Finite Group Databasebeta

← C2×#13119516 #16032008

Subgroups — C2×#13119516 #16032008

Order 3328.

2466 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic, complemented
2#13119516C2116yesmaximal, direct product factor
3C2×#11718610C211yesmaximal, characteristic
4C2×#11718645C211yesmaximal, characteristic, complemented
5C2×#11718641C211yesmaximal, characteristic, complemented
6C2×#11718609C211yesmaximal, characteristic
7C2×#11718633C211yesmaximal, characteristic, complemented
8C2×#11718606C211yesmaximal, characteristic
9C2×#11718606C211yesmaximal, characteristic
10C2×#11718606C211yesmaximal, characteristic
11C2×#11718605C211yesmaximal, characteristic
12C2×#11718594C211yesmaximal, characteristic, complemented
13C2×#11718638C211yesmaximal, characteristic, complemented
14C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
15C2×C4×#6101C211yesmaximal, characteristic, complemented
16C22×C13×#126C211yesmaximal, characteristic
17C2×C13×#126—28no—
18C2×C13×#126C2218yes—
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×#6101C2211yescharacteristic
39C22×#6101C2211yescharacteristic
40C22×C4×Dic13C2211yescharacteristic
41C22×C4×Dic13C2211yescharacteristic
42C22×C4×Dic13C2211yescharacteristic
43C22×C4×Dic13C2211yescharacteristic
44C2×#88143—28no—
45C2×#88143C2218yescomplemented
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56#11718645C2218yescomplemented
57#11718641C2218yescomplemented
58#11718638C2218yescomplemented
59C4⋊C4×Dic13C2218yescomplemented
60#11718633C2218yescomplemented
61#11718610C2218yes—
62#11718609C2218yes—
63#11718606C2218yes—
64#11718606C2218yes—
65#11718606C2218yes—
66#11718605C2218yes—
67#11718594C2218yescomplemented
68C4×#6101C2218yescomplemented
69C25×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C13×#126—232no—
85C2×C13×C4⋊C4—24no—
86C2×C13×C4⋊C4—24no—
87C2×C13×C4⋊C4D418yes—
88C2×C13×C4⋊C4C2314yes—
89C2×C13×C4⋊C4C2314yes—
90C2×C13×C4⋊C4C2314yes—
91C2×C13×C22⋊C4—24no—
92C2×C13×C22⋊C4—24no—
93C2×C13×C22⋊C4—24no—
94C2×C13×C22⋊C4C2314yes—
95C2×C13×C22⋊C4C2314yes—
96C2×C13×C22⋊C4C2314yes—
97C2×C42×C13—24no—
98C2×C42×C13C2314yes—
99C2×C22⋊Dic13—24no—
100C2×C22⋊Dic13—24no—
101C2×C22⋊Dic13—24no—
102C2×C22⋊Dic13—24no—
103C2×C22⋊Dic13C2314yes—
104C2×C22⋊Dic13C2314yes—
105C2×C22⋊Dic13C2314yes—
106C2×C22⋊Dic13C2314yes—
107C2×C4⋊Dic13—24no—
108C2×C4⋊Dic13—24no—
109C2×C4⋊Dic13C2314yes—
110C2×C4⋊Dic13C2314yes—
111C2×#6101—24no—
112C2×#6101—24no—
113C2×#6101—24no—
114C2×#6101—24no—
115C2×#6101—24no—
116C2×#6101—24no—
117C2×#6101—24no—
118C2×#6101—24no—
119C2×#6101C2314yes—
120C2×#6101C2314yes—
121C2×#6101C2314yes—
122C2×#6101C2314yes—
123C2×#6101C2314yes—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×#6101C2314yes—
127C2×C4×Dic13—24no—
128C2×C4×Dic13—24no—
129C2×C4×Dic13—24no—
130C2×C4×Dic13—24no—
131C2×C4×Dic13C2314yes—
132C2×C4×Dic13C2314yes—
133C2×C4×Dic13C2314yes—
134C2×C4×Dic13C2314yes—
135#88143—232no—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#88071C2314yes—
146C2×#2519—131nomaximal, Sylow
147C24×C13—22no—
148C24×C13—22no—
149C24×C13—22no—
150C24×C13—22no—
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13C2412yes—
155C24×C13C2411yescharacteristic
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13C2×D414yes—
172C22×C4×C13C2×D414yes—
173C22×C4×C13C2×D414yes—
174C22×C4×C13C2412yes—
