Finite Group Databasebeta

← C2×#21456673 #30550668

Subgroups — C2×#21456673 #30550668

Order 15616.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840340C211yesmaximal, characteristic, complemented
2C2×#16840326C211yesmaximal, characteristic, complemented
3#21456673C2116yesmaximal, direct product factor
4C2×#16840081C211yesmaximal, characteristic, complemented
5C2×#16840104C211yesmaximal, characteristic, complemented
6C2×#16840087C211yesmaximal, characteristic, complemented
7C2×#16840076C211yesmaximal, characteristic, complemented
8C2×#16840015C211yesmaximal, characteristic, complemented
9C2×#16840008C211yesmaximal, characteristic, complemented
10C2×#16839998C211yesmaximal, characteristic, complemented
11C2×#16839991C211yesmaximal, characteristic, complemented
12C2×#16839909C211yesmaximal, characteristic, complemented
13C2×#16839909C211yesmaximal, characteristic, complemented
14C2×#16839915C211yesmaximal, characteristic, complemented
15C2×#16839898C211yesmaximal, characteristic, complemented
16C2×C61×#408C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic, complemented
18C23×D244C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×D488C2211yescharacteristic
22C22×D488C2211yescharacteristic
23#16840340—24no—
24#16840340C2218yescomplemented
25#16840326—24no—
26#16840326C2218yescomplemented
27C2×#14519773—21no—
28C2×#14519766—21no—
29C2×#14519756C2211yescharacteristic
30C2×#14519756C2211yescharacteristic, complemented
31C2×#14519753—21no—
32C2×#14519751C2211yescharacteristic
33C2×#14519751C2211yescharacteristic
34C2×#14519751C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36C2×#14519751C2211yescharacteristic
37C2×#14519751C2211yescharacteristic, complemented
38C2×#14519749—21no—
39C2×#14519749—21no—
40C2×#14519748—21no—
41C2×#14519745—21no—
42C2×#14519745—21no—
43C2×#14519736C2211yescharacteristic
44C22×C4⋊Dic61C2211yescharacteristic, complemented
45#16840104C2218yescomplemented
46#16840087C2218yescomplemented
47#16840081C2218yescomplemented
48#16840076C2218yescomplemented
49#16840015C2218yescomplemented
50#16840008C2218yescomplemented
51#16839998C2218yescomplemented
52#16839991C2218yescomplemented
53#16839915C2218yescomplemented
54#16839909C2218yescomplemented
55#16839909C2218yescomplemented
56#16839898C2218yescomplemented
57C2×#14519711C2211yescharacteristic, complemented
58C2×#14519711C2211yescharacteristic, complemented
59C2×#14519709C2211yescharacteristic, complemented
60C2×#14519709C2211yescharacteristic, complemented
61C2×#14519702C2211yescharacteristic, complemented
62C2×#14519702C2211yescharacteristic, complemented
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic, complemented
68C2×#14519699C2211yescharacteristic, complemented
69C22×#41×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic, complemented
71C23×C8×C61C2211yescharacteristic, complemented
72C61×#408C2218yescomplemented
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×C22⋊C8×C61C2211yescharacteristic, complemented
76C2×C22⋊C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—22no—
79C2×#11758222—42no—
80C2×#11758222—42no—
81C2×#11758222C2314yescomplemented
82C22×Dic122C2311yescharacteristic
83C22×D244—21no—
84C22×D244—22no—
85C22×D244—42no—
86C22×D244—42no—
87C22×D244C2311yescharacteristic
88C22×D244C2311yescharacteristic
