Finite Group Databasebeta

← C2×#10594546 #11901528

Subgroups — C2×#10594546 #11901528

Order 1152.

2691 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64103C211yesmaximal, characteristic, complemented
2C2×C3×#894C211yesmaximal, characteristic, complemented
3C2×C3×#892C211yesmaximal, characteristic, complemented
4C2×#63912C211yesmaximal, characteristic, complemented
5C2×#63911C211yesmaximal, characteristic, complemented
6C2×#63910C211yesmaximal, characteristic, complemented
7C2×#63906C211yesmaximal, characteristic, complemented
8C2×#63906C211yesmaximal, characteristic, complemented
9C2×#63906C211yesmaximal, characteristic, complemented
10C2×C4×#626C211yesmaximal, characteristic, complemented
11C2×#63890C211yesmaximal, characteristic, complemented
12C2×#63885C211yesmaximal, characteristic, complemented
13C2×#63880C211yesmaximal, characteristic, complemented
14C2×#63867C211yesmaximal, characteristic, complemented
15C2×#63854C211yesmaximal, characteristic, complemented
16#10594546C2116yesmaximal, direct product factor
17C2×#5663—31nomaximal
18C2×#5535—31nomaximal
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C22×#625C2211yescharacteristic
32C22×#624C2211yescharacteristic
33C22×D3×Dic3C2211yescharacteristic
34C2×C32×C4⋊C4C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3750C2211yescharacteristic
39#64103C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×C4⋊Dic3C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×C4×Dic3C2211yescharacteristic
48C2×C3×C4×Dic3C2211yescharacteristic
49C3×#894C2218yescomplemented
50C3×#892C2218yescomplemented
51C2×#3724C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57#63912C2218yescomplemented
58#63911C2218yescomplemented
59#63910C2218yescomplemented
60#63906C2218yescomplemented
61#63906C2218yescomplemented
62#63906C2218yescomplemented
63C4×#626C2218yescomplemented
64#63890C2218yescomplemented
65#63885C2218yescomplemented
66#63880C2218yescomplemented
67#63867C2218yescomplemented
68#63854C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#117—31no—
71C2×#940—31no—
72C2×#939—31no—
73C2×#930—31no—
74C2×#930—31no—
75C2×#930—31no—
76C2×C4×#67—31no—
77#5663—316no—
78#5535—316no—
79C2×#895—31no—
80C2×#894—31no—
81C2×#894—31no—
82C2×#894—31no—
83C2×#894—31no—
84C2×#894—61no—
85C2×#894D311yescharacteristic, complemented
86C2×#892D311yescharacteristic, complemented
87C2×#889—31no—
88C2×#886—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#883—31no—
97C2×#67⋊C4—31no—
98C2×#874—31no—
99C2×C4×D12—31no—
100C2×C4×D12—31no—
101C2×#870—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×C4⋊(C3⋊D3)—42no—
113C2×C4⋊(C3⋊D3)C2314yes—
114C2×C4×C3⋊D3—42no—
115C2×C4×C3⋊D3C2314yes—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×D12—42no—
122C2×C3×D12C2314yes—
123C2×C3×C4×D3—24no—
124C2×C3×C4×D3—42no—
125C2×C3×C4×D3C2314yes—
126C2×C3×C4×D3C2314yes—
127C2×#626—24no—
128C2×#626—24no—
129C2×#626—42no—
130C2×#626—42no—
131C2×#626—42no—
132C2×#626—42no—
133C2×#626C2314yes—
134C2×#626C2314yes—
135C2×#626C2314yes—
136C2×#626C2314yes—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#625—42no—
140C2×#625—42no—
141C2×#625C2314yes—
142C2×#625C2314yes—
143C2×#624—42no—
144C2×#624C2314yes—
145C2×D3×Dic3—42no—
146C2×D3×Dic3C2314yes—
147C32×C4⋊C4C2314yes—
148#3752C2314yes—
149#3752C2314yes—
150#3752C2314yes—
151#3750C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×C4⋊Dic3C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×C4×Dic3C2314yes—
160C3×C4×Dic3C2314yes—
161#3724C2314yes—
