Finite Group Databasebeta

← C2×#13118812 #16030907

Subgroups — C2×#13118812 #16030907

Order 3328.

2486 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic
2#13118812C2116yesmaximal, direct product factor
3C2×#11718645C211yesmaximal, characteristic
4C2×#11718644C211yesmaximal, characteristic
5C2×#11718890C211yesmaximal, characteristic
6C2×#11718890C211yesmaximal, characteristic
7C2×#11718589C211yesmaximal, characteristic
8C2×#11718633C211yesmaximal, characteristic
9C2×#11718642C211yesmaximal, characteristic
10C2×#11718594C211yesmaximal, characteristic
11C2×#11718594C211yesmaximal, characteristic
12C2×#11718594C211yesmaximal, characteristic
13C2×#11718594C211yesmaximal, characteristic
14C2×#11718639C211yesmaximal, characteristic
15C2×C4×#6101C211yesmaximal, characteristic
16C22×C4×Q8×C13C211yesmaximal, characteristic
17C23×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13—28no—
19C2×C4×Q8×C13C2218yes—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×#6101C2211yescharacteristic
36C22×#6101C2211yescharacteristic
37C22×#6101C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40C2×#88143—28no—
41C2×#88143C2218yes—
42#11718890C2218yes—
43#11718890C2218yes—
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57C2×#88071C2211yescharacteristic
58#11718645C2218yes—
59#11718644C2218yes—
60#11718642C2218yes—
61#11718639C2218yes—
62#11718633C2218yes—
63#11718594C2218yes—
64#11718594C2218yes—
65#11718594C2218yes—
66#11718594C2218yes—
67C4×#6101C2218yes—
68#11718589C2218yes—
69C22×Q8×C13—24no—
70C22×Q8×C13—24no—
71C22×Q8×C13—24no—
72C22×Q8×C13C2314yes—
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C23×Dic13C2311yescharacteristic
88C4×Q8×C13—232no—
89C2×C13×C4⋊C4—24no—
90C2×C13×C4⋊C4—24no—
91C2×C13×C4⋊C4D418yes—
92C2×C13×C4⋊C4C2314yes—
93C2×C13×C4⋊C4C2314yes—
94C2×C13×C4⋊C4C2314yes—
95C2×C42×C13—24no—
96C2×C42×C13—24no—
97C2×C42×C13—24no—
98C2×C42×C13C2314yes—
99C2×C42×C13C2314yes—
100C2×C42×C13C2314yes—
101C2×C4⋊Dic13—24no—
102C2×C4⋊Dic13—24no—
103C2×C4⋊Dic13C2314yes—
104C2×C4⋊Dic13C2314yes—
105C2×#6101—24no—
106C2×#6101—24no—
107C2×#6101—24no—
108C2×#6101—24no—
109C2×#6101—24no—
110C2×#6101—24no—
111C2×#6101—24no—
112C2×#6101—24no—
113C2×#6101—24no—
114C2×#6101Q818yescomplemented
115C2×#6101C2314yes—
116C2×#6101C2314yes—
117C2×#6101C2314yes—
118C2×#6101C2314yes—
119C2×#6101C2314yes—
120C2×#6101C2314yes—
121C2×#6101C2314yes—
122C2×#6101C2314yes—
123C2×#6101C2314yes—
124C2×#6101C2314yes—
125C2×C4×Dic13—24no—
126C2×C4×Dic13—24no—
127C2×C4×Dic13C2314yes—
128C2×C4×Dic13C2314yes—
129#88143—232no—
130#88071C2314yes—
131#88071C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144C2×#2462—131nomaximal, Sylow
145C24×C13C2411yescharacteristic
146C2×Q8×C13—232no—
147C2×Q8×C13—28no—
148C2×Q8×C13—28no—
149C2×Q8×C13—28no—
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×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13C2×D414yes—
166C22×C4×C13C2×D414yes—
167C22×C4×C13C2×D414yes—
168C22×C4×C13C2×Q814yes—
169C22×C4×C13#4114yes—