89C22×D244C2311yescharacteristic
90C22×D244C2314yes—
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C22×C22⋊D61—21no—
96C22×C22⋊D61—21no—
97C22×C22⋊D61—21no—
98C23×Dic61—21no—
99C22×C4×D61—21no—
100C2×#11758190—42no—
101C2×#11758190—42no—
102C2×#11758190C2314yes—
103C2×#11758190C2314yes—
104C2×D488—42no—
105C2×D488—42no—
106C2×D488C2314yes—
107C2×D488C2314yes—
108#14519773—28no—
109#14519766—28no—
110#14519756—22no—
111#14519756—22no—
112#14519756C2314yes—
113#14519756C2314yescomplemented
114#14519753—28no—
115#14519751—22no—
116#14519751—22no—
117#14519751—22no—
118#14519751—22no—
119#14519751—22no—
120#14519751—22no—
121#14519751C2314yes—
122#14519751C2314yes—
123#14519751C2314yes—
124#14519751C2314yes—
125#14519751C2314yes—
126#14519751C2314yescomplemented
127#14519749—28no—
128#14519749—28no—
129#14519748—28no—
130#14519745—28no—
131#14519745—28no—
132#14519736—22no—
133#14519736C2314yes—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61—22no—
136C2×C4⋊Dic61C2311yescharacteristic
137C2×C4⋊Dic61C2311yescharacteristic
138C2×C4⋊Dic61C2311yescharacteristic
139C2×C4⋊Dic61C2311yescharacteristic
140C2×C4⋊Dic61C2314yescomplemented
141C2×#11758196—21no—
142C2×#11758196—21no—
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×#11758198—21no—
151C2×#11758198—21no—
152C2×C4×Dic61—21no—
153#14519711C2314yescomplemented
154#14519711C2314yescomplemented
155#14519709C2314yescomplemented
156#14519709C2314yescomplemented
157#14519702C2314yescomplemented
158#14519702C2314yescomplemented
159#14519699C2314yes—
160#14519699C2314yes—
161#14519699C2314yes—
162#14519699C2314yes—
163#14519699C2314yescomplemented
164#14519699C2314yescomplemented
165C2×#41×C61—42no—
166C2×#41×C61—42no—
167C2×#41×C61D414yes—
168C2×#41×C61C2314yes—
169C22×Q8×C61D411yescharacteristic
170C22×D4×C61D411yescharacteristic
171C22×D4×C61D411yescharacteristic
172C22×D4×C61D411yescharacteristic
173C23×C4×C61C2311yescharacteristic
174C23×C4×C61C2311yescharacteristic
175C23×C4×C61C2311yescharacteristic
176C2×M16×C61—42no—
177C2×M16×C61C2314yescomplemented
178C22×C8×C61—42no—
179C22×C8×C61C2311yescharacteristic
180C22×C8×C61C2311yescharacteristic
181C22×C8×C61C2311yescharacteristic
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2314yescomplemented
184C22⋊C8×C61C2314yes—
185C22⋊C8×C61C2314yes—
186C22⋊C8×C61C2314yescomplemented
187C22⋊C8×C61C2314yescomplemented
188C24×C61C2×D411yescharacteristic
189C24×C61C2×D411yescharacteristic
190C24×C61C2×D411yescharacteristic
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—24no—
195C23×D61—44no—
196C23×D61—82no—
197C23×D61—82no—
198#41×C61—48no—
199#41×C61—44no—
200#41×C61—44no—
201C2×Q8×C61—42no—
202C2×Q8×C61C2×D414yes—
203C2×D4×C61—42no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61C2×D414yes—
207C2×D4×C61C2×D414yes—
208C2×D4×C61C2×D414yes—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D412yes—
218C22×C4×C61C2×D412yes—
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D412yes—
221C22×C4×C61C2412yes—
222C22×C4×C61C2412yes—
223C22×C4×C61C2412yes—
224C22×C4×C61C2411yescharacteristic
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—24no—
231C2×C22⋊D61—24no—
232C2×C22⋊D61—44no—
233C2×C22⋊D61—82no—
234C2×C22⋊D61—82no—
235C2×C22⋊D61—82no—
236C2×C22⋊D61—82no—
237C2×C22⋊D61—82no—
