Finite Group Databasebeta

← C2×#21458305 #30558593

Subgroups — C2×#21458305 #30558593

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×#16840467C211yesmaximal, characteristic, complemented
2C2×#16840456C211yesmaximal, characteristic
3#21458305C2116yesmaximal, direct product factor
4C2×#16840169C211yesmaximal, characteristic, complemented
5C2×#16840099C211yesmaximal, characteristic, complemented
6C2×#16840082C211yesmaximal, characteristic, complemented
7C2×#16840103C211yesmaximal, characteristic, complemented
8C2×#16840075C211yesmaximal, characteristic, complemented
9C2×#16840072C211yesmaximal, characteristic, complemented
10C2×#16840041C211yesmaximal, characteristic, complemented
11C2×#16840008C211yesmaximal, characteristic, complemented
12C2×#16839992C211yesmaximal, characteristic, complemented
13C2×#16839861C211yesmaximal, characteristic, complemented
14C2×#16839831C211yesmaximal, characteristic, complemented
15C2×#107×D61C211yesmaximal, characteristic, complemented
16C2×C61×#428C211yesmaximal, characteristic, complemented
17C22×#11758190C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840467—24no—
20#16840467C2218yescomplemented
21#16840456—24no—
22#16840456C2218yes—
23C2×#14519776C2211yescharacteristic
24C2×#14519771—21no—
25C2×#14519768C2211yescharacteristic
26C2×#14519767—21no—
27C2×#14519759—21no—
28C2×#14519757C2211yescharacteristic
29C2×#14519756—21no—
30C2×#14519756C2211yescharacteristic
31C2×#14519755—21no—
32C2×#14519752C2211yescharacteristic
33C2×#14519751C2211yescharacteristic
34C2×#14519750—21no—
35C2×#14519742C2211yescharacteristic
36C2×C4×D244—21no—
37C2×#14519739C2211yescharacteristic
38C2×C4×C22⋊D61—21no—
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840169C2218yescomplemented
43#16840103C2218yescomplemented
44#16840099C2218yescomplemented
45#16840082C2218yescomplemented
46#16840075C2218yescomplemented
47#16840072C2218yescomplemented
48#16840041C2218yescomplemented
49#16840008C2218yescomplemented
50#16839992C2218yescomplemented
51#16839861C2218yescomplemented
52#16839831C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519710C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57#107×D61C2218yescomplemented
58C2×#14519708C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×M16×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C22×C4⋊C4×C61C2211yescharacteristic
72C61×#428C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#107×C61C2211yescharacteristic
75C2×#106×C61C2211yescharacteristic
76C2×#106×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244—21no—
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61D411yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C2×#11758190—24no—
88C2×#11758190C2314yes—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—24no—
92C2×C8×D61C2314yes—
93#14519776—22no—
94#14519776C2314yes—
95#14519771—28no—
96#14519768—22no—
97#14519768C2314yes—
98#14519767—28no—
99#14519759—28no—
100#14519757—22no—
101#14519757C2314yes—
102#14519756—22no—
103#14519756—28no—
104#14519756C2314yes—
105#14519755—28no—
106#14519752—22no—
107#14519752C2314yes—
108#14519751—22no—
109#14519751C2314yes—
110#14519750—28no—
111#14519742—22no—
112#14519742C2314yes—
113C4×D244—28no—
114#14519739—22no—
115#14519739C2314yes—
116C4×C22⋊D61—28no—
117C4×C22⋊D61D414yes—
118C4×C22⋊D61C2314yes—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196D411yescharacteristic
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C4⋊C4×D61C2314yes—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61D411yescharacteristic
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198D411yescharacteristic
