Finite Group Databasebeta

← C2×#21456674 #30550669

Subgroups — C2×#21456674 #30550669

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×#16840342C211yesmaximal, characteristic, complemented
2C2×#16840328C211yesmaximal, characteristic, complemented
3#21456674C2116yesmaximal, direct product factor
4C2×#16840082C211yesmaximal, characteristic, complemented
5C2×#16840102C211yesmaximal, characteristic, complemented
6C2×#16840088C211yesmaximal, characteristic, complemented
7C2×#16840074C211yesmaximal, characteristic, complemented
8C2×#16840013C211yesmaximal, characteristic, complemented
9C2×#16840010C211yesmaximal, characteristic, complemented
10C2×#16839998C211yesmaximal, characteristic, complemented
11C2×#16839910C211yesmaximal, characteristic, complemented
12C2×#16839906C211yesmaximal, characteristic, complemented
13C2×#16839911C211yesmaximal, characteristic, complemented
14C2×#16839897C211yesmaximal, characteristic, complemented
15C2×#16839728C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic, complemented
18C22×#11758222C2211yescharacteristic
19C22×D4×D61C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×D488C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758194C2211yescharacteristic, complemented
24#16840342—24no—
25#16840342C2218yescomplemented
26#16840328—24no—
27#16840328C2218yescomplemented
28C2×#14519773—21no—
29C2×#14519763—21no—
30C2×#14519755—21no—
31C2×#14519753C2211yescharacteristic
32C2×#14519752—21no—
33C2×#14519752C2211yescharacteristic
34C2×#14519752C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36C2×#14519751C2211yescharacteristic, complemented
37C2×#14519750—21no—
38C2×#14519750—21no—
39C2×#14519748C2211yescharacteristic
40C2×#14519747—21no—
41C2×#14519745—21no—
42C2×#14519735C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic, complemented
44#16840102C2218yescomplemented
45#16840088C2218yescomplemented
46#16840082C2218yescomplemented
47#16840074C2218yescomplemented
48#16840013C2218yescomplemented
49#16840010C2218yescomplemented
50#16839998C2218yescomplemented
51#16839911C2218yescomplemented
52#16839910C2218yescomplemented
53#16839906C2218yescomplemented
54#16839897C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519701C2211yescharacteristic, complemented
59C2×#14519699C2211yescharacteristic
60C2×#14519699C2211yescharacteristic, complemented
61C2×#14519698C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic, complemented
64#16839728C2218yescomplemented
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic, complemented
69C22×SD16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic, complemented
71C2×C22⋊Q8×C61C2211yescharacteristic, complemented
72C2×#121×C61C2211yescharacteristic
73C61×#465C2218yescomplemented
74C2×#106×C61C2211yescharacteristic, complemented
75C2×#103×C61C2211yescharacteristic, complemented
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C2×#11758226—22no—
79C2×#11758226—42no—
80C2×#11758226—42no—
81C2×#11758226C2314yescomplemented
82C2×#11758222—42no—
83C2×#11758222—42no—
84C2×#11758222D414yes—
85C2×#11758222C2314yes—
86C22×Dic122D411yescharacteristic
87C22×D244—21no—
88C22×D244—21no—
89C22×D244—21no—
90C22×D244D411yescharacteristic
91C22×D244C2311yescharacteristic
92C22×D244C2311yescharacteristic
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C22×C22⋊D61—21no—
96C22×C22⋊D61—21no—
97C22×C22⋊D61D411yescharacteristic
98C22×C22⋊D61D411yescharacteristic
99C2×D4×D61—22no—
100C2×D4×D61—42no—
101C2×D4×D61—42no—
102C2×D4×D61C2314yes—
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C2×#11758201—42no—
108C2×#11758201C2314yes—
109C2×D488—42no—
110C2×D488C2314yes—
111C2×#11758199—42no—
112C2×#11758199C2314yes—
113C2×#11758194—42no—