175C22×C4×C13C2412yes—
176C22×C4×C13C2412yes—
177C22×C4×C13C2412yes—
178C22×C4×C13C2412yes—
179C22×C4×C13C2412yes—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13#4114yes—
201C22×Dic13#4114yes—
202C22×Dic13#4114yes—
203C22×Dic13#4114yes—
204C22×Dic13C2412yes—
205C22×Dic13C2412yes—
206C22×Dic13C2412yes—
207C22×Dic13C2412yes—
208C22×Dic13C2412yes—
209C22×Dic13C2412yes—
210C22×Dic13C2412yes—
211C22×Dic13C2412yes—
212C13×C4⋊C4—28no—
213C13×C4⋊C4—28no—
214C13×C4⋊C4C2×D4116yes—
215C13×C22⋊C4—28no—
216C13×C22⋊C4—28no—
217C13×C22⋊C4—28no—
218C42×C13—28no—
219C22⋊Dic13—28no—
220C22⋊Dic13—28no—
221C22⋊Dic13—28no—
222C22⋊Dic13—28no—
223C4⋊Dic13—28no—
224C4⋊Dic13—28no—
225#6101—28no—
226#6101—28no—
227#6101—28no—
228#6101—28no—
229#6101—28no—
230#6101—28no—
231#6101—28no—
232#6101—28no—
233C4×Dic13—28no—
234C4×Dic13—28no—
235C4×Dic13—28no—
236C4×Dic13—28no—
237C22×#126D1311yescharacteristic
238C22×#125—131no—
239#2519—1316no—
240C2×#399—131no—
241C2×#398—131no—
242C2×#398—131no—
243C2×#396—131no—
244C2×#389—131no—
245C2×#388—131no—
246C2×#388—131no—
247C2×#388—131no—
248C2×#388—131no—
249C2×#387—131no—
250C2×#382—131no—
251C2×C4×C4⋊C4—131no—
252C2×C4×C4⋊C4—131no—
253C23×C13—22no—
254C23×C13—22no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—44no—
261C23×C13—44no—
262C23×C13—44no—
263C23×C13—44no—
264C23×C13—44no—
265C23×C13—44no—
266C23×C13—44no—
267C23×C13C22×D412yes—
268C23×C13C2×#4112yes—
269C23×C13C2×#4112yes—
270C23×C13C2×#4112yes—
271C23×C13C2×#4112yes—
272C23×C132−1+412yes—
273C23×C132−1+412yes—
274C23×C13C2511yescharacteristic
275C2×C4×C13—28no—
276C2×C4×C13—28no—
277C2×C4×C13—28no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—44no—
294C2×C4×C13—44no—
295C2×C4×C13—44no—
296C2×C4×C13C22×D414yes—
297C2×C4×C13C22×D414yes—
298C2×C4×C13C22×D414yes—
299C2×Dic13—28no—
300C2×Dic13—28no—
301C2×Dic13—28no—
302C2×Dic13—28no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—44no—
324C2×Dic13—44no—
325C2×Dic13—44no—
326C2×Dic13—44no—
327C2×Dic13C2×#4114yes—
328C2×Dic13C2×#4114yes—
329C2×Dic13C2×#4114yes—
330C2×Dic13C2×#4114yes—
331C2×#126—28no—
332C2×#126C2×D1318yes—
333C2×#125—138no—
334C2×#125—268no—
335C22×C4⋊C4—131no—
336C22×C4⋊C4—131no—
337C22×C4⋊C4—131no—
338C22×C4⋊C4—131no—
339C22×C4⋊C4—131no—
340C22×C4⋊C4—131no—
341C22×C4⋊C4—131no—
342C22×C4⋊C4—131no—
343C22×C4⋊C4—131no—
344C22×C4⋊C4—131no—
345C22×C4⋊C4C2×D1311yescharacteristic
346C22×C4⋊C4C2×D1311yescharacteristic
347C22×C4⋊C4C2×D1311yescharacteristic
348C22×C22⋊C4—131no—
349C22×C22⋊C4—131no—
350C22×C22⋊C4—131no—
351C22×C22⋊C4—131no—
352C22×C22⋊C4C2×D1311yescharacteristic
353C22×C22⋊C4C2×D1311yescharacteristic
354C22×C22⋊C4C2×D1311yescharacteristic
355C22×C42—131no—
356C22×C42—131no—
357C22×C42—131no—
358C22×C42—131no—
359C22×C42C2×D1311yescharacteristic
360#399—138no—
361#398—138no—
362#398—138no—
363#396—138no—
364#389—138no—
365#388—138no—
366#388—138no—
367#388—138no—
368#388—138no—
369#387—138no—
370#382—138no—
371C4×C4⋊C4—138no—
372C4×C4⋊C4—138no—
373C2×#95—131no—
374C2×#95—131no—
375C2×#95—131no—
376C2×#95—131no—
377C2×#95—131no—
378C2×#95—131no—
379C2×#95—131no—
380C2×#95—131no—
381C2×#95—131no—
382C2×#95—131no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13—42no—
386C22×C13—42no—
387C22×C13—42no—
388C22×C13—42no—
389C22×C13—42no—
390C22×C13—88no—