141C2×C4×Dic61—21no—
142C2×C4×Dic61C2311yescharacteristic
143#14519711C2314yes—
144#14519710C2314yes—
145#14519710C2314yes—
146#14519710C2314yes—
147#14519708C2314yes—
148#14519706C2314yes—
149#14519702C2314yes—
150#14519700C2314yes—
151#14519700C2314yes—
152#14519699C2314yes—
153#14519697C2314yes—
154#14519697C2314yes—
155C22⋊#92418C2314yes—
156#14519689C2314yes—
157#14519687C2314yes—
158C23×C4×C61—21no—
159C23×C4×C61C2311yescharacteristic
160C2×M16×C61—24no—
161C2×M16×C61C2314yes—
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164#117×C61—22no—
165#117×C61C2314yes—
166C2×C4⋊C4×C61—22no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2314yes—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C42×C61—21no—
175#107×C61C2314yes—
176#107×C61C2314yes—
177#106×C61C2314yes—
178#106×C61C2314yes—
179C24×C61C2×D411yescharacteristic
180C23×D61—21no—
181C23×D61C2×D411yescharacteristic
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—24no—
189C22×C4×C61—82no—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—24no—
195C2×C22⋊D61—24no—
196C2×C22⋊D61—82no—
197C2×C22⋊D61C2×D414yes—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C2×D244—22no—
205C2×D244—22no—
206C2×D244—24no—
207C2×D244—21no—
208C2×D244—44no—
209C2×D244C2412yes—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—24no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—82no—
216C2×C4×D61—82no—
217C2×C4×D61—82no—
218C2×C4×D61C2×D412yes—
219C2×C4×D61C2412yes—
220C2×Dic122—22no—
221C2×Dic122—22no—
222C2×Dic122—21no—
223C2×Dic122—24no—
224C2×Dic122—82no—
225C2×Dic122C2412yes—
226M16×C61—28no—
227C2×C8×C61—22no—
228C2×C8×C61#4114yes—
229C2×C8×C61C2412yes—
230C2×C8×C61C2412yes—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61C2412yes—
237C4⋊C4×C61C2412yes—
238C4⋊C4×C61C2412yes—
239C4⋊C4×C61C2412yes—
240C22⋊C4×C61—24no—
241C42×C61—24no—
242C22⋊Dic61—24no—
243C22⋊Dic61C2×D414yes—
244#11758198—24no—
245#11758198—24no—
246#11758198—24no—
247#11758198—24no—
248#11758198C2×D414yes—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—24no—
252C4⋊Dic61—24no—
253C4⋊Dic61C2412yes—
254C4⋊Dic61C2412yes—
255#11758196—24no—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196C2×D414yes—
262C4×Dic61—24no—
263C4×Dic61C2×D412yes—
264C4×Dic61C2412yes—
265C2×#92418—22no—
266C2×#92418—22no—
267C2×#92418C2412yes—
268C2×#92418C2412yes—
269#11758190—28no—
270C8×D61—28no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61C22×D412yes—
275C23×C61C22×D411yescharacteristic
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61#13714yes—
283C22×D61C22×D412yes—
284C2×C4×C61—22no—
285C2×C4×C61—24no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—84no—
297C2×C4×C61C22×D412yes—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C2×#4112yes—
300C2×C4×C612−1+412yes—
301C2×C4×C61C2511yescharacteristic
302C22⋊D61—28no—
303C22⋊D61—84no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61C22×D412yes—
314C2×Dic61C22×D412yes—
315C2×Dic61C22×D412yes—
316D244—22no—
317D244—22no—
318D244—48no—
319D244—42no—
320C4×D61—24no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—84no—
324C4×D61—84no—
325C4×D61—84no—
326Dic122—22no—
327Dic122—22no—
328Dic122—42no—
329Dic122—84no—
330C8×C61—22no—
331C8×C61C2×#4114yes—
332#92418—22no—
333#92418—22no—
334C2×#3346—611nomaximal, Sylow
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—44no—
339C22×C61#54712yes—
340C22×C61C2×#13712yes—
341C22×C61#57612yes—
342C22×C61C23×D411yescharacteristic
343C2×D61—28no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—84no—
350C2×D61C2×#13714yes—
351C4×C61—22no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61#54712yes—
