Finite Group Databasebeta

← C2×#13118437 #16030940

Subgroups — C2×#13118437 #16030940

Order 3328.

3246 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88198C211yesmaximal, characteristic, complemented
2C22×#88178C211yesmaximal, characteristic
3C22×Q8×Dic13C211yesmaximal, characteristic, complemented
4#13118437C2116yesmaximal, direct product factor
5C2×#11718645C212yesmaximal, complemented
6C2×#11718609C212yesmaximal
7C2×#11718635C211yesmaximal, characteristic, complemented
8C2×#11718634C211yesmaximal, characteristic, complemented
9C2×#11718633C212yesmaximal, complemented
10C2×#11718606C212yesmaximal
11C2×C4×C22⋊Dic13C211yesmaximal, characteristic
12C22×C13×C22⋊Q8C211yesmaximal, characteristic
13C23×Q8×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C23×Dic26C2211yescharacteristic
16C2×C13×C22⋊Q8—28no—
17C2×C13×C22⋊Q8C2218yes—
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2212yes—
21C22×C22⋊Dic13C2212yes—
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C2×Q8×Dic13—28no—
25C2×Q8×Dic13C2218yescomplemented
26C2×#88198—28no—
27C2×#88198C2218yescomplemented
28C22×C4⋊Dic13C2212yes—
29C22×C4⋊Dic13C2211yescharacteristic
30C2×#88178—28no—
31C2×#88178C2218yes—
32C22×#6101C2212yes—
33C22×#6101C2212yes—
34C22×#6101C2212yes—
35C22×#6101C2212yes—
36C22×C4×Dic13C2212yes—
37C22×C4×Dic13C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C4×C22⋊Dic13C2218yes—
40C2×#88071C2212yes—
41C2×#88071C2212yes—
42C2×#88071C2211yescharacteristic
43C2×#88071C2212yes—
44C2×#88071C2211yescharacteristic
45#11718645C22116yescomplemented
46#11718635C2218yescomplemented
47#11718634C2218yescomplemented
48#11718633C22116yescomplemented
49#11718609C22116yes—
50#11718606C22116yes—
51C25×C13C2311yescharacteristic
52C22×Q8×C13—24no—
53C22×Q8×C13—24no—
54C22×Q8×C13D418yes—
55C22×Q8×C13C2314yes—
56C23×C4×C13—24no—
57C23×C4×C13—24no—
58C23×C4×C13—24no—
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2312yes—
61C23×C4×C13C2314yes—
62C23×C4×C13C2312yes—
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2312yes—
66C23×Dic13C2312yes—
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C22×Dic26—24no—
71C22×Dic26—24no—
72C22×Dic26—24no—
73C22×Dic26C2314yes—
74C13×C22⋊Q8—232no—
75C2×C13×C4⋊C4—24no—
76C2×C13×C4⋊C4—28no—
77C2×C13×C4⋊C4C2318yes—
78C2×C13×C4⋊C4C2314yes—
79C2×C13×C22⋊C4—28no—
80C2×C13×C22⋊C4C2318yes—
81C2×C22⋊Dic13—28no—
82C2×C22⋊Dic13—24no—
83C2×C22⋊Dic13Q818yescomplemented
84C2×C22⋊Dic13C2318yes—
85C2×C22⋊Dic13C2314yes—
86C2×C22⋊Dic13C2314yes—
87Q8×Dic13—232no—
88#88198—232no—
89C2×C4⋊Dic13—28no—
90C2×C4⋊Dic13D418yes—
91C2×C4⋊Dic13C2318yes—
92C2×C4⋊Dic13C2314yes—
93#88178—232no—
94C2×#6101—28no—
95C2×#6101—28no—
96C2×#6101—28no—
97C2×#6101—28no—
98C2×#6101C2318yes—
99C2×#6101C2318yes—
100C2×#6101C2318yes—
101C2×#6101C2318yes—
102C2×C4×Dic13—24no—
103C2×C4×Dic13—24no—
104C2×C4×Dic13—28no—
105C2×C4×Dic13C2314yes—
106C2×C4×Dic13C2318yes—
107C2×C4×Dic13C2314yes—
108#88071C2318yes—
109#88071C2318yes—
110#88071C2318yes—
111#88071C2314yes—
112#88071C2314yes—
113C2×#2429—131nomaximal, Sylow
114C24×C13—22no—
115C24×C13—22no—
116C24×C13—22no—
117C24×C13—22no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13C2×Q814yes—
121C24×C13C2412yes—