238C2×C22⋊D61—82no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—24no—
245C22×Dic61—82no—
246#11758222—44no—
247#11758222—44no—
248#11758222—48no—
249C2×D244—22no—
250C2×D244—22no—
251C2×D244—22no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—22no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—24no—
258C2×D244—21no—
259C2×D244—44no—
260C2×D244—44no—
261C2×D244—44no—
262C2×D244—48no—
263C2×D244C2412yes—
264C2×D244C2412yes—
265C2×D244C2412yes—
266C2×C4×D61—24no—
267C2×C4×D61—44no—
268C2×Dic122—22no—
269C2×Dic122—22no—
270C2×Dic122—21no—
271C2×Dic122C2412yes—
272M16×C61—44no—
273C2×C8×C61—22no—
274C2×C8×C61—22no—
275C2×C8×C61—22no—
276C2×C8×C61—22no—
277C2×C8×C61—44no—
278C2×C8×C61C2412yes—
279C2×C8×C61C2412yes—
280C2×C8×C61C2412yes—
281C2×C8×C61C2412yes—
282C22⋊Dic61—24no—
283C22⋊Dic61—24no—
284C22⋊Dic61—24no—
285#11758198—24no—
286#11758198—24no—
287#11758198—24no—
288#11758198—24no—
289#11758198—24no—
290#11758198—24no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61—24no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61C2412yes—
297C4⋊Dic61C2412yes—
298C4⋊Dic61C2412yes—
299C4⋊Dic61C2412yes—
300#11758196—24no—
301#11758196—24no—
302C4×Dic61—24no—
303D488—44no—
304D488—44no—
305#11758190—44no—
306#11758190—44no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61C22×D412yes—
317C23×C61C22×D412yes—
318C23×C61C22×D412yes—
319C23×C61C22×D411yescharacteristic
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—48no—
324C22×D61—42no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—84no—
334C22×D61—84no—
335C22×D61—816no—
336Q8×C61—44no—
337D4×C61—44no—
338D4×C61—44no—
339D4×C61—44no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—24no—
344C2×C4×C61—24no—
345C2×C4×C61—24no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D412yes—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61H(5,𝔽2)12yes—
357C2×C4×C61H(5,𝔽2)12yes—
358C2×C4×C61C2511yescharacteristic
359C22⋊D61—48no—
360C22⋊D61—84no—
361C22⋊D61—84no—
362C22⋊D61—84no—
363C22⋊D61—84no—
364C22⋊D61—84no—
365C22⋊D61—84no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—84no—
377D244—22no—
378D244—22no—
379D244—22no—
380D244—22no—
381D244—22no—
382D244—22no—
383D244—48no—
384D244—42no—
385D244—42no—
386D244—42no—
387C4×D61—48no—
388Dic122—22no—
389Dic122—22no—
390Dic122—42no—
391C8×C61—22no—
392C8×C61—22no—
393C8×C61—22no—
394C8×C61—22no—
395C2×#3198—611nomaximal, Sylow
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—44no—
406C22×C61—44no—
407C22×C61—44no—
408C22×C61#53412yes—
409C22×C61#57612yes—
410C22×C61#57712yes—
411C22×C61C23×D411yescharacteristic
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—816no—
422C2×D61—84no—
423C2×D61—84no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—22no—
427C4×C61—22no—
428C4×C61#53412yes—
429C4×C61C2×H(5,𝔽2)11yescharacteristic
430C4×C61C2×H(5,𝔽2)11yescharacteristic
431Dic61—42no—
432Dic61—42no—
433Dic61—42no—
434Dic61—42no—
435Dic61—42no—
436C2×#537—611no—
437C2×#535—611no—
438#3198—6116no—
439C2×#481—611no—
440C2×#485—611no—
441C2×#482—611no—
442C2×#480—611no—
443C2×#469—611no—
444C2×#468—611no—
445C2×#466—611no—
446C2×#465—611no—
447C2×#449—611no—
448C2×#449—611no—
449C2×#450—611no—
450C2×#447—611no—
451C2×#408D6111yescharacteristic, complemented
452C2×C61—42no—
