Finite Group Databasebeta

← C2×#13124873 #16730955

Subgroups — C2×#13124873 #16730955

Order 3328.

2138 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719283C211yesmaximal, characteristic
2C2×C4×Q8×D13C211yesmaximal, characteristic
3#13124873C2116yesmaximal, direct product factor
4C2×#11718545C211yesmaximal, characteristic
5C2×#11718470C211yesmaximal, characteristic
6C2×#11718536C211yesmaximal, characteristic, complemented
7C2×#11718455C211yesmaximal, characteristic, complemented
8C2×#11718454C211yesmaximal, characteristic, complemented
9C2×#11718843C211yesmaximal, characteristic, complemented
10C2×#11718469C211yesmaximal, characteristic
11C2×#11718847C211yesmaximal, characteristic
12C2×C4×Dic52C211yesmaximal, characteristic, complemented
13C2×C4×#6107C211yesmaximal, characteristic, complemented
14C2×C4×#6107C211yesmaximal, characteristic, complemented
15C2×#11718346C211yesmaximal, characteristic
16C2×C4×C13×Q16C211yesmaximal, characteristic, complemented
17C22×Q8×D13C2211yescharacteristic
18C22×C13×Q16C2211yescharacteristic
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×#88200C2211yescharacteristic
22C2×Q8×Dic13C2211yescharacteristic
23C2×#88198C2211yescharacteristic
24C22×#6107C2211yescharacteristic
25C22×#6107C2211yescharacteristic
26C22×Dic52C2211yescharacteristic
27#11719283—24no—
28#11719283C2218yes—
29C4×Q8×D13—24no—
30C4×Q8×D13C2218yes—
31C2×#88151C2211yescharacteristic
32C2×#88150—21no—
33C2×C4⋊C4×D13—21no—
34C2×C4⋊C4×D13C2211yescharacteristic
35C2×#88143—21no—
36C2×#88142C2211yescharacteristic
37C2×#88141—21no—
38C2×#88141C2211yescharacteristic
39C2×#88126—21no—
40C2×C42×D13—21no—
41C2×C42×D13C2211yescharacteristic
42C2×C4×Dic26—21no—
43C2×C4×Dic26—21no—
44C2×C4×Dic26C2211yescharacteristic
45C2×C4×Dic26C2211yescharacteristic
46C4×C13×Q16C2218yescomplemented
47C2×C13×#107C2211yescharacteristic
48C2×C13×#103C2211yescharacteristic
49C2×C13×#103C2211yescharacteristic
50C2×C4×C8×C13C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53#11718847C2218yes—
54#11718843C2218yescomplemented
55C2×#88060C2211yescharacteristic
56C2×#88060C2211yescharacteristic
57C2×#88058C2211yescharacteristic
58C2×#88056C2211yescharacteristic
59C2×#88056C2211yescharacteristic
60C2×#88054C2211yescharacteristic
61C2×#88054C2211yescharacteristic
62C4×#6107C2218yescomplemented
63C4×#6107C2218yescomplemented
64C2×#88050C2211yescharacteristic
65C2×#88050C2211yescharacteristic
66C2×#88047C2211yescharacteristic
67C2×#88047C2211yescharacteristic
68C2×C4×#1055C2211yescharacteristic
69#11718545C2218yes—
70#11718536C2218yescomplemented
71#11718470C2218yes—
72#11718469C2218yes—
73#11718455C2218yescomplemented