122C24×C13C2411yescharacteristic
123C2×Q8×C13—232no—
124C2×Q8×C13—28no—
125C2×Q8×C13—28no—
126C2×Q8×C13C2×D4116yes—
127C22×C4×C13—24no—
128C22×C4×C13—24no—
129C22×C4×C13—22no—
130C22×C4×C13—24no—
131C22×C4×C13—22no—
132C22×C4×C13—24no—
133C22×C4×C13—22no—
134C22×C4×C13—24no—
135C22×C4×C13—28no—
136C22×C4×C13—28no—
137C22×C4×C13—28no—
138C22×C4×C13—416no—
139C22×C4×C13C2×D414yes—
140C22×C4×C13C2×D418yes—
141C22×C4×C13C2×D414yes—
142C22×C4×C13#4114yes—
143C22×C4×C13C2414yes—
144C22×C4×C13C2412yes—
145C22×C4×C13C2414yes—
146C22×C4×C13C2412yes—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—24no—
151C22×Dic13—24no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—24no—
157C22×Dic13—24no—
158C22×Dic13—22no—
159C22×Dic13—24no—
160C22×Dic13—22no—
161C22×Dic13C2×D418yes—
162C22×Dic13C2×Q814yes—
163C22×Dic13C2×Q814yes—
164C22×Dic13#4114yes—
165C22×Dic13C2412yes—
166C22×Dic13C2414yes—
167C22×Dic13C2414yes—
168C22×Dic13C2412yes—
169C22×Dic13C2412yes—
170C22×Dic13C2412yes—
171C2×Dic26—28no—
172C2×Dic26—28no—
173C2×Dic26—28no—
174C2×Dic26—416no—
175C13×C4⋊C4—28no—
176C13×C4⋊C4—216no—
177C13×C22⋊C4—216no—
178C22⋊Dic13—216no—
179C22⋊Dic13—28no—
180C22⋊Dic13C2×Q8116yescomplemented
181C4⋊Dic13—216no—
182C4⋊Dic13C2×D4116yes—
183#6101—216no—
184#6101—216no—
185#6101—216no—
186#6101—216no—
187C4×Dic13—28no—
188C4×Dic13—28no—
189C4×Dic13—216no—
190C22×C4⋊Q8—131no—
191C22×C22⋊Q8—131no—
192C22×C22⋊Q8D1311yescharacteristic
193C22×C4×Q8—131no—
194#2429—1316no—
195C2×#398—132no—
196C2×#396—132no—
197C2×#391—131no—
198C2×#389—132no—
199C2×#389—131no—
200C2×#388—132no—
201C2×C4×C22⋊C4—131no—
202C23×C13—28no—
203C23×C13—28no—
204C23×C13—28no—
205C23×C13—22no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13—44no—
212C23×C13—44no—
213C23×C13—44no—
214C23×C13—44no—
215C23×C13C22×D412yes—
216C23×C13C22×D412yes—
217C23×C13C22×Q814yes—
218C23×C13C22×Q812yes—
219C23×C13C2×#4112yes—
220C23×C13C2×#4112yes—
221C23×C132−1+412yes—
222C23×C132−1+412yes—
223C23×C13C2511yescharacteristic
224Q8×C13—232no—
225C2×C4×C13—216no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—22no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—24no—
232C2×C4×C13—22no—
233C2×C4×C13—24no—
234C2×C4×C13—44no—
235C2×C4×C13—48no—
236C2×C4×C13—416no—
237C2×C4×C13#121116yes—
238C2×C4×C13C22×D418yes—
239C2×C4×C13C22×D414yes—
240C2×C4×C13C22×D414yes—
241C2×C4×C13C2×#4114yes—
242C2×Dic13—216no—
243C2×Dic13—28no—
244C2×Dic13—28no—
245C2×Dic13—28no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—22no—
258C2×Dic13—24no—
259C2×Dic13—22no—
260C2×Dic13—48no—
261C2×Dic13—44no—
262C2×Dic13C22×D418yes—
263C2×Dic13C22×Q814yes—
264C2×Dic13C22×Q814yes—
265C2×Dic13C2×#4114yes—
266Dic26—416no—
267C23×Q8—131no—
268C23×Q8C2×D1311yescharacteristic
269C24×C4C2×D1311yescharacteristic
270C2×C4⋊Q8—138no—
271C2×C4⋊Q8—268no—
272C2×C22⋊Q8—28no—
273C2×C22⋊Q8—138no—
274C2×C22⋊Q8—268no—
275C2×C22⋊Q8C2×D1318yes—
276C2×C4×Q8—138no—
277C2×C4×Q8—268no—
278C22×C4⋊C4—131no—
279C22×C4⋊C4—132no—
280C22×C4⋊C4—132no—
281C22×C4⋊C4—132no—
282C22×C4⋊C4—132no—
283C22×C4⋊C4—132no—
284C22×C4⋊C4C2×D1312yes—
285C22×C4⋊C4C2×D1311yescharacteristic
286C22×C22⋊C4—131no—
287C22×C22⋊C4—131no—
288C22×C22⋊C4—132no—
289C22×C22⋊C4C2×D1312yes—