453C2×C61—42no—
454C2×C61—42no—
455C2×C61#319814yescomplemented
456C2×C61C2×#53411yescharacteristic
457C2×C61C2×#57611yescharacteristic
458C2×C61C2×#57711yescharacteristic
459D61—82no—
460D61—82no—
461D61—82no—
462C22×#41—611no—
463C22×#41C2×D6111yescharacteristic
464C23×D4—611no—
465C22×SD16—611no—
466C22×SD16—611no—
467C22×D8—611no—
468C22×D8—611no—
469C22×M16C2×D6111yescharacteristic, complemented
470C23×C8C2×D6111yescharacteristic, complemented
471#537—618no—
472#537—1224no—
473#535—618no—
474#535—1224no—
475C2×#127—1221no—
476C2×#124—1221no—
477C2×C22⋊Q8—611no—
478C2×C22⋊Q8—611no—
479C2×C22⋊Q8—1221no—
480C2×#121—611no—
481C2×#121—611no—
482C2×#121—611no—
483C2×#121—611no—
484C2×#121—611no—
485C2×#121—611no—
486C2×#121—1221no—
487C2×#121—1221no—
488C2×#121—1221no—
489C2×#120—1221no—
490C2×#120—1221no—
491C2×#117—611no—
492C22×C4⋊C4—611no—
493#485—618no—
494#482—618no—
495#481—618no—
496#480—618no—
497#469—618no—
498#468—618no—
499#466—618no—
500#465—618no—
501#450—618no—
502#449—618no—
503#449—618no—
504#447—618no—
505C2×#107—611no—
506C2×#107—611no—
507C2×#106—611no—
508C2×#106—611no—
509C2×#103—611no—
510C2×#103—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102—611no—
515C2×#102—611no—
516C2×#102—611no—
517#408C2×D6118yescomplemented
518C2×C22⋊C8C2×D6111yescharacteristic
519C2×C22⋊C8C2×D6111yescharacteristic
520C2×C22⋊C8C2×D6111yescharacteristic, complemented
521C2×C22⋊C8C2×D6111yescharacteristic, complemented
522C61C2×#319811yescharacteristic, complemented, Sylow
523C25—1221no—
524C2×#41—42no—
525C2×#41—42no—
526C2×#41—614no—
527C2×#41—1222no—
528C2×#41—2442no—
529C2×#41—2442no—
530C2×#41D24414yes—
531C2×#41C22×D6114yes—
532C22×Q8—611no—
533C22×Q8D24411yescharacteristic
534C22×D4—611no—
535C22×D4—611no—
536C22×D4—611no—
537C22×D4—614no—
538C22×D4—1221no—
539C22×D4—1221no—
540C22×D4—1221no—
541C22×D4—1221no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4—1221no—
545C22×D4—1221no—
546C22×D4—1222no—
547C22×D4—2442no—
548C22×D4—2442no—
549C22×D4D24411yescharacteristic
550C22×D4D24411yescharacteristic
551C22×D4D24411yescharacteristic
552C23×C4—1221no—
553C23×C4—1221no—
554C23×C4C22×D6111yescharacteristic
555C23×C4C22×D6111yescharacteristic
556C23×C4C22×D6111yescharacteristic
557C2×SD16—614no—
558C2×SD16—614no—
559C2×SD16—2442no—
560C2×SD16—2442no—
561C2×D8—614no—
562C2×D8—614no—
563C2×D8—2442no—
564C2×D8—2442no—
565C2×M16—42no—
566C2×M16C22×D6114yescomplemented
567C22×C8—42no—
568C22×C8C22×D6111yescharacteristic
569C22×C8C22×D6111yescharacteristic
570C22×C8C22×D6111yescharacteristic
571C22×C8C22×D6111yescharacteristic
572C22×C8C22×D6114yescomplemented
573#127—1228no—
574#124—1228no—
575C22⋊Q8—614no—
576C22⋊Q8—614no—
577C22⋊Q8—1228no—
578C22⋊Q8—1222no—
579C22⋊Q8—1222no—
580#121—614no—
581#121—614no—
582#121—614no—
583#121—614no—
584#121—614no—
585#121—614no—
586#121—1228no—
587#121—1228no—
588#121—1228no—
589#121—1222no—
590#121—1222no—
591#121—1222no—
592#121—1222no—
593#121—1222no—
594#121—1222no—
595#120—1228no—
596#120—1228no—
597#117—614no—
598#117—1222no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—614no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4—1221no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C42—1221no—
618#107—614no—
619#107—614no—
620#106—614no—
621#106—614no—
