Finite Group Databasebeta

← C2×#21458310 #30558598

Subgroups — C2×#21458310 #30558598

Order 15616.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic, complemented
2C2×#16840464C211yesmaximal, characteristic
3#21458310C2116yesmaximal, direct product factor
4C2×#16840169C211yesmaximal, characteristic, complemented
5C2×#16840095C211yesmaximal, characteristic, complemented
6C2×#16840078C211yesmaximal, characteristic, complemented
7C2×#16840102C211yesmaximal, characteristic, complemented
8C2×#16840074C211yesmaximal, characteristic, complemented
9C2×#16840071C211yesmaximal, characteristic, complemented
10C2×#16840040C211yesmaximal, characteristic, complemented
11C2×#16840005C211yesmaximal, characteristic, complemented
12C2×#16839863C211yesmaximal, characteristic, complemented
13C2×#16839833C211yesmaximal, characteristic, complemented
14C2×#16839801C211yesmaximal, characteristic, complemented
15C22×#14519711C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×#11758189C2211yescharacteristic
18#16840470—24no—
19#16840470C2218yescomplemented
20#16840464—24no—
21#16840464C2218yes—
22C2×#14519776C2211yescharacteristic
23C2×#14519770—21no—
24C2×#14519768C2211yescharacteristic
25C2×#14519767—21no—
26C2×#14519761—21no—
27C2×#14519757—21no—
28C2×#14519754—21no—
29C2×#14519753C2211yescharacteristic
30C2×#14519749—21no—
31C2×#14519748C2211yescharacteristic
32C2×Q8×Dic61C2211yescharacteristic
33C2×D4×Dic61—21no—
34C2×D4×Dic61C2211yescharacteristic
35C2×C4×C22⋊D61C2211yescharacteristic
36C2×#14519737—21no—
37C2×#14519735C2211yescharacteristic
38C22×C4⋊Dic61C2211yescharacteristic
39C22×C4⋊Dic61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41#16840169C2218yescomplemented
42#16840102C2218yescomplemented
43#16840095C2218yescomplemented
44#16840078C2218yescomplemented
45#16840074C2218yescomplemented
46#16840071C2218yescomplemented
47#16840040C2218yescomplemented
48#16840005C2218yescomplemented
49#16839863C2218yescomplemented
50#16839833C2218yescomplemented
51#16839801C2218yescomplemented
52C2×#14519711C2211yescharacteristic
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519711C2211yescharacteristic
56C2×#14519711C2218yescomplemented
57C2×#14519710C2211yescharacteristic
58C2×#14519710C2211yescharacteristic
59C2×#14519708C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#465C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C23×Dic61—21no—
81C23×Dic61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—24no—
86C2×#11758189C2314yes—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89#14519776—22no—
90#14519776C2314yes—
91#14519770—28no—
92#14519768—22no—
93#14519768C2314yes—
94#14519767—28no—
95#14519761—28no—
96#14519757—28no—
97#14519754—28no—
98#14519753—22no—
99#14519753C2314yes—
100#14519749—28no—
101#14519748—22no—
102#14519748C2314yes—
103Q8×Dic61—22no—
104Q8×Dic61C2314yes—
105D4×Dic61—28no—
106D4×Dic61—22no—
107D4×Dic61C2314yes—
108C4×C22⋊D61D414yes—
109C4×C22⋊D61C2314yes—
110#14519737—28no—
111#14519735—22no—
112#14519735C2314yes—
113C2×C4⋊Dic61—22no—
114C2×C4⋊Dic61—22no—
115C2×C4⋊Dic61—21no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61C2314yes—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2314yes—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196D411yescharacteristic
130C4⋊C4×D61—22no—
131C4⋊C4×D61C2314yes—
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61D411yescharacteristic
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198D411yescharacteristic
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61C2311yescharacteristic
141#14519711C2314yes—
142#14519711C2314yes—
143#14519711C2314yes—
144#14519711C2314yes—
145#14519710C2314yes—
