Finite Group Databasebeta

← C2×#21456668 #30550663

Subgroups — C2×#21456668 #30550663

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×#16840328C211yesmaximal, characteristic, complemented
3#21456668C2116yesmaximal, direct product factor
4C2×#16840078C211yesmaximal, characteristic, complemented
5C2×#16840102C211yesmaximal, characteristic, complemented
6C2×#16840084C211yesmaximal, characteristic, complemented
7C2×#16840076C211yesmaximal, characteristic, complemented
8C2×#16840014C211yesmaximal, characteristic, complemented
9C2×#16840005C211yesmaximal, characteristic, complemented
10C2×#16839995C211yesmaximal, characteristic, complemented
11C2×#16839994C211yesmaximal, characteristic, complemented
12C2×#16839907C211yesmaximal, characteristic, complemented
13C2×#16839911C211yesmaximal, characteristic, complemented
14C2×#16839894C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758189C2211yescharacteristic, complemented
22C22×C8×D61C2211yescharacteristic, complemented
23#16840340—24no—
24#16840340C2218yescomplemented
25#16840328—24no—
26#16840328C2218yescomplemented
27C2×#14519773—21no—
28C2×#14519763—21no—
29C2×#14519756—21no—
30C2×#14519753C2211yescharacteristic
31C2×#14519753C2211yescharacteristic, complemented
32C2×#14519752C2211yescharacteristic
33C2×#14519751—21no—
34C2×#14519751C2211yescharacteristic
35C2×#14519749—21no—
36C2×#14519749—21no—
37C2×#14519748C2211yescharacteristic
38C2×#14519748C2211yescharacteristic
39C2×#14519748C2211yescharacteristic, complemented
40C2×#14519747—21no—
41C2×#14519745—21no—
42C2×#14519735C2211yescharacteristic
43C22×C4⋊Dic61C2211yescharacteristic, complemented
44#16840102C2218yescomplemented
45#16840084C2218yescomplemented
46#16840078C2218yescomplemented
47#16840076C2218yescomplemented
48#16840014C2218yescomplemented
49#16840005C2218yescomplemented
50#16839995C2218yescomplemented
51#16839994C2218yescomplemented
52#16839911C2218yescomplemented
53#16839907C2218yescomplemented
54#16839894C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519711C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519708C2211yescharacteristic, complemented
59C2×#14519701C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic, complemented
65#16839727C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic, complemented
70C22×SD16×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#449C2218yescomplemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic, complemented
76C2×C22⋊C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222D414yes—
81C2×#11758222C2314yes—
82C22×Dic122D411yescharacteristic
83C22×D244—21no—
84C22×D244D411yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61D411yescharacteristic
92C22×C22⋊D61D411yescharacteristic
93C2×D4×D61—22no—
94C2×D4×D61—42no—
95C2×D4×D61—42no—
96C2×D4×D61C2314yes—
97C23×Dic61—21no—
98C22×C4×D61C2311yescharacteristic
99C22×C4×D61C2311yescharacteristic
100C2×#11758201—42no—
101C2×#11758201C2314yes—
102C2×#11758199—42no—
103C2×#11758199C2314yes—
104C2×#11758189—42no—
105C2×#11758189C2314yescomplemented
106C22×#92418C2311yescharacteristic
107C22×#92418C2311yescharacteristic
108C2×C8×D61—42no—
109C2×C8×D61C2314yescomplemented
110#14519773—28no—
111#14519763—28no—
112#14519756—28no—
113#14519753—22no—
114#14519753—22no—
115#14519753C2314yes—
116#14519753C2314yescomplemented
117#14519752—22no—
118#14519752C2314yes—
119#14519751—22no—
120#14519751—28no—
121#14519751C2314yes—
122#14519749—28no—
123#14519749—28no—
124#14519748—22no—
125#14519748—22no—
126#14519748—22no—
127#14519748C2314yes—
128#14519748C2314yes—
129#14519748C2314yescomplemented
130#14519747—28no—
131#14519745—28no—
132#14519735—22no—
133#14519735C2314yes—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61—22no—
136C2×C4⋊Dic61C2311yescharacteristic
137C2×C4⋊Dic61C2311yescharacteristic
