no—
539C23×C4—611no—
540C23×C4—1221no—
541C23×C4C22×D6111yescharacteristic
542C2×SD16—42no—
543C2×SD16—614no—
544C2×SD16—614no—
545C2×SD16—614no—
546C2×SD16—2442no—
547C2×SD16—2442no—
548C2×SD16—2442no—
549C2×SD16C22×D6114yes—
550C2×M16—42no—
551C2×M16C22×D6114yescomplemented
552C22×C8—611no—
553C22×C8—611no—
554C22×C8—614no—
555C22×C8—2442no—
556C22×C8C22×D6111yescharacteristic
557C22×C8C22×D6111yescharacteristic
558C4⋊Q8—1228no—
559#127—1228no—
560#124—1228no—
561#124—1228no—
562#123—1228no—
563#123—1228no—
564C22⋊Q8—22no—
565C22⋊Q8—614no—
566C22⋊Q8—614no—
567C22⋊Q8—614no—
568C22⋊Q8—1222no—
569C22⋊Q8—1222no—
570C22⋊Q8—1222no—
571C22⋊Q8C22×D6114yescomplemented
572#121—22no—
573#121—614no—
574#121—614no—
575#121—614no—
576#121—1222no—
577#121—1222no—
578#121—1222no—
579#121C22×D6114yes—
580#120—1228no—
581#120—1228no—
582#117—614no—
583#117—614no—
584#117—1222no—
585#117—1222no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4C22×D6111yescharacteristic
593C2×C4⋊C4C22×D6111yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C42—1221no—
605C2×C42—1221no—
606#107—614no—
607#107C22×D6114yescomplemented
608#106—614no—
609#106—614no—
610#103—614no—
611#103—614no—
612#103—614no—
613#103C22×D6114yescomplemented
614#102—614no—
615#102—614no—
616#102—614no—
617#102C22×D6114yes—
618C22⋊C8—614no—
619C22⋊C8—614no—
620C22⋊C8—614no—
621C22⋊C8—614no—
622C24—21no—
623C24—611no—
624C24—611no—
625C24—1224no—
626C24—1221no—
627C24—4882no—
628C24—4882no—
629C24—2444no—
630C24D4×D6111yescharacteristic
631#41—2448no—
632#41—2444no—
633#41—2444no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—614no—
638C2×Q8—612no—
639C2×Q8—1224no—
640C2×Q8—1221no—
641C2×Q8—1222no—
642C2×Q8—1222no—
643C2×Q8—2442no—
644C2×Q8—2444no—
645C2×Q8—2444no—
646C2×Q8—2444no—
647C2×Q8—2448no—
648C2×Q8C23×D6112yes—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—82no—
654C2×D4—614no—
655C2×D4—614no—
656C2×D4—614no—
657C2×D4—612no—
658C2×D4—1224no—
659C2×D4—1224no—
660C2×D4—1224no—
661C2×D4—1224no—
662C2×D4—1221no—
663C2×D4—1222no—
664C2×D4—1222no—
665C2×D4—4882no—
666C2×D4—4882no—
667C2×D4—4882no—
668C2×D4—2442no—
669C2×D4—2444no—
670C2×D4—2444no—
671C2×D4—2448no—
672C2×D4—2442no—
673C2×D4—2442no—
674C2×D4—2444no—
675C2×D4C23×D6112yes—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—612no—
684C22×C4—612no—
685C22×C4—612no—
686C22×C4—612no—
687C22×C4—1224no—
688C22×C4—1222no—
689C22×C4—1222no—
690C22×C4—1222no—
691C22×C4—1222no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—2444no—
696C22×C4D4×D6112yes—
697C22×C4D4×D6111yescharacteristic
698C22×C4C23×D6112yes—
699C22×C4C23×D6111yescharacteristic
700SD16—44no—
701SD16—2444no—
702SD16—2444no—
703SD16—2444no—
704M16—44no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—612no—
708C2×C8—612no—
709C2×C8—1222no—
710C2×C8—1222no—
711C2×C8—2444no—
712C2×C8C23×D6112yes—
713C2×C8C23×D6112yes—
714C4⋊C4—24no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—612no—
718C4⋊C4—612no—
719C4⋊C4—1224no—
720C4⋊C4—1224no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1224no—
724C4⋊C4C23×D6112yes—
725C4⋊C4C23×D6112yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—1224no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C42—1224no—
737C42—1224no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—612no—
746C23—612no—
747C23—1222no—
748C23—1222no—
749C23—1222no—
750C23—1222no—
751C23—1222no—
752C23—1222no—
753C23—1222no—
754C23—4884no—
755C23—4884no—
756C23—48816no—
757C23—2448no—
758C23—2442no—
759C23—2442no—
760C23—2442no—
761C23C2×D4×D6112yes—
762C23C2×D4×D6111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—1222no—
767Q8—1222no—
768Q8—2444no—
769Q8—2448no—
770Q8—2442no—
771D4—22no—
772D4—22no—
773D4—42no—
774D4—84no—
775D4—1222no—
776D4—1222no—
777D4—4884no—
778D4—4884no—
779D4—4884no—
780D4—2444no—
