Finite Group Databasebeta

← C2×#21457797 #30556653

Subgroups — C2×#21457797 #30556653

Order 15616.

2190 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic, complemented
2C2×#16840417C211yesmaximal, characteristic, complemented
3#21457797C2116yesmaximal, direct product factor
4C2×#16840131C211yesmaximal, characteristic, complemented
5C2×#16840104C211yesmaximal, characteristic, complemented
6C2×#16840093C211yesmaximal, characteristic, complemented
7C2×#16840063C211yesmaximal, characteristic, complemented
8C2×#16840008C211yesmaximal, characteristic, complemented
9C2×#16839991C211yesmaximal, characteristic, complemented
10C2×#16839968C211yesmaximal, characteristic, complemented
11C2×#16839909C211yesmaximal, characteristic, complemented
12C2×#16839909C211yesmaximal, characteristic, complemented
13C2×#16839875C211yesmaximal, characteristic, complemented
14C2×#16839764C211yesmaximal, characteristic, complemented
15C2×#16839759C211yesmaximal, characteristic, complemented
16C2×C61×#435C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758222C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×D488C2211yescharacteristic
22#16840458—24no—
23#16840458C2218yescomplemented
24#16840417—24no—
25#16840417C2218yescomplemented
26C2×#14519777C2211yescharacteristic
27C2×#14519772—21no—
28C2×#14519769C2211yescharacteristic
29C2×#14519759—21no—
30C2×#14519759—21no—
31C2×#14519759—21no—
32C2×#14519756C2211yescharacteristic
33C2×#14519756C2211yescharacteristic
34C2×#14519751C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36C2×#14519749—21no—
37C2×#14519748—21no—
38C2×C4×D244C2211yescharacteristic
39C2×C4×D244C2211yescharacteristic
40C2×#14519737—21no—
41C2×#14519736C2211yescharacteristic
42C22×C4⋊Dic61C2211yescharacteristic
43C2×C4⋊C4×D61—21no—
44#16840131C2218yescomplemented
45#16840104C2218yescomplemented
46#16840093C2218yescomplemented
47#16840063C2218yescomplemented
48#16840008C2218yescomplemented
49#16839991C2218yescomplemented
50#16839968C2218yescomplemented
51#16839909C2218yescomplemented
52#16839909C2218yescomplemented
53#16839875C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57#16839764C2218yescomplemented
58#16839759C2218yescomplemented
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#435C2218yescomplemented
73C2×C4⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—22no—
79C2×#11758222—24no—
80C2×#11758222—24no—
81C2×#11758222—42no—
82C2×#11758222—42no—
83C2×#11758222C2314yes—
84C2×#11758222C2314yes—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2311yescharacteristic
87C22×D244C2311yescharacteristic
88C22×D244C2311yescharacteristic
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C23×Dic61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C2×#11758190—42no—
99C2×#11758190—42no—
100C2×#11758190C2314yes—
101C2×#11758190C2314yes—
102C2×D488—24no—
103C2×D488C2314yes—
104#14519777—22no—
105#14519777C2314yes—
106#14519772—28no—
107#14519769—22no—
108#14519769C2314yes—
109#14519759—28no—
110#14519759—28no—
111#14519759—28no—
112#14519756—22no—
113#14519756—22no—
114#14519756C2314yes—
115#14519756C2314yes—
116#14519751—22no—
117#14519751—22no—
118#14519751C2314yes—
119#14519751C2314yes—
120#14519749—28no—
121#14519748—28no—
122C4×D244—22no—
123C4×D244—22no—
124C4×D244C2314yes—
125C4×D244C2314yes—
126#14519737—28no—
127#14519736—22no—
128#14519736C2314yes—
129C2×C4⋊Dic61—22no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61C2314yes—
134C2×C4⋊Dic61C2311yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C4⋊C4×D61—28no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yes—
152#14519709C2314yes—
153#14519709C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519702C2314yes—
159#14519702C2314yes—
160#14519699C2314yes—
161#14519699C2314yes—
162#14519699C2314yes—
163#14519699C2314yes—
164C22×D4×C61D411yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C2×M16×C61—42no—
168C2×M16×C61C2314yes—
