Finite Group Databasebeta

← C2×#13127285 #16741460

Subgroups — C2×#13127285 #16741460

Order 3328.

1878 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
1C2×#11719246C211yesmaximal, characteristic
2#13127285C2116yesmaximal, direct product factor
3C2×#11718741C211yesmaximal, characteristic, complemented
4C2×#11718631C211yesmaximal, characteristic, complemented
5C2×#11718706C211yesmaximal, characteristic, complemented
6C2×#11718632C211yesmaximal, characteristic, complemented
7C2×#11718704C211yesmaximal, characteristic, complemented
8C2×#11718683C211yesmaximal, characteristic, complemented
9C2×#11718755C211yesmaximal, characteristic, complemented
10C2×#11718713C211yesmaximal, characteristic, complemented
11C2×#11718712C211yesmaximal, characteristic, complemented
12C2×#11718691C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic
14C2×#11718625C211yesmaximal, characteristic, complemented
15C22×#88048C211yesmaximal, characteristic, complemented
16C2×C13×#554C211yesmaximal, characteristic
17C13×#554—24no—
18C13×#554C2218yes—
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#125—21no—
21C2×C13×C22⋊Q8—21no—
22C2×C13×C22⋊Q8—21no—
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×D4×C13—21no—
27C2×C4×D4×C13C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C4⋊C4C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C2×#88189—21no—
32C2×#88180C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C2×#88178C2211yescharacteristic
35C2×#88178C2211yescharacteristic
36C22×#6099C2211yescharacteristic
37C23×#1055C2211yescharacteristic
38#11719246—24no—
39#11719246C2218yes—
40C2×#88143—21no—
41C2×#88133—21no—
42C2×#88131—21no—
43C2×#88124C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C2×#88075C2211yescharacteristic
46C2×#88075C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718755C2218yescomplemented
51#11718741C2218yescomplemented
52#11718713C2218yescomplemented
53#11718712C2218yescomplemented
54#11718706C2218yescomplemented
55#11718704C2218yescomplemented
56#11718691C2218yescomplemented
57#11718683C2218yescomplemented
58#11718672C2218yes—
59#11718632C2218yescomplemented
60#11718631C2218yescomplemented
61C2×#88050C2211yescharacteristic
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64#11718625C2218yescomplemented
65C2×#88048C2211yescharacteristic
66C2×#88048C2211yescharacteristic
67C2×#88048C2211yescharacteristic
68C2×#88048C2211yescharacteristic
69C2×#88048C2211yescharacteristic
70C2×#88048C2211yescharacteristic
71C2×#88048C2218yescomplemented
72C2×#88047C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
77C22×Q8×C13—21no—
78C22×Q8×C13C2311yescharacteristic
79C22×D4×C13D411yescharacteristic
80C23×C4×C13—21no—
81C23×C4×C13—21no—
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×Dic13—21no—
85C22×Dic26C2311yescharacteristic
86C13×C4⋊Q8—22no—
87C13×C4⋊Q8C2314yes—
88C13×#125—28no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—28no—
92C13×C22⋊Q8—28no—
93C13×C22⋊Q8C2314yes—
94C13×C22⋊Q8C2314yes—
95C4×Q8×C13—22no—
96C4×Q8×C13C2314yes—
97C4×D4×C13—28no—
98C4×D4×C13D414yes—
99C4×D4×C13C2314yes—