162Dic3⋊Dic3C2314yes—
163Dic3⋊Dic3C2314yes—
164Dic3⋊Dic3C2314yes—
165#3722C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167C2×#540—91noSylow
168C22×C3×D4—31no—
169C23×C3×C4—31no—
170C23×C3×C4—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C23×Dic3—31no—
182C22×D12—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—31no—
188C22×D12—31no—
189C22×D12—31no—
190C22×D12—61no—
191C22×D12C2×D311yescharacteristic
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×C4×D3C2×D311yescharacteristic
199C22×C4×D3C2×D311yescharacteristic
200C3×#123—38no—
201C3×#117—38no—
202C2×C3×C4⋊C4—21no—
203C2×C3×C4⋊C4—31no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C4⋊C4C2×D311yescharacteristic
206C2×C3×C4⋊C4C2×D311yescharacteristic
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4—31no—
210C2×C3×C22⋊C4—31no—
211C2×C3×C22⋊C4—31no—
212C2×C3×C42—31no—
213C2×C3×C42—31no—
214C2×#217—31no—
215#940—38no—
216#939—38no—
217#930—38no—
218#930—38no—
219#930—38no—
220C4×#67—38no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—61no—
231C2×(C2×D3)⋊C4—61no—
232C2×(C2×D3)⋊C4—61no—
233C2×(C2×D3)⋊C4C2×D311yescharacteristic
234C2×(C2×D3)⋊C4C2×D311yescharacteristic
235C2×(C2×D3)⋊C4C2×D311yescharacteristic
236C2×(C2×D3)⋊C4C2×D311yescharacteristic
237C2×(C2×D3)⋊C4C2×D311yescharacteristic
238C2×C4⋊Dic3—31no—
239C2×C4⋊Dic3—31no—
240C2×C4⋊Dic3—31no—
241C2×C4⋊Dic3C2×D311yescharacteristic
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—61no—
250C2×Dic3⋊C4C2×D311yescharacteristic
251C2×C4×Dic3C2×D311yescharacteristic
252C2×C4×Dic3C2×D311yescharacteristic
253#895—38no—
254#894—38no—
255#894—38no—
256#894—38no—
257#894—38no—
258#894—68no—
259#894C2×D318yescomplemented
260#892C2×D318yescomplemented
261#889—38no—
262#886—38no—
263#884—38no—
264#884—38no—
265#884—38no—
266#884—38no—
267#884—38no—
268#884—38no—
269#884—38no—
270#883—38no—
271#67⋊C4—38no—
272#874—38no—
273C4×D12—38no—
274C4×D12—38no—
275#870—38no—
276C23×C32C2411yescharacteristic
277C22×C3⋊D3—22no—
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3—22no—
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3C2412yes—
284C22×C3⋊D3C2412yes—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3C2412yes—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C2×C32×C4—22no—
298C2×C32×C4—22no—
299C2×C32×C4—22no—
300C2×C32×C4C2412yes—
301C2×C32×C4C2412yes—
302C2×C32×C4C2412yes—
303C2×C3⋊Dic3—22no—
304C2×C3⋊Dic3—22no—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2412yes—
307C4⋊(C3⋊D3)—44no—
308C4×C3⋊D3—44no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3#4114yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C3×D12—44no—
320C3×C4×D3—28no—
321C3×C4×D3—44no—
322#626—28no—
323#626—28no—
324#626—44no—
325#626—44no—
326#626—44no—
327#626—44no—
328#625—44no—
329#625—44no—
330#624—44no—
331D3×Dic3—44no—
332#540—916no—
333C2×#127—91no—
334C2×#125—91no—
335C2×#123—31no—
336C2×#123—91no—
337C2×#123—91no—
338C2×#123—91no—
339C2×#121—91no—
340C2×#121—91no—
341C2×#121—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#121—91no—
345C2×C4×D4—91no—
346C2×C4×D4—91no—
347C2×#117—31no—
348C24×C3—31no—
349C24×C3—31no—
350C24×C3—31no—
351C23×D3—31no—
352C23×D3—31no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—61no—
356C23×D3—61no—
357C23×D3C22×D311yescharacteristic
358C23×D3C22×D311yescharacteristic
359C23×D3C22×D311yescharacteristic
360C2×C3×D4—34no—
361C2×C3×D4—122no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—34no—
371C22×C3×C4—34no—
372C22×C3×C4—64no—
