Finite Group Databasebeta

← C2×#21456666 #30550661

Subgroups — C2×#21456666 #30550661

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×#16840341C211yesmaximal, characteristic, complemented
2C2×#16840328C211yesmaximal, characteristic, complemented
3#21456666C2116yesmaximal, direct product factor
4C2×#16840082C211yesmaximal, characteristic, complemented
5C2×#16840106C211yesmaximal, characteristic, complemented
6C2×#16840084C211yesmaximal, characteristic, complemented
7C2×#16840074C211yesmaximal, characteristic, complemented
8C2×#16840008C211yesmaximal, characteristic, complemented
9C2×#16839996C211yesmaximal, characteristic, complemented
10C2×#16839989C211yesmaximal, characteristic, complemented
11C2×#16839908C211yesmaximal, characteristic, complemented
12C2×#16839904C211yesmaximal, characteristic, complemented
13C2×#16839914C211yesmaximal, characteristic, complemented
14C2×#16839894C211yesmaximal, characteristic, complemented
15C2×#16839730C211yesmaximal, characteristic, complemented
16C2×C61×#469C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758224C2211yescharacteristic, complemented
19C22×D4×D61C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C23×#92418C2211yescharacteristic, complemented
24#16840341—24no—
25#16840341C2218yescomplemented
26#16840328—24no—
27#16840328C2218yescomplemented
28C2×#14519773—21no—
29C2×#14519763—21no—
30C2×#14519757C2211yescharacteristic
31C2×#14519756C2211yescharacteristic, complemented
32C2×#14519754—21no—
33C2×#14519752C2211yescharacteristic
34C2×#14519751C2211yescharacteristic
35C2×#14519750—21no—
36C2×#14519749—21no—
37C2×#14519748—21no—
38C2×#14519748C2211yescharacteristic
39C2×#14519748C2211yescharacteristic
40C2×#14519747—21no—
41C2×#14519745—21no—
42C2×#14519735C2211yescharacteristic
43C2×C4⋊C4×D61C2211yescharacteristic, complemented
44#16840106C2218yescomplemented
45#16840084C2218yescomplemented
46#16840082C2218yescomplemented
47#16840074C2218yescomplemented
48#16840008C2218yescomplemented
49#16839996C2218yescomplemented
50#16839989C2218yescomplemented
51#16839914C2218yescomplemented
52#16839908C2218yescomplemented
53#16839904C2218yescomplemented
54#16839894C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519702C2211yescharacteristic, complemented
59C2×#14519700C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic
61C2×#14519698C2211yescharacteristic
62C2×#14519698C2211yescharacteristic, complemented
63C2×#14519697C2211yescharacteristic
64#16839730C2218yescomplemented
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic, complemented
68C2×#14519689C2211yescharacteristic, complemented
69C22×D8×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic, complemented
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic, complemented
73C61×#469C2218yescomplemented
74C2×#106×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222D414yes—
81C2×#11758222C2314yes—
82C2×#11758224—22no—
83C2×#11758224—42no—
84C2×#11758224—42no—
85C2×#11758224C2314yescomplemented
86C22×Dic122D411yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×D244—21no—
89C22×D244D411yescharacteristic
90C22×D244C2311yescharacteristic
91C22×C22⋊D61—21no—
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C22×C22⋊D61—21no—
96C22×C22⋊D61D411yescharacteristic
97C22×C22⋊D61D411yescharacteristic
98C2×D4×D61—22no—
99C2×D4×D61—42no—
100C2×D4×D61—42no—
101C2×D4×D61C2314yes—
102C23×Dic61—21no—
103C22×C4×D61—21no—
104C22×C4×D61C2311yescharacteristic
105C22×C4×D61C2311yescharacteristic
106C2×#11758190—42no—
107C2×#11758190C2314yes—
108C2×#11758200—42no—
