Finite Group Databasebeta

← C2×#21457360 #30555027

Subgroups — C2×#21457360 #30555027

Order 15616.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519802C211yesmaximal, characteristic, complemented
2C22×#14519797C211yesmaximal, characteristic, complemented
3C2×#16840408C211yesmaximal, characteristic, complemented
4#21457360C2116yesmaximal, direct product factor
5C2×#16840149C211yesmaximal, characteristic, complemented
6C2×#16840006C211yesmaximal, characteristic, complemented
7C2×#16839996C211yesmaximal, characteristic, complemented
8C2×#16839984C211yesmaximal, characteristic, complemented
9C2×#16839954C211yesmaximal, characteristic, complemented
10C2×#16839924C211yesmaximal, characteristic, complemented
11C2×#16839907C211yesmaximal, characteristic, complemented
12C2×#16839905C211yesmaximal, characteristic, complemented
13C2×#16839895C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×#16839834C211yesmaximal, characteristic, complemented
16C2×C61×#550C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C2×#14519802—28no—
20C2×#14519802C2218yescomplemented
21C2×#14519797—28no—
22C2×#14519797C2218yescomplemented
23C22×#11758202C2211yescharacteristic, complemented
24C22×#11758200C2211yescharacteristic, complemented
25C22×#11758200C2211yescharacteristic, complemented
26C22×#11758201C2211yescharacteristic
27C22×#11758201C2211yescharacteristic
28C22×#11758199C2211yescharacteristic
29C22×#11758199C2211yescharacteristic
30C22×#11758199C2211yescharacteristic
31C22×#11758199C2211yescharacteristic
32C22×#11758194C2211yescharacteristic
33C23×#92418C2211yescharacteristic, complemented
34#16840408—24no—
35#16840408C2218yescomplemented
36C2×#14519765C2211yescharacteristic
37C2×#14519762—21no—
38C2×#14519756C2211yescharacteristic
39C2×#14519751C2211yescharacteristic
40C2×#14519750—21no—
41C2×#14519745—21no—
42C2×C4×D244C2211yescharacteristic
43C2×C22⋊C4×D61—21no—
44#16840149C2218yescomplemented
45#16840006C2218yescomplemented
46#16839996C2218yescomplemented
47#16839984C2218yescomplemented
48#16839954C2218yescomplemented
49#16839924C2218yescomplemented
50#16839907C2218yescomplemented
51#16839905C2218yescomplemented
52#16839895C2218yescomplemented
53#16839860C2218yescomplemented
54#16839834C2218yescomplemented
55C2×#14519710C2211yescharacteristic, complemented
56C2×C4⋊#92418C2211yescharacteristic, complemented
57C2×#14519701C2211yescharacteristic, complemented
58C2×#14519700C2211yescharacteristic, complemented
59C2×#14519698C2211yescharacteristic, complemented
60C2×#14519698C2211yescharacteristic, complemented
61C2×#14519697C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×C22⋊#92418C2211yescharacteristic
64C2×C22⋊#92418C2211yescharacteristic, complemented
65C2×#14519688C2211yescharacteristic, complemented
66C22×#41×C61C2211yescharacteristic
67C22×#41×C61C2211yescharacteristic, complemented
68C61×#550—24no—
69C61×#550C2218yescomplemented
70C2×#127×C61—21no—
71C2×#127×C61C2211yescharacteristic, complemented
72C2×#121×C61—21no—
73C2×#121×C61—21no—
74C2×#121×C61C2211yescharacteristic
75C2×#121×C61C2211yescharacteristic, complemented
76C2×C4×Q8×C61C2211yescharacteristic, complemented