290C22×C42—131no—
291C22×C42—132no—
292C22×C42—131no—
293#398—1316no—
294#396—1316no—
295#391—138no—
296#389—1316no—
297#389—138no—
298#388—1316no—
299C4×C22⋊C4—138no—
300C2×#95—132no—
301C2×#95—131no—
302C2×#95—132no—
303C2×#95—131no—
304C2×#95—132no—
305C22×C13—24no—
306C22×C13—24no—
307C22×C13—24no—
308C22×C13—42no—
309C22×C13—416no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—42no—
313C22×C13C2×#12114yes—
314C22×C13#53314yes—
315C22×C13#54114yes—
316C22×C13#54714yes—
317C22×C13#54814yes—
318C22×C13D4×Q814yes—
319C22×C13D4×Q814yes—
320C22×C13C23×D411yescharacteristic
321C22×C13C23×D411yescharacteristic
322C22×C13C23×Q811yescharacteristic
323C22×C13C22×#4111yescharacteristic
324C22×C13C22×#4111yescharacteristic
325C22×C13C2×2−1+411yescharacteristic
326C22×C13C2×2−1+411yescharacteristic
327C4×C13—28no—
328C4×C13—42no—
329C4×C13—44no—
330C4×C13C2×#12118yes—
331Dic13—28no—
332Dic13—24no—
333Dic13—24no—
334Dic13—24no—
335Dic13—44no—
336Dic13—42no—
337C25C22×D1311yescharacteristic
338C22×Q8—24no—
339C22×Q8—24no—
340C22×Q8—134no—
341C22×Q8—264no—
342C22×Q8—264no—
343C22×Q8—264no—
344C22×Q8C22⋊D1318yes—
345C22×Q8C22×D1314yes—
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—132no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—131no—
353C23×C4—132no—
354C23×C4—131no—
355C23×C4C22×D1314yes—
356C23×C4C22×D1312yes—
357C23×C4C22×D1311yescharacteristic
358C23×C4C22×D1312yes—
359C23×C4C22×D1311yescharacteristic
360C4⋊Q8—2632no—
361C22⋊Q8—232no—
362C22⋊Q8—2632no—
363C4×Q8—2632no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—138no—
367C2×C4⋊C4—134no—
368C2×C4⋊C4—138no—
369C2×C4⋊C4—138no—
370C2×C4⋊C4—138no—
371C2×C4⋊C4—138no—
372C2×C4⋊C4—138no—
373C2×C4⋊C4—268no—
374C2×C4⋊C4—268no—
375C2×C4⋊C4—268no—
376C2×C4⋊C4—268no—
377C2×C4⋊C4—268no—
378C2×C4⋊C4C22×D1314yes—
379C2×C4⋊C4C22×D1318yes—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—138no—
382C2×C22⋊C4—134no—
383C2×C22⋊C4—138no—
384C2×C22⋊C4—134no—
385C2×C22⋊C4—268no—
386C2×C22⋊C4—264no—
387C2×C22⋊C4C22×D1318yes—
388C2×C42—134no—
389C2×C42—138no—
390C2×C42—134no—
391C2×C42—268no—
392C2×C42—264no—
393C2×C42—264no—
394#95—134no—
395#95—134no—
396#95—138no—
397#95—138no—
398#95—138no—
399C2×C13—44no—
400C2×C13#242918yescomplemented
401C2×C13C22×#12111yescharacteristic
402C2×C13C2×#53311yescharacteristic
403C2×C13C2×#54111yescharacteristic
404C2×C13C2×#54711yescharacteristic
405C2×C13C2×#54811yescharacteristic
406C2×C13C2×D4×Q811yescharacteristic
407C2×C13C2×D4×Q811yescharacteristic
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24Q8×D1314yes—
415C24C23×D1312yes—
416C24C23×D1311yescharacteristic
417C2×Q8—232no—
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—268no—
421C2×Q8—268no—
422C2×Q8—268no—
423C2×Q8—5216no—
424C2×Q8C2×C22⋊D13116yes—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—416no—
437C22×C4—138no—
438C22×C4—134no—
439C22×C4—134no—
440C22×C4—134no—
441C22×C4—132no—
442C22×C4—132no—
443C22×C4—134no—
444C22×C4—132no—
445C22×C4—132no—
446C22×C4—134no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—264no—
450C22×C4—264no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—264no—
457C22×C4—264no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—264no—