109C2×#11758200C2314yes—
110C2×#11758199—42no—
111C2×#11758199C2314yes—
112C22×#92418—42no—
113C22×#92418C2311yescharacteristic
114C22×#92418C2311yescharacteristic
115C22×#92418C2314yescomplemented
116#14519773—28no—
117#14519763—28no—
118#14519757—22no—
119#14519757C2314yes—
120#14519756—22no—
121#14519756C2314yescomplemented
122#14519754—28no—
123#14519752—22no—
124#14519752C2314yes—
125#14519751—22no—
126#14519751C2314yes—
127#14519750—28no—
128#14519749—28no—
129#14519748—28no—
130#14519748—22no—
131#14519748—22no—
132#14519748C2314yes—
133#14519748C2314yes—
134#14519747—28no—
135#14519745—28no—
136#14519735—22no—
137#14519735C2314yes—
138C2×C4⋊Dic61—21no—
139C2×C4⋊Dic61C2311yescharacteristic
140C2×C4⋊Dic61C2311yescharacteristic
141C2×#11758196—21no—
142C2×#11758196—21no—
143C4⋊C4×D61—22no—
144C4⋊C4×D61C2314yescomplemented
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×C4×Dic61—21no—
153#14519711C2314yescomplemented
154#14519710C2314yescomplemented
155#14519708C2314yescomplemented
156#14519702C2314yescomplemented
157#14519700C2314yescomplemented
158#14519699C2314yes—
159#14519698C2314yes—
160#14519698C2314yescomplemented
161#14519697C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164#14519689C2314yescomplemented
165#14519689C2314yescomplemented
166C22×D4×C61—21no—
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61C2311yescharacteristic
171C2×D8×C61—42no—
172C2×D8×C61C2314yes—
173C2×M16×C61—42no—
174C2×M16×C61C2314yescomplemented
175C22×C8×C61C2311yescharacteristic
176C22×C8×C61C2311yescharacteristic
177#121×C61—22no—
178#121×C61—22no—
179#121×C61C2314yes—
180#121×C61C2314yescomplemented
181C2×C4⋊C4×C61C2311yescharacteristic
182C2×C4⋊C4×C61C2311yescharacteristic
183C2×C22⋊C4×C61—21no—
184C2×C22⋊C4×C61—21no—
185#106×C61C2314yescomplemented
186#102×C61C2314yes—
187#102×C61C2314yescomplemented
188C24×C61—21no—
189C24×C61—21no—
190C24×C61C2×D411yescharacteristic
191C23×D61—21no—
192C23×D61—24no—
193C23×D61—44no—
194C23×D61—82no—
195C23×D61—82no—
196C23×D61C2×D411yescharacteristic
197C23×D61C2×D411yescharacteristic
198C2×D4×C61—24no—
199C2×D4×C61—24no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—22no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—82no—
207C2×D4×C61—82no—
208C2×D4×C61C2412yes—
209C2×D4×C61C2412yes—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—24no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—42no—
224C2×C22⋊D61—42no—
225C2×C22⋊D61—44no—
226C2×C22⋊D61—44no—
227C2×C22⋊D61—82no—
228C2×C22⋊D61—82no—
229C2×C22⋊D61—82no—
230C2×C22⋊D61C2×D414yes—
231C2×C22⋊D61C2×D414yes—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—24no—
236C22×Dic61—44no—
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239#11758224—44no—
240#11758224—44no—
241#11758224—48no—
242D4×D61—44no—
243D4×D61—44no—
244D4×D61—48no—
245#11758222—48no—
246#11758222—44no—
247#11758222—44no—
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—21no—
251C2×D244—24no—
252C2×D244—42no—
253C2×D244—82no—
254C2×D244C2×D414yes—
255C2×D244C2412yes—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—24no—
261C2×C4×D61—82no—
262C2×C4×D61C2×D412yes—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2412yes—
265C2×C4×D61C2412yes—
266C2×Dic122—22no—
267C2×Dic122—22no—
268C2×Dic122—21no—
269C2×Dic122—42no—
270C2×Dic122C2×D414yes—
271C2×Dic122C2412yes—
272D8×C61—44no—
273M16×C61—44no—
274C2×C8×C61—22no—
275C2×C8×C61—22no—
276C2×C8×C61C2412yes—
277C2×C8×C61C2412yes—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C2412yes—
281C4⋊C4×C61C2412yes—