169C22×C8×C61—42no—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2314yes—
175C4×D4×C61D414yes—
176C4×D4×C61C2314yes—
177C2×C4⋊C4×C61D411yescharacteristic
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C22⋊C4×C61D411yescharacteristic
180C2×C42×C61C2311yescharacteristic
181C4⋊C8×C61C2314yes—
182C22⋊C8×C61C2314yes—
183C22⋊C8×C61C2314yes—
184#97×C61C2314yes—
185C24×C61C2×D411yescharacteristic
186C24×C61C2×D411yescharacteristic
187C23×D61—21no—
188C23×D61—21no—
189C2×D4×C61—42no—
190C2×D4×C61C2×D414yes—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D412yes—
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2412yes—
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—44no—
209C2×C22⋊D61—44no—
210C2×C22⋊D61—44no—
211C2×C22⋊D61—82no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—82no—
220#11758222—28no—
221#11758222—28no—
222#11758222—44no—
223#11758222—44no—
224#11758222—48no—
225#11758222—48no—
226C2×D244—21no—
227C2×D244—22no—
228C2×D244—22no—
229C2×D244—22no—
230C2×D244—21no—
231C2×D244#4114yes—
232C2×D244C2412yes—
233C2×D244C2412yes—
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—44no—
239C2×C4×D61—44no—
240C2×C4×D61—44no—
241C2×C4×D61—82no—
242C2×Dic122—22no—
243C2×Dic122—22no—
244C2×Dic122—22no—
245C2×Dic122—22no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122C2412yes—
249C2×Dic122C2412yes—
250M16×C61—44no—
251C2×C8×C61—22no—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C2×C8×C61—44no—
256C2×C8×C61C2412yes—
257C2×C8×C61C2412yes—
258C2×C8×C61C2412yes—
259C2×C8×C61C2412yes—
260C4⋊C4×C61C2×D414yes—
261C22⋊C4×C61C2×D414yes—
262C22⋊C4×C61C2×D414yes—
263C42×C61C2×D412yes—
264C42×C61C2412yes—
265C22⋊Dic61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272C4⋊Dic61—24no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—24no—
276C4⋊Dic61—24no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61C2412yes—
280C4⋊Dic61C2412yes—
281C4⋊Dic61C2412yes—
282C4⋊Dic61C2412yes—
283#11758196—24no—
284#11758196—24no—
285#11758196—24no—
286#11758196—24no—
287C4×Dic61—24no—
288D488—28no—
289#11758190—44no—
290#11758190—44no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61C22×D412yes—
298C23×C61C22×D412yes—
299C23×C61C22×D411yescharacteristic
300C22×D61—24no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—42no—
308D4×C61—44no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—24no—
314C2×C4×C61—24no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D412yes—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4112yes—
325C2×C4×C61H(5,𝔽2)12yes—
326C2×C4×C61C2511yescharacteristic
327C22⋊D61—48no—
328C22⋊D61—48no—
329C22⋊D61—48no—
330C22⋊D61—84no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—84no—
344D244—24no—
345D244—22no—
346D244—22no—
347D244—22no—
348D244—42no—
349D244C2×#4114yes—
350C4×D61—48no—
351C4×D61—48no—
352C4×D61—48no—
353C4×D61—84no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—42no—
359Dic122—42no—
360C8×C61—22no—
361C8×C61—22no—
362C8×C61—22no—
363C8×C61—22no—
364C2×#3307—611nomaximal, Sylow
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—44no—
372C22×C61—44no—
373C22×C61#54612yes—
374C22×C61#57512yes—
375C22×C61#57712yes—
376C22×C61C23×D411yescharacteristic
377C2×D61—24no—
378C2×D61—48no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C2×D61—84no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61#54612yes—
390C4×C61C22×#4111yescharacteristic
391C4×C61C2×H(5,𝔽2)11yescharacteristic
392Dic61—42no—
393Dic61—42no—
394Dic61—42no—
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#553—611no—
399C2×#547—611no—
400#3307—6116no—
401C2×#491—611no—
402C2×#485—611no—
403C2×#483—611no—
404C2×#478—611no—
405C2×#468—611no—
406C2×#465—611no—
407C2×#461—611no—
408C2×#449—611no—
409C2×#449—611no—
410C2×#442—611no—
411C2×#435D6111yescharacteristic, complemented
412C2×#417—611no—
413C2×#416—611no—
414C2×C61—42no—
415C2×C61—42no—
416C2×C61#330714yescomplemented