138C2×C4⋊Dic61C2311yescharacteristic
139C2×C4⋊Dic61C2314yescomplemented
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yescomplemented
152#14519711C2314yescomplemented
153#14519708C2314yescomplemented
154#14519708C2314yescomplemented
155#14519701C2314yescomplemented
156#14519699C2314yes—
157#14519699C2314yes—
158#14519698C2314yes—
159#14519698C2314yes—
160#14519698C2314yescomplemented
161C22⋊#92418C2314yescomplemented
162#14519689C2314yes—
163#14519689C2314yes—
164C2×#41×C61—22no—
165C2×#41×C61—42no—
166C2×#41×C61—42no—
167C2×#41×C61C2314yescomplemented
168C22×Q8×C61C2311yescharacteristic
169C22×D4×C61—21no—
170C22×D4×C61—21no—
171C22×D4×C61C2311yescharacteristic
172C22×D4×C61C2311yescharacteristic
173C23×C4×C61—21no—
174C23×C4×C61C2311yescharacteristic
175C2×SD16×C61—42no—
176C2×SD16×C61C2314yes—
177C2×D8×C61—42no—
178C2×D8×C61C2314yes—
179C22×C8×C61C2311yescharacteristic
180C22×C8×C61C2311yescharacteristic
181#121×C61—22no—
182#121×C61C2314yes—
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185#103×C61C2314yescomplemented
186#102×C61C2314yescomplemented
187C22⋊C8×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
198#41×C61—44no—
199#41×C61—44no—
200#41×C61—48no—
201C2×Q8×C61—21no—
202C2×Q8×C61—22no—
203C2×Q8×C61—22no—
204C2×Q8×C61C2412yes—
205C2×D4×C61—24no—
206C2×D4×C61—24no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—22no—
210C2×D4×C61—22no—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61—44no—
214C2×D4×C61—82no—
215C2×D4×C61C2412yes—
216C2×D4×C61C2412yes—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—24no—
222C22×C4×C61—44no—
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D412yes—
225C22×C4×C61C2412yes—
226C22×C4×C61C2411yescharacteristic
227C2×C22⋊D61—24no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—24no—
231C2×C22⋊D61—24no—
232C2×C22⋊D61—42no—
233C2×C22⋊D61—42no—
234C2×C22⋊D61—44no—
235C2×C22⋊D61—82no—
236C2×C22⋊D61—82no—
237C2×C22⋊D61—82no—
238C2×C22⋊D61—82no—
239C2×C22⋊D61C2×D414yes—
240C2×C22⋊D61C2×D414yes—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—24no—
245C22×Dic61—82no—
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248D4×D61—44no—
249D4×D61—44no—
250D4×D61—48no—
251#11758222—48no—
252#11758222—44no—
253#11758222—44no—
254C2×D244—22no—
255C2×D244—22no—
256C2×D244—21no—
257C2×D244—24no—
258C2×D244—42no—
259C2×D244—82no—
260C2×D244C2×D414yes—
261C2×D244C2412yes—
262C2×C4×D61—22no—
263C2×C4×D61—22no—
264C2×C4×D61—22no—
265C2×C4×D61—22no—
266C2×C4×D61C2×D412yes—
267C2×C4×D61C2×D412yes—
268C2×C4×D61C2412yes—
269C2×C4×D61C2412yes—
270C2×Dic122—42no—
271C2×Dic122C2×D414yes—
272SD16×C61—44no—
273D8×C61—44no—
274C2×C8×C61—22no—
275C2×C8×C61—22no—
276C2×C8×C61C2412yes—
277C2×C8×C61C2412yes—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C2412yes—
280C22⋊C4×C61—24no—
281C22⋊Dic61—24no—
282C22⋊Dic61—24no—
283C22⋊Dic61—24no—
284#11758201—44no—
285#11758199—44no—
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⋊Dic61C2412yes—
296C4⋊Dic61C2412yes—
297C4⋊Dic61C2412yes—
298#11758196—24no—
299#11758196—24no—
300C4×Dic61—24no—
301C2×#92418—22no—
302C2×#92418—22no—
303C2×#92418C2412yes—
304C2×#92418C2412yes—
305#11758189—44no—
306C8×D61—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—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—42no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—22no—
343D4×C61—48no—
344D4×C61—42no—
345D4×C61—42no—
346D4×C61—84no—
347C2×C4×C61—22no—
348C2×C4×C61—24no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—48no—
354C2×C4×C61—42no—
355C2×C4×C61—42no—
356C2×C4×C61C22×D412yes—
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61H(5,𝔽2)12yes—
359C2×C4×C61H(5,𝔽2)12yes—
360C2×C4×C61C2511yescharacteristic
361C22⋊D61—44no—
362C22⋊D61—44no—
363C22⋊D61—48no—
364C22⋊D61—84no—
365C22⋊D61—84no—
366C22⋊D61—84no—
