Finite Group Databasebeta

← C2×#21456678 #30550673

Subgroups — C2×#21456678 #30550673

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×#16840343C211yesmaximal, characteristic, complemented
2C2×#16840328C211yesmaximal, characteristic, complemented
3#21456678C2116yesmaximal, direct product factor
4C2×#16840080C211yesmaximal, characteristic, complemented
5C2×#16840105C211yesmaximal, characteristic, complemented
6C2×#16840089C211yesmaximal, characteristic, complemented
7C2×#16840014C211yesmaximal, characteristic, complemented
8C2×#16840009C211yesmaximal, characteristic, complemented
9C2×#16839999C211yesmaximal, characteristic, complemented
10C2×#16839990C211yesmaximal, characteristic, complemented
11C2×#16839909C211yesmaximal, characteristic, complemented
12C2×#16839905C211yesmaximal, characteristic, complemented
13C2×#16839914C211yesmaximal, characteristic, complemented
14C2×#16839897C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#480C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758222C2211yescharacteristic, complemented
19C22×D4×D61C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×D488C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758189C2211yescharacteristic, complemented
25C22×C8×D61C2211yescharacteristic, complemented
26#16840343—24no—
27#16840343C2218yescomplemented
28#16840328—24no—
29#16840328C2218yescomplemented
30C2×#14519773—21no—
31C2×#14519763—21no—
32C2×#14519757—21no—
33C2×#14519757C2211yescharacteristic
34C2×#14519757C2211yescharacteristic, complemented
35C2×#14519752—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519752C2211yescharacteristic
38C2×#14519752C2211yescharacteristic, complemented
39C2×#14519751—21no—
40C2×#14519751—21no—
41C2×#14519751C2211yescharacteristic
42C2×#14519748C2211yescharacteristic
43C2×#14519747—21no—
44C2×#14519745—21no—
45C2×#14519735C2211yescharacteristic
46#16840105C2218yescomplemented
47#16840089C2218yescomplemented
48#16840080C2218yescomplemented
49#16840014C2218yescomplemented
50#16840009C2218yescomplemented
51#16839999C2218yescomplemented
52#16839990C2218yescomplemented
53#16839914C2218yescomplemented
54#16839909C2218yescomplemented
55#16839905C2218yescomplemented
56#16839897C2218yescomplemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519708C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519700C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic, complemented
65#16839727C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×#121×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic, complemented
71C61×#480C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#107×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—22no—
79C2×#11758222—42no—
80C2×#11758222—42no—
81C2×#11758222—42no—
82C2×#11758222—42no—
83C2×#11758222D414yes—
84C2×#11758222C2314yes—
85C2×#11758222C2314yescomplemented
86C22×Dic122D411yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×D244—21no—
89C22×D244—21no—
90C22×D244—21no—
91C22×D244D411yescharacteristic
92C22×D244C2311yescharacteristic
93C22×D244C2311yescharacteristic
94C22×C22⋊D61—21no—
95C22×C22⋊D61—21no—
96C22×C22⋊D61—21no—
97C22×C22⋊D61—21no—
98C22×C22⋊D61D411yescharacteristic
99C22×C22⋊D61D411yescharacteristic
100C2×D4×D61—22no—
101C2×D4×D61—42no—
102C2×D4×D61—42no—
103C2×D4×D61C2314yes—
104C22×C4×D61—21no—
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C2×#11758190—42no—
108C2×#11758190C2314yes—
109C2×#11758200—42no—
110C2×#11758200C2314yes—
111C2×D488—42no—
112C2×D488C2314yes—
113C2×#11758199—42no—
114C2×#11758199C2314yes—
115C2×#11758189—42no—
116C2×#11758189C2314yescomplemented
117C22×#92418C2311yescharacteristic
118C22×#92418C2311yescharacteristic