373C22×C3×C4—122no—
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—34no—
383C2×#67—34no—
384C2×#67—34no—
385C2×#67—34no—
386C2×#67—34no—
387C2×#67—34no—
388C2×#67—34no—
389C2×#67—34no—
390C2×#67—64no—
391C2×#67—64no—
392C2×#67—122no—
393C2×#67—122no—
394C2×#67—122no—
395C2×#67—122no—
396C2×#67—122no—
397C2×#67—122no—
398C2×#67—122no—
399C2×#67—122no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—31no—
404C22×Dic3—34no—
405C22×Dic3—61no—
406C22×Dic3—61no—
407C22×Dic3—122no—
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C2×D12—34no—
414C2×D12—34no—
415C2×D12—34no—
416C2×D12—34no—
417C2×D12—34no—
418C2×D12—34no—
419C2×D12—34no—
420C2×D12—34no—
421C2×D12—42no—
422C2×D12—64no—
423C2×D12—64no—
424C2×D12—64no—
425C2×D12—122no—
426C2×D12—122no—
427C2×D12—124no—
428C2×D12—122no—
429C2×D12—122no—
430C2×D12—122no—
431C2×D12—122no—
432C2×D12C22×D314yes—
433C2×C4×D3—24no—
434C2×C4×D3—34no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—42no—
440C2×C4×D3—64no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3—122no—
446C2×C4×D3—124no—
447C2×C4×D3C22×D314yes—
448C2×C4×D3C22×D314yes—
449C3×C4⋊C4—24no—
450C3×C4⋊C4—34no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4C22×D314yes—
453C3×C4⋊C4C22×D314yes—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459C3×C42—34no—
460C3×C42—34no—
461#217—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—34no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—64no—
472(C2×D3)⋊C4—64no—
473(C2×D3)⋊C4—64no—
474(C2×D3)⋊C4C22×D314yes—
475(C2×D3)⋊C4C22×D314yes—
476(C2×D3)⋊C4C22×D314yes—
477(C2×D3)⋊C4C22×D314yes—
478(C2×D3)⋊C4C22×D314yes—
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3C22×D314yes—
483Dic3⋊C4—34no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—64no—
491Dic3⋊C4C22×D314yes—
492C4×Dic3C22×D314yes—
493C4×Dic3C22×D314yes—
494C22×C32C2×#4112yes—
495C22×C32H(5,𝔽2)12yes—
496C22×C32H(5,𝔽2)12yes—
497C22×C32C2511yescharacteristic
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—22no—
504C2×C3⋊D3—44no—
505C2×C3⋊D3—44no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—44no—
516C2×C3×D3—44no—
517C2×C3×D3—44no—
518C32×C4—22no—
519C32×C4—22no—
520C32×C4—22no—
521C3⋊Dic3—22no—
522C3⋊Dic3—22no—
523C3×Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3C2×#4114yes—
528C22×D4—31no—
529C22×D4—91no—
530C22×D4—91no—
531C22×D4—91no—
532C22×D4—91no—
533C22×D4—91no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C23×C4—31no—
539C23×C4—31no—
540C23×C4—91no—
541C23×C4—91no—
542C23×C4—91no—
543#127—98no—
544#125—98no—
545#123—38no—
546#123—98no—
547#123—98no—
548#123—98no—
549#121—98no—
550#121—98no—
551#121—98no—
552#121—98no—
553#121—98no—
554#121—98no—
555C4×D4—98no—
556C4×D4—98no—
557#117—38no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4D3211yescharacteristic
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C42—31no—
577C2×C42—31no—
578C23×C3—21no—
579C23×C3—32no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—62no—
583C23×C3—62no—
584C23×C3—62no—
585C23×C3—62no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—62no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3C23×D311yescharacteristic
592C23×C3C23×D311yescharacteristic
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—32no—
603C22×D3—32no—
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—62no—
607C22×D3—62no—
608C22×D3—64no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—122no—
622C22×D3—122no—
623C22×D3—122no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3C23×D312yes—