77C2×C4×D4×C61—21no—
78C2×C4×D4×C61C2211yescharacteristic
79C24×D61—21no—
80C2×#11758222—22no—
81C2×#11758222—24no—
82C2×#11758222—42no—
83C2×#11758222C2314yes—
84C22×Dic122C2311yescharacteristic
85C22×D244—24no—
86C22×D244—21no—
87C22×D244—22no—
88C22×D244—42no—
89C22×D244C2311yescharacteristic
90C22×D244C2314yes—
91C22×D244C2311yescharacteristic
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96#14519802—232no—
97#14519797—232no—
98C2×#11758202—24no—
99C2×#11758202C2314yescomplemented
100C2×#11758200—24no—
101C2×#11758200—42no—
102C2×#11758200C2314yescomplemented
103C2×#11758200C2314yescomplemented
104C2×#11758201—24no—
105C2×#11758201D418yescomplemented
106C2×#11758201C2314yes—
107C2×#11758201C2314yes—
108C2×#11758199—24no—
109C2×#11758199—24no—
110C2×#11758199—24no—
111C2×#11758199—42no—
112C2×#11758199C2314yes—
113C2×#11758199C2314yes—
114C2×#11758199C2314yes—
115C2×#11758199C2314yes—
116C2×#11758194—24no—
117C2×#11758194C2314yes—
118C22×#92418—24no—
119C22×#92418C2311yescharacteristic
120C22×#92418C2311yescharacteristic
121C22×#92418C2311yescharacteristic
122C22×#92418C2311yescharacteristic
123C22×#92418C2314yescomplemented
124#14519765—22no—
125#14519765C2314yes—
126#14519762—28no—
127#14519756—22no—
128#14519756C2314yes—
129#14519751—22no—
130#14519751C2314yes—
131#14519750—28no—
132#14519745—28no—
133C4×D244—22no—
134C4×D244C2314yes—
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C22⋊C4×D61—28no—
143#14519710C2314yescomplemented
144C4⋊#92418C2314yescomplemented
145#14519701C2314yescomplemented
146#14519700C2314yescomplemented
147#14519698C2314yescomplemented
148#14519698C2314yescomplemented
149#14519697C2314yes—
150#14519697C2314yes—
151C22⋊#92418C2314yes—
152C22⋊#92418C2314yescomplemented
153#14519688C2314yescomplemented
154C2×#41×C61—22no—
155C2×#41×C61—22no—
156C2×#41×C61—24no—
157C2×#41×C61—24no—
158C2×#41×C61—42no—
159C2×#41×C61—42no—
160C2×#41×C61C2314yes—
161C2×#41×C61C2314yescomplemented
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61—21no—
164C22×D4×C61—21no—
165C22×D4×C61—21no—
166C22×D4×C61—21no—
167C22×D4×C61—21no—
168C22×D4×C61—21no—
169C22×D4×C61D411yescharacteristic
170C22×D4×C61C2311yescharacteristic
171C22×D4×C61C2311yescharacteristic
172C23×C4×C61—21no—
173C23×C4×C61—21no—
174C23×C4×C61C2311yescharacteristic
175C23×C4×C61C2311yescharacteristic
176#127×C61—28no—
177#127×C61—22no—
178#127×C61C2314yescomplemented
179#121×C61—22no—
180#121×C61—22no—
181#121×C61—28no—
182#121×C61—28no—
183#121×C61C2314yes—
184#121×C61C2314yescomplemented
185C4×Q8×C61—22no—
186C4×Q8×C61C2314yescomplemented
187C4×D4×C61—28no—
188C4×D4×C61D414yes—
189C4×D4×C61C2314yes—
190C2×C4⋊C4×C61—21no—
191C2×C4⋊C4×C61D411yescharacteristic
192C2×C4⋊C4×C61C2311yescharacteristic
193C2×C22⋊C4×C61—21no—
194C2×C22⋊C4×C61—21no—
195C2×C22⋊C4×C61D411yescharacteristic
196C2×C22⋊C4×C61D411yescharacteristic
197C2×C42×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C24×C61—21no—
200C24×C61—21no—
201C24×C61C2×D411yescharacteristic
202C24×C61C2×D411yescharacteristic
203C23×D61—21no—
204C23×D61—21no—
205C23×D61—24no—
206C23×D61—44no—
207C23×D61—44no—
208C23×D61—82no—