367C22⋊D61—84no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—84no—
377C2×Dic61C22×D412yes—
378C2×Dic61C22×D412yes—
379D244—22no—
380D244—22no—
381D244—44no—
382D244—42no—
383D244—84no—
384C4×D61—24no—
385C4×D61—24no—
386C4×D61—22no—
387C4×D61—22no—
388C4×D61—22no—
389C4×D61—22no—
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—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×#469—611no—
444C2×#468—611no—
445C2×#466—611no—
446C2×#465—611no—
447C2×#449—611no—
448C2×#449D6111yescharacteristic, complemented
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×#41C2×D6111yescharacteristic, complemented
464C23×D4—611no—
465C22×SD16—611no—
466C22×SD16C2×D6111yescharacteristic
467C22×D8—611no—
468C22×D8C2×D6111yescharacteristic
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⋊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#449C2×D6118yescomplemented
504#447—618no—
505C2×#107—611no—
506C2×#107—611no—
507C2×#106—611no—
508C2×#106—611no—
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, complemented
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—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—614no—
528C2×#41—614no—
529C2×#41—2442no—
530C2×#41—2442no—
531C2×#41C22×D6114yescomplemented
532C22×Q8—611no—
533C22×Q8C22×D6111yescharacteristic
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—21no—
553C23×C4—611no—
554C23×C4—611no—
555C23×C4—1221no—
556C23×C4C22×D6111yescharacteristic
557C2×SD16—42no—
558C2×SD16—614no—
559C2×SD16—2442no—
560C2×SD16C22×D6114yes—
561C2×D8—42no—
562C2×D8—614no—
563C2×D8—2442no—
564C2×D8C22×D6114yes—
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—1228no—
578C22⋊Q8—1222no—
579C22⋊Q8—1222no—
580#121—22no—
581#121—614no—
582#121—614no—
583#121—614no—
584#121—614no—
585#121—614no—
586#121—1222no—
587#121—1228no—
588#121—1222no—
589#121—1222no—
590#121—1222no—
591#121—1228no—
592#121—1228no—
593#121—1222no—
594#121C22×D6114yes—
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—1221no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4C22×D6111yescharacteristic
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#107—614no—
619#107—614no—
620#106—614no—
621#106—614no—
622#103—614no—
623#103C22×D6114yescomplemented
624#102—614no—
625#102—614no—
626#102—614no—
627#102—614no—
628#102—614no—
629#102C22×D6114yescomplemented
630C22⋊C8—614no—
631C22⋊C8—614no—
632C22⋊C8—614no—
633C22⋊C8C22×D6114yescomplemented
634C24—21no—
635C24—21no—
636C24—611no—
637C24—611no—
638C24—1224no—
639C24—1221no—
640C24—4882no—
641C24—4882no—
642C24—2444no—
643C24D4×D6111yescharacteristic
644#41—44no—
645#41—44no—
646#41—48no—
647#41—2448no—
648#41—2444no—
649#41—2444no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—614no—
654C2×Q8—2442no—
655C2×Q8C23×D6112yes—
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—44no—
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—4882no—
684C2×D4—2442no—
685C2×D4—2444no—
686C2×D4—2444no—
687C2×D4—2448no—
688C2×D4—2442no—
689C2×D4—2442no—
690C2×D4—2444no—
691C2×D4C23×D6112yes—
692C2×D4C23×D6112yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—44no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—612no—
702C22×C4—612no—
703C22×C4—612no—
704C22×C4—612no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1224no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—4882no—
714C22×C4D4×D6112yes—
715C22×C4D4×D6111yescharacteristic
716C22×C4C23×D6112yes—
717C22×C4C23×D6111yescharacteristic
718SD16—44no—
719SD16—2444no—
720D8—44no—
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—612no—
734C4⋊C4—612no—
735C4⋊C4—612no—
736C4⋊C4—1224no—
737C4⋊C4—1224no—
738C4⋊C4—1224no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
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—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—22no—