74#11718454C2218yescomplemented
75C4×Dic52C2218yescomplemented
76#11718346C2218yes—
77C22×Q8×C13C2311yescharacteristic
78C22×Q8×C13C2311yescharacteristic
79C2×Q8×D13—24no—
80C2×Q8×D13—22no—
81C2×Q8×D13—24no—
82C2×Q8×D13C2314yes—
83C22×C4×D13—21no—
84C22×C4×D13—21no—
85C22×C4×D13D411yescharacteristic
86C22×C4×D13D411yescharacteristic
87C22×C4×D13C2311yescharacteristic
88C22×Dic26—21no—
89C22×Dic26—21no—
90C22×Dic26C2311yescharacteristic
91C22×Dic26C2311yescharacteristic
92C2×C13×Q16—24no—
93C2×C13×Q16C2314yes—
94C22×C8×C13C2311yescharacteristic
95C22×C8×C13C2311yescharacteristic
96C4×Q8×C13—22no—
97C4×Q8×C13—22no—
98C4×Q8×C13C2314yes—
99C4×Q8×C13C2314yes—
100C2×C13×C4⋊C4—21no—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C42×C13—21no—
105C2×C42×C13—21no—
106C2×C42×C13C2311yescharacteristic
107#88200—22no—
108#88200C2314yes—
109Q8×Dic13—22no—
110Q8×Dic13C2314yes—
111#88198—22no—
112#88198C2314yes—
113C2×#6107—24no—
114C2×#6107—24no—
115C2×#6107C2314yes—
116C2×#6107C2314yes—
117C2×#6103—21no—
118C2×#6103—21no—
119C2×C4⋊Dic13—21no—
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13C2311yescharacteristic
122C2×C4⋊Dic13C2311yescharacteristic
123C2×#6101—21no—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×#6101—21no—
127C2×#6101—21no—
128C2×#6101—21no—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×C4×Dic13—21no—
132C2×C4×Dic13—21no—
133C2×C4×Dic13—21no—
134C2×C4×Dic13—21no—
135C2×C4×Dic13D411yescharacteristic
136C2×C4×Dic13D411yescharacteristic
137C2×C4×Dic13C2311yescharacteristic
138C22×#1055C2311yescharacteristic
139C22×#1055C2311yescharacteristic
140C2×Dic52—24no—
141C2×Dic52C2314yes—
142#88151—22no—
143#88151C2314yes—
144#88150—28no—
145C4⋊C4×D13—28no—
146C4⋊C4×D13—22no—
147C4⋊C4×D13C2314yes—
148#88143—28no—
149#88142—22no—
150#88142C2314yes—
151#88141—28no—
152#88141—22no—
153#88141C2314yes—
154#88126—28no—
155C42×D13—28no—
156C42×D13D414yes—
157C42×D13C2314yes—
158C4×Dic26—22no—
159C4×Dic26—22no—
160C4×Dic26—28no—
161C4×Dic26—28no—
162C4×Dic26C2314yes—
163C4×Dic26C2314yes—
164C13×#107C2314yes—
165C13×#103C2314yes—
166C13×#103C2314yes—
167C4×C8×C13C2314yes—
168#88075C2314yes—
169#88075C2314yes—
170#88060C2314yes—
171#88060C2314yes—
172#88058C2314yes—
173#88056C2314yes—
174#88056C2314yes—
175#88054C2314yes—
176#88054C2314yes—
177#88050C2314yes—
178#88050C2314yes—
179#88047C2314yes—
180#88047C2314yes—
181C4×#1055C2314yes—
182C2×#3104—131nomaximal, Sylow
183C23×D13C2×D411yescharacteristic
184C2×Q8×C13—21no—
185C2×Q8×C13—21no—
186C2×Q8×C13—22no—
187C2×Q8×C13—22no—
188C2×Q8×C13—22no—
189C2×Q8×C13#4114yes—
190C2×Q8×C13C2412yes—
191C2×Q8×C13C2412yes—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2411yescharacteristic