146#14519710C2314yes—
147#14519708C2314yes—
148#14519708C2314yes—
149#14519706C2314yes—
150#14519701C2314yes—
151#14519701C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154C22⋊#92418C2314yes—
155#14519689C2314yes—
156#14519687C2314yes—
157C22×Q8×C61C2311yescharacteristic
158C22×D4×C61—21no—
159C22×D4×C61C2311yescharacteristic
160C23×C4×C61C2311yescharacteristic
161C2×SD16×C61—24no—
162C2×SD16×C61C2314yes—
163C22×C8×C61—24no—
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2314yes—
166C22×C8×C61C2311yescharacteristic
167C22⋊Q8×C61—22no—
168C22⋊Q8×C61C2314yes—
169#121×C61—22no—
170#121×C61C2314yes—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176#106×C61C2314yes—
177#103×C61C2314yes—
178#102×C61C2314yes—
179C24×C61—21no—
180C24×C61C2×D411yescharacteristic
181C23×D61C2×D411yescharacteristic
182C2×Q8×C61—21no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61C2412yes—
186C2×D4×C61—24no—
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—44no—
191C2×D4×C61C2412yes—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—82no—
204C2×C22⋊D61C2×D414yes—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—24no—
210C22×Dic61—24no—
211C22×Dic61—24no—
212C22×Dic61—82no—
213C22×Dic61—82no—
214C22×Dic61—82no—
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—24no—
221C2×C4×D61—82no—
222C2×C4×D61C2×D412yes—
223C2×C4×D61C2412yes—
224C2×Dic122—24no—
225C2×Dic122—82no—
226SD16×C61—28no—
227C2×C8×C61—22no—
228C2×C8×C61—28no—
229C2×C8×C61#4114yes—
230C2×C8×C61C2412yes—
231C2×C8×C61C2412yes—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2412yes—
236C4⋊C4×C61C2412yes—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C22⋊Dic61—24no—
240C22⋊Dic61—24no—
241C22⋊Dic61C2×D414yes—
242#11758198—24no—
243#11758198—24no—
244#11758198C2×D414yes—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—24no—
250C4⋊Dic61—24no—
251C4⋊Dic61—24no—
252C4⋊Dic61—24no—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255C4⋊Dic61C2412yes—
256C4⋊Dic61C2412yes—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196C2×D414yes—
262C4×Dic61—24no—
263C4×Dic61—24no—
264C4×Dic61C2×D412yes—
265C4×Dic61C2412yes—
266C2×#92418—22no—
267C2×#92418—22no—
268C2×#92418C2412yes—
269C2×#92418C2412yes—
270#11758189—28no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—42no—
275C23×C61—42no—
276C23×C61—42no—
277C23×C61#13714yes—
278C23×C61C22×D412yes—
279C23×C61C22×D411yescharacteristic
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61C22×D412yes—
284Q8×C61—22no—
285Q8×C61—22no—
286Q8×C61—42no—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—48no—
290D4×C61—42no—
291C2×C4×C61—22no—
292C2×C4×C61—24no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61C22×D412yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4112yes—
304C2×C4×C612−1+412yes—
305C2×C4×C61C2511yescharacteristic
306C22⋊D61—28no—
307C22⋊D61—84no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—84no—
320C2×Dic61—84no—
321C2×Dic61—84no—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324C2×Dic61C22×D412yes—
325C4×D61—24no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—84no—
329Dic122—84no—
330C8×C61—22no—
331C8×C61C2×#4114yes—
332#92418—22no—
333#92418—22no—
334C2×#3346—611nomaximal, Sylow
335C22×C61—28no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—84no—
342C22×C61#54712yes—
343C22×C61C2×#13714yes—
344C22×C61C2×#13712yes—
345C22×C61#57612yes—
346C22×C61C23×D411yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—44no—
351C4×C61—22no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61#54712yes—
356C4×C61C22×#4111yescharacteristic
357C4×C61C2×2−1+411yescharacteristic
358Dic61—22no—
359Dic61—22no—
360Dic61—22no—