170C22×C4×C13#4114yes—
171C22×C4×C13C2412yes—
172C22×C4×C13C2412yes—
173C22×C4×C13C2412yes—
174C22×C4×C13C2412yes—
175C22×C4×C13C2412yes—
176C22×C4×C13C2412yes—
177C22×C4×C13C2412yes—
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×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×Dic13C2×Q814yes—
200C22×Dic13C2×Q814yes—
201C22×Dic13#4114yes—
202C22×Dic13C2412yes—
203C22×Dic13C2412yes—
204C22×Dic13C2412yes—
205C22×Dic13C2412yes—
206C22×Dic13C2412yes—
207C22×Dic13C2412yes—
208C22×Dic13C2412yes—
209C22×Dic13C2412yes—
210C13×C4⋊C4—28no—
211C13×C4⋊C4—28no—
212C13×C4⋊C4C2×D4116yes—
213C42×C13—28no—
214C42×C13—28no—
215C42×C13—28no—
216C4⋊Dic13—28no—
217C4⋊Dic13—28no—
218#6101—28no—
219#6101—28no—
220#6101—28no—
221#6101—28no—
222#6101—28no—
223#6101—28no—
224#6101—28no—
225#6101—28no—
226#6101—28no—
227#6101C2×Q8116yescomplemented
228C4×Dic13—28no—
229C4×Dic13—28no—
230C22×#125—131no—
231C22×C4×Q8D1311yescharacteristic
232#2462—1316no—
233C2×#398—131no—
234C2×#398—131no—
235C2×#395—131no—
236C2×#395—131no—
237C2×#389—131no—
238C2×#389—131no—
239C2×#387—131no—
240C2×#387—131no—
241C2×#387—131no—
242C2×#387—131no—
243C2×#387—131no—
244C2×#387—131no—
245C2×C4×C4⋊C4—131no—
246C23×C13C22×D412yes—
247C23×C13C22×Q812yes—
248C23×C13C2×#4112yes—
249C23×C13C2×#4112yes—
250C23×C13C2×#4112yes—
251C23×C132−1+412yes—
252C23×C132−1+412yes—
253C23×C13C2511yescharacteristic
254Q8×C13—232no—
255C2×C4×C13—28no—
256C2×C4×C13—28no—
257C2×C4×C13—28no—
258C2×C4×C13—28no—
259C2×C4×C13—28no—
260C2×C4×C13—28no—
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—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—44no—
277C2×C4×C13C22×D414yes—
278C2×C4×C13C22×D414yes—
279C2×C4×C13C22×D414yes—
280C2×C4×C13C22×Q814yes—
281C2×C4×C13C2×#4114yes—
282C2×C4×C13C2×#4114yes—
283C2×Dic13—28no—
284C2×Dic13—28no—
285C2×Dic13—28no—
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—22no—
299C2×Dic13—22no—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—44no—
308C2×Dic13—44no—
309C2×Dic13—44no—
310C2×Dic13—44no—
311C2×Dic13—44no—
312C2×Dic13C22×Q814yes—
313C2×Dic13C22×Q814yes—
314C2×Dic13C2×#4114yes—
315C23×Q8C2×D1311yescharacteristic
316C2×#125—138no—
317C2×#125—268no—
318C2×C4×Q8—28no—
319C2×C4×Q8C2×D1318yes—
320C22×C4⋊C4—131no—
321C22×C4⋊C4—131no—
322C22×C4⋊C4—131no—
323C22×C4⋊C4—131no—
324C22×C4⋊C4—131no—
325C22×C4⋊C4—131no—
326C22×C4⋊C4—131no—
327C22×C4⋊C4—131no—
328C22×C4⋊C4—131no—
329C22×C4⋊C4—131no—
330C22×C4⋊C4—131no—
331C22×C4⋊C4—131no—
332C22×C4⋊C4C2×D1311yescharacteristic
333C22×C4⋊C4C2×D1311yescharacteristic
334C22×C4⋊C4C2×D1311yescharacteristic
335C22×C42—131no—
336C22×C42—131no—
337C22×C42C2×D1311yescharacteristic
338C22×C42C2×D1311yescharacteristic
339C22×C42C2×D1311yescharacteristic
340#398—138no—
341#398—138no—
342#395—138no—
343#395—138no—
344#389—138no—
345#389—138no—
346#387—138no—
347#387—138no—
348#387—138no—
349#387—138no—
350#387—138no—
351#387—138no—
352C4×C4⋊C4—138no—
353C2×#95—131no—
354C2×#95—131no—
355C2×#95—131no—