114C2×#11758194C2314yescomplemented
115C22×#92418C2311yescharacteristic
116C22×#92418C2311yescharacteristic
117#14519773—28no—
118#14519763—28no—
119#14519755—28no—
120#14519753—22no—
121#14519753C2314yes—
122#14519752—28no—
123#14519752—22no—
124#14519752—22no—
125#14519752C2314yes—
126#14519752C2314yes—
127#14519751—22no—
128#14519751—22no—
129#14519751C2314yes—
130#14519751C2314yescomplemented
131#14519750—28no—
132#14519750—28no—
133#14519748—22no—
134#14519748C2314yes—
135#14519747—28no—
136#14519745—28no—
137#14519735—22no—
138#14519735C2314yes—
139C2×C4⋊Dic61C2311yescharacteristic
140C2×C4⋊Dic61C2311yescharacteristic
141C2×#11758196—21no—
142C2×#11758196—21no—
143C4⋊C4×D61—22no—
144C4⋊C4×D61C2314yescomplemented
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#14519710C2314yescomplemented
155#14519708C2314yescomplemented
156#14519701C2314yescomplemented
157#14519699C2314yes—
158#14519699C2314yescomplemented
159#14519698C2314yes—
160#14519697C2314yes—
161#14519697C2314yescomplemented
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—
172C22×C8×C61—42no—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175C22×C8×C61C2314yescomplemented
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#106×C61C2314yescomplemented
186#103×C61C2314yescomplemented
187#102×C61C2314yes—
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—24no—
193C23×D61—44no—
194C23×D61—82no—
195C23×D61—82no—
196C23×D61C2×D411yescharacteristic
197C23×D61C2×D411yescharacteristic
198C2×Q8×C61—21no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61C2412yes—
202C2×D4×C61—24no—
203C2×D4×C61—21no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—82no—
207C2×D4×C61C2412yes—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2412yes—
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—42no—
223C2×C22⋊D61—44no—
224C2×C22⋊D61—82no—
225C2×C22⋊D61—82no—
226C2×C22⋊D61—82no—
227C2×C22⋊D61C2×D414yes—
228C2×C22⋊D61C2×D414yes—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233#11758226—44no—
234#11758226—44no—
235#11758226—48no—
236D4×D61—44no—
237D4×D61—44no—
238D4×D61—48no—
239#11758222—48no—
240#11758222—44no—
241#11758222—44no—
242C2×D244—22no—
243C2×D244—22no—
244C2×D244—22no—
245C2×D244—22no—
246C2×D244—24no—
247C2×D244—21no—
248C2×D244—21no—
249C2×D244—24no—
250C2×D244—24no—
251C2×D244—42no—
252C2×D244—44no—
253C2×D244—82no—
254C2×D244—82no—
255C2×D244C2×D414yes—
256C2×D244C2412yes—
257C2×D244C2412yes—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—24no—
263C2×C4×D61—24no—
264C2×C4×D61—44no—
265C2×C4×D61—82no—
266C2×C4×D61C2×D412yes—
267C2×C4×D61C2×D412yes—
268C2×C4×D61C2412yes—
269C2×C4×D61C2412yes—
270C2×Dic122—42no—
271C2×Dic122C2×D414yes—
272SD16×C61—44no—
273C2×C8×C61—22no—
274C2×C8×C61—22no—
275C2×C8×C61—44no—
276C2×C8×C61C2412yes—
277C2×C8×C61C2412yes—
278C4⋊C4×C61—24no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61C2412yes—
282C4⋊C4×C61C2412yes—
283C22⋊C4×C61—24no—
284C22⋊C4×C61—24no—
285C22⋊Dic61—24no—
286#11758201—44no—
287#11758199—44no—
288#11758198—24no—
289#11758198—24no—
290#11758198—24no—
291#11758198—24no—
292#11758198—24no—
293#11758198—24no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61C2412yes—
297C4⋊Dic61C2412yes—
298#11758196—24no—
299#11758196—24no—
300C4×Dic61—24no—
301#11758194—44no—
302C2×#92418—22no—
303C2×#92418—22no—
304C2×#92418C2412yes—
305C2×#92418C2412yes—
306D488—44no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61C22×D412yes—
315C23×C61C22×D411yescharacteristic
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—48no—
325C22×D61—42no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—84no—
332C22×D61—84no—
333C22×D61—816no—
334C22×D61C22×D412yes—