209#41×C61—28no—
210#41×C61—28no—
211#41×C61—44no—
212#41×C61—44no—
213#41×C61—48no—
214#41×C61—48no—
215C2×Q8×C61—21no—
216C2×Q8×C61—22no—
217C2×Q8×C61C2×D414yes—
218C2×Q8×C61C2412yes—
219C2×D4×C61—24no—
220C2×D4×C61—24no—
221C2×D4×C61—24no—
222C2×D4×C61—24no—
223C2×D4×C61—22no—
224C2×D4×C61—22no—
225C2×D4×C61—24no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—24no—
229C2×D4×C61—22no—
230C2×D4×C61—22no—
231C2×D4×C61—42no—
232C2×D4×C61—44no—
233C2×D4×C61—44no—
234C2×D4×C61—44no—
235C2×D4×C61—82no—
236C2×D4×C61—82no—
237C2×D4×C61—82no—
238C2×D4×C61C2×D414yes—
239C2×D4×C61C2412yes—
240C2×D4×C61C2412yes—
241C22×C4×C61—21no—
242C22×C4×C61—22no—
243C22×C4×C61—22no—
244C22×C4×C61—22no—
245C22×C4×C61—22no—
246C22×C4×C61—21no—
247C22×C4×C61—24no—
248C22×C4×C61—24no—
249C22×C4×C61—44no—
250C22×C4×C61—44no—
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D412yes—
255C22×C4×C61C2×D412yes—
256C22×C4×C61C2×D411yescharacteristic
257C22×C4×C61C2412yes—
258C22×C4×C61C2412yes—
259C22×C4×C61C2411yescharacteristic
260C2×C22⋊D61—24no—
261C2×C22⋊D61—24no—
262C2×C22⋊D61—44no—
263C2×C22⋊D61—82no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266#11758222—28no—
267#11758222—44no—
268#11758222—48no—
269C2×D244—21no—
270C2×D244—22no—
271C2×D244—22no—
272C2×D244—22no—
273C2×D244—28no—
274C2×D244—24no—
275C2×D244—21no—
276C2×D244—44no—
277C2×D244—48no—
278C2×D244—44no—
279C2×D244C2×D414yes—
280C2×D244C2412yes—
281C2×D244C2412yes—
282C2×C4×D61—24no—
283C2×C4×D61—24no—
284C2×C4×D61—44no—
285C2×C4×D61—82no—
286C2×Dic122—22no—
287C2×Dic122—22no—
288C2×Dic122—21no—
289C2×Dic122C2412yes—
290C4⋊C4×C61—24no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61C2×D414yes—
293C4⋊C4×C61C2412yes—
294C22⋊C4×C61—24no—
295C22⋊C4×C61—24no—
296C22⋊C4×C61C2×D414yes—
297C22⋊C4×C61C2×D414yes—
298C42×C61—24no—
299C42×C61C2×D412yes—
300C42×C61C2412yes—
301C22⋊Dic61—24no—
302#11758202—28no—
303#11758201—28no—
304#11758201C2×D4116yescomplemented
305#11758200—28no—
306#11758200—44no—
307#11758199—28no—
308#11758199—28no—
309#11758199—28no—
310#11758199—44no—
311#11758198—24no—
312#11758198—24no—
313#11758198—24no—
314#11758198—24no—
315C4⋊Dic61—21no—
316C4⋊Dic61C2412yes—
317#11758196—24no—
318#11758194—28no—
319C2×#92418—22no—
320C2×#92418—22no—
321C2×#92418—22no—
322C2×#92418—28no—
323C2×#92418C2×D414yes—
324C2×#92418C2412yes—
325C2×#92418C2412yes—
326C2×#92418C2412yes—
327C2×#92418C2412yes—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—42no—
337C23×C61—42no—
338C23×C61—42no—
339C23×C61—42no—
340C23×C61—42no—
341C23×C61—42no—
342C23×C61C22×D412yes—
343C23×C61C22×D412yes—
344C23×C61C22×D411yescharacteristic
345C22×D61—24no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—48no—
349C22×D61—42no—
350C22×D61—42no—
351C22×D61—48no—
352C22×D61—42no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—84no—
356C22×D61—816no—
357Q8×C61—24no—
358Q8×C61—22no—
359Q8×C61C22×D414yes—
360D4×C61—22no—
361D4×C61—22no—
362D4×C61—22no—
363D4×C61—22no—
364D4×C61—44no—
365D4×C61—48no—
366D4×C61—48no—
367D4×C61—48no—
368D4×C61—42no—
369D4×C61—42no—
370D4×C61—84no—
371D4×C61—84no—