100C2×C13×C4⋊C4—21no—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—21no—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4D411yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C4⋊C4C2311yescharacteristic
111C2×C13×C4⋊C4C2311yescharacteristic
112C2×C13×C4⋊C4C2314yes—
113C2×C13×C4⋊C4C2314yes—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C13×C22⋊C4D411yescharacteristic
117C2×C13×C22⋊C4D411yescharacteristic
118C2×C42×C13—21no—
119C2×C42×C13C2311yescharacteristic
120C2×C22⋊Dic13—21no—
121C2×C22⋊Dic13—21no—
122C2×C22⋊Dic13—21no—
123C2×#6107—24no—
124C2×#6107C2314yes—
125#88189—28no—
126#88180—22no—
127#88180C2314yes—
128C2×C4⋊Dic13—21no—
129C2×C4⋊Dic13—22no—
130C2×C4⋊Dic13C2311yescharacteristic
131C2×C4⋊Dic13C2311yescharacteristic
132C2×C4⋊Dic13C2311yescharacteristic
133C2×C4⋊Dic13C2314yes—
134#88178—22no—
135#88178—22no—
136#88178C2314yes—
137#88178C2314yes—
138C2×#6101—21no—
139C2×#6101—21no—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×#6101—21no—
143C2×C4×Dic13—21no—
144C2×C4×Dic13—21no—
145C2×#6099—24no—
146C2×#6099C2314yes—
147C22×#1055—24no—
148C22×#1055C2314yes—
149C22×#1055C2311yescharacteristic
150C22×#1055C2311yescharacteristic
151C22×#1055C2311yescharacteristic
152C22×#1055C2311yescharacteristic
153#88143—28no—
154#88133—28no—
155#88131—28no—
156#88124—22no—
157#88124C2314yes—
158C4×Dic26—22no—
159C4×Dic26C2314yes—
160#88075C2314yes—
161#88075C2314yes—
162#88075C2314yes—
163C22⋊#1055C2314yes—
164C22⋊#1055C2314yes—
165#88050C2314yes—
166#88050C2314yes—
167#88050C2314yes—
168#88048C2314yes—
169#88048C2314yes—
170#88048C2314yes—
171#88048C2314yes—
172#88048C2314yes—
173#88048C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176#88047C2314yes—
177C4⋊#1055C2314yes—
178#88043C2314yes—
179C2×#3344—131nomaximal, Sylow
180C24×C13C2×D411yescharacteristic
181C24×C13C2×D411yescharacteristic
182C2×Q8×C13—21no—
183C2×Q8×C13—24no—
184C2×Q8×C13—22no—
185C2×Q8×C13—22no—
186C2×Q8×C13—82no—
187C2×Q8×C13C2412yes—
188C2×D4×C13—24no—
189C2×D4×C13C2×D414yes—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—22no—
193C22×C4×C13—22no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—24no—
199C22×C4×C13—24no—
200C22×C4×C13—82no—
201C22×C4×C13—82no—
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×D412yes—
208C22×C4×C13C2412yes—
209C22×C4×C13C2412yes—
210C22×C4×C13C2411yescharacteristic
211C22×Dic13—24no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—44no—
217C2×Dic26—22no—
218C2×Dic26—22no—
219C2×Dic26—21no—
220C2×Dic26C2412yes—
221C13×C4⋊C4—21no—
222C13×C4⋊C4—24no—
223C13×C4⋊C4—24no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4—24no—
227C13×C4⋊C4—24no—
228C13×C4⋊C4—24no—
229C13×C4⋊C4—24no—
230C13×C4⋊C4C2×D414yes—
231C13×C4⋊C4C2412yes—
232C13×C4⋊C4C2412yes—
233C13×C4⋊C4C2412yes—
234C13×C22⋊C4—24no—
235C13×C22⋊C4—24no—
236C13×C22⋊C4C2×D414yes—
237C13×C22⋊C4C2×D414yes—
238C42×C13—24no—
239C42×C13C2×D412yes—
240C42×C13C2412yes—
241C22⋊Dic13—24no—
242C22⋊Dic13—24no—
243C22⋊Dic13—24no—
244#6107—28no—
245C4⋊Dic13—21no—
246C4⋊Dic13—21no—
247C4⋊Dic13—21no—
248C4⋊Dic13—24no—