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13C2×D411yescharacteristic
204C22×Dic13C2×D411yescharacteristic
205C22×Dic13C2×D411yescharacteristic
206Q8×D13—216no—
207Q8×D13—28no—
208Q8×D13—28no—
209C2×C4×D13—28no—
210C2×C4×D13—24no—
211C2×C4×D13—22no—
212C2×C4×D13—22no—
213C2×C4×D13—24no—
214C2×C4×D13—42no—
215C2×C4×D13—44no—
216C2×C4×D13Q1618yescomplemented
217C2×C4×D13C2×D412yes—
218C2×C4×D13C2×D414yes—
219C2×C4×D13C2×D414yes—
220C2×C4×D13C2412yes—
221C2×Dic26—28no—
222C2×Dic26—21no—
223C2×Dic26—22no—
224C2×Dic26—24no—
225C2×Dic26—22no—
226C2×Dic26—22no—
227C2×Dic26—21no—
228C2×Dic26—24no—
229C2×Dic26—44no—
230C2×Dic26#4114yes—
231C2×Dic26C2412yes—
232C2×Dic26C2412yes—
233C13×Q16—28no—
234C2×C8×C13—22no—
235C2×C8×C13—22no—
236C2×C8×C13C2412yes—
237C2×C8×C13C2412yes—
238C13×C4⋊C4—24no—
239C13×C4⋊C4—21no—
240C13×C4⋊C4—21no—
241C13×C4⋊C4—24no—
242C13×C4⋊C4C2412yes—
243C13×C4⋊C4C2412yes—
244C42×C13—24no—
245C42×C13—24no—
246C42×C13C2×D412yes—
247C42×C13C2412yes—
248#6107—28no—
249#6107—28no—
250#6103—24no—
251#6103—24no—
252C4⋊Dic13—21no—
253C4⋊Dic13—21no—
254C4⋊Dic13—24no—
255C4⋊Dic13—24no—
256C4⋊Dic13C2412yes—
257C4⋊Dic13C2412yes—
258#6101—24no—
259#6101—24no—
260#6101—24no—
261#6101—24no—
262#6101—24no—
263#6101—24no—
264#6101—24no—
265#6101—24no—
266C4×Dic13—24no—
267C4×Dic13—24no—
268C4×Dic13—24no—
269C4×Dic13—24no—
270C4×Dic13C2×D414yes—
271C4×Dic13C2×D412yes—
272C4×Dic13C2×D414yes—
273C4×Dic13C2412yes—
274C2×#1055—22no—
275C2×#1055—22no—
276C2×#1055C2412yes—
277C2×#1055C2412yes—
278Dic52—28no—
279C2×#533—131no—
280C22×C4×Q8—131no—
281#3104—1316no—
282C2×#484—131no—
283C2×#484—131no—
284C2×#477—131no—
285C2×#477—131no—
286C2×#462—131no—
287C2×#462—131no—
288C2×#451—131no—
289C2×#451—131no—
290C2×C4×Q16—131no—
291C2×C4×Q16—131no—
292C2×C4×Q16—131no—
293C2×C4×Q16D1311yescharacteristic, complemented
294C2×#431—131no—
295C23×C13C22×D411yescharacteristic
296C22×D13—22no—
297C22×D13—22no—
298C22×D13C2×Q1614yes—
299C22×D13C22×D412yes—
300Q8×C13—24no—
301Q8×C13—22no—
302Q8×C13—22no—
303Q8×C13—22no—
304Q8×C13—42no—
305Q8×C13C2×#4114yes—
306C2×C4×C13—24no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13C2×Q1614yes—
316C2×C4×C13C22×D412yes—
317C2×C4×C13C22×D411yescharacteristic
318C2×C4×C13C22×D412yes—
319C2×C4×C13C2×#4112yes—
320C2×C4×C13C2×#4112yes—
321C2×C4×C13C2511yescharacteristic
322C2×Dic13—22no—
323C2×Dic13—24no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332C2×Dic13C2×Q1614yes—
333C2×Dic13C22×D412yes—
334C2×Dic13C22×D412yes—
335C2×Dic13C22×D412yes—
336C4×D13—216no—
337C4×D13—24no—
338C4×D13—22no—
339C4×D13—22no—
340C4×D13—44no—
341C4×D13—48no—
342C4×D13C2×Q16116yescomplemented