783Q8—22no—
784Q8—42no—
785Q8—2444no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—42no—
793D4—84no—
794D4—1222no—
795D4—1222no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—4884no—
800D4—4884no—
801D4—2444no—
802D4—2444no—
803D4—2444no—
804D4—2448no—
805D4—2442no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—48no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—612no—
816C2×C4—612no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1224no—
820C2×C4—1224no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—4884no—
829C2×C4—2442no—
830C2×C4—2442no—
831C2×C4—2442no—
832C2×C4C2×D4×D6112yes—
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4#1451982212yes—
835C2×C4#1451982212yes—
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#1684032212yes—
867C22#1684056412yes—
868C22#1684057212yes—
869C22C22×D4×D6111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—1222no—
874C4—1222no—
875C4—2442no—
876C4—2442no—
877C4—2442no—
878C4#1684032212yes—
879C4C2×#1451982211yescharacteristic
880C4C2×#1451982211yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—4882no—
885C2—2442no—
886C2—2442no—
887C2#2145666814yesdirect product factor
888C2C2×#1684032211yescharacteristic
889C2C2×#1684056411yescharacteristic
890C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3198
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16840340C2semidirect
2. C2×#16840328C2semidirect
3. #21456668C2direct (N × H)
4. C2×#16840078C2semidirect
5. C2×#16840102C2semidirect
6. C2×#16840084C2semidirect
7. C2×#16840076C2semidirect
8. C2×#16840014C2semidirect
9. C2×#16840005C2semidirect
10. C2×#16839995C2semidirect
11. C2×#16839994C2semidirect
12. C2×#16839907C2semidirect
13. C2×#16839911C2semidirect
14. C2×#16839894C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#449C2semidirect
21. C22×#11758189C22semidirect
22. C22×C8×D61C22semidirect
24. #16840340C22semidirect
26. #16840328C22semidirect
31. C2×#14519753C22semidirect
39. C2×#14519748C22semidirect
43. C22×C4⋊Dic61C22semidirect
44. #16840102C22semidirect
45. #16840084C22semidirect
46. #16840078C22semidirect
47. #16840076C22semidirect
48. #16840014C22semidirect
49. #16840005C22semidirect
50. #16839995C22semidirect
51. #16839994C22semidirect
52. #16839911C22semidirect
53. #16839907C22semidirect
54. #16839894C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519711C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519708C22semidirect
59. C2×#14519701C22semidirect
64. C2×#14519698C22semidirect
65. #16839727C22semidirect
66. C2×C22⋊#92418C22semidirect
69. C22×#41×C61C22semidirect
73. C61×#449C22semidirect
74. C2×#103×C61C22semidirect
75. C2×#102×C61C22semidirect
76. C2×C22⋊C8×C61C22semidirect
105. C2×#11758189C23semidirect
109. C2×C8×D61C23semidirect
116. #14519753C23semidirect
129. #14519748C23semidirect
139. C2×C4⋊Dic61C23semidirect
151. #14519711C23semidirect
152. #14519711C23semidirect
153. #14519708C23semidirect
154. #14519708C23semidirect
155. #14519701C23semidirect
160. #14519698C23semidirect
161. C22⋊#92418C23semidirect
167. C2×#41×C61C23semidirect
185. #103×C61C23semidirect
186. #102×C61C23semidirect
187. C22⋊C8×C61C23semidirect
448. C2×#449D61semidirect
455. C2×C61#3198semidirect
463. C22×#41C2×D61semidirect
503. #449C2×D61semidirect
510. C2×#103C2×D61semidirect
516. C2×#102C2×D61semidirect
521. C2×C22⋊C8C2×D61semidirect
522. C61C2×#3198semidirect
531. C2×#41C22×D61semidirect
623. #103C22×D61semidirect
629. #102C22×D61semidirect
633. C22⋊C8C22×D61semidirect
887. C2#21456668direct (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×#168403282
#214566682
C2×#168400782
C2×#168401022
C2×#168400842
C2×#168400762
C2×#168400142
C2×#168400052
C2×#168399952
C2×#168399942
C2×#168399072
C2×#168399112
C2×#168398942
C2×#168397272
C2×C61×#4492
C2×#319861