Finite Group Databasebeta

← C2×#21457014 #30552153

Subgroups — C2×#21457014 #30552153

Order 15616.

2038 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840315C211yesmaximal, characteristic, complemented
2C2×#16840307C211yesmaximal, characteristic
3#21457014C2116yesmaximal, direct product factor
4C2×#16840170C211yesmaximal, characteristic, complemented
5C2×#16840169C211yesmaximal, characteristic, complemented
6C2×#16840125C211yesmaximal, characteristic, complemented
7C2×#16840125C211yesmaximal, characteristic, complemented
8C2×#16840087C211yesmaximal, characteristic, complemented
9C2×#16840086C211yesmaximal, characteristic, complemented
10C2×#16840083C211yesmaximal, characteristic, complemented
11C2×#16840051C211yesmaximal, characteristic, complemented
12C2×#16840050C211yesmaximal, characteristic, complemented
13C2×#16840041C211yesmaximal, characteristic, complemented
14C2×#16840040C211yesmaximal, characteristic, complemented
15C2×#16839816C211yesmaximal, characteristic, complemented
16C2×C61×#482C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18#16840315—24no—
19#16840315C2218yescomplemented
20#16840307—24no—
21#16840307C2218yes—
22C2×#14519776C2211yescharacteristic
23C2×#14519776C2211yescharacteristic
24C2×#14519776C2211yescharacteristic
25C2×#14519773C2211yescharacteristic
26C2×#14519768C2211yescharacteristic
27C2×#14519768C2211yescharacteristic
28C2×#14519763—21no—
29C2×#14519754—21no—
30C2×#14519754—21no—
31C2×#14519751C2211yescharacteristic
32C2×#14519749—21no—
33C2×C4×Dic122—21no—
34C2×C4×Dic122—21no—
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519737—21no—
38C2×#14519736C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40#16840170C2218yescomplemented
41#16840169C2218yescomplemented
42#16840125C2218yescomplemented
43#16840125C2218yescomplemented
44#16840087C2218yescomplemented
45#16840086C2218yescomplemented
46#16840083C2218yescomplemented
47#16840051C2218yescomplemented
48#16840050C2218yescomplemented
49#16840041C2218yescomplemented
50#16840040C2218yescomplemented
51#16839816C2218yescomplemented
52C2×#14519711C2211yescharacteristic
53C2×#14519710C2211yescharacteristic
54C2×#14519710C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C2×#121×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C61×#482C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122—21no—
80C22×Dic122—21no—
81C22×Dic122—21no—
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C23×Dic61—21no—
87C23×Dic61D411yescharacteristic
88C23×Dic61D411yescharacteristic
89C22×C4×D61—21no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92#14519776—22no—
93#14519776—22no—
94#14519776—22no—
95#14519776C2314yes—
96#14519776C2314yes—
97#14519776C2314yes—
98#14519773—22no—
99#14519773C2314yes—
100#14519768—22no—
101#14519768—22no—
102#14519768C2314yes—
103#14519768C2314yes—
104#14519763—28no—
105#14519754—28no—
106#14519754—28no—
107#14519751—22no—
108#14519751C2314yes—
109#14519749—28no—
110C4×Dic122—28no—
111C4×Dic122—28no—
112D4×Dic61—22no—
113D4×Dic61C2314yes—
114#14519739—22no—
115#14519739C2314yes—
116#14519737—28no—
117#14519736—22no—
118#14519736C2314yes—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—21no—
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×C22⋊Dic61—21no—
130C2×C22⋊Dic61—21no—
131C2×#11758198—21no—
132C2×#11758198—21no—
133C2×C4×Dic61—21no—
134C2×C4×Dic61D411yescharacteristic
135C2×C4×Dic61D411yescharacteristic
136C2×C4×Dic61D414yes—
137C2×C4×Dic61C2311yescharacteristic
138C2×C4×Dic61C2311yescharacteristic
139C2×C4×Dic61C2314yes—
140#14519711C2314yes—
141#14519710C2314yes—
142#14519710C2314yes—
143#14519709C2314yes—
144#14519708C2314yes—
145#14519708C2314yes—
146#14519706C2314yes—
147#14519706C2314yes—
148#14519699C2314yes—
149#14519699C2314yes—
150#14519698C2314yes—
151#14519698C2314yes—
