Finite Group Databasebeta

← C2×#10594980 #11901439

Subgroups — C2×#10594980 #11901439

Order 1152.

2501 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic, complemented
3C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C2×#63966C212yesmaximal, complemented
5C2×#63952C212yesmaximal, complemented
6#10594980C2116yesmaximal, direct product factor
7C2×#63897C212yesmaximal, complemented
8C2×#63888C212yesmaximal, complemented
9C2×#63848C212yesmaximal, complemented
10C2×#63845C212yesmaximal, complemented
11C2×#5645—31nomaximal
12C2×#5515—31nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2212yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#624C2212yes—
20#64139C2218yes—
21C2×#3752C2212yes—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924C2218yescomplemented
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2218yescomplemented
30C2×#3724C2212yes—
31#63966C22116yescomplemented
32C2×Dic3⋊Dic3C2212yes—
33C2×Dic3⋊Dic3C2212yes—
34C2×#3722C2212yes—
35C2×#3722C2212yes—
36C2×#3722C2212yes—
37C2×Dic32C2212yes—
38#63952C22116yescomplemented
39#63897C22116yescomplemented
40#63888C22116yescomplemented
41#63848C22116yescomplemented
42#63845C22116yescomplemented
43C2×C3×C22⋊Q8—31no—
44C22×C3×C4⋊C4—31no—
45C2×#946—32no—
46C2×#930—31no—
47C2×#930—31no—
48C2×#930—61no—
49C2×#929—32no—
50C2×C4×#67—32no—
51C2×#924D311yescharacteristic, complemented
52C22×Dic3⋊C4D311yescharacteristic, complemented
53#5645—316no—
54#5515—316no—
55C2×#898—32no—
56C2×#898—32no—
57C2×#896—32no—
58C2×#894—32no—
59C2×#894—32no—
60C2×#890—32no—
61C2×#889—32no—
62C2×#886—32no—
63C2×#67⋊C4—32no—
64C24×C32C2311yescharacteristic
65C23×C3⋊D3C2312yes—
66C22×C32×C4—42no—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2314yes—
70C2×#638—28no—
71C2×#638C2318yes—
72C22×C3⋊Dic3C2312yes—
73C2×C4⋊(C3⋊D3)—42no—
74C2×C4⋊(C3⋊D3)C2314yes—
75C22×C3×Dic3—24no—
76C22×C3×Dic3—42no—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2314yes—
82C22×C3×Dic3C2314yes—
83C2×C3×Dic6—42no—
84C2×C3×Dic6C2314yes—
85C2×#624—44no—
86C2×#624C2318yes—
87#3752C2318yes—
88C4⋊(C3⋊Dic3)C2314yes—
89C3×#217C2318yes—
90C3×C4⋊Dic3C2314yes—
91C3×Dic3⋊C4C2318yes—
92C3×Dic3⋊C4C2318yes—
93C3×Dic3⋊C4C2318yes—
94#3724C2318yes—
95Dic3⋊Dic3C2318yes—
96Dic3⋊Dic3C2318yes—
97#3722C2318yes—
98#3722C2318yes—
99#3722C2318yes—
100Dic32C2318yes—
101C2×#539—91noSylow
102C22×C3×Q8—31no—
103C23×C3×C4—21no—
104C23×C3×C4—31no—
105C23×C3×C4—31no—
106C23×C3×C4C2×D311yescharacteristic
107C23×C3×C4C2×D311yescharacteristic
108C22×#67—32no—
109C22×#67—32no—
110C22×#67—62no—
111C23×Dic3C2×D311yescharacteristic
112C23×Dic3C2×D311yescharacteristic
113C22×D12—31no—
114C22×D12—31no—
115C22×D12—61no—
116C22×C4×D3—32no—
117C22×C4×D3—32no—
118C22×Dic6C2×D311yescharacteristic
119C3×C22⋊Q8—38no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4—38no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C22⋊C4—32no—
126C2×#217C2×D312yes—
127#946—316no—
128#930—38no—
129#930—38no—
130#930—68no—
131#929—316no—
132C4×#67—316no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—62no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—32no—
145C2×C4⋊Dic3—32no—