372D4×C61—84no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—24no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—24no—
380C2×C4×C61—24no—
381C2×C4×C61—22no—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—48no—
387C2×C4×C61—48no—
388C2×C4×C61—42no—
389C2×C4×C61C22×D412yes—
390C2×C4×C61C22×D412yes—
391C2×C4×C61C22×D412yes—
392C2×C4×C61C22×D412yes—
393C2×C4×C61C22×D411yescharacteristic
394C2×C4×C61C22×D412yes—
395C2×C4×C61H(5,𝔽2)12yes—
396C2×C4×C61C2511yescharacteristic
397C22⋊D61—48no—
398C22⋊D61—84no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—42no—
402C2×Dic61—42no—
403D244—24no—
404D244—22no—
405D244—22no—
406D244—22no—
407D244—48no—
408D244—42no—
409D244C22×D414yes—
410C4×D61—48no—
411C4×D61—84no—
412Dic122—22no—
413Dic122—22no—
414Dic122—42no—
415#92418—22no—
416#92418—22no—
417#92418—22no—
418#92418C22×D414yes—
419C2×#3268—611nomaximal, Sylow
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—22no—
423C22×C61—22no—
424C22×C61—22no—
425C22×C61—22no—
426C22×C61—44no—
427C22×C61—44no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61—84no—
435C22×C61—84no—
436C22×C61D4212yes—
437C22×C61#57512yes—
438C22×C61#57612yes—
439C22×C61C23×D411yescharacteristic
440C2×D61—24no—
441C2×D61—48no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—42no—
445C2×D61—42no—
446C2×D61—42no—
447C2×D61—816no—
448C2×D61—84no—
449C4×C61—22no—
450C4×C61—22no—
451C4×C61—24no—
452C4×C61—22no—
453C4×C61—22no—
454C4×C61—42no—
455C4×C61D4212yes—
456C4×C61C23×D411yescharacteristic
457C4×C61C2×H(5,𝔽2)11yescharacteristic
458Dic61—42no—
459Dic61—42no—
460C22×AGL(1,ℤ/8)—611no—
461C22×#135—611no—
462C2×#550D6111yescharacteristic, complemented
463C2×#546—611no—
464#3268—6116no—
465C2×#496—611no—
466C2×#468—611no—
467C2×#466—611no—
468C2×#464—611no—
469C2×#459—611no—
470C2×#452—611no—
471C2×#449—611no—
472C2×#449—611no—
473C2×#447—611no—
474C2×#440—611no—
475C2×#435—611no—
476C2×C61—42no—
477C2×C61—42no—
478C2×C61—82no—
479C2×C61—82no—
480C2×C61#326814yescomplemented
481C2×C61C2×D4211yescharacteristic
482C2×C61C2×#57511yescharacteristic
483C2×C61C2×#57611yescharacteristic
484D61—44no—
485D61—82no—
486C22×#41—611no—
487C22×#41C2×D6111yescharacteristic
488C22×#41C2×D6111yescharacteristic, complemented
489C23×D4—611no—
490C2×AGL(1,ℤ/8)—618no—
491C2×AGL(1,ℤ/8)—1228no—
492C2×#135—618no—
493C2×#135—1228no—
494C22×Q16—611no—
495C22×SD16—611no—
496C22×SD16—611no—
497C22×SD16—611no—
498C22×SD16—611no—
499C22×D8—611no—
500C22×D8—611no—
501C22×D8—611no—
502C22×D8—611no—
503C22×M16—611no—
504C23×C8—611no—
505#550—24no—
506#550C2×D6118yescomplemented
507#546—618no—
508#546—1224no—
509C2×#127—21no—
510C2×#127C2×D6111yescharacteristic, complemented
511C2×#124—611no—
512C2×#123—1221no—
513C2×C22⋊Q8—611no—
514C2×#121—21no—
515C2×#121—21no—
516C2×#121—611no—
517C2×#121—1221no—
518C2×#121C2×D6111yescharacteristic
519C2×#121C2×D6111yescharacteristic, complemented
520C2×#120—1221no—
521C2×C4×Q8C2×D6111yescharacteristic, complemented
522C2×C4×D4—21no—
523C2×C4×D4—611no—
524C2×C4×D4C2×D6111yescharacteristic
525C22×C22⋊C4—1221no—
526#496—618no—
527#468—618no—
528#466—618no—
529#464—618no—
530#459—618no—
531#452—618no—
532#449—618no—
533#449—618no—