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364Dic61—42no—
365C2×#554—611no—
366C2×#553—611no—
367#3346—6116no—
368C2×#501—611no—
369C2×#484—611no—
370C2×#481—611no—
371C2×#485—611no—
372C2×#480—611no—
373C2×#479—611no—
374C2×#474—611no—
375C2×#468—611no—
376C2×#465D6111yescharacteristic, complemented
377C2×#440—611no—
378C2×#435—611no—
379C2×#428—611no—
380C22×#107—611no—
381C2×C61—24no—
382C2×C61—82no—
383C2×C61#334614yescomplemented
384C2×C61C2×#54711yescharacteristic
385C2×C61C22×#13711yescharacteristic
386C2×C61C2×#57611yescharacteristic
387D61—42no—
388C22×SD16C2×D6111yescharacteristic
389C22×M16—611no—
390C23×C8C2×D6111yescharacteristic
391#554—618no—
392#554—1224no—
393#553—618no—
394#553—1224no—
395C2×C4⋊Q8—611no—
396C2×#126—1221no—
397C2×#125—611no—
398C2×#125—1221no—
399C2×#123—1221no—
400C2×C22⋊Q8—611no—
401C2×C22⋊Q8—1221no—
402C2×C22⋊Q8—1221no—
403C2×C22⋊Q8C2×D6111yescharacteristic
404C2×#121—611no—
405C2×#121—1221no—
406C2×#121C2×D6111yescharacteristic
407C2×C4×Q8—611no—
408C2×C4×D4—611no—
409C2×C4×D4—611no—
410C2×C4×D4—1221no—
411C2×C4×D4—1221no—
412C2×#117—611no—
413C22×C4⋊C4—611no—
414C22×C4⋊C4—611no—
415C22×C4⋊C4—611no—
416#501—618no—
417#485—618no—
418#484—618no—
419#481—618no—
420#480—618no—
421#479—618no—
422#474—618no—
423#468—618no—
424#465C2×D6118yescomplemented
425#440—618no—
426#435—618no—
427#428—618no—
428C2×#107—611no—
429C2×#107—611no—
430C2×#107—618no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#107—611no—
434C2×#107—611no—
435C2×#106—611no—
436C2×#106—611no—
437C2×#106C2×D6111yescharacteristic
438C2×C4⋊C8—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103C2×D6111yescharacteristic
442C2×#102—611no—
443C2×#102—611no—
444C2×#102C2×D6111yescharacteristic
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×#97—611no—
448C61C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—1221no—
450C22×Q8C22×D6111yescharacteristic
451C22×D4—21no—
452C22×D4—611no—
453C22×D4—1221no—
454C22×D4C22×D6111yescharacteristic
455C23×C4—611no—
456C23×C4—1221no—
457C23×C4—1221no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461C2×SD16—24no—
462C2×SD16C22×D6114yes—
463C2×M16—614no—
464C2×M16—1224no—
465C22×C8—24no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8C22×D6111yescharacteristic
469C22×C8C22×D6114yes—
470C22×C8C22×D6111yescharacteristic
471C4⋊Q8—614no—
472C4⋊Q8—1222no—
473#126—1228no—
474#125—614no—
475#125—1222no—
476#125—1228no—
477#123—1228no—
478C22⋊Q8—22no—
479C22⋊Q8—614no—
480C22⋊Q8—1228no—
481C22⋊Q8—1228no—
482C22⋊Q8—1222no—
483C22⋊Q8C22×D6114yes—
484#121—22no—
485#121—614no—
486#121—1222no—
487#121—1228no—
488#121C22×D6114yes—
489C4×Q8—614no—
490C4×Q8—1222no—
491C4×D4—614no—
492C4×D4—614no—
493C4×D4—614no—
494C4×D4—1222no—
495C4×D4—1228no—
496C4×D4—1228no—
497#117—614no—
498#117—1222no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—614no—
506C2×C4⋊C4—614no—
507C2×C4⋊C4—614no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C42—611no—
530C2×C42—1221no—
531C2×C42—1221no—
532#107—614no—
533#107—614no—
534#107—614no—
535#107—614no—
536#107—614no—
537#107—614no—
538#106—614no—
539#106—614no—
540#106C22×D6114yes—
541C4⋊C8—614no—
542#103—614no—
543#103—614no—
544#103C22×D6114yes—
545#102—614no—
546#102—614no—
547#102C22×D6114yes—
548C22⋊C8—614no—
549C22⋊C8—614no—
550#97—614no—
551C24—21no—
552C24—611no—
553C24D4×D6111yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—1224no—
558C2×Q8—4882no—
559C2×Q8C23×D6112yes—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—44no—
565C2×D4—614no—
566C2×D4—1224no—
567C2×D4—1224no—
568C2×D4—4882no—
569C2×D4C23×D6112yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—1224no—