119C2×C8×D61—42no—
120C2×C8×D61C2314yescomplemented
121#14519773—28no—
122#14519763—28no—
123#14519757—22no—
124#14519757—22no—
125#14519757—28no—
126#14519757C2314yes—
127#14519757C2314yescomplemented
128#14519752—28no—
129#14519752—22no—
130#14519752—22no—
131#14519752—22no—
132#14519752C2314yes—
133#14519752C2314yes—
134#14519752C2314yescomplemented
135#14519751—22no—
136#14519751—28no—
137#14519751—28no—
138#14519751C2314yes—
139#14519748—22no—
140#14519748C2314yes—
141#14519747—28no—
142#14519745—28no—
143#14519735—22no—
144#14519735C2314yes—
145C2×C4⋊Dic61—21no—
146C2×C4⋊Dic61—21no—
147C2×C4⋊Dic61C2311yescharacteristic
148C2×C22⋊Dic61—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×C4×Dic61—21no—
157#14519708C2314yescomplemented
158#14519708C2314yescomplemented
159#14519702C2314yescomplemented
160#14519700C2314yescomplemented
161#14519699C2314yescomplemented
162#14519697C2314yes—
163#14519697C2314yes—
164#14519697C2314yescomplemented
165C22⋊#92418C2314yescomplemented
166#14519689C2314yes—
167#14519689C2314yes—
168C22×D4×C61—21no—
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61—21no—
171C23×C4×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174#121×C61—22no—
175#121×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61—22no—
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C4⋊C4×C61C2314yescomplemented
182C2×C22⋊C4×C61—21no—
183#107×C61C2314yescomplemented
184#107×C61C2314yescomplemented
185#102×C61C2314yes—
186#102×C61C2314yes—
187C22⋊C8×C61C2314yescomplemented
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×D4×C61—24no—
199C2×D4×C61—21no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—82no—
203C2×D4×C61C2412yes—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—24no—
210C22×C4×C61—82no—
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2411yescharacteristic
215C2×C22⋊D61—24no—
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—44no—
223C2×C22⋊D61—82no—
224C2×C22⋊D61—82no—
225C2×C22⋊D61C2×D414yes—
226C2×C22⋊D61C2×D414yes—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231D4×D61—44no—
232D4×D61—44no—
233D4×D61—48no—
234#11758222—44no—
235#11758222—44no—
236#11758222—48no—
237#11758222—44no—
238#11758222—44no—
239#11758222—48no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—22no—
243C2×D244—22no—
244C2×D244—21no—
245C2×D244—21no—
246C2×D244—24no—
247C2×D244—24no—
248C2×D244—24no—
249C2×D244—42no—
250C2×D244—82no—
251C2×D244—82no—
252C2×D244—82no—
253C2×D244C2×D414yes—
254C2×D244C2412yes—
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—44no—
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—
272C2×C8×C61—22no—
273C2×C8×C61—22no—
274C2×C8×C61C2412yes—
275C2×C8×C61C2412yes—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—24no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C2412yes—
281C4⋊C4×C61C2412yes—
282C4⋊C4×C61C2412yes—
283C22⋊C4×C61—24no—
284C22⋊Dic61—24no—
285#11758200—44no—
286#11758199—44no—
287#11758198—24no—
288#11758198—24no—
289#11758198—24no—
290#11758198—24no—
291#11758198—24no—
292#11758198—24no—
293#11758198—24no—
294C4⋊Dic61—21no—
295C4⋊Dic61—24no—
296C4⋊Dic61—24no—
297C4⋊Dic61C2412yes—
298C4×Dic61—24no—
299C2×#92418—22no—
300C2×#92418—22no—
301C2×#92418C2412yes—
302C2×#92418C2412yes—
303D488—44no—
304#11758190—44no—
305#11758189—44no—
306C8×D61—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—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—42no—
339D4×C61—84no—
340C2×C4×C61—22no—
341C2×C4×C61—24no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—42no—
348C2×C4×C61—42no—
349C2×C4×C61—42no—
350C2×C4×C61—84no—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61H(5,𝔽2)12yes—