282C22⋊C4×C61—24no—
283C22⋊C4×C61—24no—
284C22⋊Dic61—24no—
285C22⋊Dic61—24no—
286C22⋊Dic61—24no—
287#11758200—44no—
288#11758199—44no—
289#11758198—24no—
290#11758198—24no—
291#11758198—24no—
292#11758198—24no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—24no—
296C4⋊Dic61C2412yes—
297C4⋊Dic61C2412yes—
298#11758196—24no—
299#11758196—24no—
300C4×Dic61—24no—
301C2×#92418—22no—
302C2×#92418—22no—
303C2×#92418—44no—
304C2×#92418C2412yes—
305C2×#92418C2412yes—
306#11758190—44no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61C22×D412yes—
319C23×C61C22×D411yescharacteristic
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—48no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—84no—
332C22×D61—84no—
333C22×D61—816no—
334C22×D61C22×D412yes—
335C22×D61C22×D412yes—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—42no—
341D4×C61—42no—
342D4×C61—84no—
343D4×C61—84no—
344C2×C4×C61—22no—
345C2×C4×C61—24no—
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×C61C22×D412yes—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61H(5,𝔽2)12yes—
355C2×C4×C61H(5,𝔽2)12yes—
356C2×C4×C61C2511yescharacteristic
357C22⋊D61—44no—
358C22⋊D61—44no—
359C22⋊D61—48no—
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—22no—
369C2×Dic61—48no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61C22×D412yes—
374C2×Dic61C22×D412yes—
375D244—22no—
376D244—22no—
377D244—44no—
378D244—42no—
379D244—84no—
380C4×D61—24no—
381C4×D61—24no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—84no—
387Dic122—22no—
388Dic122—22no—
389Dic122—44no—
390Dic122—42no—
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—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—84no—
407C22×C61—84no—
408C22×C61#53412yes—
409C22×C61#57612yes—
410C22×C61#57712yes—
411C22×C61C23×D411yescharacteristic
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—44no—
419C2×D61—44no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—816no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—42no—
427C4×C61—42no—
428C4×C61#53412yes—
429C4×C61C2×H(5,𝔽2)11yescharacteristic
430C4×C61C2×H(5,𝔽2)11yescharacteristic
431Dic61—22no—
432Dic61—22no—
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×#469D6111yescharacteristic, complemented
444C2×#468—611no—
445C2×#466—611no—
446C2×#465—611no—
447C2×#449—611no—
448C2×#449—611no—
449C2×#450—611no—
450C2×#447—611no—
451C2×#408—611no—
452C2×C61—42no—
453C2×C61—82no—
454C2×C61—82no—
455C2×C61#319814yescomplemented
456C2×C61C2×#53411yescharacteristic
457C2×C61C2×#57611yescharacteristic
458C2×C61C2×#57711yescharacteristic
459D61—42no—
460D61—42no—
461D61—82no—
462C22×#41—611no—
463C22×#41—611no—
464C23×D4—611no—
465C22×SD16—611no—
466C22×SD16—611no—
467C22×D8—611no—
468C22×D8C2×D6111yescharacteristic
469C22×M16C2×D6111yescharacteristic, complemented
470C23×C8—611no—
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—1221no—
485C2×#121—1221no—
486C2×#121—1221no—
487C2×#121C2×D6111yescharacteristic
488C2×#121C2×D6111yescharacteristic, complemented
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#469C2×D6118yescomplemented
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×#106C2×D6111yescharacteristic, complemented
509C2×#103—611no—
510C2×#103—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102—611no—
515C2×#102C2×D6111yescharacteristic
516C2×#102C2×D6111yescharacteristic, complemented
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×Q8—611no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—611no—
537C22×D4—611no—
538C22×D4—614no—
539C22×D4—611no—