335C22×D61C22×D412yes—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—42no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—42no—
342D4×C61—84no—
343C2×C4×C61—22no—
344C2×C4×C61—24no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—42no—
351C2×C4×C61—42no—
352C2×C4×C61—42no—
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61H(5,𝔽2)12yes—
356C2×C4×C61H(5,𝔽2)12yes—
357C2×C4×C61C2511yescharacteristic
358C22⋊D61—44no—
359C22⋊D61—44no—
360C22⋊D61—48no—
361C22⋊D61—84no—
362C22⋊D61—84no—
363C22⋊D61—84no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—42no—
369C2×Dic61—42no—
370C2×Dic61C22×D412yes—
371C2×Dic61C22×D412yes—
372D244—22no—
373D244—22no—
374D244—22no—
375D244—22no—
376D244—44no—
377D244—48no—
378D244—42no—
379D244—42no—
380D244—84no—
381D244—84no—
382C4×D61—24no—
383C4×D61—24no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—22no—
387C4×D61—22no—
388C4×D61—48no—
389C4×D61—84no—
390Dic122—44no—
391C8×C61—22no—
392C8×C61—22no—
393#92418—22no—
394#92418—22no—
395C2×#3198—611nomaximal, Sylow
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—44no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—84no—
404C22×C61#53412yes—
405C22×C61#57612yes—
406C22×C61#57712yes—
407C22×C61C23×D411yescharacteristic
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—44no—
415C2×D61—44no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—816no—
423C2×D61—84no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—42no—
427C4×C61—42no—
428C4×C61—42no—
429C4×C61#53412yes—
430C4×C61C2×H(5,𝔽2)11yescharacteristic
431C4×C61C2×H(5,𝔽2)11yescharacteristic
432Dic61—22no—
433Dic61—22no—
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×#465D6111yescharacteristic, complemented
447C2×#449—611no—
448C2×#449—611no—
449C2×#450—611no—
450C2×#447—611no—
451C2×#408—611no—
452C2×C61—42no—
453C2×C61—82no—
454C2×C61#319814yescomplemented
455C2×C61C2×#53411yescharacteristic
456C2×C61C2×#57611yescharacteristic
457C2×C61C2×#57711yescharacteristic
458D61—42no—
459D61—42no—
460D61—82no—
461D61—82no—
462C22×#41—611no—
463C22×#41—611no—
464C23×D4—611no—
465C22×SD16—611no—
466C22×SD16C2×D6111yescharacteristic
467C22×D8—611no—
468C22×D8—611no—
469C22×M16—611no—
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—1221no—
479C2×C22⋊Q8C2×D6111yescharacteristic, complemented
480C2×#121—611no—
481C2×#121—611no—
482C2×#121—611no—
483C2×#121—611no—
484C2×#121—611no—
485C2×#121—1221no—
486C2×#121—1221no—
487C2×#121—1221no—
488C2×#121C2×D6111yescharacteristic
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#465C2×D6118yescomplemented
501#450—618no—
502#449—618no—
503#449—618no—
504#447—618no—
505C2×#107—611no—
506C2×#107—611no—
507C2×#106—611no—
508C2×#106C2×D6111yescharacteristic, complemented
509C2×#103—611no—
510C2×#103C2×D6111yescharacteristic, complemented
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102—611no—
515C2×#102—611no—
516C2×#102C2×D6111yescharacteristic
517#408—618no—
518C2×C22⋊C8—611no—
519C2×C22⋊C8—611no—
520C2×C22⋊C8—611no—
521C2×C22⋊C8—611no—
522C61C2×#319811yescharacteristic, complemented, Sylow
523C25—1221no—
524C2×#41—614no—
525C2×#41—614no—
526C2×#41—614no—
527C2×#41—1222no—
528C2×#41—2442no—
529C2×#41—2442no—
530C2×#41—2442no—
531C2×#41—2442no—
532C22×Q8—611no—
533C22×Q8C22×D6111yescharacteristic
534C22×D4—21no—
535C22×D4—611no—
536C22×D4—611no—
537C22×D4—614no—
538C22×D4—611no—
539C22×D4—611no—
540C22×D4—611no—
541C22×D4—1221no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4—1222no—
545C22×D4—1221no—
546C22×D4—1221no—
547C22×D4—1221no—
548C22×D4—1221no—
549C22×D4—2442no—
550C22×D4—2442no—
551C22×D4C22×D6111yescharacteristic
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4C22×D6111yescharacteristic