356C2×#95—131no—
357C2×#95—131no—
358C2×#95—131no—
359C2×#95—131no—
360C2×#95—131no—
361C2×#95—131no—
362C2×#95—131no—
363C2×#95—131no—
364C2×#95—131no—
365C2×#95—131no—
366C2×#95—131no—
367C22×C13#52514yes—
368C22×C13#53314yes—
369C22×C13#54114yes—
370C22×C13#54714yes—
371C22×C13D4×Q814yes—
372C22×C13#55214yes—
373C22×C13#55714yes—
374C22×C13C23×D411yescharacteristic
375C22×C13C23×Q811yescharacteristic
376C22×C13C22×#4111yescharacteristic
377C22×C13C22×#4111yescharacteristic
378C22×C13C22×#4111yescharacteristic
379C22×C13C2×2−1+411yescharacteristic
380C22×C13C2×2−1+411yescharacteristic
381C4×C13—24no—
382C4×C13—24no—
383C4×C13—24no—
384C4×C13—24no—
385C4×C13—24no—
386C4×C13—24no—
387C4×C13—42no—
388Dic13—24no—
389Dic13—24no—
390Dic13—24no—
391Dic13—42no—
392Dic13—42no—
393Dic13—42no—
394Dic13—42no—
395Dic13—42no—
396C22×Q8—24no—
397C22×Q8—24no—
398C22×Q8—24no—
399C22×Q8C22×D1314yes—
400C23×C4—131no—
401C23×C4—131no—
402C23×C4—131no—
403C23×C4—131no—
404C23×C4—131no—
405C23×C4—131no—
406C23×C4—131no—
407C23×C4—131no—
408C23×C4C22×D1311yescharacteristic
409C23×C4C22×D1311yescharacteristic
410C23×C4C22×D1311yescharacteristic
411C23×C4C22×D1311yescharacteristic
412C23×C4C22×D1311yescharacteristic
413C23×C4C22×D1311yescharacteristic
414C23×C4C22×D1311yescharacteristic
415#125—2632no—
416C4×Q8—232no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—138no—
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—134no—
427C2×C4⋊C4—134no—
428C2×C4⋊C4—134no—
429C2×C4⋊C4—134no—
430C2×C4⋊C4—134no—
431C2×C4⋊C4—134no—
432C2×C4⋊C4—264no—
433C2×C4⋊C4—264no—
434C2×C4⋊C4—264no—
435C2×C4⋊C4—264no—
436C2×C4⋊C4—264no—
437C2×C4⋊C4—264no—
438C2×C4⋊C4—264no—
439C2×C4⋊C4—264no—
440C2×C4⋊C4—264no—
441C2×C4⋊C4—264no—
442C2×C4⋊C4—264no—
443C2×C4⋊C4C22⋊D1318yes—
444C2×C4⋊C4C22×D1314yes—
445C2×C4⋊C4C22×D1314yes—
446C2×C4⋊C4C22×D1314yes—
447C2×C42—24no—
448C2×C42—24no—
449C2×C42—24no—
450C2×C42—134no—
451C2×C42—134no—
452C2×C42—264no—
453C2×C42—264no—
454C2×C42C22×D1314yes—
455C2×C42C22×D1314yes—
456C2×C42C22×D1314yes—
457#95—134no—
458#95—134no—
459#95—134no—
460#95—134no—
461#95—134no—
462#95—134no—
463#95—134no—
464#95—134no—
465#95—134no—
466#95—134no—
467#95—134no—
468#95—134no—
469#95—134no—
470#95—134no—
471C2×C13#246218yescomplemented
472C2×C13C2×#52511yescharacteristic
473C2×C13C2×#53311yescharacteristic
474C2×C13C2×#54111yescharacteristic
475C2×C13C2×#54711yescharacteristic
476C2×C13C2×D4×Q811yescharacteristic
477C2×C13C2×#55211yescharacteristic
478C2×C13C2×#55711yescharacteristic
479C24C23×D1311yescharacteristic
480C2×Q8—232no—
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—28no—
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—22no—
498C22×C4—22no—
499C22×C4—134no—
500C22×C4—134no—
501C22×C4—134no—
502C22×C4—132no—
503C22×C4—132no—
504C22×C4—132no—
505C22×C4—132no—
506C22×C4—132no—
507C22×C4—132no—
508C22×C4—132no—
509C22×C4—132no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4—262no—
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×C4—262no—