343Dic26—216no—
344Dic26—24no—
345Dic26—22no—
346Dic26—22no—
347Dic26—22no—
348Dic26—48no—
349Dic26—42no—
350Dic26C2×#4114yes—
351C8×C13—22no—
352C8×C13—22no—
353#1055—22no—
354#1055—22no—
355C23×Q8—131no—
356C22×Q16—131no—
357C22×Q16—131no—
358C22×Q16—131no—
359C22×Q16C2×D1311yescharacteristic
360#533—138no—
361#533—264no—
362C2×C4⋊Q8—131no—
363C2×C4⋊Q8—131no—
364C2×#125—261no—
365C2×C22⋊Q8—131no—
366C2×C22⋊Q8—131no—
367C2×C22⋊Q8—261no—
368C2×C4×Q8—131no—
369C2×C4×Q8—138no—
370C2×C4×Q8—131no—
371C2×C4×Q8—131no—
372C2×C4×Q8—131no—
373C2×C4×Q8—261no—
374C2×C4×Q8—261no—
375C2×C4×Q8—261no—
376C2×C4×Q8—264no—
377C2×C4×Q8C2×D1311yescharacteristic
378C2×C4×Q8C2×D1311yescharacteristic
379C2×#117—261no—
380C22×C4⋊C4—131no—
381C22×C4⋊C4—261no—
382C22×C42—131no—
383C22×C42—261no—
384#484—138no—
385#484—138no—
386#477—138no—
387#477—138no—
388#462—138no—
389#462—138no—
390#451—138no—
391#451—138no—
392C4×Q16—138no—
393C4×Q16—138no—
394C4×Q16—138no—
395C4×Q16C2×D1318yescomplemented
396#431—138no—
397C2×#107—131no—
398C2×#107—131no—
399C2×#107—131no—
400C2×#107C2×D1311yescharacteristic
401C2×C4⋊C8—131no—
402C2×C4⋊C8—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#103—131no—
409C2×#103C2×D1311yescharacteristic
410C2×#103C2×D1311yescharacteristic
411C2×C22⋊C8—131no—
412C2×C22⋊C8—131no—
413C2×C4×C8—131no—
414C2×C4×C8C2×D1311yescharacteristic
415C22×C13#52512yes—
416C22×C13C22×Q1612yes—
417C22×C13#57512yes—
418C22×C13C23×D411yescharacteristic
419C2×D13—28no—
420C2×D13—22no—
421C2×D13—22no—
422C2×D13C22×Q1614yes—
423C4×C13—24no—
424C4×C13—22no—
425C4×C13—42no—
426C4×C13—42no—
427C4×C13—42no—
428C4×C13#52512yes—
429C4×C13C22×Q1614yes—
430C4×C13C22×#4111yescharacteristic
431C4×C13C22×#4111yescharacteristic
432Dic13—22no—
433Dic13—24no—
434Dic13—22no—
435Dic13—42no—
436Dic13—42no—
437Dic13—42no—
438Dic13C22×Q1614yes—
439C22×Q8—134no—
440C22×Q8—131no—
441C22×Q8—131no—
442C22×Q8—261no—
443C22×Q8—261no—
444C22×Q8—262no—
445C22×Q8—264no—
446C22×Q8—264no—
447C22×Q8C22×D1311yescharacteristic
448C22×Q8C22×D1311yescharacteristic
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4—261no—
453C23×C4—261no—
454C2×Q16—24no—
455C2×Q16—134no—
456C2×Q16—134no—
457C2×Q16—134no—
458C2×Q16—264no—
459C2×Q16—264no—
460C2×Q16—264no—
461C2×Q16C22×D1314yes—
462C22×C8—131no—
463C22×C8—131no—
464C22×C8C22×D1311yescharacteristic
465C22×C8C22×D1311yescharacteristic
466C4⋊Q8—134no—
467C4⋊Q8—134no—
468C4⋊Q8—262no—
469C4⋊Q8—262no—
470#125—268no—
471C22⋊Q8—134no—
472C22⋊Q8—134no—
473C22⋊Q8—262no—
474C22⋊Q8—268no—
475C22⋊Q8—262no—
476C4×Q8—22no—
477C4×Q8—22no—
478C4×Q8—134no—
479C4×Q8—134no—
480C4×Q8—134no—
481C4×Q8—134no—
482C4×Q8—268no—