540C22×D4—611no—
541C22×D4—1221no—
542C22×D4—1222no—
543C22×D4—1221no—
544C22×D4—1221no—
545C22×D4—1221no—
546C22×D4—1221no—
547C22×D4—1221no—
548C22×D4—2442no—
549C22×D4—2442no—
550C22×D4C22×D6111yescharacteristic
551C22×D4C22×D6111yescharacteristic
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4C22×D6111yescharacteristic
557C2×SD16—614no—
558C2×SD16—614no—
559C2×SD16—2442no—
560C2×SD16—2442no—
561C2×D8—42no—
562C2×D8—614no—
563C2×D8—2442no—
564C2×D8C22×D6114yes—
565C2×M16—42no—
566C2×M16C22×D6114yescomplemented
567C22×C8—611no—
568C22×C8—611no—
569C22×C8—614no—
570C22×C8—2442no—
571C22×C8C22×D6111yescharacteristic
572C22×C8C22×D6111yescharacteristic
573#127—1228no—
574#124—1228no—
575C22⋊Q8—614no—
576C22⋊Q8—614no—
577C22⋊Q8—1228no—
578C22⋊Q8—1222no—
579C22⋊Q8—1222no—
580#121—22no—
581#121—22no—
582#121—614no—
583#121—614no—
584#121—614no—
585#121—614no—
586#121—1228no—
587#121—1222no—
588#121—1222no—
589#121—1222no—
590#121—1228no—
591#121—1228no—
592#121—1222no—
593#121C22×D6114yes—
594#121C22×D6114yescomplemented
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—1222no—
603C2×C4⋊C4—1221no—
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#103—614no—
624#102—614no—
625#102—614no—
626#102—614no—
627#102—614no—
628#102C22×D6114yes—
629#102C22×D6114yescomplemented
630C22⋊C8—614no—
631C22⋊C8—614no—
632C22⋊C8—614no—
633C22⋊C8—614no—
634C24—21no—
635C24—21no—
636C24—611no—
637C24—611no—
638C24—1224no—
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—614no—
651C2×Q8—612no—
652C2×Q8—1221no—
653C2×Q8—1222no—
654C2×Q8—1222no—
655C2×Q8—2442no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—82no—
665C2×D4—82no—
666C2×D4—614no—
667C2×D4—614no—
668C2×D4—614no—
669C2×D4—612no—
670C2×D4—1224no—
671C2×D4—1224no—
672C2×D4—1224no—
673C2×D4—1224no—
674C2×D4—1224no—
675C2×D4—1224no—
676C2×D4—1221no—
677C2×D4—1222no—
678C2×D4—1222no—
679C2×D4—4882no—
680C2×D4—4882no—
681C2×D4—4882no—
682C2×D4—4882no—
683C2×D4—2442no—
684C2×D4—2444no—
685C2×D4—2444no—
686C2×D4—2448no—
687C2×D4—2442no—
688C2×D4—2442no—
689C2×D4—2444no—
690C2×D4—2444no—
691C2×D4C23×D6112yes—
692C2×D4C23×D6112yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—612no—
700C22×C4—612no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—1224no—
704C22×C4—1224no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1221no—
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—2444no—
719SD16—2444no—
720D8—44no—
721D8—2444no—
722M16—44no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—612no—
726C2×C8—612no—
727C2×C8—1222no—
728C2×C8—1222no—
729C2×C8—2444no—
730C2×C8C23×D6112yes—
731C2×C8C23×D6112yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—612no—
735C4⋊C4—612no—
736C4⋊C4—1224no—
737C4⋊C4—1224no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1224no—
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—22no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—612no—
765C23—612no—
766C23—1222no—
767C23—1222no—
768C23—1222no—
769C23—1222no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—4884no—
774C23—4884no—
775C23—48816no—
776C23—2448no—
777C23—2442no—
778C23—2442no—
779C23—2442no—
780C23C2×D4×D6112yes—
781C23C2×D4×D6111yescharacteristic
782Q8—1222no—
783Q8—1222no—
784Q8—2444no—
785Q8—2442no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—42no—
791D4—42no—
792D4—84no—
793D4—84no—
794D4—1222no—
795D4—1222no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—4884no—
800D4—2444no—
801D4—2444no—
802D4—2444no—
803D4—2448no—
804D4—2448no—
805D4—2442no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—612no—