557C2×SD16—42no—
558C2×SD16—614no—
559C2×SD16—2442no—
560C2×SD16C22×D6114yes—
561C2×D8—614no—
562C2×D8—614no—
563C2×D8—2442no—
564C2×D8—2442no—
565C2×M16—614no—
566C2×M16—2442no—
567C22×C8—42no—
568C22×C8—611no—
569C22×C8—611no—
570C22×C8C22×D6111yescharacteristic
571C22×C8C22×D6111yescharacteristic
572C22×C8C22×D6114yescomplemented
573#127—1228no—
574#124—1228no—
575C22⋊Q8—22no—
576C22⋊Q8—614no—
577C22⋊Q8—1228no—
578C22⋊Q8—1222no—
579C22⋊Q8C22×D6114yescomplemented
580#121—22no—
581#121—614no—
582#121—614no—
583#121—614no—
584#121—614no—
585#121—614no—
586#121—1228no—
587#121—1228no—
588#121—1222no—
589#121—1222no—
590#121—1228no—
591#121—1222no—
592#121—1222no—
593#121—1222no—
594#121C22×D6114yes—
595#120—1228no—
596#120—1228no—
597#117—614no—
598#117—1222no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—614no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4C22×D6111yescharacteristic
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
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#106C22×D6114yescomplemented
622#103—614no—
623#103C22×D6114yescomplemented
624#102—614no—
625#102—614no—
626#102—614no—
627#102—614no—
628#102—614no—
629#102C22×D6114yes—
630C22⋊C8—614no—
631C22⋊C8—614no—
632C22⋊C8—614no—
633C22⋊C8—614no—
634C24—21no—
635C24—611no—
636C24—611no—
637C24—1224no—
638C24—1221no—
639C24—1221no—
640C24—4882no—
641C24—4882no—
642C24—2444no—
643C24D4×D6111yescharacteristic
644#41—2448no—
645#41—2444no—
646#41—2444no—
647#41—2444no—
648#41—2444no—
649#41—2448no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—614no—
654C2×Q8—2442no—
655C2×Q8C23×D6112yes—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—614no—
662C2×D4—614no—
663C2×D4—614no—
664C2×D4—612no—
665C2×D4—612no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—1224no—
671C2×D4—1224no—
672C2×D4—1224no—
673C2×D4—1221no—
674C2×D4—1221no—
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—2442no—
685C2×D4—2444no—
686C2×D4—2444no—
687C2×D4—2444no—
688C2×D4—2448no—
689C2×D4—2442no—
690C2×D4—2442no—
691C2×D4—2444no—
692C2×D4C23×D6112yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—1224no—
705C22×C4—1224no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—4882no—
713C22×C4—2444no—
714C22×C4D4×D6112yes—
715C22×C4D4×D6111yescharacteristic
716C22×C4C23×D6112yes—
717C22×C4C23×D6111yescharacteristic
718SD16—44no—
719SD16—2444no—
720D8—2444no—
721D8—2444no—
722M16—2444no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—44no—
726C2×C8—612no—
727C2×C8—612no—
728C2×C8—1222no—
729C2×C8—1222no—
730C2×C8C23×D6112yes—
731C2×C8C23×D6112yes—
732C4⋊C4—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—612no—
736C4⋊C4—612no—
737C4⋊C4—1224no—
738C4⋊C4—1224no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4C23×D6112yes—
742C4⋊C4C23×D6112yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
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—42no—
758C23—42no—
759C23—42no—
760C23—612no—
761C23—612no—
762C23—1222no—
763C23—1222no—
764C23—1222no—
765C23—1222no—
766C23—1222no—
767C23—1222no—
768C23—1222no—
769C23—1222no—
770C23—4884no—
771C23—4884no—
772C23—48816no—
773C23—2448no—
774C23—2442no—
775C23—2442no—
776C23—2442no—
777C23—2442no—
778C23—2442no—
779C23—2442no—
780C23C2×D4×D6112yes—
781C23C2×D4×D6111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—2444no—
786D4—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—1222no—
791D4—1222no—
792D4—1222no—
793D4—1222no—
794D4—4884no—
795D4—4884no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—2444no—
800D4—2448no—
801D4—2444no—
802D4—2444no—
803D4—2448no—
804D4—2442no—
805D4—2442no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—612no—
