Finite Group Databasebeta

← C2×#10595029 #11900786

Subgroups — C2×#10595029 #11900786

Order 1152.

3901 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C22×C3×#235C211yesmaximal, characteristic, complemented
3C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63978C214yesmaximal, complemented
5#10595029C2116yesmaximal, direct product factor
6C2×#63911C211yesmaximal, characteristic, complemented
7C2×C4×#626C214yesmaximal, complemented
8C2×#63866C211yesmaximal, characteristic, complemented
9C2×#63864C211yesmaximal, characteristic, complemented
10C2×#63860C211yesmaximal, characteristic, complemented
11C2×#5832—31nomaximal
12C2×#5477—31nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2212yes—
15C2×#3828—28no—
16C2×#3828C2218yescomplemented
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C4×C3⋊D3C2212yes—
19C22×#634C2211yescharacteristic
20C22×C3×#67C2212yes—
21C23×C3×Dic3C2212yes—
22C2×C3×#235—28no—
23C2×C3×#235C2218yescomplemented
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2212yes—
26C22×C3×Dic6C2211yescharacteristic
27C22×#626C2214yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2212yes—
31C2×C3×C4×Dic3C2218yescomplemented
32#63978C22132yescomplemented
33C2×Dic3⋊Dic3C2214yes—
34C2×#3722C2214yes—
35C2×(C2×D3)⋊Dic3C2214yes—
36#63911C2218yescomplemented
37C4×#626C22132yescomplemented
38#63866C2218yescomplemented
39#63864C2218yescomplemented
40#63860C2218yescomplemented
41C22×C3×#41—31no—
42C22×#235—31no—
43C22×#235—31no—
44C22×#235—61no—
45C22×#235D311yescharacteristic, complemented
46C22×C3×C42—31no—
47#5832—316no—
48C2×#947—31no—
49C2×#944—31no—
50C2×#940—31no—
51C2×#939—34no—
52C2×#936—31no—
53C2×#930—34no—
54C2×C4×#67—34no—
55C22×C4×Dic3D311yescharacteristic, complemented
56#5477—316no—
57C2×#875—31no—
58C2×#875—31no—
59C2×#874—31no—
60C2×C4×D12—34no—
61C2×#869—31no—
62C24×C32C2311yescharacteristic
63C23×C3⋊D3C2312yes—
64C23×C3×D3C2312yes—
65C22×C32×C4D418yescomplemented
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2314yes—
69C2×#638—28no—
70C2×#638C2318yes—
71C22×C3⋊Dic3C2312yes—
72#3828—232no—
73C2×C4⋊(C3⋊D3)—24no—
74C2×C4⋊(C3⋊D3)C2314yes—
75C2×C4×C3⋊D3—28no—
76C2×C4×C3⋊D3C2318yes—
77C2×#634—24no—
78C2×#634C2314yes—
79C2×C3×#67—28no—
80C2×C3×#67C2318yes—
81C22×C3×Dic3—28no—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2318yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C3×#235—232no—
87C2×C3×D12—24no—
88C2×C3×D12C2314yes—
89C2×C3×C4×D3—28no—
90C2×C3×C4×D3C2318yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6C2314yes—
93C2×#626—216no—
94C2×#626C23116yes—
95C3×C4×Dic3C2314yes—
96C3×C4×Dic3C2314yes—
97C3×C4×Dic3C2318yes—
98Dic3⋊Dic3C23116yes—
99#3722C23116yes—
100(C2×D3)⋊Dic3C23116yes—
101C2×#532—91noSylow