249C4⋊Dic13C2412yes—
250C4⋊Dic13C2412yes—
251C4⋊Dic13C2412yes—
252#6101—24no—
253#6101—24no—
254#6101—24no—
255#6101—24no—
256#6101—24no—
257C4×Dic13—24no—
258C4×Dic13—24no—
259#6099—28no—
260C2×#1055—22no—
261C2×#1055—22no—
262C2×#1055—22no—
263C2×#1055—28no—
264C2×#1055#4114yes—
265C2×#1055C2412yes—
266C2×#1055C2412yes—
267C2×#1055C2412yes—
268C2×#1055C2412yes—
269C2×#554D1311yescharacteristic
270C2×#552—131no—
271#3344—1316no—
272C2×#501—131no—
273C2×#484—131no—
274C2×#485—131no—
275C2×#483—131no—
276C2×#483—131no—
277C2×#479—131no—
278C2×#475—131no—
279C2×#470—131no—
280C2×#467—131no—
281C2×#441—131no—
282C2×#435—131no—
283C2×#428—131no—
284C22×#106—131no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13#13714yes—
291C23×C13C22×D412yes—
292C23×C13C22×D412yes—
293C23×C13C22×D411yescharacteristic
294Q8×C13—22no—
295Q8×C13—22no—
296Q8×C13—42no—
297Q8×C13—84no—
298D4×C13—28no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—24no—
304C2×C4×C13—24no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13—84no—
318C2×C4×C13—84no—
319C2×C4×C13C22×D412yes—
320C2×C4×C13C22×D412yes—
321C2×C4×C13C22×D412yes—
322C2×C4×C13C22×D412yes—
323C2×C4×C13C22×D411yescharacteristic
324C2×C4×C13C2×#4112yes—
325C2×C4×C132−1+412yes—
326C2×C4×C13C2511yescharacteristic
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—42no—
332C2×Dic13—48no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336Dic26—22no—
337Dic26—22no—
338Dic26—42no—
339#1055—22no—
340#1055—22no—
341#1055—22no—
342#1055C2×#4114yes—
343C22×Q16—131no—
344C22×M16—131no—
345C23×C8—131no—
346#554—24no—
347#554C2×D1318yes—
348#552—138no—
349#552—264no—
350C2×C4⋊Q8C2×D1311yescharacteristic
351C2×#126—261no—
352C2×#125—21no—
353C2×#125—131no—
354C2×#125—261no—
355C2×#123—261no—
356C2×C22⋊Q8—21no—
357C2×C22⋊Q8—21no—
358C2×C22⋊Q8—131no—
359C2×C22⋊Q8—131no—
360C2×C22⋊Q8C2×D1311yescharacteristic
361C2×C22⋊Q8C2×D1311yescharacteristic
362C2×C4×Q8—131no—
363C2×C4×Q8C2×D1311yescharacteristic
364C2×C4×D4—21no—
365C2×C4×D4C2×D1311yescharacteristic
366C2×#117—131no—
367C2×#117—261no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4C2×D1311yescharacteristic
370C22×C4⋊C4C2×D1311yescharacteristic
371#501—138no—
372#485—138no—
373#484—138no—
374#483—138no—
375#483—138no—
376#479—138no—
377#475—138no—
378#470—138no—
379#467—138no—
380#441—138no—
381#435—138no—
382#428—138no—
383C2×#107—131no—
384C2×#107—131no—
385C2×#107—131no—
386C2×#106—131no—
387C2×#106—131no—
388C2×#106—131no—
389C2×#106—131no—
390C2×#106—138no—
391C2×#106—131no—
392C2×#106—131no—
393C2×C4⋊C8—131no—
394C2×#103—131no—
395C2×#103—131no—
396C2×#103—131no—
397C2×#103—131no—
398C2×#103—131no—
399C2×#103—131no—
400C2×C22⋊C8—131no—
401C2×C22⋊C8—131no—
402C2×#97—131no—
403C22×C13—28no—
404C22×C13—22no—
405C22×C13—22no—
406C22×C13—22no—
407C22×C13—22no—
408C22×C13—22no—
409C22×C13—44no—
410C22×C13#54712yes—
411C22×C13C2×#13714yes—
412C22×C13C2×#13712yes—
413C22×C13#57712yes—
414C22×C13C23×D411yescharacteristic
415C4×C13—22no—
416C4×C13—22no—
417C4×C13—22no—
418C4×C13—22no—
419C4×C13—42no—
420C4×C13—42no—
421C4×C13—42no—