581C22×C4—1224no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—4882no—
591C22×C4—4882no—
592C22×C4—4882no—
593C22×C4—4882no—
594C22×C4D4×D6112yes—
595C22×C4D4×D6111yescharacteristic
596C22×C4C23×D6112yes—
597C22×C4C23×D6111yescharacteristic
598SD16—28no—
599M16—1228no—
600C2×C8—22no—
601C2×C8—28no—
602C2×C8—612no—
603C2×C8—612no—
604C2×C8—1222no—
605C2×C8—1222no—
606C2×C8#1175822414yes—
607C2×C8C23×D6112yes—
608C2×C8C23×D6112yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—614no—
613C4⋊C4—612no—
614C4⋊C4—612no—
615C4⋊C4—612no—
616C4⋊C4—612no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1224no—
627C4⋊C4—1221no—
628C4⋊C4—1224no—
629C4⋊C4C23×D6112yes—
630C4⋊C4C23×D6112yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—614no—
634C22⋊C4—614no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C42—612no—
640C42—612no—
641C42—1224no—
642C42—1224no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—612no—
650C23—1222no—
651C23—1222no—
652C23—1222no—
653C23#1451980614yes—
654C23C2×D4×D6112yes—
655C23C2×D4×D6111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—4884no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—42no—
664D4—1228no—
665D4—4884no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—612no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1224no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—4884no—
690C2×C4—4884no—
691C2×C4—4884no—
692C2×C4—4884no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4C2×D4×D6112yes—
698C2×C4C2×D4×D6111yescharacteristic
699C2×C4C2×#1175822412yes—
700C2×C4#1451982412yes—
701C2×C4C24×D6111yescharacteristic
702C8—22no—
703C8—1222no—
704C8—1222no—
705C8C2×#1175822414yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—84no—
713C22—1222no—
714C22—1222no—
715C22—1222no—
716C22—2444no—
717C22#1684041212yes—
718C22C2×#1451980614yes—
719C22C2×#1451980612yes—
720C22#1684056412yes—
721C22C22×D4×D6111yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—1222no—
727C4—1222no—
728C4—1222no—
729C4—2442no—
730C4—2442no—
731C4—2442no—
732C4—2442no—
733C4#1684041212yes—
734C4C22×#1175822411yescharacteristic
735C4C2×#1451982411yescharacteristic
736C2—24no—
737C2—82no—
738C2—2442no—
739C2#2145831014yesdirect product factor
740C2C2×#1684041211yescharacteristic
741C2C22×#1451980611yescharacteristic
742C2C2×#1684056411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radicalC2×#16840464C2
hypercenterC2×#465D61
hypocenterC61C2×#3346
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×#16840470C2semidirect
3. #21458310C2direct (N × H)
4. C2×#16840169C2semidirect
5. C2×#16840095C2semidirect
6. C2×#16840078C2semidirect
7. C2×#16840102C2semidirect
8. C2×#16840074C2semidirect
9. C2×#16840071C2semidirect
10. C2×#16840040C2semidirect
11. C2×#16840005C2semidirect
12. C2×#16839863C2semidirect
13. C2×#16839833C2semidirect
14. C2×#16839801C2semidirect
15. C22×#14519711C2semidirect
16. C2×C61×#465C2semidirect
19. #16840470C22semidirect
41. #16840169C22semidirect
42. #16840102C22semidirect
43. #16840095C22semidirect
44. #16840078C22semidirect
45. #16840074C22semidirect
46. #16840071C22semidirect
47. #16840040C22semidirect
48. #16840005C22semidirect
49. #16839863C22semidirect
50. #16839833C22semidirect
51. #16839801C22semidirect
56. C2×#14519711C22semidirect
73. C61×#465C22semidirect
376. C2×#465D61semidirect
383. C2×C61#3346semidirect
424. #465C2×D61semidirect
448. C61C2×#3346semidirect
739. C2#21458310direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168404642
#214583102
C2×#168401692
C2×#168400952
C2×#168400782
C2×#168401022
C2×#168400742
C2×#168400712
C2×#168400402
C2×#168400052
C2×#168398632
C2×#168398332
C2×#168398012
C22×#145197112
C2×C61×#4652
C2×#334661