391C22×C13#52914yes—
392C22×C13#53214yes—
393C22×C13#54114yes—
394C22×C13#54714yes—
395C22×C13#54814yes—
396C22×C13#55214yes—
397C22×C13#55214yes—
398C22×C13C23×D411yescharacteristic
399C22×C13C22×#4111yescharacteristic
400C22×C13C22×#4111yescharacteristic
401C22×C13C22×#4111yescharacteristic
402C22×C13C22×#4111yescharacteristic
403C22×C13C2×2−1+411yescharacteristic
404C22×C13C2×2−1+411yescharacteristic
405C4×C13—24no—
406C4×C13—24no—
407C4×C13—24no—
408C4×C13—42no—
409C4×C13—42no—
410C4×C13—42no—
411Dic13—24no—
412Dic13—24no—
413Dic13—24no—
414Dic13—24no—
415Dic13—42no—
416Dic13—42no—
417Dic13—42no—
418Dic13—42no—
419C25C22×D1311yescharacteristic
420C23×C4—131no—
421C23×C4—131no—
422C23×C4—131no—
423C23×C4—131no—
424C23×C4—131no—
425C23×C4—131no—
426C23×C4—131no—
427C23×C4—131no—
428C23×C4C22×D1311yescharacteristic
429C23×C4C22×D1311yescharacteristic
430C23×C4C22×D1311yescharacteristic
431C23×C4C22×D1311yescharacteristic
432C23×C4C22×D1311yescharacteristic
433C23×C4C22×D1311yescharacteristic
434#126—232no—
435#125—2632no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—134no—
439C2×C4⋊C4—134no—
440C2×C4⋊C4—134no—
441C2×C4⋊C4—134no—
442C2×C4⋊C4—134no—
443C2×C4⋊C4—134no—
444C2×C4⋊C4—134no—
445C2×C4⋊C4—134no—
446C2×C4⋊C4—134no—
447C2×C4⋊C4—134no—
448C2×C4⋊C4—264no—
449C2×C4⋊C4—264no—
450C2×C4⋊C4—264no—
451C2×C4⋊C4—264no—
452C2×C4⋊C4—264no—
453C2×C4⋊C4—264no—
454C2×C4⋊C4—264no—
455C2×C4⋊C4—264no—
456C2×C4⋊C4—264no—
457C2×C4⋊C4—264no—
458C2×C4⋊C4C22⋊D1318yes—
459C2×C4⋊C4C22×D1314yes—
460C2×C4⋊C4C22×D1314yes—
461C2×C4⋊C4C22×D1314yes—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—134no—
466C2×C22⋊C4—134no—
467C2×C22⋊C4—134no—
468C2×C22⋊C4—134no—
469C2×C22⋊C4—264no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—264no—
472C2×C22⋊C4—264no—
473C2×C22⋊C4C22×D1314yes—
474C2×C22⋊C4C22×D1314yes—
475C2×C22⋊C4C22×D1314yes—
476C2×C42—24no—
477C2×C42—134no—
478C2×C42—134no—
479C2×C42—134no—
480C2×C42—134no—
481C2×C42—264no—
482C2×C42—264no—
483C2×C42—264no—
484C2×C42—264no—
485C2×C42C22×D1314yes—
486#95—134no—
487#95—134no—
488#95—134no—
489#95—134no—
490#95—134no—
491#95—134no—
492#95—134no—
493#95—134no—
494#95—134no—
495#95—134no—
496C2×C13—82no—
497C2×C13#251918yescomplemented
498C2×C13C2×#52911yescharacteristic
499C2×C13C2×#53211yescharacteristic
500C2×C13C2×#54111yescharacteristic
501C2×C13C2×#54711yescharacteristic
502C2×C13C2×#54811yescharacteristic
503C2×C13C2×#55211yescharacteristic
504C2×C13C2×#55211yescharacteristic
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24C23×D1312yes—
513C24C23×D1311yescharacteristic
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—134no—
530C22×C4—134no—
531C22×C4—134no—
532C22×C4—134no—
533C22×C4—132no—
534C22×C4—132no—
535C22×C4—132no—
536C22×C4—132no—
537C22×C4—132no—
538C22×C4—132no—
539C22×C4—132no—
540C22×C4—132no—
541C22×C4—262no—
542C22×C4—262no—
543C22×C4—262no—
544C22×C4—262no—
545C22×C4—262no—
546C22×C4—262no—
547C22×C4—262no—
548C22×C4—262no—
549C22×C4—262no—
550C22×C4—262no—
551C22×C4—262no—
552C22×C4—262no—
553C22×C4—262no—
554C22×C4—262no—
555C22×C4—262no—
556C22×C4—262no—
557C22×C4—262no—
558C22×C4—262no—
559C22×C4—262no—
560C22×C4—262no—
561C22×C4C2×C22⋊D1314yes—
562C22×C4C2×C22⋊D1314yes—
563C22×C4C2×C22⋊D1314yes—
564C22×C4C23×D1312yes—
565C22×C4C23×D1312yes—