422C4×C13—42no—
423C4×C13#54712yes—
424C4×C13C22×#4111yescharacteristic
425C4×C13C2×2−1+411yescharacteristic
426Dic13—42no—
427Dic13—42no—
428Dic13—42no—
429Dic13—42no—
430C22×Q8—21no—
431C22×Q8—131no—
432C22×Q8C22×D1311yescharacteristic
433C22×D4C22⋊D1311yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—261no—
437C23×C4C22×D1311yescharacteristic
438C23×C4C22×D1311yescharacteristic
439C2×Q16—134no—
440C2×Q16—264no—
441C2×M16—134no—
442C2×M16—264no—
443C22×C8—131no—
444C22×C8—131no—
445C22×C8—134no—
446C22×C8—131no—
447C22×C8—131no—
448C22×C8—264no—
449C4⋊Q8—22no—
450C4⋊Q8C22×D1314yes—
451#126—268no—
452#125—28no—
453#125—134no—
454#125—268no—
455#125—262no—
456#123—268no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—28no—
460C22⋊Q8—28no—
461C22⋊Q8—134no—
462C22⋊Q8—134no—
463C22⋊Q8—262no—
464C22⋊Q8—262no—
465C22⋊Q8C22×D1314yes—
466C22⋊Q8C22×D1314yes—
467C4×Q8—22no—
468C4×Q8—134no—
469C4×Q8—262no—
470C4×Q8C22×D1314yes—
471C4×D4—28no—
472C4×D4C22⋊D1314yes—
473C4×D4C22×D1314yes—
474#117—134no—
475#117—262no—
476#117—268no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—131no—
486C2×C4⋊C4—131no—
487C2×C4⋊C4—134no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—261no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—261no—
492C2×C4⋊C4—261no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4—261no—
495C2×C4⋊C4—261no—
496C2×C4⋊C4C22⋊D1311yescharacteristic
497C2×C4⋊C4C22×D1311yescharacteristic
498C2×C4⋊C4C22×D1311yescharacteristic
499C2×C4⋊C4C22×D1311yescharacteristic
500C2×C4⋊C4C22×D1314yes—
501C2×C4⋊C4C22×D1314yes—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—261no—
505C2×C22⋊C4—261no—
506C2×C22⋊C4—261no—
507C2×C22⋊C4C22⋊D1311yescharacteristic
508C2×C22⋊C4C22⋊D1311yescharacteristic
509C2×C42—21no—
510C2×C42—261no—
511C2×C42—261no—
512C2×C42C22×D1311yescharacteristic
513#107—134no—
514#107—134no—
515#107—134no—
516#106—134no—
517#106—134no—
518#106—134no—
519#106—134no—
520#106—134no—
521#106—134no—
522C4⋊C8—134no—
523#103—134no—
524#103—134no—
525#103—134no—
526#103—134no—
527#103—134no—
528#103—134no—
529C22⋊C8—134no—
530C22⋊C8—134no—
531#97—134no—
532C2×C13—24no—
533C2×C13—42no—
534C2×C13#334414yescomplemented
535C2×C13C2×#54711yescharacteristic
536C2×C13C22×#13711yescharacteristic
537C2×C13C2×#57711yescharacteristic
538C24C2×C22⋊D1311yescharacteristic
539C24C2×C22⋊D1311yescharacteristic
540C2×Q8—21no—
541C2×Q8—24no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—82no—
545C2×Q8—132no—
546C2×Q8—261no—
547C2×Q8—262no—
548C2×Q8—262no—
549C2×Q8C23×D1312yes—
550C2×D4—24no—
551C2×D4C2×C22⋊D1314yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4—264no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—524no—
570C22×C4C2×C22⋊D1312yes—
571C22×C4C2×C22⋊D1312yes—
572C22×C4C2×C22⋊D1311yescharacteristic
573C22×C4C2×C22⋊D1311yescharacteristic
574C22×C4C2×C22⋊D1311yescharacteristic
575C22×C4C2×C22⋊D1311yescharacteristic
576C22×C4C23×D1312yes—
577C22×C4C23×D1312yes—
578C22×C4C23×D1311yescharacteristic
579Q16—268no—
580M16—268no—
581C2×C8—134no—
582C2×C8—132no—
583C2×C8—132no—
584C2×C8—132no—
