Finite Group Databasebeta

← C2×#13117790 #16022274

Subgroups — C2×#13117790 #16022274

Order 3328.

2638 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic
2#13117790C2116yesmaximal, direct product factor
3C2×#11718307C211yesmaximal, characteristic
4C2×#11718307C211yesmaximal, characteristic
5C2×#11718316C211yesmaximal, characteristic
6C2×#11718642C211yesmaximal, characteristic
7C2×#11718639C211yesmaximal, characteristic
8C2×#11718637C211yesmaximal, characteristic
9C2×#11718311C211yesmaximal, characteristic
10C2×#11718311C211yesmaximal, characteristic
11C2×C4×#6101C211yesmaximal, characteristic
12C2×C4×#6101C211yesmaximal, characteristic
13C2×#11718310C211yesmaximal, characteristic
14C2×#11718310C211yesmaximal, characteristic
15C2×#11718310C211yesmaximal, characteristic
16C2×C13×#387C211yesmaximal, characteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6101C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C2×#88141C4116yescomplemented
39C2×#88141C2218yes—
40C13×#387C2218yes—
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718642C2218yes—
56#11718639C2218yes—
57#11718637C2218yes—
58C4×#6101C2218yes—
59C4×#6101C2218yes—
60#11718316C2218yes—
61#11718311C2218yes—
62#11718311C2218yes—
63#11718310C2218yes—
64#11718310C2218yes—
65#11718310C2218yes—
66#11718307C2218yes—
67#11718307C2218yes—
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C22×Dic26—24no—
84C22×Dic26—24no—
85C22×Dic26C2×C418yes—
86C22×Dic26C2314yes—
87C2×C13×C4⋊C4—42no—
88C2×C13×C4⋊C4C2×C418yes—
89C2×C13×C4⋊C4C2314yes—
90C2×C13×C4⋊C4C2314yes—
91C2×C42×C13—42no—
92C2×C42×C13C2314yes—
93C2×C4⋊Dic13—42no—
94C2×C4⋊Dic13C2314yes—
95C2×#6101—24no—
96C2×#6101—24no—
97C2×#6101—24no—
98C2×#6101—24no—
99C2×#6101—24no—
100C2×#6101C2×C418yes—
101C2×#6101C2×C418yes—
102C2×#6101Q818yescomplemented
103C2×#6101C2314yes—
104C2×#6101C2314yes—
105C2×#6101C2314yes—
106C2×#6101C2314yes—
107C2×#6101C2314yes—
108C2×#6101C2314yes—
109C2×#6101C2314yes—
110C2×#6101C2314yes—
111C2×C4×Dic13—24no—
112C2×C4×Dic13—24no—
113C2×C4×Dic13—42no—
114C2×C4×Dic13—42no—
115C2×C4×Dic13—42no—
116C2×C4×Dic13C2×C418yes—
117C2×C4×Dic13C2×C418yes—
118C2×C4×Dic13C2×C418yes—
119C2×C4×Dic13C2314yes—
120C2×C4×Dic13C2314yes—
121C2×C4×Dic13C2314yes—
122C2×C4×Dic13C2314yes—
123C2×C4×Dic13C2314yes—
124C2×C4×Dic13C2314yes—
125C2×C4×Dic13C2314yes—
126C2×C4×Dic13C2314yes—
127#88141C2×C4164yescomplemented
128C13×#95C2314yes—
129C13×#95C2314yes—
130C13×#95C2314yes—
131C13×#95C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142C2×#2355—131nomaximal, Sylow
143C24×C13C2411yescharacteristic
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13C22×C414yes—
162C22×C4×C13C22×C414yes—
163C22×C4×C13C22×C414yes—
164C22×C4×C13C2×Q814yes—
165C22×C4×C13C2412yes—
166C22×C4×C13C2412yes—
167C22×C4×C13C2412yes—
168C22×C4×C13C2412yes—
169C22×C4×C13C2412yes—
170C22×C4×C13C2412yes—
171C22×C4×C13C2412yes—
172C22×Dic13—22no—
173C22×Dic13—22no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13C22×C414yes—
188C22×Dic13C22×C414yes—
189C22×Dic13C22×C414yes—
190C22×Dic13C22×C414yes—
191C22×Dic13C2×Q814yes—
192C22×Dic13C2×Q814yes—
193C22×Dic13#4114yes—