534#447—618no—
535#440—618no—
536#435—618no—
537C2×#107—611no—
538C2×C4⋊C8—611no—
539C2×#103—611no—
540C2×#103—611no—
541C2×#102—611no—
542C2×#102—611no—
543C2×#102—611no—
544C2×#102—611no—
545C2×C22⋊C8—611no—
546C2×C22⋊C8—611no—
547C2×#97—611no—
548C61C2×#326811yescharacteristic, complemented, Sylow
549C25—1221no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—24no—
553C2×#41—24no—
554C2×#41—42no—
555C2×#41—42no—
556C2×#41—614no—
557C2×#41—1224no—
558C2×#41—1222no—
559C2×#41—2442no—
560C2×#41C22×D6114yes—
561C2×#41C22×D6114yescomplemented
562C22×Q8—611no—
563C22×Q8C22×D6111yescharacteristic
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—21no—
569C22×D4—21no—
570C22×D4—611no—
571C22×D4—611no—
572C22×D4—614no—
573C22×D4—1224no—
574C22×D4—1221no—
575C22×D4—1221no—
576C22×D4—1221no—
577C22×D4—1222no—
578C22×D4—2442no—
579C22×D4C22⋊D6111yescharacteristic
580C22×D4C22×D6111yescharacteristic
581C22×D4C22×D6111yescharacteristic
582C23×C4—21no—
583C23×C4—21no—
584C23×C4—1221no—
585C23×C4—1221no—
586C23×C4C22×D6111yescharacteristic
587C23×C4C22×D6111yescharacteristic
588AGL(1,ℤ/8)—12232no—
589#135—12232no—
590C2×Q16—614no—
591C2×Q16—1224no—
592C2×SD16—618no—
593C2×SD16—614no—
594C2×SD16—614no—
595C2×SD16—614no—
596C2×SD16—614no—
597C2×SD16—1224no—
598C2×SD16—1224no—
599C2×SD16—2442no—
600C2×D8—614no—
601C2×D8—614no—
602C2×D8—614no—
603C2×D8—614no—
604C2×D8—1224no—
605C2×D8—1224no—
606C2×D8—1224no—
607C2×D8—2442no—
608C2×M16—614no—
609C2×M16—1224no—
610C22×C8—611no—
611C22×C8—611no—
612C22×C8—614no—
613C22×C8—611no—
614C22×C8—611no—
615C22×C8—1224no—
616#127—28no—
617#127—22no—
618#127C22×D6114yescomplemented
619#124—614no—
620#124—1222no—
621#123—1228no—
622C22⋊Q8—614no—
623C22⋊Q8—1222no—
624#121—22no—
625#121—22no—
626#121—28no—
627#121—28no—
628#121—614no—
629#121—1222no—
630#121—1228no—
631#121C22×D6114yes—
632#121C22×D6114yescomplemented
633#120—1228no—
634C4×Q8—22no—
635C4×Q8C22×D6114yescomplemented
636C4×D4—28no—
637C4×D4—614no—
638C4×D4—1222no—
639C4×D4C22⋊D6114yes—
640C4×D4C22×D6114yes—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—1221no—
644C2×C4⋊C4C22⋊D6111yescharacteristic
645C2×C4⋊C4C22×D6111yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—1221no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4—1221no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—1228no—
654C2×C22⋊C4C22⋊D6111yescharacteristic
655C2×C22⋊C4C22⋊D6111yescharacteristic
656C2×C42—21no—
657C2×C42C22×D6111yescharacteristic
658#107—614no—
659C4⋊C8—614no—
660#103—614no—
661#103—614no—
662#102—614no—
663#102—614no—
664#102—614no—
665#102—614no—
666C22⋊C8—614no—
667C22⋊C8—614no—
668#97—614no—
669C24—21no—
670C24—21no—
671C24—1221no—
672C24—1224no—
673C24—1221no—
674C24—4882no—
675C24—2444no—
676C24—2444no—
677C24C2×C22⋊D6111yescharacteristic
678C24C2×C22⋊D6111yescharacteristic
679#41—28no—
680#41—28no—
681#41—44no—
682#41—44no—
683#41—48no—
684#41—48no—
685#41—1228no—
686#41—2444no—
687#41—2448no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—612no—
691C2×Q8—1221no—
692C2×Q8—1222no—
693C2×Q8—1222no—
694C2×Q8D4×D6114yes—