102C2×C3×#41—38no—
103C2×C3×#41—68no—
104C22×C3×Q8—31no—
105C22×C3×D4—32no—
106C22×C3×D4—31no—
107C23×C3×C4—21no—
108C23×C3×C4—32no—
109C23×C3×C4—32no—
110C23×C3×C4C2×D311yescharacteristic
111C23×C3×C4C2×D311yescharacteristic
112C22×#67—32no—
113C22×#67—32no—
114C22×#67—34no—
115C22×#67—62no—
116C22×#67C2×D312yes—
117C23×Dic3C2×D312yes—
118C2×#235—28no—
119C2×#235—38no—
120C2×#235—38no—
121C2×#235—68no—
122C2×#235—616no—
123C2×#235—68no—
124C2×#235—68no—
125C2×#235C2×D318yescomplemented
126C22×D12—34no—
127C22×D12—31no—
128C22×D12—31no—
129C22×D12—61no—
130C22×D12C2×D311yescharacteristic
131C22×C4×D3—32no—
132C22×C4×D3—32no—
133C22×C4×D3—62no—
134C22×C4×D3C2×D312yes—
135C22×Dic6—31no—
136C22×Dic6—31no—
137C22×Dic6—61no—
138C22×Dic6C2×D311yescharacteristic
139C2×C3×C42—31no—
140C2×C3×C42—32no—
141C2×C3×C42—31no—
142C2×C3×C42—38no—
143C2×#217—34no—
144#947—38no—
145#944—38no—
146#940—38no—
147#939—332no—
148#936—38no—
149#930—332no—
150C4×#67—332no—
151C2×(C2×D3)⋊C4—34no—
152C2×(C2×D3)⋊C4—34no—
153C2×(C2×D3)⋊C4—34no—
154C2×C4⋊Dic3—34no—
155C2×Dic3⋊C4—34no—
156C2×C4×Dic3C2×D312yes—
157C2×C4×Dic3C2×D311yescharacteristic
158C2×C4×Dic3C2×D311yescharacteristic
159C2×C4×Dic3C2×D318yescomplemented
160#875—38no—
161#875—38no—
162#874—38no—
163C4×D12—332no—
164#869—38no—
165C23×C32—24no—
166C23×C32C2×D414yes—
167C23×C32C2412yes—
168C23×C32C2411yescharacteristic
169C22×C3⋊D3—24no—
170C22×C3⋊D3—28no—
171C22×C3⋊D3C2414yes—
172C22×C3×D3—24no—
173C22×C3×D3—28no—
174C22×C3×D3C2414yes—
175C2×C32×C4C2×D414yes—
176C2×C32×C4C2×D414yes—
177C2×C32×C4C2×D4116yescomplemented
178C2×C32×C4C2412yes—
179C2×C32×C4C2412yes—
180#638—216no—
181C2×C3⋊Dic3—24no—
182C2×C3⋊Dic3C2414yes—
183C4⋊(C3⋊D3)—28no—
184C4×C3⋊D3—216no—
185#634—28no—
186C3×#67—216no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—216no—
190C2×C3×Dic3#4118yescomplemented
191C2×C3×Dic3C2414yes—
192C2×C3×Dic3C2414yes—
193C2×C3×Dic3C2414yes—
194C3×D12—28no—
195C3×C4×D3—216no—
196C3×Dic6—28no—
197#626—232no—
198C22×#41—31no—
199C22×#41—91no—
200#532—916no—
201C2×C4⋊Q8—91no—
202C2×#127—91no—
203C2×#124—91no—
204C2×#124—91no—
205C2×#121—94no—
206C2×C4×D4—94no—
207C22×C42—31no—
208C24×C3—21no—
209C24×C3—32no—
210C24×C3C22×D311yescharacteristic
211C24×C3C22×D311yescharacteristic
212C23×D3—32no—
213C23×D3—32no—
214C23×D3—62no—
215C23×D3C22×D312yes—
216C3×#41—632no—
217C2×C3×Q8—34no—
218C2×C3×Q8—64no—
219C2×C3×D4—38no—
220C2×C3×D4—34no—
221C2×C3×D4—68no—
222C2×C3×D4—64no—
223C22×C3×C4—28no—
224C22×C3×C4—21no—
225C22×C3×C4—24no—
226C22×C3×C4—21no—
227C22×C3×C4—32no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4—38no—
231C22×C3×C4—38no—
232C22×C3×C4—68no—
233C22×C3×C4—68no—
234C22×C3×C4D1218yescomplemented
235C22×C3×C4#6718yescomplemented