483C4×Q8—268no—
484C4×Q8—268no—
485C4×Q8—262no—
486C4×Q8—262no—
487C4×Q8—262no—
488C4×Q8—262no—
489C4×Q8C22×D1314yes—
490C4×Q8C22×D1314yes—
491#117—268no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—131no—
495C2×C4⋊C4—131no—
496C2×C4⋊C4—134no—
497C2×C4⋊C4—262no—
498C2×C4⋊C4—268no—
499C2×C4⋊C4—261no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—261no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4C22×D1311yescharacteristic
510C2×C4⋊C4C22×D1311yescharacteristic
511C2×C22⋊C4—261no—
512C2×C22⋊C4—261no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—131no—
516C2×C42—131no—
517C2×C42—131no—
518C2×C42—134no—
519C2×C42—134no—
520C2×C42—268no—
521C2×C42—261no—
522C2×C42—261no—
523C2×C42—261no—
524C2×C42—261no—
525C2×C42C22×D1311yescharacteristic
526#107—134no—
527#107—134no—
528#107—134no—
529#107C22×D1314yes—
530C4⋊C8—134no—
531C4⋊C8—134no—
532#103—134no—
533#103—134no—
534#103—134no—
535#103—134no—
536#103—134no—
537#103—134no—
538#103C22×D1314yes—
539#103C22×D1314yes—
540C22⋊C8—134no—
541C22⋊C8—134no—
542C4×C8—134no—
543C4×C8C22×D1314yes—
544C2×C13#310414yescomplemented
545C2×C13C2×#52511yescharacteristic
546C2×C13C23×Q1611yescharacteristic
547C2×C13C2×#57511yescharacteristic
548D13—24no—
549C24—131no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—134no—
556C2×Q8—132no—
557C2×Q8—132no—
558C2×Q8—264no—
559C2×Q8—264no—
560C2×Q8—268no—
561C2×Q8—268no—
562C2×Q8—2616no—
563C2×Q8—268no—
564C2×Q8—262no—
565C2×Q8—261no—
566C2×Q8—261no—
567C2×Q8—262no—
568C2×Q8—262no—
569C2×Q8—524no—
570C2×Q8#612714yes—
571C2×Q8C23×D1312yes—
572C2×Q8C23×D1312yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—131no—
578C22×C4—138no—
579C22×C4—134no—
580C22×C4—131no—
581C22×C4—131no—
582C22×C4—132no—
583C22×C4—132no—
584C22×C4—134no—
585C22×C4—264no—
586C22×C4—268no—
587C22×C4—264no—
588C22×C4—261no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—522no—
595C22×C4—524no—
596C22×C4D4×D1311yescharacteristic
597C22×C4D4×D1311yescharacteristic
598C22×C4C23×D1311yescharacteristic
599Q16—28no—
600Q16—268no—
601Q16—268no—
602Q16—268no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—132no—
606C2×C8—132no—
607C2×C8—262no—
608C2×C8—262no—
609C2×C8C23×D1312yes—
610C2×C8C23×D1312yes—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—132no—
616C4⋊C4—132no—
617C4⋊C4—264no—
618C4⋊C4—264no—
619C4⋊C4—264no—
620C4⋊C4—264no—
621C4⋊C4—264no—
622C4⋊C4—264no—
623C4⋊C4—264no—
624C4⋊C4—264no—
625C4⋊C4—261no—
626C4⋊C4—261no—
627C4⋊C4—264no—
628C4⋊C4—264no—
629C4⋊C4C23×D1312yes—
630C4⋊C4C23×D1312yes—
631C22⋊C4—264no—
632C22⋊C4—264no—
633C42—24no—
634C42—24no—
635C42—134no—
636C42—134no—
637C42—132no—
638C42—132no—
639C42—264no—