695C2×Q8C23×D6112yes—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—24no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—24no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—42no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—82no—
713C2×D4—82no—
714C2×D4—82no—
715C2×D4—614no—
716C2×D4—612no—
717C2×D4—612no—
718C2×D4—1228no—
719C2×D4—1224no—
720C2×D4—1224no—
721C2×D4—1222no—
722C2×D4—1221no—
723C2×D4—1224no—
724C2×D4—1221no—
725C2×D4—1222no—
726C2×D4—1222no—
727C2×D4—4882no—
728C2×D4—2444no—
729C2×D4—2448no—
730C2×D4—2444no—
731C2×D4—2444no—
732C2×D4C2×C22⋊D6114yes—
733C2×D4C23×D6112yes—
734C2×D4C23×D6112yes—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1224no—
748C22×C4—1224no—
749C22×C4—4882no—
750C22×C4—2444no—
751C22×C4C2×C22⋊D6112yes—
752C22×C4C2×C22⋊D6112yes—
753C22×C4C2×C22⋊D6111yescharacteristic
754C22×C4C2×C22⋊D6111yescharacteristic
755C22×C4C2×C22⋊D6111yescharacteristic
756C22×C4C2×C22⋊D6111yescharacteristic
757C22×C4C23×D6112yes—
758C22×C4C23×D6112yes—
759C22×C4C23×D6111yescharacteristic
760Q16—1228no—
761SD16—6116no—
762SD16—1228no—
763SD16—1228no—
764SD16—2444no—
765D8—1228no—
766D8—1228no—
767D8—1228no—
768D8—2444no—
769M16—1228no—
770C2×C8—614no—
771C2×C8—612no—
772C2×C8—612no—
773C2×C8—612no—
774C2×C8—612no—
775C2×C8—1228no—
776C2×C8—1222no—
777C2×C8—1222no—
778C2×C8—1222no—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—612no—
782C4⋊C4—1221no—
783C4⋊C4—1224no—
784C4⋊C4C2×C22⋊D6114yes—
785C4⋊C4C23×D6112yes—
786C22⋊C4—24no—
787C22⋊C4—24no—
788C22⋊C4—1224no—
789C22⋊C4—1224no—
790C22⋊C4—1224no—
791C22⋊C4—1224no—
792C22⋊C4—1224no—
793C22⋊C4C2×C22⋊D6114yes—
794C22⋊C4C2×C22⋊D6114yes—
795C42—24no—
796C42C2×C22⋊D6112yes—
797C42C23×D6112yes—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—1222no—
813C23—1224no—
814C23—1222no—
815C23—4884no—
816C23—48816no—
817C23—2448no—
818C23—2448no—
819C23—2442no—
820C23—2442no—
821C23—2442no—
822C23—2442no—
823C23—2442no—
824C23C22×C22⋊D6112yes—
825C23C22×C22⋊D6112yes—
826C23C22×C22⋊D6111yescharacteristic
827Q8—22no—
828Q8—24no—
829Q8—1222no—
830Q8—1222no—
831Q8—2442no—
832Q8C2×D4×D6114yes—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—44no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—42no—
842D4—42no—
843D4—84no—
844D4—84no—
845D4—84no—
846D4—614no—
847D4—1222no—
848D4—1222no—
849D4—1222no—
850D4—1224no—
851D4—4884no—
852D4—2448no—
853D4—2448no—
854D4—2442no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—48no—
869C2×C4—48no—
870C2×C4—42no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—4884no—
874C2×C4—2448no—
875C2×C4—2442no—
876C2×C4—2442no—
877C2×C4C2×D4×D6112yes—
878C2×C4C22×C22⋊D6112yes—
879C2×C4C22×C22⋊D6112yes—
880C2×C4C22×C22⋊D6112yes—
881C2×C4C22×C22⋊D6112yes—
882C2×C4C22×C22⋊D6111yescharacteristic
883C2×C4#1451982212yes—
884C2×C4C24×D6111yescharacteristic
885C8—614no—
886C8—1222no—
887C8—1222no—
888C8—1222no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—44no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—84no—
904C22—84no—
905C22—1224no—
906C22—48816no—
907C22—4884no—
908C22—2442no—
909C22—2442no—
910C22—2442no—
911C22—2442no—
912C22—2442no—
913C22—2448no—
914C22D4×C22⋊D6112yes—
915C22#1684056012yes—