354C2×C4×C61H(5,𝔽2)12yes—
355C2×C4×C61C2511yescharacteristic
356C22⋊D61—44no—
357C22⋊D61—44no—
358C22⋊D61—48no—
359C22⋊D61—48no—
360C22⋊D61—84no—
361C22⋊D61—84no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—42no—
367C2×Dic61—42no—
368C2×Dic61C22×D412yes—
369C2×Dic61C22×D412yes—
370D244—22no—
371D244—22no—
372D244—22no—
373D244—22no—
374D244—44no—
375D244—42no—
376D244—42no—
377D244—84no—
378D244—84no—
379D244—84no—
380C4×D61—24no—
381C4×D61—24no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—48no—
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—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×#480D6111yescharacteristic, complemented
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×#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×SD16—611no—
467C22×D8—611no—
468C22×D8—611no—
469C22×M16—611no—
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—611no—
485C2×#121—1221no—
486C2×#121—1221no—
487C2×#121—1221no—
488C2×#121C2×D6111yescharacteristic
489C2×#120—1221no—
490C2×#120—1221no—
491C2×#117—611no—
492C22×C4⋊C4C2×D6111yescharacteristic, complemented
493#485—618no—
494#482—618no—
495#481—618no—
496#480C2×D6118yescomplemented
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×#107C2×D6111yescharacteristic, complemented
506C2×#107C2×D6111yescharacteristic, complemented
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×#102C2×D6111yescharacteristic
516C2×#102C2×D6111yescharacteristic
517#408—618no—
518C2×C22⋊C8—611no—
519C2×C22⋊C8—611no—
520C2×C22⋊C8—611no—
521C2×C22⋊C8C2×D6111yescharacteristic, complemented
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—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—21no—
553C23×C4—611no—
554C23×C4—611no—
555C23×C4—1221no—
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—614no—
566C2×M16—2442no—
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—1222no—
578C22⋊Q8—1222no—
579C22⋊Q8—1228no—
580#121—22no—
581#121—614no—
582#121—614no—
583#121—614no—
584#121—614no—
585#121—614no—
586#121—1222no—
587#121—1222no—
588#121—1222no—
589#121—1228no—
590#121—1228no—
591#121—1228no—
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—22no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4C22×D6111yescharacteristic
605C2×C4⋊C4C22×D6111yescharacteristic
606C2×C4⋊C4C22×D6111yescharacteristic
607C2×C4⋊C4C22×D6114yescomplemented
608C2×C22⋊C4—21no—
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#107C22×D6114yescomplemented
619#107C22×D6114yescomplemented
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#102C22×D6114yes—
629#102C22×D6114yes—
630C22⋊C8—614no—
631C22⋊C8—614no—
632C22⋊C8—614no—
633C22⋊C8C22×D6114yescomplemented
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—614no—
651C2×Q8—612no—
652C2×Q8—1221no—
653C2×Q8—1222no—
654C2×Q8—1222no—
655C2×Q8—2442no—
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—2448no—
688C2×D4—2442no—
689C2×D4—2442no—
690C2×D4—2444no—
691C2×D4—2444no—
692C2×D4C23×D6112yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—82no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—612no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1224no—
713C22×C4—2444no—
714C22×C4D4×D6112yes—
715C22×C4D4×D6111yescharacteristic
716C22×C4C23×D6112yes—
717C22×C4C23×D6111yescharacteristic
718SD16—2444no—
719SD16—2444no—
720D8—2444no—
721D8—2444no—
722M16—2444no—
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—24no—
735C4⋊C4—21no—
736C4⋊C4—612no—
737C4⋊C4—1224no—
738C4⋊C4—1224no—
739C4⋊C4—1221no—
740C4⋊C4C23×D6112yes—
741C4⋊C4C23×D6112yes—
742C4⋊C4C23×D6112yes—
743C22⋊C4—24no—
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—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—1222no—