566C22×C4C23×D1312yes—
567C22×C4C23×D1312yes—
568C22×C4C23×D1312yes—
569C22×C4C23×D1312yes—
570C4⋊C4—28no—
571C4⋊C4—28no—
572C4⋊C4—268no—
573C4⋊C4—268no—
574C4⋊C4—268no—
575C4⋊C4—268no—
576C4⋊C4—268no—
577C4⋊C4—268no—
578C4⋊C4—268no—
579C4⋊C4—268no—
580C4⋊C4—268no—
581C4⋊C4—268no—
582C4⋊C4C2×C22⋊D13116yes—
583C22⋊C4—28no—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—268no—
587C22⋊C4—268no—
588C22⋊C4—268no—
589C22⋊C4—268no—
590C42—28no—
591C42—268no—
592C42—268no—
593C42—268no—
594C42—268no—
595C13C2×#251911yescharacteristic, complemented, Sylow
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23#41×D1312yes—
611C23#41×D1312yes—
612C23#41×D1312yes—
613C23#41×D1312yes—
614C23#8825712yes—
615C23#8825712yes—
616C23C22×C22⋊D1312yes—
617C23C24×D1311yescharacteristic
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—134no—
640C2×C4—134no—
641C2×C4—134no—
642C2×C4—134no—
643C2×C4—268no—
644C2×C4—262no—
645C2×C4—262no—
646C2×C4—262no—
647C2×C4—262no—
648C2×C4—262no—
649C2×C4—262no—
650C2×C4—262no—
651C2×C4—262no—
652C2×C4—268no—
653C2×C4—268no—
654C2×C4—268no—
655C2×C4—262no—
656C2×C4—262no—
657C2×C4—262no—
658C2×C4—262no—
659C2×C4—262no—
660C2×C4—262no—
661C2×C4—262no—
662C2×C4—262no—
663C2×C4—262no—
664C2×C4—262no—
665C2×C4—262no—
666C2×C4—262no—
667C2×C4—524no—
668C2×C4—524no—
669C2×C4—524no—
670C2×C4—524no—
671C2×C4C22×C22⋊D1314yes—
672C2×C4C22×C22⋊D1314yes—
673C2×C4C22×C22⋊D1314yes—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—88no—
682C22#1171940614yes—
683C22#1171941114yes—
684C22#1171941314yes—
685C22#1171941314yes—
686C22#1171952914yes—
687C22#1171953614yes—
688C22#1171953714yes—
689C22C2×#41×D1311yescharacteristic
690C22C2×#41×D1311yescharacteristic
691C22C2×#41×D1311yescharacteristic
692C22C2×#41×D1311yescharacteristic
693C22C2×#8825711yescharacteristic
694C22C2×#8825711yescharacteristic
695C22C23×C22⋊D1311yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—264no—
703C4—264no—
704C4—264no—
705C4—264no—
706C4—522no—
707C4—522no—
708C4—522no—
709C4—522no—
710C2—82no—
711C2#1311951618yesdirect product factor
712C2C2×#1171941111yescharacteristic
713C2C2×#1171953711yescharacteristic
714C2C2×#1171940611yescharacteristic
715C2C2×#1171952911yescharacteristic
716C2C2×#1171953611yescharacteristic
717C2C2×#1171941311yescharacteristic
718C2C2×#1171941311yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#126C2
socleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×#126D13
hypocenterC13C2×#2519
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×#88143C2semidirect
2. #13119516C2direct (N × H)
4. C2×#11718645C2semidirect
5. C2×#11718641C2semidirect
7. C2×#11718633C2semidirect
12. C2×#11718594C2semidirect
13. C2×#11718638C2semidirect
14. C2×C4⋊C4×Dic13C2semidirect
15. C2×C4×#6101C2semidirect
45. C2×#88143C22semidirect
56. #11718645C22semidirect
57. #11718641C22semidirect
58. #11718638C22semidirect
59. C4⋊C4×Dic13C22semidirect
60. #11718633C22semidirect
67. #11718594C22semidirect
68. C4×#6101C22semidirect
497. C2×C13#2519semidirect
595. C13C2×#2519semidirect
711. C2#13119516direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881432
#131195162
C2×#117186102
C2×#117186452
C2×#117186412
C2×#117186092
C2×#117186332
C2×#117186062
C2×#117186052
C2×#117185942
C2×#117186382
C2×C4⋊C4×Dic132
C2×C4×#61012
C22×C13×#1262
C2×#251913