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D314yes—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D314yes—
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C2×#67—28no—
243C2×#67—38no—
244C2×#67—38no—
245C2×#67—316no—
246C2×#67—68no—
247C2×#67—616no—
248C2×#67—68no—
249C2×#67—68no—
250C2×#67—616no—
251C2×#67C22×D318yes—
252C22×Dic3—28no—
253C22×Dic3—32no—
254C22×Dic3—32no—
255C22×Dic3—62no—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D318yes—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D312yes—
260#235—232no—
261#235—664no—
262#235—632no—
263#235—632no—
264C2×D12—24no—
265C2×D12—316no—
266C2×D12—34no—
267C2×D12—34no—
268C2×D12—64no—
269C2×D12—68no—
270C2×D12—616no—
271C2×D12—64no—
272C2×D12—64no—
273C2×D12C22×D314yes—
274C2×C4×D3—28no—
275C2×C4×D3—38no—
276C2×C4×D3—38no—
277C2×C4×D3—68no—
278C2×C4×D3—616no—
279C2×C4×D3—68no—
280C2×C4×D3—68no—
281C2×C4×D3C22×D318yes—
282C2×Dic6—24no—
283C2×Dic6—34no—
284C2×Dic6—34no—
285C2×Dic6—64no—
286C2×Dic6—68no—
287C2×Dic6—64no—
288C2×Dic6—64no—
289C2×Dic6C22×D314yes—
290C3×C42—34no—
291C3×C42—38no—
292C3×C42—34no—
293#217—316no—
294(C2×D3)⋊C4—316no—
295(C2×D3)⋊C4—316no—
296(C2×D3)⋊C4—316no—
297C4⋊Dic3—316no—
298Dic3⋊C4—316no—
299C4×Dic3C22×D318yes—
300C4×Dic3C22×D314yes—
301C4×Dic3C22×D314yes—
302C22×C32—28no—
303C22×C32—24no—
304C22×C32C22×D414yes—
305C22×C32C22×D412yes—
306C22×C32C2×#4114yes—
307C22×C32C2511yescharacteristic
308C2×C3⋊D3—24no—
309C2×C3⋊D3—28no—
310C2×C3⋊D3—48no—
311C2×C3×D3—24no—
312C2×C3×D3—28no—
313C2×C3×D3—48no—
314C32×C4C22×D414yes—
315C32×C4C22×D414yes—
316C3⋊Dic3—24no—
317C3×Dic3—24no—
318C3×Dic3—24no—
319C3×Dic3C2×#4118yescomplemented
320C2×#41—38no—
321C2×#41—68no—
322C2×#41—98no—
323C2×#41—188no—
324C22×Q8—31no—
325C22×Q8—91no—
326C22×D4—32no—
327C22×D4—31no—
328C22×D4—94no—
329C22×D4—92no—
330C22×D4—91no—
331C23×C4—32no—
332C23×C4—32no—
333C23×C4—92no—
334C23×C4D3211yescharacteristic
335C4⋊Q8—98no—
336#127—98no—
337#124—98no—
338#124—98no—
339#121—932no—
340C4×D4—932no—
341C2×C4⋊C4—94no—
342C2×C22⋊C4—94no—
343C2×C22⋊C4—94no—
344C2×C42—31no—
345C2×C42—31no—
346C2×C42—38no—
347C2×C42—32no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—21no—
351C23×C3—22no—
352C23×C3—24no—
353C23×C3—34no—
354C23×C3—44no—
355C23×C3—64no—
356C23×C3—68no—
357C23×C3C2×D1214yes—
358C23×C3C2×#6714yes—
359C23×C3C23×D312yes—
360C23×C3C23×D312yes—
361C23×C3C23×D311yescharacteristic
362C23×C3C23×D311yescharacteristic
363C22×D3—28no—
364C22×D3—24no—
365C22×D3—34no—
366C22×D3—34no—
367C22×D3—64no—
368C22×D3—68no—
369C22×D3—64no—
370C22×D3—68no—
371C22×D3—68no—
372C22×D3—64no—
373C22×D3—128no—
374C22×D3C23×D314yes—
375C3×Q8—68no—
376C3×D4—616no—