781D4—2444no—
782D4—2444no—
783D4—2448no—
784D4—2442no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—612no—
796C2×C4—612no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1224no—
800C2×C4—1224no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—2448no—
809C2×C4—2442no—
810C2×C4—2442no—
811C2×C4—2442no—
812C2×C4C2×D4×D6112yes—
813C2×C4C2×D4×D6111yescharacteristic
814C2×C4#1451982212yes—
815C2×C4#1451982312yes—
816C2×C4C24×D6111yescharacteristic
817C8—22no—
818C8—22no—
819C8—1222no—
820C8—1222no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—1222no—
830C22—1222no—
831C22—1222no—
832C22—1222no—
833C22—1222no—
834C22—1222no—
835C22—48816no—
836C22—4884no—
837C22—2442no—
838C22—2442no—
839C22—2442no—
840C22—2444no—
841C22—2444no—
842C22#1684032012yes—
843C22#1684057112yes—
844C22#1684057212yes—
845C22C22×D4×D6111yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—1222no—
851C4—1222no—
852C4—2442no—
853C4—2442no—
854C4—2442no—
855C4#1684032012yes—
856C4C2×#1451982211yescharacteristic
857C4C2×#1451982311yescharacteristic
858C2—42no—
859C2—82no—
860C2—4882no—
861C2—2442no—
862C2—2442no—
863C2#2145668714yesdirect product factor
864C2C2×#1684032011yescharacteristic
865C2C2×#1684057111yescharacteristic
866C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#468C2
socleC23×C61C22×D4
prime radicalC2×#16840328C2
hypercenterC2×#468D61
hypocenterC61C2×#3200
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#16840335C2semidirect
3. #21456687C2direct (N × H)
4. C2×#16840105C2semidirect
5. C2×#16840102C2semidirect
6. C2×#16840089C2semidirect
7. C2×#16840084C2semidirect
8. C2×#16840008C2semidirect
9. C2×#16839993C2semidirect
10. C2×#16839989C2semidirect
11. C2×#16839902C2semidirect
12. C2×#16839899C2semidirect
13. C2×#16839914C2semidirect
14. C2×#16839911C2semidirect
15. C2×#16839730C2semidirect
16. C2×C61×#468C2semidirect
18. C22×Q8×D61C22semidirect
23. C23×#92418C22semidirect
25. #16840335C22semidirect
35. C2×#14519756C22semidirect
43. C2×#14519735C22semidirect
44. #16840105C22semidirect
45. #16840102C22semidirect
46. #16840089C22semidirect
47. #16840084C22semidirect
48. #16840008C22semidirect
49. #16839993C22semidirect
50. #16839989C22semidirect
51. #16839914C22semidirect
52. #16839911C22semidirect
53. #16839902C22semidirect
54. #16839899C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519708C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519702C22semidirect
59. C2×#14519701C22semidirect
60. C2×#14519700C22semidirect
64. #16839730C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519689C22semidirect
70. C22×M16×C61C22semidirect
71. C2×C22⋊Q8×C61C22semidirect
73. C61×#468C22semidirect
74. C2×#107×C61C22semidirect
75. C2×#103×C61C22semidirect
88. C2×Q8×D61C23semidirect
113. C22×#92418C23semidirect
123. #14519756C23semidirect
137. #14519735C23semidirect
153. #14519711C23semidirect
154. #14519708C23semidirect
155. #14519708C23semidirect
156. #14519702C23semidirect
157. #14519701C23semidirect
158. #14519700C23semidirect
164. #14519689C23semidirect
165. #14519689C23semidirect
173. C2×M16×C61C23semidirect
177. C22⋊Q8×C61C23semidirect
185. #107×C61C23semidirect
186. #103×C61C23semidirect
433. C2×#468D61semidirect
443. C2×C61#3200semidirect
457. C22×M16C2×D61semidirect
472. C2×C22⋊Q8C2×D61semidirect
486. #468C2×D61semidirect
494. C2×#107C2×D61semidirect
500. C2×#103C2×D61semidirect
510. C61C2×#3200semidirect
551. C2×M16C22×D61semidirect
571. C22⋊Q8C22×D61semidirect
607. #107C22×D61semidirect
613. #103C22×D61semidirect
863. C2#21456687direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403352
C2×#168403282
#214566872
C2×#168401052
C2×#168401022
C2×#168400892
C2×#168400842
C2×#168400082
C2×#168399932
C2×#168399892
C2×#168399022
C2×#168398992
C2×#168399142
C2×#168399112
C2×#168397302
C2×C61×#4682
C2×#320061