640C42—264no—
641C42—264no—
642C42—264no—
643C42D4×D1312yes—
644C42C23×D1312yes—
645C13C2×#310411yescharacteristic, complemented, Sylow
646C23—134no—
647C23—132no—
648C23—262no—
649C23—262no—
650C23C2×D4×D1311yescharacteristic
651Q8—24no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—134no—
657Q8—2616no—
658Q8—264no—
659Q8—262no—
660Q8—262no—
661Q8—262no—
662Q8—528no—
663Q8—522no—
664Q8C2×#612714yes—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—134no—
675C2×C4—132no—
676C2×C4—1316no—
677C2×C4—132no—
678C2×C4—132no—
679C2×C4—2616no—
680C2×C4—262no—
681C2×C4—262no—
682C2×C4—264no—
683C2×C4—262no—
684C2×C4—264no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—524no—
691C2×C4—528no—
692C2×C4—522no—
693C2×C4—522no—
694C2×C4—522no—
695C2×C4Q16×D1314yes—
696C2×C4C2×#612712yes—
697C2×C4C2×D4×D1312yes—
698C2×C4C2×D4×D1312yes—
699C2×C4C2×D4×D1311yescharacteristic
700C2×C4#41×D1312yes—
701C2×C4C24×D1311yescharacteristic
702C8—22no—
703C8—22no—
704C8—262no—
705C8—262no—
706C22—134no—
707C22—268no—
708C22—262no—
709C22—262no—
710C22#1171925212yes—
711C22C2×Q16×D1312yes—
712C22#1171947312yes—
713C22C22×D4×D1311yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—134no—
720C4—262no—
721C4—262no—
722C4—264no—
723C4—522no—
724C4—522no—
725C4—522no—
726C4#1171925212yes—
727C4C2×Q16×D1314yes—
728C4C22×#612711yescharacteristic
729C4C2×#41×D1311yescharacteristic
730C2—264no—
731C2#1312487314yesdirect product factor
732C2C2×#1171925211yescharacteristic
733C2C22×Q16×D1311yescharacteristic
734C2C2×#1171947311yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C4×C13×Q16C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×C4×Q16D13
hypocenterC13C2×#3104
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #13124873C2direct (N × H)
6. C2×#11718536C2semidirect
7. C2×#11718455C2semidirect
8. C2×#11718454C2semidirect
9. C2×#11718843C2semidirect
12. C2×C4×Dic52C2semidirect
13. C2×C4×#6107C2semidirect
14. C2×C4×#6107C2semidirect
16. C2×C4×C13×Q16C2semidirect
46. C4×C13×Q16C22semidirect
54. #11718843C22semidirect
62. C4×#6107C22semidirect
63. C4×#6107C22semidirect
70. #11718536C22semidirect
73. #11718455C22semidirect
74. #11718454C22semidirect
75. C4×Dic52C22semidirect
216. C2×C4×D13Q16semidirect
293. C2×C4×Q16D13semidirect
342. C4×D13C2×Q16semidirect
395. C4×Q16C2×D13semidirect
544. C2×C13#3104semidirect
645. C13C2×#3104semidirect
731. C2#13124873direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192832
C2×C4×Q8×D132
#131248732
C2×#117185452
C2×#117184702
C2×#117185362
C2×#117184552
C2×#117184542
C2×#117188432
C2×#117184692
C2×#117188472
C2×C4×Dic522
C2×C4×#61072
C2×#117183462
C2×C4×C13×Q162
C2×#310413