377C3×D4—68no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—216no—
383C2×C3×C4—38no—
384C2×C3×C4—34no—
385C2×C3×C4—34no—
386C2×C3×C4—34no—
387C2×C3×C4—616no—
388C2×C3×C4—64no—
389C2×C3×C4—64no—
390C2×C3×C4—616no—
391C2×C3×C4C2×D1214yes—
392C2×C3×C4C2×D1214yes—
393C2×C3×C4C2×D12116yescomplemented
394C2×C3×C4C2×#6714yes—
395C2×C3×C4C2×#6714yes—
396C2×C3×C4C2×#67116yescomplemented
397C2×C3×C4C23×D312yes—
398C2×C3×C4C23×D312yes—
399C2×C3×C4C23×D312yes—
400C2×C3×C4C23×D312yes—
401#67—216no—
402#67—632no—
403#67—616no—
404#67—616no—
405#67—632no—
406C2×Dic3—24no—
407C2×Dic3—24no—
408C2×Dic3—216no—
409C2×Dic3—34no—
410C2×Dic3—34no—
411C2×Dic3—64no—
412C2×Dic3—68no—
413C2×Dic3—64no—
414C2×Dic3—64no—
415C2×Dic3#23518yescomplemented
416C2×Dic3C23×D314yes—
417C2×Dic3C23×D314yes—
418C2×Dic3C23×D314yes—
419D12—28no—
420D12—616no—
421D12—632no—
422D12—68no—
423D12—68no—
424C4×D3—216no—
425C4×D3—632no—
426C4×D3—616no—
427C4×D3—616no—
428Dic6—28no—
429Dic6—616no—
430Dic6—68no—
431Dic6—68no—
432C2×C32—24no—
433C2×C32#53214yescomplemented
434C2×C32C23×D411yescharacteristic
435C2×C32C22×#4112yes—
436C3⋊D3—44no—
437C3×D3—44no—
438C24—32no—
439C24—92no—
440C24C2×D3211yescharacteristic
441#41—632no—
442#41—1832no—
443C2×Q8—34no—
444C2×Q8—64no—
445C2×Q8—94no—
446C2×Q8—184no—
447C2×D4—38no—
448C2×D4—34no—
449C2×D4—68no—
450C2×D4—64no—
451C2×D4—916no—
452C2×D4—98no—
453C2×D4—94no—
454C2×D4—1816no—
455C2×D4—188no—
456C2×D4—184no—
457C22×C4—32no—
458C22×C4—32no—
459C22×C4—38no—
460C22×C4—32no—
461C22×C4—38no—
462C22×C4—68no—
463C22×C4—68no—
464C22×C4—92no—
465C22×C4—98no—
466C22×C4—188no—
467C22×C4#62618yescomplemented
468C22×C4C2×D3211yescharacteristic
469C22×C4C2×D3214yes—
470C22×C4C2×D3211yescharacteristic
471C4⋊C4—916no—
472C22⋊C4—916no—
473C22⋊C4—916no—
474C42—38no—
475C42—34no—
476C42—34no—
477C22×C3—24no—
478C22×C3—24no—
479C22×C3—28no—
480C22×C3—28no—
481C22×C3—24no—
482C22×C3—22no—
483C22×C3—24no—
484C22×C3—21no—
485C22×C3—44no—
486C22×C3—48no—
487C22×C3—64no—
488C22×C3—68no—
489C22×C3—128no—
490C22×C3C22×D1214yes—
491C22×C3C22×D1212yes—
492C22×C3C2×#23514yes—
493C22×C3D3×#4114yes—
494C22×C3C22×#6714yes—
495C22×C3C22×#6712yes—
496C22×C3C24×D311yescharacteristic
497C22×C3C24×D311yescharacteristic
498C2×D3—28no—
499C2×D3—24no—
500C2×D3—48no—
501C2×D3—68no—
502C2×D3—64no—
503C2×D3—68no—
504C2×D3—68no—
505C2×D3—64no—
506C2×D3—128no—
507C2×D3—1216no—
508C2×D3—128no—
509C2×D3—128no—
510C3×C4—24no—
511C3×C4—24no—
512C3×C4—38no—
513C3×C4—64no—
514C3×C4—64no—
515C3×C4C22×D1214yes—
516C3×C4C22×D1214yes—
517C3×C4C22×#6714yes—
518C3×C4C22×#6714yes—
519Dic3—24no—
520Dic3—24no—
521Dic3—68no—
522Dic3—64no—
523Dic3—64no—
524Dic3C2×#23518yescomplemented
525C32C2×#53211yescharacteristic, complemented, Sylow
526C23—24no—