357C4×C61C22×#4111yescharacteristic
358C4×C61C2×2−1+411yescharacteristic
359Dic61—22no—
360Dic61—22no—
361Dic61—22no—
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×#465—611no—
377C2×#440—611no—
378C2×#435—611no—
379C2×#428D6111yescharacteristic, complemented
380C22×#107—611no—
381C2×C61—42no—
382C2×C61#334614yescomplemented
383C2×C61C2×#54711yescharacteristic
384C2×C61C22×#13711yescharacteristic
385C2×C61C2×#57611yescharacteristic
386D61—24no—
387D61—82no—
388C22×SD16—611no—
389C22×M16C2×D6111yescharacteristic
390C23×C8—611no—
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—611no—
402C2×C22⋊Q8—1221no—
403C2×C22⋊Q8—1221no—
404C2×#121—611no—
405C2×#121—611no—
406C2×#121—1221no—
407C2×C4×Q8—611no—
408C2×C4×D4—611no—
409C2×C4×D4—611no—
410C2×C4×D4—1221no—
411C2×C4×D4—1221no—
412C2×#117C2×D6111yescharacteristic
413C22×C4⋊C4—611no—
414C22×C4⋊C4—611no—
415C22×C4⋊C4C2×D6111yescharacteristic
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#465—618no—
425#440—618no—
426#435—618no—
427#428C2×D6118yescomplemented
428C2×#107—611no—
429C2×#107—611no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#107—618no—
433C2×#107C2×D6111yescharacteristic
434C2×#107C2×D6111yescharacteristic
435C2×#106—611no—
436C2×#106C2×D6111yescharacteristic
437C2×#106C2×D6111yescharacteristic
438C2×C4⋊C8—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×#102—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×#97—611no—
448C61C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—611no—
450C22×Q8—1221no—
451C22×D4—611no—
452C22×D4—611no—
453C22×D4—1221no—
454C22×D4—1221no—
455C23×C4—21no—
456C23×C4—611no—
457C23×C4—1221no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461C2×SD16—614no—
462C2×SD16—1224no—
463C2×M16—24no—
464C2×M16C22×D6114yes—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—614no—
468C22×C8—1224no—
469C22×C8C22×D6111yescharacteristic
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—614no—
479C22⋊Q8—614no—
480C22⋊Q8—1228no—
481C22⋊Q8—1228no—
482C22⋊Q8—1222no—
483C22⋊Q8—1222no—
484#121—614no—
485#121—614no—
486#121—1228no—
487#121—1222no—
488#121—1222no—
489C4×Q8—614no—
490C4×Q8—1222no—
491C4×D4—614no—
492C4×D4—614no—
493C4×D4—614no—
494C4×D4—1228no—
495C4×D4—1222no—
496C4×D4—1228no—
497#117—22no—
498#117C22×D6114yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—614no—
505C2×C4⋊C4—614no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1222no—
508C2×C4⋊C4—1221no—
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⋊C4C22×D6111yescharacteristic
517C2×C4⋊C4C22×D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C4⋊C4C22×D6114yes—
520C2×C4⋊C4C22×D6111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C42—21no—
530C2×C42—611no—
531C2×C42—1221no—
532#107—614no—
533#107—614no—
534#107—614no—
535#107—614no—
536#107C22×D6114yes—
537#107C22×D6114yes—
538#106—614no—
539#106C22×D6114yes—
540#106C22×D6114yes—
541C4⋊C8—614no—
542#103—614no—
543#103—614no—
544#103—614no—
545#102—614no—
546#102—614no—
547#102—614no—
548C22⋊C8—614no—
549C22⋊C8—614no—
550#97—614no—
551C24—611no—
552C24—1221no—
553C24D4×D6111yescharacteristic
554C2×Q8—612no—
555C2×Q8—1224no—
556C2×Q8—1221no—
557C2×Q8—1222no—
558C2×Q8—1222no—
559C2×Q8—4882no—
560C2×D4—614no—
561C2×D4—612no—
562C2×D4—1224no—
563C2×D4—1224no—
564C2×D4—1224no—
565C2×D4—1221no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—4882no—
569C2×D4—2444no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—82no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—1224no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—4882no—
592C22×C4—4882no—