627C22×D3C23×D312yes—
628C22×D3C23×D312yes—
629C3×D4—124no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—34no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—42no—
646C2×C3×C4—42no—
647C2×C3×C4—42no—
648C2×C3×C4—68no—
649C2×C3×C4—62no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—124no—
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D312yes—
656C2×C3×C4C23×D312yes—
657C2×C3×C4C23×D312yes—
658C2×C3×C4C23×D312yes—
659C2×C3×C4C23×D312yes—
660#67—68no—
661#67—68no—
662#67—124no—
663#67—124no—
664#67—124no—
665#67—124no—
666#67—124no—
667#67—124no—
668#67—124no—
669#67—124no—
670C2×Dic3—22no—
671C2×Dic3—22no—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—62no—
679C2×Dic3—62no—
680C2×Dic3—62no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—122no—
685C2×Dic3—122no—
686C2×Dic3—124no—
687C2×Dic3#23514yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D312yes—
690C2×Dic3C23×D312yes—
691C2×Dic3C23×D312yes—
692C2×Dic3C23×D312yes—
693D12—44no—
694D12—68no—
695D12—68no—
696D12—124no—
697D12—124no—
698D12—128no—
699D12—124no—
700D12—124no—
701D12—124no—
702D12—124no—
703C4×D3—28no—
704C4×D3—44no—
705C4×D3—124no—
706C4×D3—124no—
707C4×D3—124no—
708C4×D3—124no—
709C4×D3—124no—
710C4×D3—128no—
711C2×C32#54014yescomplemented
712C2×C32C22×#4111yescharacteristic
713C2×C32C2×H(5,𝔽2)11yescharacteristic
714C2×C32C2×H(5,𝔽2)11yescharacteristic
715C3⋊D3—42no—
716C3⋊D3—42no—
717C3×D3—42no—
718C3×D3—42no—
719C3×D3—42no—
720C24—31no—
721C24—31no—
722C24—31no—
723C24—91no—
724C24—91no—
725C2×D4—34no—
726C2×D4—94no—
727C2×D4—94no—
728C2×D4—94no—
729C2×D4—94no—
730C2×D4—94no—
731C2×D4—94no—
732C2×D4—94no—
733C2×D4—94no—
734C2×D4—94no—
735C2×D4—122no—
736C2×D4—184no—
737C2×D4—184no—
738C2×D4—362no—
739C2×D4—362no—
740C2×D4—362no—
741C2×D4—362no—
742C2×D4—362no—
743C2×D4—362no—
744C2×D4—362no—
745C22×C4—31no—
746C22×C4—31no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—34no—
751C22×C4—34no—
752C22×C4—64no—
753C22×C4—94no—
754C22×C4—94no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—94no—
758C22×C4—122no—
759C22×C4—362no—
760C22×C4—362no—
761C22×C4—362no—
762C22×C4C2×D3211yescharacteristic
763C22×C4C2×D3211yescharacteristic
764C22×C4C2×D3211yescharacteristic
765C4⋊C4—34no—
766C4⋊C4—34no—
767C4⋊C4—94no—
768C4⋊C4—94no—
769C4⋊C4—94no—
770C4⋊C4—94no—
771C4⋊C4—94no—
772C4⋊C4C2×D3214yes—
773C22⋊C4—34no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—34no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C42—34no—
784C42—34no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—21no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—124no—
799C22×C3—124no—
800C22×C3—124no—
801C22×C3C2×#23512yes—
802C22×C3#100412yes—
803C22×C3D3×#4112yes—
804C22×C3#100912yes—
805C22×C3#100912yes—
806C22×C3#100912yes—
807C22×C3C24×D311yescharacteristic
808C22×C3C24×D311yescharacteristic
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—44no—
819C2×D3—44no—
820C2×D3—44no—
821C2×D3—64no—
822C2×D3—62no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—122no—
835C2×D3—122no—
836C2×D3—122no—
837C2×D3—122no—
838C2×D3—122no—
839C2×D3—128no—
840C2×D3—124no—
841C2×D3—124no—
842C2×D3—124no—
843C2×D3—124no—
844C2×D3—244no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—22no—
848C3×C4—22no—
849C3×C4—22no—
850C3×C4—22no—
851C3×C4—34no—
852C3×C4—42no—
853C3×C4—42no—
854C3×C4—42no—
855C3×C4—62no—
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—62no—
859Dic3—22no—
860Dic3—22no—
861Dic3—22no—