527C23—34no—
528C23—68no—
529C23—64no—
530C23—94no—
531C23—188no—
532C23—184no—
533C23C2×#62614yes—
534C23C22×D3212yes—
535C23C22×D3211yescharacteristic
536Q8—68no—
537Q8—188no—
538D4—616no—
539D4—68no—
540D4—1832no—
541D4—1816no—
542D4—188no—
543C2×C4—38no—
544C2×C4—34no—
545C2×C4—34no—
546C2×C4—34no—
547C2×C4—616no—
548C2×C4—64no—
549C2×C4—64no—
550C2×C4—616no—
551C2×C4—94no—
552C2×C4—184no—
553C2×C4—1816no—
554C2×C4C2×#62614yes—
555C2×C4C2×#62614yes—
556C2×C4C2×#626116yescomplemented
557C2×C4C22×D3212yes—
558C2×C4C22×D3212yes—
559C2×C3—24no—
560C2×C3—24no—
561C2×C3—22no—
562C2×C3—21no—
563C2×C3—24no—
564C2×C3—44no—
565C2×C3—124no—
566C2×C3#547714yescomplemented
567C2×C3#583214yescomplemented
568C2×C3C23×D1211yescharacteristic
569C2×C3C22×#23512yes—
570C2×C3C2×D3×#4112yes—
571C2×C3C23×#6711yescharacteristic
572D3—44no—
573D3—128no—
574D3—124no—
575D3—124no—
576C22—24no—
577C22—28no—
578C22—68no—
579C22—64no—
580C22—128no—
581C22—188no—
582C22—184no—
583C22—368no—
584C22D3×#23514yes—
585C22C22×#62614yes—
586C22C22×#62612yes—
587C22C23×D3211yescharacteristic
588C4—38no—
589C4—64no—
590C4—64no—
591C4—184no—
592C4C22×#62614yes—
593C4C22×#62614yes—
594C3—21no—
595C3C2×#547711yescharacteristic, complemented
596C3C2×#583211yescharacteristic, complemented
597C2—24no—
598C2—124no—
599C2—364no—
600C2#1059502914yesdirect product factor
601C2C2×D3×#23512yes—
602C2C23×#62611yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C22×C3×#235C2semidirect
3. C22×C3×C4×Dic3C2semidirect
4. C2×#63978C2semidirect
5. #10595029C2direct (N × H)
6. C2×#63911C2semidirect
7. C2×C4×#626C2semidirect
8. C2×#63866C2semidirect
9. C2×#63864C2semidirect
10. C2×#63860C2semidirect
16. C2×#3828C22semidirect
23. C2×C3×#235C22semidirect
31. C2×C3×C4×Dic3C22semidirect
32. #63978C22semidirect
36. #63911C22semidirect
37. C4×#626C22semidirect
38. #63866C22semidirect
39. #63864C22semidirect
40. #63860C22semidirect
45. C22×#235D3semidirect
55. C22×C4×Dic3D3semidirect
65. C22×C32×C4D4semidirect
125. C2×#235C2×D3semidirect
159. C2×C4×Dic3C2×D3semidirect
177. C2×C32×C4C2×D4semidirect
190. C2×C3×Dic3#41semidirect
234. C22×C3×C4D12semidirect
235. C22×C3×C4#67semidirect
319. C3×Dic3C2×#41semidirect
393. C2×C3×C4C2×D12semidirect
396. C2×C3×C4C2×#67semidirect
415. C2×Dic3#235semidirect
433. C2×C32#532semidirect
467. C22×C4#626semidirect
524. Dic3C2×#235semidirect
525. C32C2×#532semidirect
556. C2×C4C2×#626semidirect
566. C2×C3#5477semidirect
567. C2×C3#5832semidirect
595. C3C2×#5477semidirect
596. C3C2×#5832semidirect
600. C2#10595029direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×C3×#2352
C22×C3×C4×Dic32
C2×#639782
#105950292
C2×#639112
C2×C4×#6262
C2×#638662
C2×#638642
C2×#638602
C2×#58323
C2×#54773