152#14519697C2314yes—
153#14519697C2314yes—
154C22⋊#92418C2314yes—
155#14519687C2314yes—
156#14519687C2314yes—
157C22×D4×C61—21no—
158C22×D4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160C22×C8×C61C2311yescharacteristic
161C22×C8×C61C2311yescharacteristic
162#121×C61—22no—
163#121×C61C2314yes—
164#117×C61—22no—
165#117×C61C2314yes—
166C2×C4⋊C4×C61C2311yescharacteristic
167C2×C4⋊C4×C61C2311yescharacteristic
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C22⋊C4×C61—21no—
170C2×C22⋊C4×C61—21no—
171C2×C42×C61—21no—
172#107×C61C2314yes—
173#106×C61C2314yes—
174#102×C61C2314yes—
175#102×C61C2314yes—
176C22⋊C8×C61C2314yes—
177C24×C61—21no—
178C24×C61C2×D411yescharacteristic
179C23×D61—21no—
180C2×D4×C61—24no—
181C2×D4×C61—21no—
182C2×D4×C61—22no—
183C2×D4×C61—22no—
184C2×D4×C61—44no—
185C2×D4×C61C2412yes—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—24no—
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—44no—
199C2×C22⋊D61—44no—
200C2×C22⋊D61—44no—
201C22×Dic61—24no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—24no—
206C22×Dic61—42no—
207C22×Dic61—44no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D414yes—
212C22×Dic61C2×D414yes—
213C22×Dic61C2×D411yescharacteristic
214#11758224—432no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—21no—
218C2×D244C2412yes—
219C2×C4×D61—24no—
220C2×C4×D61—44no—
221C2×Dic122—24no—
222C2×Dic122—24no—
223C2×Dic122—24no—
224C2×Dic122—44no—
225C2×Dic122—44no—
226C2×Dic122—44no—
227C2×C8×C61—22no—
228C2×C8×C61—22no—
229C2×C8×C61C2412yes—
230C2×C8×C61C2412yes—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C2412yes—
235C4⋊C4×C61C2412yes—
236C4⋊C4×C61C2412yes—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C42×C61—24no—
240C22⋊Dic61—24no—
241C22⋊Dic61—24no—
242#11758198—24no—
243#11758198—24no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61—24no—
248C4⋊Dic61—24no—
249C4⋊Dic61C2412yes—
250C4⋊Dic61C2412yes—
251C4⋊Dic61C2412yes—
252#11758196—24no—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256#11758196—24no—
257C4×Dic61—24no—
258C4×Dic61C2×D414yes—
259C4×Dic61C2×D412yes—
260C4×Dic61C2×D414yes—
261C4×Dic61C2×D412yes—
262C4×Dic61C2412yes—
263C4×Dic61C2412yes—
264C2×#92418—22no—
265C2×#92418—22no—
266C2×#92418C2412yes—
267C2×#92418C2412yes—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—42no—
273C23×C61—42no—
274C23×C61—42no—
275C23×C61C22×D412yes—
276C23×C61C22×D411yescharacteristic
277C22×D61—22no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—48no—
284D4×C61—42no—
285C2×C4×C61—22no—
286C2×C4×C61—24no—
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×C61C22×D412yes—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C612−1+412yes—
298C2×C4×C612−1+412yes—
299C2×C4×C61C2511yescharacteristic
300C22⋊D61—48no—
301C22⋊D61—48no—
302C22⋊D61—48no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—28no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—44no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—48no—
315C2×Dic61AGL(1,ℤ/8)14yes—
316C2×Dic61C22×D412yes—
317C2×Dic61C22×D412yes—
318C2×Dic61C22×D412yes—
319C2×Dic61C22×D412yes—
320D244—22no—
321D244—22no—
322D244—42no—
323C4×D61—48no—
324Dic122—48no—
325Dic122—48no—
326Dic122—48no—
327C8×C61—22no—
328C8×C61—22no—
329#92418—22no—
330#92418—22no—
331C2×#3235—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—44no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—84no—
340C22×C61#53612yes—
341C22×C61C2×AGL(1,ℤ/8)12yes—
342C22×C61#57512yes—
343C22×C61C23×D411yescharacteristic
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—84no—
348C4×C61—22no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61—42no—
352C4×C61#53612yes—
353C4×C61C2×2−1+411yescharacteristic
354C4×C61C2×2−1+411yescharacteristic
355Dic61—22no—
356Dic61—22no—
357Dic61—22no—
358Dic61—42no—
359Dic61—42no—