622#103—614no—
623#103—614no—
624#102—614no—
625#102—614no—
626#102—614no—
627#102—614no—
628#102—614no—
629#102—614no—
630C22⋊C8C22×D6114yes—
631C22⋊C8C22×D6114yes—
632C22⋊C8C22×D6114yescomplemented
633C22⋊C8C22×D6114yescomplemented
634C24—1224no—
635C24—1221no—
636C24—1221no—
637C24—1221no—
638C24—4882no—
639C24—4882no—
640C24—2444no—
641C24C2×D24411yescharacteristic
642C24C2×D24411yescharacteristic
643C24C2×D24411yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—2444no—
648#41—2444no—
649#41—2448no—
650C2×Q8—42no—
651C2×Q8—612no—
652C2×Q8—1221no—
653C2×Q8—1222no—
654C2×Q8—1222no—
655C2×Q8C2×D24414yes—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—612no—
660C2×D4—612no—
661C2×D4—612no—
662C2×D4—1224no—
663C2×D4—1224no—
664C2×D4—1224no—
665C2×D4—1224no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1224no—
673C2×D4—1222no—
674C2×D4—1222no—
675C2×D4—1222no—
676C2×D4—1222no—
677C2×D4—1222no—
678C2×D4—1222no—
679C2×D4—4882no—
680C2×D4—4882no—
681C2×D4—4882no—
682C2×D4—4882no—
683C2×D4—4882no—
684C2×D4—4882no—
685C2×D4—2444no—
686C2×D4—2444no—
687C2×D4—2444no—
688C2×D4—2448no—
689C2×D4—2444no—
690C2×D4C2×D24414yes—
691C2×D4C2×D24414yes—
692C2×D4C2×D24414yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—1224no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1224no—
706C22×C4—4882no—
707C22×C4—2444no—
708C22×C4C2×D24412yes—
709C22×C4C2×D24412yes—
710C22×C4C2×D24412yes—
711C22×C4C2×D24411yescharacteristic
712C22×C4C2×D24411yescharacteristic
713C22×C4C2×D24411yescharacteristic
714C22×C4C23×D6112yes—
715C22×C4C23×D6112yes—
716C22×C4C23×D6112yes—
717C22×C4C23×D6111yescharacteristic
718SD16—2444no—
719SD16—2444no—
720D8—2444no—
721D8—2444no—
722M16—44no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—44no—
728C2×C8C23×D6112yes—
729C2×C8C23×D6112yes—
730C2×C8C23×D6112yes—
731C2×C8C23×D6112yes—
732C4⋊C4—612no—
733C4⋊C4—612no—
734C4⋊C4—612no—
735C4⋊C4—612no—
736C4⋊C4—1224no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1224no—
742C4⋊C4—1224no—
743C22⋊C4—1224no—
744C22⋊C4—1224no—
745C22⋊C4—1224no—
746C22⋊C4—1224no—
747C22⋊C4—1224no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C22⋊C4—1224no—
752C42—1224no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—4884no—
766C23—4884no—
767C23—48816no—
768C23—2448no—
769C23—2442no—
770C23—2442no—
771C23—2442no—
772C23—2442no—
773C23—2442no—
774C23—2442no—
775C23—2442no—
776C23—2442no—
777C23—2442no—
778C23C22×D24412yes—
779C23C22×D24412yes—
780C23C22×D24412yes—
781C23C22×D24411yescharacteristic
782Q8—44no—
783Q8—1222no—
784Q8—1222no—
785Q8—2442no—
786D4—44no—
787D4—44no—
788D4—44no—
789D4—1222no—
790D4—1222no—
791D4—1222no—
792D4—1222no—
793D4—1222no—
794D4—1222no—
795D4—4884no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—4884no—
800D4—4884no—
801D4—2448no—
802D4—2448no—
803D4—2442no—
804D4—2442no—
805D4—2442no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—4884no—
824C2×C4—2448no—
825C2×C4—2442no—
826C2×C4—2442no—
827C2×C4—2442no—
828C2×C4—2442no—
829C2×C4—2442no—
830C2×C4C22×D24412yes—
831C2×C4C22×D24412yes—
832C2×C4C22×D24412yes—
833C2×C4C22×D24411yescharacteristic
834C2×C4#1451982212yes—
835C2×C4#1451982212yes—
836C2×C4C24×D6111yescharacteristic
837C8—22no—
838C8—22no—
839C8—22no—
840C8—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—48816no—