530C22×C4—262no—
531C22×C4#612714yes—
532C22×C4#612714yes—
533C22×C4Q8×D1314yes—
534C22×C4C2×C22⋊D1314yes—
535C22×C4C2×C22⋊D1314yes—
536C22×C4C2×C22⋊D1314yes—
537C22×C4C23×D1312yes—
538C22×C4C23×D1312yes—
539C22×C4C23×D1312yes—
540C22×C4C23×D1312yes—
541C22×C4C23×D1312yes—
542C22×C4C23×D1312yes—
543C22×C4C23×D1312yes—
544C4⋊C4—28no—
545C4⋊C4—28no—
546C4⋊C4—1316no—
547C4⋊C4—268no—
548C4⋊C4—268no—
549C4⋊C4—268no—
550C4⋊C4—268no—
551C4⋊C4—268no—
552C4⋊C4—268no—
553C4⋊C4—268no—
554C4⋊C4—268no—
555C4⋊C4—268no—
556C4⋊C4—268no—
557C4⋊C4—268no—
558C4⋊C4C2×C22⋊D13116yes—
559C42—28no—
560C42—28no—
561C42—28no—
562C42—268no—
563C42—268no—
564C13C2×#246211yescharacteristic, complemented, Sylow
565C23C2×#612712yes—
566C23C2×#612712yes—
567C23C2×Q8×D1312yes—
568C23#8825412yes—
569C23#41×D1312yes—
570C23#8825712yes—
571C23C22×C22⋊D1312yes—
572C23C24×D1311yescharacteristic
573Q8—232no—
574C2×C4—28no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—28no—
578C2×C4—28no—
579C2×C4—28no—
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—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—44no—
596C2×C4—134no—
597C2×C4—134no—
598C2×C4—134no—
599C2×C4—268no—
600C2×C4—268no—
601C2×C4—268no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—262no—
606C2×C4—262no—
607C2×C4—262no—
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×C4—524no—
627C2×C4—524no—
628C2×C4C2×#612714yes—
629C2×C4C2×#612714yes—
630C2×C4C2×Q8×D1314yes—
631C2×C4C22×C22⋊D1314yes—
632C2×C4C22×C22⋊D1314yes—
633C2×C4C22×C22⋊D1314yes—
634C22#1171927214yes—
635C22#1171928314yes—
636C22#1171928614yes—
637C22#1171928814yes—
638C22#1171949614yes—
639C22Q8×C22⋊D1314yes—
640C22#1171952914yes—
641C22C22×#612711yescharacteristic
642C22C22×#612711yescharacteristic
643C22C22×Q8×D1311yescharacteristic
644C22C2×#8825411yescharacteristic
645C22C2×#41×D1311yescharacteristic
646C22C2×#8825711yescharacteristic
647C22C23×C22⋊D1311yescharacteristic
648C4—24no—
649C4—24no—
650C4—24no—
651C4—24no—
652C4—24no—
653C4—24no—
654C4—42no—
655C4—264no—
656C4—264no—
657C4—264no—
658C4—522no—
659C4—522no—
660C4—522no—
661C4—522no—
662C4—522no—
663C2#1311881218yesdirect product factor
664C2C2×#1171949611yescharacteristic
665C2C2×#1171928311yescharacteristic
666C2C2×#1171928811yescharacteristic
667C2C2×#1171952911yescharacteristic
668C2C2×Q8×C22⋊D1311yescharacteristic
669C2C2×#1171928611yescharacteristic
670C2C2×#1171927211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C4×Q8×C13C2
socle, prime radicalC24×C13C24
hypercenterC22×C4×Q8D13
hypocenterC13C2×#2462
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13118812C2direct (N × H)
114. C2×#6101Q8semidirect
227. #6101C2×Q8semidirect
471. C2×C13#2462semidirect
564. C13C2×#2462semidirect
663. C2#13118812direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881432
#131188122
C2×#117186452
C2×#117186442
C2×#117188902
C2×#117185892
C2×#117186332
C2×#117186422
C2×#117185942
C2×#117186392
C2×C4×#61012
C22×C4×Q8×C132
C2×#246213