360Dic61—42no—
361Dic61C2×AGL(1,ℤ/8)14yes—
362C2×#533—611no—
363C2×#532—611no—
364#3235—6116no—
365C2×#501—611no—
366C2×#501—611no—
367C2×#490—611no—
368C2×#490—611no—
369C2×#482—611no—
370C2×#482—611no—
371C2×#482—611no—
372C2×#482D6111yescharacteristic, complemented
373C2×#476—611no—
374C2×#476—611no—
375C2×#474—611no—
376C2×#474—611no—
377C2×#432—611no—
378C2×C61—42no—
379C2×C61—82no—
380C2×C61#323514yescomplemented
381C2×C61C2×#53611yescharacteristic
382C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
383C2×C61C2×#57511yescharacteristic
384D61—82no—
385C22×#41—1221no—
386#533—618no—
387#533—1224no—
388#532—618no—
389#532—1224no—
390C2×C4⋊Q8—611no—
391C2×C4⋊Q8—611no—
392C2×C4⋊Q8—611no—
393C2×#127—611no—
394C2×#125—611no—
395C2×#125—611no—
396C2×#124—1221no—
397C2×C22⋊Q8—1221no—
398C2×C22⋊Q8—1221no—
399C2×#121—611no—
400C2×#121—1221no—
401C2×#121C2×D6111yescharacteristic
402C2×C4×Q8—1221no—
403C2×C4×Q8—1221no—
404C2×C4×D4—611no—
405C2×C4×D4—611no—
406C2×C4×D4—1221no—
407C2×#117—611no—
408C2×#117C2×D6111yescharacteristic
409C22×C42—611no—
410#501—618no—
411#501—618no—
412#490—618no—
413#490—618no—
414#482—618no—
415#482—618no—
416#482—618no—
417#482C2×D6118yescomplemented
418#476—618no—
419#476—618no—
420#474—618no—
421#474—618no—
422#432—618no—
423C2×#107—611no—
424C2×#107—611no—
425C2×#107—611no—
426C2×#107C2×D6111yescharacteristic
427C2×#106—611no—
428C2×#106—611no—
429C2×#106—611no—
430C2×#106C2×D6111yescharacteristic
431C2×C4⋊C8—611no—
432C2×C4⋊C8—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×#102C2×D6111yescharacteristic
440C2×#102C2×D6111yescharacteristic
441C2×C22⋊C8—611no—
442C2×C22⋊C8C2×D6111yescharacteristic
443C2×#97—611no—
444C2×#97—611no—
445C61C2×#323511yescharacteristic, complemented, Sylow
446C2×#41—1228no—
447C2×#41—2448no—
448C22×Q8—1221no—
449C22×Q8—1221no—
450C22×Q8—1221no—
451C22×D4—21no—
452C22×D4—611no—
453C22×D4—1221no—
454C22×D4—1221no—
455C22×D4—1221no—
456C22×D4C22×D6111yescharacteristic
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—1221no—
460C23×C4—1221no—
461C23×C4C22×D6111yescharacteristic
462C22×C8—611no—
463C22×C8—611no—
464C22×C8C22×D6111yescharacteristic
465C22×C8C22×D6111yescharacteristic
466C4⋊Q8—614no—
467C4⋊Q8—614no—
468C4⋊Q8—614no—
469C4⋊Q8—1222no—
470C4⋊Q8—1222no—
471C4⋊Q8—1222no—
472#127—614no—
473#127—1222no—
474#125—614no—
475#125—614no—
476#125—1222no—
477#125—1222no—
478#124—1228no—
479C22⋊Q8—1228no—
480C22⋊Q8—1228no—
481#121—22no—
482#121—614no—
483#121—1228no—
484#121—1222no—
485#121C22×D6114yes—
486C4×Q8—1228no—
487C4×Q8—1228no—
488C4×D4—614no—
489C4×D4—614no—
490C4×D4—1228no—
491C4×D4—1222no—
492C4×D4—1222no—
493#117—22no—
494#117—614no—
495#117—1222no—
496#117C22×D6114yes—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C4⋊C4C22×D6111yescharacteristic
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C42—21no—
517C2×C42—611no—
518C2×C42—611no—
519C2×C42—614no—
520C2×C42—611no—
521C2×C42—611no—
522C2×C42—614no—
523C2×C42—1221no—
524#107—614no—
525#107—614no—
526#107—614no—
527#107C22×D6114yes—
528#106—614no—
529#106—614no—
530#106—614no—
531#106C22×D6114yes—
532C4⋊C8—614no—
533C4⋊C8—614no—
534#102—614no—
535#102—614no—
536#102—614no—
537#102—614no—
538#102—614no—
539#102—614no—
540#102C22×D6114yes—
541#102C22×D6114yes—
542C22⋊C8—614no—
543C22⋊C8C22×D6114yes—
544#97—614no—
545#97—614no—
546C24—21no—
547C24—1221no—
548C24D4×D6111yescharacteristic
549#41—24432no—
550C2×Q8—1224no—
551C2×Q8—1224no—
552C2×Q8—1224no—
553C2×Q8—2444no—
554C2×Q8—2444no—
555C2×Q8—2444no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—44no—
561C2×D4—612no—
562C2×D4—1224no—
563C2×D4—1224no—
564C2×D4—1224no—
565C2×D4—1221no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—2444no—
569C2×D4—2444no—
570C2×D4—2444no—
571C2×D4C23×D6112yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—611no—