815C2×C4—612no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1224no—
819C2×C4—1224no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—4884no—
828C2×C4—2448no—
829C2×C4—2442no—
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—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—84no—
853C22—1222no—
854C22—1222no—
855C22—1222no—
856C22—1222no—
857C22—1222no—
858C22—1222no—
859C22—48816no—
860C22—4884no—
861C22—2442no—
862C22—2442no—
863C22—2442no—
864C22—2444no—
865C22—2444no—
866C22#1684032012yes—
867C22#1684056612yes—
868C22#1684057212yes—
869C22C22×D4×D6111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—1222no—
874C4—1222no—
875C4—2442no—
876C4—2442no—
877C4—2442no—
878C4#1684032012yes—
879C4C2×#1451982211yescharacteristic
880C4C2×#1451982311yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—4882no—
885C2—2442no—
886C2—2442no—
887C2#2145666614yesdirect product factor
888C2C2×#1684032011yescharacteristic
889C2C2×#1684056611yescharacteristic
890C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#469C2
socleC23×C61C22×D4
hypercenterC2×#469D61
hypocenterC61C2×#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#16840341C2semidirect
2. C2×#16840328C2semidirect
3. #21456666C2direct (N × H)
4. C2×#16840082C2semidirect
5. C2×#16840106C2semidirect
6. C2×#16840084C2semidirect
7. C2×#16840074C2semidirect
8. C2×#16840008C2semidirect
9. C2×#16839996C2semidirect
10. C2×#16839989C2semidirect
11. C2×#16839908C2semidirect
12. C2×#16839904C2semidirect
13. C2×#16839914C2semidirect
14. C2×#16839894C2semidirect
15. C2×#16839730C2semidirect
16. C2×C61×#469C2semidirect
18. C22×#11758224C22semidirect
23. C23×#92418C22semidirect
25. #16840341C22semidirect
27. #16840328C22semidirect
31. C2×#14519756C22semidirect
43. C2×C4⋊C4×D61C22semidirect
44. #16840106C22semidirect
45. #16840084C22semidirect
46. #16840082C22semidirect
47. #16840074C22semidirect
48. #16840008C22semidirect
49. #16839996C22semidirect
50. #16839989C22semidirect
51. #16839914C22semidirect
52. #16839908C22semidirect
53. #16839904C22semidirect
54. #16839894C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519702C22semidirect
59. C2×#14519700C22semidirect
62. C2×#14519698C22semidirect
64. #16839730C22semidirect
67. C2×#14519689C22semidirect
68. C2×#14519689C22semidirect
70. C22×M16×C61C22semidirect
72. C2×#121×C61C22semidirect
73. C61×#469C22semidirect
74. C2×#106×C61C22semidirect
76. C2×#102×C61C22semidirect
85. C2×#11758224C23semidirect
115. C22×#92418C23semidirect
121. #14519756C23semidirect
144. C4⋊C4×D61C23semidirect
153. #14519711C23semidirect
154. #14519710C23semidirect
155. #14519708C23semidirect
156. #14519702C23semidirect
157. #14519700C23semidirect
160. #14519698C23semidirect
164. #14519689C23semidirect
165. #14519689C23semidirect
174. C2×M16×C61C23semidirect
180. #121×C61C23semidirect
185. #106×C61C23semidirect
187. #102×C61C23semidirect
443. C2×#469D61semidirect
455. C2×C61#3198semidirect
469. C22×M16C2×D61semidirect
488. C2×#121C2×D61semidirect
497. #469C2×D61semidirect
508. C2×#106C2×D61semidirect
516. C2×#102C2×D61semidirect
522. C61C2×#3198semidirect
566. C2×M16C22×D61semidirect
594. #121C22×D61semidirect
621. #106C22×D61semidirect
629. #102C22×D61semidirect
887. C2#21456666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403412
C2×#168403282
#214566662
C2×#168400822
C2×#168401062
C2×#168400842
C2×#168400742
C2×#168400082
C2×#168399962
C2×#168399892
C2×#168399082
C2×#168399042
C2×#168399142
C2×#168398942
C2×#168397302
C2×C61×#4692
C2×#319861