862Dic3—22no—
863Dic3—62no—
864Dic3—62no—
865Dic3—62no—
866Dic3—62no—
867Dic3—122no—
868Dic3—122no—
869Dic3C2×#23514yes—
870C32C2×#54011yescharacteristic, complemented, Sylow
871C23—32no—
872C23—32no—
873C23—32no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—92no—
884C23—92no—
885C23—182no—
886C23—182no—
887C23—182no—
888C23—182no—
889C23—182no—
890C23—182no—
891C23C22×D3211yescharacteristic
892D4—124no—
893D4—188no—
894D4—188no—
895D4—364no—
896D4—364no—
897D4—364no—
898D4—364no—
899D4—364no—
900D4—364no—
901D4—364no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—34no—
906C2×C4—32no—
907C2×C4—32no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—32no—
911C2×C4—68no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—62no—
916C2×C4—92no—
917C2×C4—92no—
918C2×C4—124no—
919C2×C4—182no—
920C2×C4—182no—
921C2×C4—364no—
922C2×C4—364no—
923C2×C4—364no—
924C2×C4C22×D3212yes—
925C2×C4C22×D3212yes—
926C2×C4C22×D3212yes—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—24no—
931C2×C3—122no—
932C2×C3—122no—
933C2×C3—122no—
934C2×C3#553514yescomplemented
935C2×C3#566314yescomplemented
936C2×C3C22×#23511yescharacteristic
937C2×C3C2×#100411yescharacteristic
938C2×C3C2×D3×#4111yescharacteristic
939C2×C3C2×#100911yescharacteristic
940C2×C3C2×#100911yescharacteristic
941C2×C3C2×#100911yescharacteristic
942D3—42no—
943D3—42no—
944D3—42no—
945D3—124no—
946D3—122no—
947D3—122no—
948D3—122no—
949D3—122no—
950D3—242no—
951C22—62no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—124no—
961C22—124no—
962C22—124no—
963C22—182no—
964C22—182no—
965C22—182no—
966C22—182no—
967C22—182no—
968C22—182no—
969C22—364no—
970C22—364no—
971C22D3×#23512yes—
972C22#6431412yes—
973C22#6432012yes—
974C22C23×D3211yescharacteristic
975C4—22no—
976C4—22no—
977C4—22no—
978C4—34no—
979C4—62no—
980C4—62no—
981C4—62no—
982C4—62no—
983C4—182no—
984C4—182no—
985C3—21no—
986C3C2×#553511yescharacteristic, complemented
987C3C2×#566311yescharacteristic, complemented
988C2—122no—
989C2—122no—
990C2—122no—
991C2—362no—
992C2—362no—
993C2#1059454614yesdirect product factor
994C2C2×D3×#23511yescharacteristic
995C2C2×#6431411yescharacteristic
996C2C2×#6432011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64103C2semidirect
2. C2×C3×#894C2semidirect
3. C2×C3×#892C2semidirect
4. C2×#63912C2semidirect
5. C2×#63911C2semidirect
6. C2×#63910C2semidirect
7. C2×#63906C2semidirect
8. C2×#63906C2semidirect
9. C2×#63906C2semidirect
10. C2×C4×#626C2semidirect
11. C2×#63890C2semidirect
12. C2×#63885C2semidirect
13. C2×#63880C2semidirect
14. C2×#63867C2semidirect
15. C2×#63854C2semidirect
16. #10594546C2direct (N × H)
39. #64103C22semidirect
49. C3×#894C22semidirect
50. C3×#892C22semidirect
57. #63912C22semidirect
58. #63911C22semidirect
59. #63910C22semidirect
60. #63906C22semidirect
61. #63906C22semidirect
62. #63906C22semidirect
63. C4×#626C22semidirect
64. #63890C22semidirect
65. #63885C22semidirect
66. #63880C22semidirect
67. #63867C22semidirect
68. #63854C22semidirect
85. C2×#894D3semidirect
86. C2×#892D3semidirect
259. #894C2×D3semidirect
260. #892C2×D3semidirect
711. C2×C32#540semidirect
870. C32C2×#540semidirect
934. C2×C3#5535semidirect
935. C2×C3#5663semidirect
986. C3C2×#5535semidirect
987. C3C2×#5663semidirect
993. C2#10594546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641032
C2×C3×#8942
C2×C3×#8922
C2×#639122
C2×#639112
C2×#639102
C2×#639062
C2×C4×#6262
C2×#638902
C2×#638852
C2×#638802
C2×#638672
C2×#638542
#105945462
C2×#56633
C2×#55353