578C22×C4—614no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—614no—
583C22×C4—1224no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—2444no—
590C22×C4—2444no—
591C22×C4—2442no—
592C22×C4D4×D6112yes—
593C22×C4D4×D6111yescharacteristic
594C22×C4C23×D6112yes—
595C22×C4C23×D6111yescharacteristic
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—612no—
599C2×C8—612no—
600C2×C8—1222no—
601C2×C8—1222no—
602C2×C8C23×D6112yes—
603C2×C8C23×D6112yes—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—612no—
608C4⋊C4—612no—
609C4⋊C4—612no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1224no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4C23×D6112yes—
621C4⋊C4C23×D6112yes—
622C4⋊C4C23×D6112yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—1224no—
626C22⋊C4—1224no—
627C22⋊C4—1224no—
628C22⋊C4—1224no—
629C42—24no—
630C42—614no—
631C42—612no—
632C42—614no—
633C42—612no—
634C42—612no—
635C42—612no—
636C42—1224no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—1222no—
645C23—2442no—
646C23—2442no—
647C23—2442no—
648C23C2×D4×D6112yes—
649C23C2×D4×D6111yescharacteristic
650Q8—2448no—
651Q8—2448no—
652Q8—2448no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—1222no—
658D4—1222no—
659D4—2448no—
660D4—2448no—
661D4—2448no—
662D4—2442no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—614no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—1228no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—2448no—
686C2×C4—2448no—
687C2×C4—2444no—
688C2×C4—2442no—
689C2×C4—2442no—
690C2×C4—2442no—
691C2×C4C2×D4×D6112yes—
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4#1451982412yes—
694C2×C4#1451982412yes—
695C2×C4C24×D6111yescharacteristic
696C8—22no—
697C8—22no—
698C8—1222no—
699C8—1222no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22—4884no—
709C22—2442no—
710C22—2442no—
711C22—2442no—
712C22#1684033412yes—
713C22AGL(1,ℤ/8)×D6112yes—
714C22#1684055912yes—
715C22C22×D4×D6111yescharacteristic
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—614no—
721C4—1222no—
722C4—1222no—
723C4—1222no—
724C4—2442no—
725C4—2442no—
726C4—2442no—
727C4#1684033412yes—
728C4C2×#1451982411yescharacteristic
729C4C2×#1451982411yescharacteristic
730C2—42no—
731C2—82no—
732C2—4882no—
733C2#2145701414yesdirect product factor
734C2C2×#1684033411yescharacteristic
735C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
736C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#482C2
socleC23×C61C22×D4
prime radicalC2×#16840307C2
hypercenterC2×#482D61
hypocenterC61C2×#3235
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16840315C2semidirect
3. #21457014C2direct (N × H)
4. C2×#16840170C2semidirect
5. C2×#16840169C2semidirect
6. C2×#16840125C2semidirect
7. C2×#16840125C2semidirect
8. C2×#16840087C2semidirect
9. C2×#16840086C2semidirect
10. C2×#16840083C2semidirect
11. C2×#16840051C2semidirect
12. C2×#16840050C2semidirect
13. C2×#16840041C2semidirect
14. C2×#16840040C2semidirect
15. C2×#16839816C2semidirect
16. C2×C61×#482C2semidirect
19. #16840315C22semidirect
40. #16840170C22semidirect
41. #16840169C22semidirect
42. #16840125C22semidirect
43. #16840125C22semidirect
44. #16840087C22semidirect
45. #16840086C22semidirect
46. #16840083C22semidirect
47. #16840051C22semidirect
48. #16840050C22semidirect
49. #16840041C22semidirect
50. #16840040C22semidirect
51. #16839816C22semidirect
71. C61×#482C22semidirect
372. C2×#482D61semidirect
380. C2×C61#3235semidirect
417. #482C2×D61semidirect
445. C61C2×#3235semidirect
733. C2#21457014direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403152
C2×#168403072
#214570142
C2×#168401702
C2×#168401692
C2×#168401252
C2×#168400872
C2×#168400862
C2×#168400832
C2×#168400512
C2×#168400502
C2×#168400412
C2×#168400402
C2×#168398162
C2×C61×#4822
C2×#323561