585C2×C8—132no—
586C2×C8—268no—
587C2×C8—262no—
588C2×C8—262no—
589C2×C8—262no—
590C4⋊C4—21no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—132no—
600C4⋊C4—132no—
601C4⋊C4—132no—
602C4⋊C4—261no—
603C4⋊C4—261no—
604C4⋊C4—264no—
605C4⋊C4—261no—
606C4⋊C4—264no—
607C4⋊C4—264no—
608C4⋊C4—264no—
609C4⋊C4—264no—
610C4⋊C4—264no—
611C4⋊C4C2×C22⋊D1314yes—
612C4⋊C4C23×D1312yes—
613C4⋊C4C23×D1312yes—
614C4⋊C4C23×D1312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—264no—
618C22⋊C4—264no—
619C22⋊C4—264no—
620C22⋊C4C2×C22⋊D1314yes—
621C22⋊C4C2×C22⋊D1314yes—
622C42—24no—
623C42—264no—
624C42—264no—
625C42C2×C22⋊D1312yes—
626C42C23×D1312yes—
627C13C2×#334411yescharacteristic, complemented, Sylow
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#8819614yes—
634C23C22×C22⋊D1312yes—
635C23C22×C22⋊D1312yes—
636C23C22×C22⋊D1311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—84no—
641Q8—262no—
642Q8—262no—
643Q8—522no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—262no—
666C2×C4—262no—
667C2×C4—262no—
668C2×C4—262no—
669C2×C4—528no—
670C2×C4—522no—
671C2×C4—522no—
672C2×C4—522no—
673C2×C4—522no—
674C2×C4#41×D1312yes—
675C2×C4#8825712yes—
676C2×C4C22×C22⋊D1312yes—
677C2×C4C22×C22⋊D1312yes—
678C2×C4C22×C22⋊D1312yes—
679C2×C4C22×C22⋊D1312yes—
680C2×C4C22×C22⋊D1311yescharacteristic
681C2×C4C24×D1311yescharacteristic
682C8—134no—
683C8—262no—
684C8—262no—
685C8—262no—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22C2×#8819614yes—
694C22C2×#8819612yes—
695C22#1171952912yes—
696C22#1171954112yes—
697C22C23×C22⋊D1311yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—522no—
707C4—522no—
708C4—522no—
709C4—522no—
710C4#1171952912yes—
711C4C2×#41×D1311yescharacteristic
712C4C2×#8825711yescharacteristic
713C2—24no—
714C2—42no—
715C2#1312728514yesdirect product factor
716C2C2×#1171952911yescharacteristic
717C2C22×#8819611yescharacteristic
718C2C2×#1171954111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#554D13
hypocenterC13C2×#3344
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #13127285C2direct (N × H)
3. C2×#11718741C2semidirect
4. C2×#11718631C2semidirect
5. C2×#11718706C2semidirect
6. C2×#11718632C2semidirect
7. C2×#11718704C2semidirect
8. C2×#11718683C2semidirect
9. C2×#11718755C2semidirect
10. C2×#11718713C2semidirect
11. C2×#11718712C2semidirect
12. C2×#11718691C2semidirect
14. C2×#11718625C2semidirect
15. C22×#88048C2semidirect
50. #11718755C22semidirect
51. #11718741C22semidirect
52. #11718713C22semidirect
53. #11718712C22semidirect
54. #11718706C22semidirect
55. #11718704C22semidirect
56. #11718691C22semidirect
57. #11718683C22semidirect
59. #11718632C22semidirect
60. #11718631C22semidirect
64. #11718625C22semidirect
71. C2×#88048C22semidirect
534. C2×C13#3344semidirect
627. C13C2×#3344semidirect
715. C2#13127285direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192462
#131272852
C2×#117187412
C2×#117186312
C2×#117187062
C2×#117186322
C2×#117187042
C2×#117186832
C2×#117187552
C2×#117187132
C2×#117187122
C2×#117186912
C2×#117186722
C2×#117186252
C22×#880482
C2×C13×#5542
C2×#334413