461C22×C4D4×D1314yes—
462C22×C4#612914yes—
463C22×C4C2×C22⋊D1318yes—
464C22×C4C2×C22⋊D1314yes—
465C22×C4C23×D1314yes—
466C22×C4C23×D1312yes—
467C22×C4C23×D1314yes—
468C22×C4C23×D1312yes—
469C4⋊C4—28no—
470C4⋊C4—216no—
471C4⋊C4—1316no—
472C4⋊C4—2616no—
473C4⋊C4—2616no—
474C4⋊C4—2616no—
475C4⋊C4—2616no—
476C4⋊C4—2616no—
477C22⋊C4—216no—
478C22⋊C4—1316no—
479C22⋊C4—2616no—
480C22⋊C4—268no—
481C42—2616no—
482C42—268no—
483C42—268no—
484C13C2×#242911yescharacteristic, complemented, Sylow
485C23—28no—
486C23—28no—
487C23—28no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23C2×D4×D1312yes—
499C23C2×#612912yes—
500C23C2×Q8×D1314yes—
501C23C2×Q8×D1312yes—
502C23#8825412yes—
503C23#41×D1312yes—
504C23#8825712yes—
505C23C22×C22⋊D1312yes—
506C23C24×D1311yescharacteristic
507Q8—232no—
508Q8—5216no—
509C2×C4—216no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—44no—
519C2×C4—48no—
520C2×C4—416no—
521C2×C4—138no—
522C2×C4—134no—
523C2×C4—134no—
524C2×C4—134no—
525C2×C4—268no—
526C2×C4—268no—
527C2×C4—2616no—
528C2×C4—268no—
529C2×C4—262no—
530C2×C4—264no—
531C2×C4—262no—
532C2×C4—264no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—262no—
536C2×C4—262no—
537C2×C4—262no—
538C2×C4—264no—
539C2×C4—264no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—264no—
543C2×C4—528no—
544C2×C4—524no—
545C2×C4#88193116yes—
546C2×C4C2×D4×D1314yes—
547C2×C4C2×#612914yes—
548C2×C4C22×C22⋊D1318yes—
549C2×C4C22×C22⋊D1314yes—
550C22—24no—
551C22—24no—
552C22—24no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—416no—
558C22#1171932714yes—
559C22#1171933014yes—
560C22#1171933614yes—
561C22#1171933714yes—
562C22C2×#8819314yes—
563C22Q8×C22⋊D1314yes—
564C22#1171953614yes—
565C22C22×D4×D1311yescharacteristic
566C22C22×#612911yescharacteristic
567C22C22×Q8×D1311yescharacteristic
568C22C2×#8825411yescharacteristic
569C22C2×#41×D1311yescharacteristic
570C22C2×#8825711yescharacteristic
571C22C23×C22⋊D1311yescharacteristic
572C4—28no—
573C4—44no—
574C4—42no—
575C4—268no—
576C4—264no—
577C4—264no—
578C4—264no—
579C4—522no—
580C4—524no—
581C4C2×#8819318yes—
582C2—44no—
583C2#1311843718yesdirect product factor
584C2C22×#8819311yescharacteristic
585C2C2×#1171932711yescharacteristic
586C2C2×#1171933011yescharacteristic
587C2C2×#1171933611yescharacteristic
588C2C2×#1171953611yescharacteristic
589C2C2×#1171933711yescharacteristic
590C2C2×Q8×C22⋊D1311yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#2429
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#88198C2semidirect
3. C22×Q8×Dic13C2semidirect
4. #13118437C2direct (N × H)
5. C2×#11718645C2semidirect
7. C2×#11718635C2semidirect
8. C2×#11718634C2semidirect
9. C2×#11718633C2semidirect
25. C2×Q8×Dic13C22semidirect
27. C2×#88198C22semidirect
45. #11718645C22semidirect
46. #11718635C22semidirect
47. #11718634C22semidirect
48. #11718633C22semidirect
83. C2×C22⋊Dic13Q8semidirect
180. C22⋊Dic13C2×Q8semidirect
400. C2×C13#2429semidirect
484. C13C2×#2429semidirect
583. C2#13118437direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881982
C22×#881782
C22×Q8×Dic132
#131184372
C2×#117186452
C2×#117186092
C2×#117186352
C2×#117186342
C2×#117186332
C2×#117186062
C2×C4×C22⋊Dic132
C22×C13×C22⋊Q82
C2×#242913