194C22×Dic13#4114yes—
195C22×Dic13#4114yes—
196C22×Dic13C2412yes—
197C22×Dic13C2412yes—
198C22×Dic13C2412yes—
199C22×Dic13C2412yes—
200C22×Dic13C2412yes—
201C22×Dic13C2412yes—
202C22×Dic13C2412yes—
203C22×Dic13C2412yes—
204C2×Dic26—232no—
205C2×Dic26—28no—
206C2×Dic26—28no—
207C2×Dic26C22×C4116yes—
208C13×C4⋊C4—44no—
209C13×C4⋊C4C22×C4116yes—
210C42×C13—44no—
211C4⋊Dic13—44no—
212#6101—28no—
213#6101—28no—
214#6101—28no—
215#6101—28no—
216#6101—28no—
217#6101C22×C4116yes—
218#6101C22×C4116yes—
219#6101C2×Q8116yescomplemented
220C4×Dic13—28no—
221C4×Dic13—28no—
222C4×Dic13—44no—
223C4×Dic13—44no—
224C4×Dic13—44no—
225C4×Dic13C22×C4116yes—
226C4×Dic13C22×C4116yes—
227C4×Dic13C22×C4116yes—
228C22×C4×Q8—131no—
229#2355—1316no—
230C2×#391—131no—
231C2×#391—131no—
232C2×#387—131no—
233C2×#387—131no—
234C2×#387—131no—
235C2×#387D1311yescharacteristic
236C2×#384—131no—
237C2×#382—131no—
238C2×#382—131no—
239C2×C4×C4⋊C4—131no—
240C2×C4×C4⋊C4—131no—
241C2×C4×C4⋊C4—131no—
242C2×C4×C4⋊C4—131no—
243C2×C4×C4⋊C4—131no—
244C23×C13C23×C412yes—
245C23×C13C22×Q812yes—
246C23×C13C2×#4112yes—
247C23×C13C2×#4112yes—
248C23×C13C2×#4112yes—
249C23×C13H(5,𝔽2)12yes—
250C23×C132−1+412yes—
251C23×C13C2511yescharacteristic
252C2×C4×C13—28no—
253C2×C4×C13—28no—
254C2×C4×C13—28no—
255C2×C4×C13—28no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—44no—
274C2×C4×C13—44no—
275C2×C4×C13—44no—
276C2×C4×C13C23×C414yes—
277C2×C4×C13C23×C414yes—
278C2×C4×C13C23×C414yes—
279C2×C4×C13C22×Q814yes—
280C2×Dic13—28no—
281C2×Dic13—28no—
282C2×Dic13—28no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—22no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—22no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—22no—
292C2×Dic13—22no—
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—22no—
296C2×Dic13—22no—
297C2×Dic13—22no—
298C2×Dic13—44no—
299C2×Dic13—44no—
300C2×Dic13—44no—
301C2×Dic13#117116yes—
302C2×Dic13C4×Q8116yes—
303C2×Dic13C23×C414yes—
304C2×Dic13C23×C414yes—
305C2×Dic13C23×C414yes—
306C2×Dic13C23×C414yes—
307C2×Dic13C22×Q814yes—
308C2×Dic13C22×Q814yes—
309C2×Dic13C2×#4114yes—
310C2×Dic13C2×#4114yes—
311C2×Dic13C2×#4114yes—
312Dic26—232no—
313C23×Q8—131no—
314C2×C4×Q8—1316no—
315C2×C4×Q8—138no—
316C22×C4⋊C4—131no—
317C22×C4⋊C4—131no—
318C22×C4⋊C4—131no—
319C22×C4⋊C4—131no—
320C22×C4⋊C4—131no—
321C22×C4⋊C4—131no—
322C22×C4⋊C4—131no—
323C22×C4⋊C4—131no—
324C22×C4⋊C4—131no—
325C22×C4⋊C4C2×D1311yescharacteristic
326C22×C4⋊C4C2×D1311yescharacteristic
327C22×C42—131no—
328C22×C42—131no—
329C22×C42—131no—
330C22×C42—131no—
331C22×C42—131no—
332C22×C42—131no—
333C22×C42—131no—
334C22×C42—131no—
335C22×C42C2×D1311yescharacteristic
336#391—138no—
337#391—138no—
338#387—138no—
339#387—138no—
340#387—138no—
341#387C2×D1318yes—
342#384—138no—
343#382—138no—
344#382—138no—
345C4×C4⋊C4—138no—
346C4×C4⋊C4—138no—
347C4×C4⋊C4—138no—
348C4×C4⋊C4—138no—
349C4×C4⋊C4—138no—
350C2×#95—131no—
351C2×#95—131no—
352C2×#95—131no—
353C2×#95—131no—
354C2×#95—131no—
355C2×#95—131no—
356C2×#95—131no—
357C2×#95—131no—
358C2×#95—131no—
359C2×#95—131no—
360C2×#95C2×D1311yescharacteristic
361C2×#95C2×D1311yescharacteristic