146C2×C4⋊Dic3—61no—
147C2×C4⋊Dic3C2×D311yescharacteristic
148#924C2×D318yescomplemented
149C2×Dic3⋊C4—32no—
150C2×Dic3⋊C4—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4C2×D312yes—
154C2×Dic3⋊C4C2×D312yes—
155C2×Dic3⋊C4C2×D312yes—
156C2×Dic3⋊C4C2×D318yescomplemented
157C2×C4×Dic3—32no—
158C2×C4×Dic3—32no—
159#898—316no—
160#898—316no—
161#896—316no—
162#894—316no—
163#894—316no—
164#890—316no—
165#889—316no—
166#886—316no—
167#67⋊C4—316no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32#4114yes—
171C23×C32C2412yes—
172C23×C32C2411yescharacteristic
173C22×C3⋊D3—24no—
174C22×C3⋊D3—24no—
175C22×C3⋊D3—24no—
176C22×C3⋊D3C2414yes—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—44no—
180C2×C32×C4C2412yes—
181C2×C32×C4C2412yes—
182#638—216no—
183C2×C3⋊Dic3—24no—
184C2×C3⋊Dic3C2414yes—
185C4⋊(C3⋊D3)—44no—
186C2×C3×Dic3—28no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—44no—
192C2×C3×Dic3C2414yes—
193C2×C3×Dic3C2414yes—
194C2×C3×Dic3C2414yes—
195C2×C3×Dic3C2414yes—
196C3×Dic6—44no—
197#624—48no—
198#539—916no—
199C2×#126—92no—
200C2×#125—92no—
201C2×#123—92no—
202C2×#123—92no—
203C2×C22⋊Q8—31no—
204C2×C22⋊Q8—92no—
205C2×#121—91no—
206C2×C4×D4—92no—
207C22×C4⋊C4—31no—
208C24×C3—21no—
209C24×C3C22×D311yescharacteristic
210C24×C3C22×D311yescharacteristic
211C23×D3—32no—
212C23×D3—32no—
213C23×D3—62no—
214C2×C3×Q8—34no—
215C2×C3×Q8—122no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—24no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—34no—
224C22×C3×C4—34no—
225C22×C3×C4—42no—
226C22×C3×C4—42no—
227C22×C3×C4—44no—
228C22×C3×C4—64no—
229C22×C3×C4—122no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D314yes—
235C22×C3×C4C22×D314yes—
236C2×#67—38no—
237C2×#67—38no—
238C2×#67—68no—
239C2×#67—68no—
240C2×#67—68no—
241C2×#67—128no—
242C22×Dic3—24no—
243C22×Dic3—32no—
244C22×Dic3—32no—
245C22×Dic3—42no—
246C22×Dic3—62no—
247C22×Dic3C22×D314yes—
248C22×Dic3C22×D312yes—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D312yes—
252C22×Dic3C22×D314yes—
253C2×D12—34no—
254C2×D12—34no—
255C2×D12—64no—
256C2×D12—122no—
257C2×D12—122no—
258C2×D12—124no—
259C2×C4×D3—38no—
260C2×C4×D3—38no—
261C2×C4×D3—124no—
262C2×C4×D3—124no—
263C2×Dic6—42no—
264C2×Dic6C22×D314yes—
265C3×C4⋊C4—38no—
266C3×C4⋊C4—38no—
267C3×C4⋊C4—38no—
268C3×C4⋊C4—34no—
269C3×C22⋊C4—38no—
270#217C22×D318yes—
271(C2×D3)⋊C4—38no—
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4—38no—
274(C2×D3)⋊C4—38no—
275(C2×D3)⋊C4—38no—
276(C2×D3)⋊C4—38no—
277(C2×D3)⋊C4—38no—
278(C2×D3)⋊C4—38no—
279(C2×D3)⋊C4—68no—
280C4⋊Dic3—34no—
281C4⋊Dic3—34no—
282C4⋊Dic3—38no—
283C4⋊Dic3—38no—
284C4⋊Dic3—64no—
285C4⋊Dic3C22×D314yes—
286Dic3⋊C4—38no—
287Dic3⋊C4—38no—
288Dic3⋊C4—38no—
289Dic3⋊C4—38no—
290Dic3⋊C4C22×D318yes—
291Dic3⋊C4C22×D318yes—
292Dic3⋊C4C22×D318yes—
293C4×Dic3—38no—
294C4×Dic3—38no—
295C22×C32—28no—
296C22×C32—22no—
297C22×C32—22no—
298C22×C32C2×#4114yes—
299C22×C32C2×#4112yes—
300C22×C32H(5,𝔽2)12yes—
301C22×C322−1+412yes—
302C22×C32C2511yescharacteristic
303C2×C3⋊D3—24no—
304C2×C3⋊D3—24no—
305C2×C3⋊D3—24no—
306C2×C3⋊D3—48no—
307C32×C4—22no—
308C32×C4—22no—
309C3⋊Dic3—24no—