783Q8—1222no—
784Q8—2444no—
785Q8—2442no—
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—2444no—
801D4—2444no—
802D4—2448no—
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—84no—
817C2×C4—612no—
818C2×C4—612no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1224no—
822C2×C4—1224no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—2448no—
830C2×C4—2442no—
831C2×C4—2442no—
832C2×C4C2×D4×D6112yes—
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4#1451982312yes—
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#1684032312yes—
867C22#1684056312yes—
868C22#1684057112yes—
869C22C22×D4×D6111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—1222no—
875C4—1222no—
876C4—2442no—
877C4—2442no—
878C4#1684032312yes—
879C4C2×#1451982311yescharacteristic
880C4C2×#1451982311yescharacteristic
881C2—42no—
882C2—82no—
883C2—4882no—
884C2—4882no—
885C2—2442no—
886C2—2442no—
887C2#2145667814yesdirect product factor
888C2C2×#1684032311yescharacteristic
889C2C2×#1684056311yescharacteristic
890C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#480C2
socleC23×C61C22×D4
hypercenterC2×#480D61
hypocenterC61C2×#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#16840343C2semidirect
2. C2×#16840328C2semidirect
3. #21456678C2direct (N × H)
4. C2×#16840080C2semidirect
5. C2×#16840105C2semidirect
6. C2×#16840089C2semidirect
7. C2×#16840014C2semidirect
8. C2×#16840009C2semidirect
9. C2×#16839999C2semidirect
10. C2×#16839990C2semidirect
11. C2×#16839909C2semidirect
12. C2×#16839905C2semidirect
13. C2×#16839914C2semidirect
14. C2×#16839897C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#480C2semidirect
18. C22×#11758222C22semidirect
24. C22×#11758189C22semidirect
25. C22×C8×D61C22semidirect
27. #16840343C22semidirect
29. #16840328C22semidirect
34. C2×#14519757C22semidirect
38. C2×#14519752C22semidirect
46. #16840105C22semidirect
47. #16840089C22semidirect
48. #16840080C22semidirect
49. #16840014C22semidirect
50. #16840009C22semidirect
51. #16839999C22semidirect
52. #16839990C22semidirect
53. #16839914C22semidirect
54. #16839909C22semidirect
55. #16839905C22semidirect
56. #16839897C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519708C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519700C22semidirect
61. C2×#14519699C22semidirect
64. C2×#14519697C22semidirect
65. #16839727C22semidirect
66. C2×C22⋊#92418C22semidirect
70. C22×C4⋊C4×C61C22semidirect
71. C61×#480C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#107×C61C22semidirect
76. C2×C22⋊C8×C61C22semidirect
85. C2×#11758222C23semidirect
116. C2×#11758189C23semidirect
120. C2×C8×D61C23semidirect
127. #14519757C23semidirect
134. #14519752C23semidirect
157. #14519708C23semidirect
158. #14519708C23semidirect
159. #14519702C23semidirect
160. #14519700C23semidirect
161. #14519699C23semidirect
164. #14519697C23semidirect
165. C22⋊#92418C23semidirect
181. C2×C4⋊C4×C61C23semidirect
183. #107×C61C23semidirect
184. #107×C61C23semidirect
187. C22⋊C8×C61C23semidirect
442. C2×#480D61semidirect
454. C2×C61#3198semidirect
492. C22×C4⋊C4C2×D61semidirect
496. #480C2×D61semidirect
505. C2×#107C2×D61semidirect
506. C2×#107C2×D61semidirect
521. C2×C22⋊C8C2×D61semidirect
522. C61C2×#3198semidirect
607. C2×C4⋊C4C22×D61semidirect
618. #107C22×D61semidirect
619. #107C22×D61semidirect
633. C22⋊C8C22×D61semidirect
887. C2#21456678direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403432
C2×#168403282
#214566782
C2×#168400802
C2×#168401052
C2×#168400892
C2×#168400142
C2×#168400092
C2×#168399992
C2×#168399902
C2×#168399092
C2×#168399052
C2×#168399142
C2×#168398972
C2×#168397272
C2×C61×#4802
C2×#319861