417C2×C61C2×#54611yescharacteristic
418C2×C61C2×#57511yescharacteristic
419C2×C61C2×#57711yescharacteristic
420D61—44no—
421D61—82no—
422C22×#41—611no—
423C22×#41—611no—
424C22×SD16—611no—
425C22×SD16—611no—
426C22×D8—611no—
427C22×M16C2×D6111yescharacteristic
428C23×C8C2×D6111yescharacteristic
429#553—618no—
430#553—1224no—
431#547—618no—
432#547—1224no—
433C2×C4⋊Q8—611no—
434C2×#126—1221no—
435C2×#125—611no—
436C2×#123—1221no—
437C2×#123—1221no—
438C2×#123—1221no—
439C2×C22⋊Q8—611no—
440C2×C22⋊Q8—611no—
441C2×#121—611no—
442C2×#121—611no—
443C2×#121—1221no—
444C2×#121—1221no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4—1221no—
448C2×C4×D4C2×D6111yescharacteristic
449C2×#117—611no—
450C22×C4⋊C4—611no—
451C22×C4⋊C4—1221no—
452#491—618no—
453#485—618no—
454#483—618no—
455#478—618no—
456#468—618no—
457#465—618no—
458#461—618no—
459#449—618no—
460#449—618no—
461#442—618no—
462#435C2×D6118yescomplemented
463C2×#107—611no—
464C2×#106—611no—
465C2×#106—611no—
466C2×C4⋊C8C2×D6111yescharacteristic
467#417—618no—
468#416—618no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×C22⋊C8C2×D6111yescharacteristic
480C2×C22⋊C8C2×D6111yescharacteristic
481C2×#97C2×D6111yescharacteristic
482C61C2×#330711yescharacteristic, complemented, Sylow
483C2×#41—614no—
484C2×#41—614no—
485C2×#41—1224no—
486C2×#41—1224no—
487C2×#41—1222no—
488C2×#41—1222no—
489C2×#41—2442no—
490C2×#41—2442no—
491C22×Q8—611no—
492C22×Q8—611no—
493C22×D4—611no—
494C22×D4—611no—
495C22×D4—1221no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4D24411yescharacteristic
500C23×C4—1221no—
501C23×C4—1221no—
502C23×C4—1221no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4C22×D6111yescharacteristic
506C23×C4C22×D6111yescharacteristic
507C2×SD16—614no—
508C2×SD16—614no—
509C2×SD16—2442no—
510C2×SD16—2442no—
511C2×D8—614no—
512C2×D8—1224no—
513C2×M16—42no—
514C2×M16C22×D6114yes—
515C22×C8—42no—
516C22×C8C22×D6111yescharacteristic
517C22×C8C22×D6111yescharacteristic
518C22×C8C22×D6111yescharacteristic
519C22×C8C22×D6111yescharacteristic
520C22×C8C22×D6114yes—
521C4⋊Q8—614no—
522C4⋊Q8—1222no—
523#126—1228no—
524#125—614no—
525#125—1222no—
526#123—1228no—
527#123—1228no—
528#123—1228no—
529C22⋊Q8—614no—
530C22⋊Q8—614no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533#121—614no—
534#121—614no—
535#121—1228no—
536#121—1228no—
537#121—1222no—
538#121—1222no—
539C4×D4—614no—
540C4×D4—614no—
541C4×D4—1228no—
542C4×D4—1222no—
543C4×D4—1222no—
544C4×D4D24414yes—
545C4×D4C22×D6114yes—
546#117—614no—
547#117—1222no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—614no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1222no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1228no—
562C2×C4⋊C4D24411yescharacteristic
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4D24411yescharacteristic
571C2×C22⋊C4D24411yescharacteristic
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574#107—614no—
575#106—614no—
576#106—614no—
577C4⋊C8C22×D6114yes—
578#103—614no—
579#103—614no—
580#103—614no—
581#103—614no—
582#103—614no—
583#103—614no—
584#102—614no—
585#102—614no—
586#102—614no—
587#102—614no—
588C22⋊C8C22×D6114yes—
589C22⋊C8C22×D6114yes—
590#97C22×D6114yes—
591C24—1221no—
592C24—1221no—
593C24C2×D24411yescharacteristic
594C24C2×D24411yescharacteristic
595#41—1228no—
596#41—1228no—
597#41—2444no—
598#41—2444no—
599#41—2448no—
600#41—2448no—
601C2×Q8—612no—
602C2×Q8—612no—
603C2×Q8—1221no—
604C2×Q8—1221no—
605C2×Q8—1222no—
606C2×Q8—1222no—
607C2×Q8—1222no—
608C2×Q8—1222no—
609C2×D4—42no—
610C2×D4—614no—
611C2×D4—612no—
612C2×D4—612no—
613C2×D4—1224no—
614C2×D4—1224no—
615C2×D4—1224no—
616C2×D4—1224no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1222no—
620C2×D4—1222no—
621C2×D4—1222no—
622C2×D4—4882no—
623C2×D4—2444no—
624C2×D4—2444no—
625C2×D4—2444no—
626C2×D4C2×D24414yes—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—1224no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1224no—