310C3×Dic3—24no—
311C3×Dic3—24no—
312C3×Dic3—24no—
313C3×Dic3—24no—
314C22×Q8—31no—
315C22×D4—92no—
316C22×D4—91no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—92no—
320C23×C4D3211yescharacteristic
321#126—916no—
322#125—916no—
323#123—916no—
324#123—916no—
325C22⋊Q8—38no—
326C22⋊Q8—916no—
327#121—98no—
328C4×D4—916no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—32no—
331C2×C4⋊C4—38no—
332C2×C4⋊C4—32no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—92no—
335C2×C4⋊C4—92no—
336C2×C4⋊C4—92no—
337C2×C4⋊C4—91no—
338C2×C22⋊C4—32no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—92no—
341C2×C22⋊C4—92no—
342C2×C22⋊C4—92no—
343C2×C42—92no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—21no—
350C23×C3—24no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3#23514yes—
354C23×C3#23914yes—
355C23×C3C23×D312yes—
356C23×C3C23×D312yes—
357C23×C3C23×D311yescharacteristic
358C23×C3C23×D311yescharacteristic
359C22×D3—34no—
360C22×D3—34no—
361C22×D3—64no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—64no—
368C22×D3—124no—
369C22×D3—124no—
370C22×D3—124no—
371C3×Q8—124no—
372C2×C3×C4—24no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—34no—
380C2×C3×C4—34no—
381C2×C3×C4—34no—
382C2×C3×C4—34no—
383C2×C3×C4—42no—
384C2×C3×C4—44no—
385C2×C3×C4—44no—
386C2×C3×C4—48no—
387C2×C3×C4—64no—
388C2×C3×C4—64no—
389C2×C3×C4—68no—
390C2×C3×C4—64no—
391C2×C3×C4—64no—
392C2×C3×C4—124no—
393C2×C3×C4C23×D312yes—
394C2×C3×C4C23×D312yes—
395C2×C3×C4C23×D312yes—
396C2×C3×C4C23×D312yes—
397#67—616no—
398#67—616no—
399#67—1216no—
400C2×Dic3—28no—
401C2×Dic3—24no—
402C2×Dic3—24no—
403C2×Dic3—24no—
404C2×Dic3—24no—
405C2×Dic3—34no—
406C2×Dic3—34no—
407C2×Dic3—44no—
408C2×Dic3—64no—
409C2×Dic3—64no—
410C2×Dic3—64no—
411C2×Dic3—124no—
412C2×Dic3C23×D314yes—
413C2×Dic3C23×D314yes—
414C2×Dic3C23×D314yes—
415C2×Dic3C23×D314yes—
416D12—124no—
417D12—124no—
418D12—128no—
419C4×D3—128no—
420C4×D3—128no—
421Dic6—44no—
422C2×C32—24no—
423C2×C32#53914yescomplemented
424C2×C32C22×#4111yescharacteristic
425C2×C32C2×H(5,𝔽2)11yescharacteristic
426C2×C32C2×2−1+411yescharacteristic
427C3⋊D3—44no—
428C24—92no—
429C24C2×D3211yescharacteristic
430C2×Q8—34no—
431C2×Q8—122no—
432C2×D4—98no—
433C2×D4—94no—
434C2×D4—188no—
435C2×D4—362no—
436C22×C4—34no—
437C22×C4—32no—
438C22×C4—32no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—34no—
442C22×C4—42no—
443C22×C4—64no—
444C22×C4—98no—
445C22×C4—92no—
446C22×C4—122no—
447C22×C4—364no—
448C22×C4C2×D3211yescharacteristic
449C22×C4C2×D3211yescharacteristic
450C22×C4C2×D3214yes—
451C4⋊C4—38no—
452C4⋊C4—38no—
453C4⋊C4—38no—
454C4⋊C4—34no—
455C4⋊C4—98no—
456C4⋊C4—98no—
457C4⋊C4—98no—
458C4⋊C4—94no—
459C22⋊C4—38no—
460C22⋊C4—98no—
461C22⋊C4—98no—
462C22⋊C4—98no—
463C22⋊C4—98no—
464C42—98no—
465C22×C3—28no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—28no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—24no—
474C22×C3—22no—
475C22×C3—21no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—48no—
479C22×C3C2×#23514yes—
480C22×C3C2×#23512yes—
481C22×C3#100412yes—
482C22×C3#100412yes—
483C22×C3C2×#23914yes—
484C22×C3C2×#23912yes—