854C22—4884no—
855C22—4884no—
856C22—4884no—
857C22—2442no—
858C22—2442no—
859C22—2442no—
860C22—2442no—
861C22—2442no—
862C22—2442no—
863C22—2442no—
864C22—2442no—
865C22—2442no—
866C22#1684032412yes—
867C22#1684056712yes—
868C22#1684057412yes—
869C22C23×D24411yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—2442no—
874C4—2442no—
875C4—2442no—
876C4—2442no—
877C4—2442no—
878C4#1684032412yes—
879C4C2×#1451982211yescharacteristic
880C4C2×#1451982211yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—4882no—
885C2—4882no—
886C2—4882no—
887C2#2145667314yesdirect product factor
888C2C2×#1684032411yescharacteristic
889C2C2×#1684056711yescharacteristic
890C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#408C2
socleC23×C61C22×D4
hypercenterC2×#408D61
hypocenterC61C2×#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#16840340C2semidirect
2. C2×#16840326C2semidirect
3. #21456673C2direct (N × H)
4. C2×#16840081C2semidirect
5. C2×#16840104C2semidirect
6. C2×#16840087C2semidirect
7. C2×#16840076C2semidirect
8. C2×#16840015C2semidirect
9. C2×#16840008C2semidirect
10. C2×#16839998C2semidirect
11. C2×#16839991C2semidirect
12. C2×#16839909C2semidirect
13. C2×#16839909C2semidirect
14. C2×#16839915C2semidirect
15. C2×#16839898C2semidirect
16. C2×C61×#408C2semidirect
17. C22×#11758222C22semidirect
24. #16840340C22semidirect
26. #16840326C22semidirect
30. C2×#14519756C22semidirect
37. C2×#14519751C22semidirect
44. C22×C4⋊Dic61C22semidirect
45. #16840104C22semidirect
46. #16840087C22semidirect
47. #16840081C22semidirect
48. #16840076C22semidirect
49. #16840015C22semidirect
50. #16840008C22semidirect
51. #16839998C22semidirect
52. #16839991C22semidirect
53. #16839915C22semidirect
54. #16839909C22semidirect
55. #16839909C22semidirect
56. #16839898C22semidirect
57. C2×#14519711C22semidirect
58. C2×#14519711C22semidirect
59. C2×#14519709C22semidirect
60. C2×#14519709C22semidirect
61. C2×#14519702C22semidirect
62. C2×#14519702C22semidirect
67. C2×#14519699C22semidirect
68. C2×#14519699C22semidirect
70. C22×M16×C61C22semidirect
71. C23×C8×C61C22semidirect
72. C61×#408C22semidirect
75. C2×C22⋊C8×C61C22semidirect
76. C2×C22⋊C8×C61C22semidirect
81. C2×#11758222C23semidirect
113. #14519756C23semidirect
126. #14519751C23semidirect
140. C2×C4⋊Dic61C23semidirect
153. #14519711C23semidirect
154. #14519711C23semidirect
155. #14519709C23semidirect
156. #14519709C23semidirect
157. #14519702C23semidirect
158. #14519702C23semidirect
163. #14519699C23semidirect
164. #14519699C23semidirect
177. C2×M16×C61C23semidirect
183. C22×C8×C61C23semidirect
186. C22⋊C8×C61C23semidirect
187. C22⋊C8×C61C23semidirect
451. C2×#408D61semidirect
455. C2×C61#3198semidirect
469. C22×M16C2×D61semidirect
470. C23×C8C2×D61semidirect
517. #408C2×D61semidirect
520. C2×C22⋊C8C2×D61semidirect
521. C2×C22⋊C8C2×D61semidirect
522. C61C2×#3198semidirect
566. C2×M16C22×D61semidirect
572. C22×C8C22×D61semidirect
632. C22⋊C8C22×D61semidirect
633. C22⋊C8C22×D61semidirect
887. C2#21456673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403402
C2×#168403262
#214566732
C2×#168400812
C2×#168401042
C2×#168400872
C2×#168400762
C2×#168400152
C2×#168400082
C2×#168399982
C2×#168399912
C2×#168399092
C2×#168399152
C2×#168398982
C2×C61×#4082
C2×#319861