362C2×#95C2×D1311yescharacteristic
363C2×#95C2×D1311yescharacteristic
364C22×C13C2×#11714yes—
365C22×C13C2×C4×Q814yes—
366C22×C13#52014yes—
367C22×C13#55414yes—
368C22×C13#55614yes—
369C22×C13#55714yes—
370C22×C13#55914yes—
371C22×C13C24×C411yescharacteristic
372C22×C13C23×Q811yescharacteristic
373C22×C13C22×#4111yescharacteristic
374C22×C13C22×#4111yescharacteristic
375C22×C13C22×#4111yescharacteristic
376C22×C13C2×H(5,𝔽2)11yescharacteristic
377C22×C13C2×2−1+411yescharacteristic
378C4×C13—24no—
379C4×C13—24no—
380C4×C13—24no—
381C4×C13—24no—
382C4×C13—42no—
383C4×C13—42no—
384C4×C13—42no—
385Dic13—24no—
386Dic13—24no—
387Dic13—24no—
388Dic13—42no—
389Dic13—42no—
390Dic13—42no—
391Dic13C2×#11718yes—
392Dic13C2×C4×Q818yes—
393C22×Q8—138no—
394C22×Q8—134no—
395C22×Q8—264no—
396C22×Q8—264no—
397C23×C4—131no—
398C23×C4—131no—
399C23×C4—131no—
400C23×C4—131no—
401C23×C4—131no—
402C23×C4—131no—
403C23×C4—131no—
404C23×C4—131no—
405C23×C4C22×D1311yescharacteristic
406C23×C4C22×D1311yescharacteristic
407C23×C4C22×D1311yescharacteristic
408C23×C4C22×D1311yescharacteristic
409C23×C4C22×D1311yescharacteristic
410C23×C4C22×D1311yescharacteristic
411C23×C4C22×D1311yescharacteristic
412C4×Q8—1364no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—138no—
415C2×C4⋊C4—138no—
416C2×C4⋊C4—138no—
417C2×C4⋊C4—134no—
418C2×C4⋊C4—134no—
419C2×C4⋊C4—134no—
420C2×C4⋊C4—134no—
421C2×C4⋊C4—134no—
422C2×C4⋊C4—134no—
423C2×C4⋊C4—134no—
424C2×C4⋊C4—134no—
425C2×C4⋊C4—134no—
426C2×C4⋊C4—264no—
427C2×C4⋊C4—264no—
428C2×C4⋊C4—264no—
429C2×C4⋊C4—264no—
430C2×C4⋊C4—264no—
431C2×C4⋊C4—522no—
432C2×C4⋊C4C4×D1318yes—
433C2×C4⋊C4C22×D1314yes—
434C2×C4⋊C4C22×D1314yes—
435C2×C42—42no—
436C2×C42—138no—
437C2×C42—138no—
438C2×C42—138no—
439C2×C42—134no—
440C2×C42—134no—
441C2×C42—134no—
442C2×C42—134no—
443C2×C42—134no—
444C2×C42—134no—
445C2×C42—134no—
446C2×C42—134no—
447C2×C42—264no—
448C2×C42—264no—
449C2×C42—522no—
450C2×C42—522no—
451C2×C42—522no—
452C2×C42C22×D1314yes—
453#95—134no—
454#95—134no—
455#95—134no—
456#95—134no—
457#95—134no—
458#95—134no—
459#95—134no—
460#95—134no—
461#95—134no—
462#95—134no—
463#95C22×D1314yes—
464#95C22×D1314yes—
465#95C22×D1314yes—
466#95C22×D1314yes—
467C2×C13#235518yescomplemented
468C2×C13C22×#11711yescharacteristic
469C2×C13C22×C4×Q811yescharacteristic
470C2×C13C2×#52011yescharacteristic
471C2×C13C2×#55411yescharacteristic
472C2×C13C2×#55611yescharacteristic
473C2×C13C2×#55711yescharacteristic
474C2×C13C2×#55911yescharacteristic
475C24C23×D1311yescharacteristic
476C2×Q8—1316no—
477C2×Q8—2632no—
478C2×Q8—268no—
479C2×Q8—268no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—134no—
498C22×C4—134no—
499C22×C4—134no—
500C22×C4—134no—
501C22×C4—134no—
502C22×C4—134no—
503C22×C4—132no—
504C22×C4—132no—
505C22×C4—134no—
506C22×C4—134no—
507C22×C4—134no—
508C22×C4—132no—
509C22×C4—132no—
510C22×C4—132no—
511C22×C4—132no—
512C22×C4—132no—
513C22×C4—132no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—262no—
517C22×C4—262no—
518C22×C4—262no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4—262no—
522C22×C4—262no—
523C22×C4—262no—
524C22×C4—262no—
525C22×C4—262no—