485C22×C3#100712yes—
486C22×C3#101012yes—
487C22×C3C24×D311yescharacteristic
488C22×C3C24×D311yescharacteristic
489C2×D3—64no—
490C2×D3—64no—
491C2×D3—64no—
492C2×D3—64no—
493C2×D3—64no—
494C2×D3—64no—
495C2×D3—124no—
496C2×D3—124no—
497C2×D3—124no—
498C2×D3—128no—
499C2×D3—128no—
500C2×D3—248no—
501C3×C4—24no—
502C3×C4—22no—
503C3×C4—22no—
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—42no—
507C3×C4—64no—
508C3×C4—64no—
509C3×C4—64no—
510C3×C4—64no—
511Dic3—24no—
512Dic3—24no—
513Dic3—24no—
514Dic3—24no—
515Dic3—64no—
516Dic3—64no—
517Dic3—124no—
518C32C2×#53911yescharacteristic, complemented, Sylow
519C23—22no—
520C23—22no—
521C23—94no—
522C23—184no—
523C23—184no—
524C23—184no—
525C23#379914yes—
526C23C22×D3212yes—
527C23C22×D3211yescharacteristic
528Q8—124no—
529D4—1816no—
530D4—364no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—34no—
534C2×C4—34no—
535C2×C4—34no—
536C2×C4—34no—
537C2×C4—44no—
538C2×C4—64no—
539C2×C4—68no—
540C2×C4—64no—
541C2×C4—64no—
542C2×C4—64no—
543C2×C4—94no—
544C2×C4—124no—
545C2×C4—184no—
546C2×C4—368no—
547C2×C4C22×D3212yes—
548C2×C4C22×D3212yes—
549C2×C3—24no—
550C2×C3—24no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—24no—
555C2×C3—44no—
556C2×C3#551514yescomplemented
557C2×C3#564514yescomplemented
558C2×C3C22×#23511yescharacteristic
559C2×C3C2×#100411yescharacteristic
560C2×C3C2×#100411yescharacteristic
561C2×C3C22×#23911yescharacteristic
562C2×C3C2×#100711yescharacteristic
563C2×C3C2×#101011yescharacteristic
564D3—124no—
565D3—124no—
566D3—244no—
567C22—22no—
568C22—22no—
569C22—28no—
570C22—184no—
571C22—184no—
572C22—184no—
573C22—368no—
574C22#6429712yes—
575C22C2×#379914yes—
576C22C2×#379912yes—
577C22#6433012yes—
578C22C23×D3211yescharacteristic
579C4—22no—
580C4—22no—
581C4—64no—
582C4—64no—
583C4—64no—
584C4—64no—
585C4—184no—
586C3—21no—
587C3C2×#551511yescharacteristic, complemented
588C3C2×#564511yescharacteristic, complemented
589C2—24no—
590C2—364no—
591C2#1059498014yesdirect product factor
592C2C2×#6429711yescharacteristic
593C2C22×#379911yescharacteristic
594C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC2×#64139C2
hypercenterC23×C4D32
hypocenterC32C2×#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#924C2semidirect
3. C22×C3×Dic3⋊C4C2semidirect
4. C2×#63966C2semidirect
5. C2×#63952C2semidirect
6. #10594980C2direct (N × H)
7. C2×#63897C2semidirect
8. C2×#63888C2semidirect
9. C2×#63848C2semidirect
10. C2×#63845C2semidirect
25. C3×#924C22semidirect
29. C2×C3×Dic3⋊C4C22semidirect
31. #63966C22semidirect
38. #63952C22semidirect
39. #63897C22semidirect
40. #63888C22semidirect
41. #63848C22semidirect
42. #63845C22semidirect
51. C2×#924D3semidirect
52. C22×Dic3⋊C4D3semidirect
148. #924C2×D3semidirect
156. C2×Dic3⋊C4C2×D3semidirect
423. C2×C32#539semidirect
518. C32C2×#539semidirect
556. C2×C3#5515semidirect
557. C2×C3#5645semidirect
587. C3C2×#5515semidirect
588. C3C2×#5645semidirect
591. C2#10594980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641392
C2×C3×#9242
C22×C3×Dic3⋊C42
C2×#639662
C2×#639522
#105949802
C2×#638972
C2×#638882
C2×#638482
C2×#638452
C2×#56453
C2×#55153