817C2×C4—612no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1224no—
821C2×C4—1224no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—4884no—
829C2×C4—2448no—
830C2×C4—2442no—
831C2×C4—2442no—
832C2×C4C2×D4×D6112yes—
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4#1451982212yes—
835C2×C4#1451982312yes—
836C2×C4C24×D6111yescharacteristic
837C8—22no—
838C8—22no—
839C8—1222no—
840C8—1222no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—84no—
849C22—1222no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22—1222no—
854C22—1222no—
855C22—48816no—
856C22—4884no—
857C22—4884no—
858C22—2442no—
859C22—2442no—
860C22—2442no—
861C22—2442no—
862C22—2442no—
863C22—2442no—
864C22—2444no—
865C22—2444no—
866C22#1684032012yes—
867C22#1684056412yes—
868C22#1684056812yes—
869C22C22×D4×D6111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—1222no—
875C4—1222no—
876C4—2442no—
877C4—2442no—
878C4#1684032012yes—
879C4C2×#1451982211yescharacteristic
880C4C2×#1451982311yescharacteristic
881C2—42no—
882C2—82no—
883C2—4882no—
884C2—4882no—
885C2—2442no—
886C2—2442no—
887C2#2145667414yesdirect product factor
888C2C2×#1684032011yescharacteristic
889C2C2×#1684056411yescharacteristic
890C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
hypercenterC2×#465D61
hypocenterC61C2×#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16840342C2semidirect
2. C2×#16840328C2semidirect
3. #21456674C2direct (N × H)
4. C2×#16840082C2semidirect
5. C2×#16840102C2semidirect
6. C2×#16840088C2semidirect
7. C2×#16840074C2semidirect
8. C2×#16840013C2semidirect
9. C2×#16840010C2semidirect
10. C2×#16839998C2semidirect
11. C2×#16839910C2semidirect
12. C2×#16839906C2semidirect
13. C2×#16839911C2semidirect
14. C2×#16839897C2semidirect
15. C2×#16839728C2semidirect
16. C2×C61×#465C2semidirect
17. C22×#11758226C22semidirect
23. C22×#11758194C22semidirect
25. #16840342C22semidirect
27. #16840328C22semidirect
36. C2×#14519751C22semidirect
43. C2×C4⋊C4×D61C22semidirect
44. #16840102C22semidirect
45. #16840088C22semidirect
46. #16840082C22semidirect
47. #16840074C22semidirect
48. #16840013C22semidirect
49. #16840010C22semidirect
50. #16839998C22semidirect
51. #16839911C22semidirect
52. #16839910C22semidirect
53. #16839906C22semidirect
54. #16839897C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519701C22semidirect
60. C2×#14519699C22semidirect
63. C2×#14519697C22semidirect
64. #16839728C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519689C22semidirect
70. C23×C8×C61C22semidirect
71. C2×C22⋊Q8×C61C22semidirect
73. C61×#465C22semidirect
74. C2×#106×C61C22semidirect
75. C2×#103×C61C22semidirect
81. C2×#11758226C23semidirect
114. C2×#11758194C23semidirect
130. #14519751C23semidirect
144. C4⋊C4×D61C23semidirect
153. #14519711C23semidirect
154. #14519710C23semidirect
155. #14519708C23semidirect
156. #14519701C23semidirect
158. #14519699C23semidirect
161. #14519697C23semidirect
164. #14519689C23semidirect
165. #14519689C23semidirect
175. C22×C8×C61C23semidirect
177. C22⋊Q8×C61C23semidirect
185. #106×C61C23semidirect
186. #103×C61C23semidirect
446. C2×#465D61semidirect
454. C2×C61#3198semidirect
470. C23×C8C2×D61semidirect
479. C2×C22⋊Q8C2×D61semidirect
500. #465C2×D61semidirect
508. C2×#106C2×D61semidirect
510. C2×#103C2×D61semidirect
522. C61C2×#3198semidirect
572. C22×C8C22×D61semidirect
579. C22⋊Q8C22×D61semidirect
621. #106C22×D61semidirect
623. #103C22×D61semidirect
887. C2#21456674direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403422
C2×#168403282
#214566742
C2×#168400822
C2×#168401022
C2×#168400882
C2×#168400742
C2×#168400132
C2×#168400102
C2×#168399982
C2×#168399102
C2×#168399062
C2×#168399112
C2×#168398972
C2×#168397282
C2×C61×#4652
C2×#319861