639C22×C4—1224no—
640C22×C4—1224no—
641C22×C4—1224no—
642C22×C4—4882no—
643C22×C4—4882no—
644C22×C4—2444no—
645C22×C4—2444no—
646C22×C4—2444no—
647C22×C4C2×D24412yes—
648C22×C4C2×D24412yes—
649C22×C4C2×D24411yescharacteristic
650C22×C4C2×D24411yescharacteristic
651C22×C4C2×D24411yescharacteristic
652C22×C4C2×D24411yescharacteristic
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656SD16—2444no—
657SD16—2444no—
658D8—1228no—
659M16—44no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—44no—
665C2×C8C23×D6112yes—
666C2×C8C23×D6112yes—
667C2×C8C23×D6112yes—
668C2×C8C23×D6112yes—
669C4⋊C4—612no—
670C4⋊C4—612no—
671C4⋊C4—612no—
672C4⋊C4—612no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1224no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4—1224no—
684C4⋊C4C2×D24414yes—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4C2×D24414yes—
693C22⋊C4C2×D24414yes—
694C42—1224no—
695C42C2×D24412yes—
696C42C23×D6112yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—1222no—
704C23—1224no—
705C23—1222no—
706C23—2442no—
707C23—2442no—
708C23—2442no—
709C23—2442no—
710C23—2442no—
711C23C22×D24412yes—
712C23C22×D24412yes—
713C23C22×D24411yescharacteristic
714Q8—1222no—
715Q8—1222no—
716Q8—1222no—
717Q8—1222no—
718Q8—2442no—
719Q8—2442no—
720D4—44no—
721D4—614no—
722D4—1222no—
723D4—1222no—
724D4—1222no—
725D4—1224no—
726D4—4884no—
727D4—2448no—
728D4—2448no—
729D4—2448no—
730D4—2442no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—4884no—
748C2×C4—4884no—
749C2×C4—2448no—
750C2×C4—2448no—
751C2×C4—2448no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4C22×D24412yes—
759C2×C4C22×D24412yes—
760C2×C4C22×D24412yes—
761C2×C4C22×D24412yes—
762C2×C4C22×D24411yescharacteristic
763C2×C4#41×D6112yes—
764C2×C4#1451982212yes—
765C2×C4C24×D6111yescharacteristic
766C8—22no—
767C8—22no—
768C8—22no—
769C8—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—1224no—
779C22—4884no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2448no—
786C22#1684040712yes—
787C22#1684056212yes—
788C22#1684057412yes—
789C22C23×D24411yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—2442no—
795C4—2442no—
796C4—2442no—
797C4—2442no—
798C4—2442no—
799C4—2442no—
800C4#1684040712yes—
801C4C2×#41×D6111yescharacteristic
802C4C2×#1451982211yescharacteristic
803C2—42no—
804C2—42no—
805C2—4882no—
806C2—2444no—
807C2#2145779714yesdirect product factor
808C2C2×#1684040711yescharacteristic
809C2C2×#1684056211yescharacteristic
810C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#435C2
socleC23×C61C22×D4
hypercenterC2×#435D61
hypocenterC61C2×#3307
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16840458C2semidirect
2. C2×#16840417C2semidirect
3. #21457797C2direct (N × H)
4. C2×#16840131C2semidirect
5. C2×#16840104C2semidirect
6. C2×#16840093C2semidirect
7. C2×#16840063C2semidirect
8. C2×#16840008C2semidirect
9. C2×#16839991C2semidirect
10. C2×#16839968C2semidirect
11. C2×#16839909C2semidirect
12. C2×#16839909C2semidirect
13. C2×#16839875C2semidirect
14. C2×#16839764C2semidirect
15. C2×#16839759C2semidirect
16. C2×C61×#435C2semidirect
23. #16840458C22semidirect
25. #16840417C22semidirect
44. #16840131C22semidirect
45. #16840104C22semidirect
46. #16840093C22semidirect
47. #16840063C22semidirect
48. #16840008C22semidirect
49. #16839991C22semidirect
50. #16839968C22semidirect
51. #16839909C22semidirect
52. #16839909C22semidirect
53. #16839875C22semidirect
57. #16839764C22semidirect
58. #16839759C22semidirect
72. C61×#435C22semidirect
411. C2×#435D61semidirect
416. C2×C61#3307semidirect
462. #435C2×D61semidirect
482. C61C2×#3307semidirect
807. C2#21457797direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404582
C2×#168404172
#214577972
C2×#168401312
C2×#168401042
C2×#168400932
C2×#168400632
C2×#168400082
C2×#168399912
C2×#168399682
C2×#168399092
C2×#168398752
C2×#168397642
C2×#168397592
C2×C61×#4352
C2×#330761