593C22×C4—4882no—
594C22×C4D4×D6112yes—
595C22×C4D4×D6111yescharacteristic
596C22×C4C23×D6112yes—
597C22×C4C23×D6111yescharacteristic
598SD16—1228no—
599M16—28no—
600C2×C8—22no—
601C2×C8—612no—
602C2×C8—612no—
603C2×C8—1222no—
604C2×C8—1222no—
605C2×C8—1228no—
606C2×C8#1175822214yes—
607C2×C8C23×D6112yes—
608C2×C8C23×D6112yes—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—614no—
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—1224no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1224no—
627C4⋊C4C23×D6112yes—
628C4⋊C4C23×D6112yes—
629C4⋊C4C23×D6112yes—
630C4⋊C4C23×D6112yes—
631C22⋊C4—24no—
632C22⋊C4—614no—
633C22⋊C4—614no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C42—24no—
640C42—612no—
641C42—612no—
642C42—1224no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—614no—
647C23—612no—
648C23—1222no—
649C23—1222no—
650C23—1222no—
651C23—2442no—
652C23—2442no—
653C23—2442no—
654C23C2×D4×D6112yes—
655C23C2×D4×D6111yescharacteristic
656Q8—1222no—
657Q8—1222no—
658Q8—4884no—
659Q8—2442no—
660D4—1228no—
661D4—1222no—
662D4—1222no—
663D4—4884no—
664D4—2448no—
665D4—2442no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—612no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1224no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—4884no—
692C2×C4—4884no—
693C2×C4—4884no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4C2×D4×D6112yes—
698C2×C4C2×D4×D6111yescharacteristic
699C2×C4C2×#1175822212yes—
700C2×C4#1451982512yes—
701C2×C4C24×D6111yescharacteristic
702C8—22no—
703C8—1222no—
704C8—1222no—
705C8C2×#1175822214yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—614no—
711C22—1222no—
712C22—1222no—
713C22—1228no—
714C22—4884no—
715C22—2442no—
716C22—2442no—
717C22—2442no—
718C22#1684041312yes—
719C22#137×D6112yes—
720C22#1684056612yes—
721C22C22×D4×D6111yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—1222no—
728C4—1222no—
729C4—1222no—
730C4—2442no—
731C4—2442no—
732C4—2442no—
733C4#1684041312yes—
734C4C22×#1175822211yescharacteristic
735C4C2×#1451982511yescharacteristic
736C2—42no—
737C2—1224no—
738C2—4882no—
739C2#2145830514yesdirect product factor
740C2C2×#1684041311yescharacteristic
741C2C2×#137×D6111yescharacteristic
742C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#428C2
socleC23×C61C22×D4
prime radicalC2×#16840456C2
hypercenterC2×#428D61
hypocenterC61C2×#3346
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#16840467C2semidirect
3. #21458305C2direct (N × H)
4. C2×#16840169C2semidirect
5. C2×#16840099C2semidirect
6. C2×#16840082C2semidirect
7. C2×#16840103C2semidirect
8. C2×#16840075C2semidirect
9. C2×#16840072C2semidirect
10. C2×#16840041C2semidirect
11. C2×#16840008C2semidirect
12. C2×#16839992C2semidirect
13. C2×#16839861C2semidirect
14. C2×#16839831C2semidirect
15. C2×#107×D61C2semidirect
16. C2×C61×#428C2semidirect
20. #16840467C22semidirect
42. #16840169C22semidirect
43. #16840103C22semidirect
44. #16840099C22semidirect
45. #16840082C22semidirect
46. #16840075C22semidirect
47. #16840072C22semidirect
48. #16840041C22semidirect
49. #16840008C22semidirect
50. #16839992C22semidirect
51. #16839861C22semidirect
52. #16839831C22semidirect
57. #107×D61C22semidirect
72. C61×#428C22semidirect
379. C2×#428D61semidirect
382. C2×C61#3346semidirect
427. #428C2×D61semidirect
448. C61C2×#3346semidirect
739. C2#21458305direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404672
C2×#168404562
#214583052
C2×#168401692
C2×#168400992
C2×#168400822
C2×#168401032
C2×#168400752
C2×#168400722
C2×#168400412
C2×#168400082
C2×#168399922
C2×#168398612
C2×#168398312
C2×#107×D612
C2×C61×#4282
C2×#334661