916C22#1684056512yes—
917C22C23×C22⋊D6111yescharacteristic
918C4—22no—
919C4—22no—
920C4—24no—
921C4—22no—
922C4—22no—
923C4—42no—
924C4—2442no—
925C4—2442no—
926C4D4×C22⋊D6112yes—
927C4C22×D4×D6111yescharacteristic
928C4C2×#1451982211yescharacteristic
929C2—42no—
930C2—42no—
931C2—82no—
932C2—82no—
933C2—4882no—
934C2—2444no—
935C2#2145736014yesdirect product factor
936C2C2×D4×C22⋊D6111yescharacteristic
937C2C2×#1684056011yescharacteristic
938C2C2×#1684056511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#550C2
socleC23×C61C22×D4
hypercenterC2×#550D61
hypocenterC61C2×#3268
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#14519802C2semidirect
2. C22×#14519797C2semidirect
3. C2×#16840408C2semidirect
4. #21457360C2direct (N × H)
5. C2×#16840149C2semidirect
6. C2×#16840006C2semidirect
7. C2×#16839996C2semidirect
8. C2×#16839984C2semidirect
9. C2×#16839954C2semidirect
10. C2×#16839924C2semidirect
11. C2×#16839907C2semidirect
12. C2×#16839905C2semidirect
13. C2×#16839895C2semidirect
14. C2×#16839860C2semidirect
15. C2×#16839834C2semidirect
16. C2×C61×#550C2semidirect
20. C2×#14519802C22semidirect
22. C2×#14519797C22semidirect
23. C22×#11758202C22semidirect
24. C22×#11758200C22semidirect
25. C22×#11758200C22semidirect
33. C23×#92418C22semidirect
35. #16840408C22semidirect
44. #16840149C22semidirect
45. #16840006C22semidirect
46. #16839996C22semidirect
47. #16839984C22semidirect
48. #16839954C22semidirect
49. #16839924C22semidirect
50. #16839907C22semidirect
51. #16839905C22semidirect
52. #16839895C22semidirect
53. #16839860C22semidirect
54. #16839834C22semidirect
55. C2×#14519710C22semidirect
56. C2×C4⋊#92418C22semidirect
57. C2×#14519701C22semidirect
58. C2×#14519700C22semidirect
59. C2×#14519698C22semidirect
60. C2×#14519698C22semidirect
64. C2×C22⋊#92418C22semidirect
65. C2×#14519688C22semidirect
67. C22×#41×C61C22semidirect
69. C61×#550C22semidirect
71. C2×#127×C61C22semidirect
75. C2×#121×C61C22semidirect
76. C2×C4×Q8×C61C22semidirect
99. C2×#11758202C23semidirect
102. C2×#11758200C23semidirect
103. C2×#11758200C23semidirect
105. C2×#11758201D4semidirect
123. C22×#92418C23semidirect
143. #14519710C23semidirect
144. C4⋊#92418C23semidirect
145. #14519701C23semidirect
146. #14519700C23semidirect
147. #14519698C23semidirect
148. #14519698C23semidirect
152. C22⋊#92418C23semidirect
153. #14519688C23semidirect
161. C2×#41×C61C23semidirect
178. #127×C61C23semidirect
184. #121×C61C23semidirect
186. C4×Q8×C61C23semidirect
304. #11758201C2×D4semidirect
462. C2×#550D61semidirect
480. C2×C61#3268semidirect
488. C22×#41C2×D61semidirect
506. #550C2×D61semidirect
510. C2×#127C2×D61semidirect
519. C2×#121C2×D61semidirect
521. C2×C4×Q8C2×D61semidirect
548. C61C2×#3268semidirect
561. C2×#41C22×D61semidirect
618. #127C22×D61semidirect
632. #121C22×D61semidirect
635. C4×Q8C22×D61semidirect
935. C2#21457360direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198022
C22×#145197972
C2×#168404082
#214573602
C2×#168401492
C2×#168400062
C2×#168399962
C2×#168399842
C2×#168399542
C2×#168399242
C2×#168399072
C2×#168399052
C2×#168398952
C2×#168398602
C2×#168398342
C2×C61×#5502
C2×#326861