526C22×C4—262no—
527C22×C4—262no—
528C22×C4—262no—
529C22×C4C2×C4×D1314yes—
530C22×C4C2×C4×D1314yes—
531C22×C4C2×C4×D1314yes—
532C22×C4Q8×D1314yes—
533C22×C4C23×D1312yes—
534C22×C4C23×D1312yes—
535C22×C4C23×D1312yes—
536C22×C4C23×D1312yes—
537C22×C4C23×D1312yes—
538C22×C4C23×D1312yes—
539C22×C4C23×D1312yes—
540C4⋊C4—44no—
541C4⋊C4—1316no—
542C4⋊C4—1316no—
543C4⋊C4—1316no—
544C4⋊C4—268no—
545C4⋊C4—268no—
546C4⋊C4—268no—
547C4⋊C4—268no—
548C4⋊C4—268no—
549C4⋊C4—524no—
550C4⋊C4C2×C4×D13116yes—
551C42—44no—
552C42—1316no—
553C42—1316no—
554C42—1316no—
555C42—268no—
556C42—268no—
557C42—524no—
558C42—524no—
559C42—524no—
560C13C2×#235511yescharacteristic, complemented, Sylow
561C23C22×C4×D1312yes—
562C23#8825112yes—
563C23C2×Q8×D1312yes—
564C23#41×D1312yes—
565C23#41×D1312yes—
566C23#41×D1312yes—
567C23#8825712yes—
568C23C24×D1311yescharacteristic
569Q8—2632no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—28no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—1316no—
595C2×C4—1316no—
596C2×C4—134no—
597C2×C4—134no—
598C2×C4—134no—
599C2×C4—134no—
600C2×C4—134no—
601C2×C4—134no—
602C2×C4—134no—
603C2×C4—134no—
604C2×C4—134no—
605C2×C4—268no—
606C2×C4—268no—
607C2×C4—268no—
608C2×C4—262no—
609C2×C4—262no—
610C2×C4—262no—
611C2×C4—262no—
612C2×C4—262no—
613C2×C4—262no—
614C2×C4—262no—
615C2×C4—262no—
616C2×C4—262no—
617C2×C4—262no—
618C2×C4—262no—
619C2×C4—262no—
620C2×C4—262no—
621C2×C4—262no—
622C2×C4—262no—
623C2×C4—524no—
624C2×C4—524no—
625C2×C4—524no—
626C2×C4C22×C4×D1314yes—
627C2×C4C22×C4×D1314yes—
628C2×C4C22×C4×D1314yes—
629C2×C4C2×Q8×D1314yes—
630C22D13×#11714yes—
631C22#1171925114yes—
632C22C4×Q8×D1314yes—
633C22#1171934114yes—
634C22#1171936914yes—
635C22#1171939014yes—
636C22#1171940714yes—
637C22C23×C4×D1311yescharacteristic
638C22C2×#8825111yescharacteristic
639C22C22×Q8×D1311yescharacteristic
640C22C2×#41×D1311yescharacteristic
641C22C2×#41×D1311yescharacteristic
642C22C2×#41×D1311yescharacteristic
643C22C2×#8825711yescharacteristic
644C4—24no—
645C4—24no—
646C4—24no—
647C4—24no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—138no—
652C4—138no—
653C4—264no—
654C4—264no—
655C4—264no—
656C4—522no—
657C4—522no—
658C4—522no—
659C2#1311779018yesdirect product factor
660C2C2×D13×#11711yescharacteristic
661C2C2×C4×Q8×D1311yescharacteristic
662C2C2×#1171925111yescharacteristic
663C2C2×#1171934111yescharacteristic
664C2C2×#1171940711yescharacteristic
665C2C2×#1171939011yescharacteristic
666C2C2×#1171936911yescharacteristic
subgroupG/H
centerC24C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC2×C13×#387C2
socle, prime radicalC24×C13C24
cosocleC23×C13C25
hypercenterC2×#387D13
hypocenterC13C2×#2355
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #13117790C2direct (N × H)
38. C2×#88141C4semidirect
102. C2×#6101Q8semidirect
127. #88141C2×C4semidirect
219. #6101C2×Q8semidirect
467. C2×C13#2355semidirect
560. C13C2×#2355semidirect
659. C2#13117790direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881412
#131177902
C2×#117183072
C2×#117183162
C2×#117186422
C2×#117186392
C2×#117186372
C2×#117183112
C2×C4×#61012
C2×#117183102
C2×C13×#3872
C2×#235513