Finite Group Databasebeta

← C2×#10594013 #11901308

Subgroups — C2×#10594013 #11901308

Order 1152.

2837 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64084C211yesmaximal, characteristic, complemented
2C2×C3×#876C211yesmaximal, characteristic, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C2×#63923C211yesmaximal, characteristic, complemented
5C2×#63922C211yesmaximal, characteristic, complemented
6C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C2×#63913C211yesmaximal, characteristic, complemented
8C2×#63910C211yesmaximal, characteristic, complemented
9C2×#63906C211yesmaximal, characteristic, complemented
10C2×#63904C211yesmaximal, characteristic, complemented
11C2×#63896C211yesmaximal, characteristic, complemented
12C2×#63886C211yesmaximal, characteristic, complemented
13C2×#63854C211yesmaximal, characteristic, complemented
14C2×#63850C211yesmaximal, characteristic, complemented
15C2×#63848C211yesmaximal, characteristic, complemented
16#10594013C2116yesmaximal, direct product factor
17C2×#5704—31nomaximal
18C2×#5560—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic, complemented
29C22×#625C2211yescharacteristic
30C22×#624C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic
32C2×C32×C42C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic, complemented
36C2×#3752C2211yescharacteristic, complemented
37#64084C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C3×#876C2218yescomplemented
48C3×C4×D12C2218yescomplemented
49C2×#3724C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×Dic32C2211yescharacteristic, complemented
57#63923C2218yescomplemented
58#63922C2218yescomplemented
59D3×(C2×D3)⋊C4C2218yescomplemented
60#63913C2218yescomplemented
61#63910C2218yescomplemented
62#63906C2218yescomplemented
63#63904C2218yescomplemented
64#63896C2218yescomplemented
65#63886C2218yescomplemented
66#63854C2218yescomplemented
67#63850C2218yescomplemented
68#63848C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#937—31no—
73C2×#930—31no—
74C2×#929—31no—
75C2×C4×#67—31no—
76C22×(C2×D3)⋊C4—31no—
77#5704—316no—
78#5560—316no—
79C2×#898—31no—
80C2×#898—31no—
81C2×#896—31no—
82C2×#895—31no—
83C2×#895—31no—
84C2×#894—31no—
85C2×#894—31no—
86C2×#893—31no—
87C2×#885—31no—
88C2×#885—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#883—31no—
92C2×#882—31no—
93C2×#882—31no—
94C2×#882—31no—
95C2×D3×C22⋊C4—31no—
96C2×#878—31no—
97C2×#876D311yescharacteristic, complemented
98C2×#875—31no—
99C2×#875—31no—
100C2×#875—61no—
101C2×C4×D12D311yescharacteristic, complemented
102C23×C3⋊D3C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C22×D32—24no—
108C22×D32—42no—
109C22×D32—42no—
110C22×D32C2314yes—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C4⋊(C3⋊D3)—42no—
117C2×C4⋊(C3⋊D3)C2314yes—
118C2×#634—42no—
119C2×#634C2314yescomplemented
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×D12—24no—
126C2×C3×D12C2314yes—
127C2×C3×C4×D3—42no—
128C2×C3×C4×D3—42no—
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2314yescomplemented
131C2×#626—24no—
132C2×#626—42no—
133C2×#626—42no—
134C2×#626—42no—
135C2×#626C2314yes—
136C2×#626C2314yes—
137C2×#626C2314yes—
138C2×#626C2314yescomplemented
139C2×#625—42no—
140C2×#625C2314yes—
141C2×#624—42no—
142C2×#624C2314yescomplemented
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yes—
145C32×C42C2314yescomplemented
146#3752C2314yes—
147#3752C2314yes—
148#3752C2314yescomplemented
149#3752C2314yescomplemented
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yescomplemented
155C3×C4⋊Dic3C2314yescomplemented
156C3×Dic3⋊C4C2314yescomplemented
157C3×Dic3⋊C4C2314yescomplemented
158C3×Dic3⋊C4C2314yescomplemented
159#3724C2314yescomplemented
160Dic3⋊Dic3C2314yescomplemented
161#3722C2314yes—
162#3722C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×D4—31no—
171C23×C3×C4—31no—
172C23×C3×C4—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C23×Dic3—31no—
180C22×D12—31no—
181C22×D12—31no—
182C22×D12—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—61no—
187C22×D12C2×D311yescharacteristic
188C22×C4×D3—31no—
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3C2×D311yescharacteristic
192C22×C4×D3C2×D311yescharacteristic, complemented
193C22×Dic6—31no—
194C22×Dic6—31no—
195C22×Dic6—61no—
196C3×#126—38no—
197C3×C4×D4—38no—
198C2×C3×C4⋊C4—31no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C42—21no—
208C2×C3×C42C2×D311yescharacteristic, complemented
209C2×C3×C42C2×D311yescharacteristic, complemented
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—31no—
213#939—38no—
214#937—38no—
215#930—38no—
216#929—38no—
217C4×#67—38no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
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—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—38no—
234C2×(C2×D3)⋊C4—61no—
235C2×(C2×D3)⋊C4—61no—
236C2×(C2×D3)⋊C4—61no—
237C2×(C2×D3)⋊C4—61no—
238C2×(C2×D3)⋊C4C2×D311yescharacteristic
239C2×(C2×D3)⋊C4C2×D311yescharacteristic
240C2×(C2×D3)⋊C4C2×D311yescharacteristic
241C2×(C2×D3)⋊C4C2×D311yescharacteristic
242C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
243C2×C4⋊Dic3—31no—
244C2×C4⋊Dic3C2×D311yescharacteristic, complemented
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4C2×D311yescharacteristic, complemented
249C2×Dic3⋊C4C2×D311yescharacteristic, complemented
250C2×Dic3⋊C4C2×D311yescharacteristic, complemented
251C2×C4×Dic3—31no—
252C2×C4×Dic3—31no—
253#898—38no—
254#898—38no—
255#896—38no—
256#895—38no—
257#895—38no—
258#894—38no—
259#894—38no—
260#893—38no—
261#885—38no—
262#885—38no—
263#884—38no—
264#884—38no—
265#883—38no—
266#882—38no—
267#882—38no—
268#882—38no—
269D3×C22⋊C4—38no—
270#878—38no—
271#876C2×D318yescomplemented
272#875—38no—
273#875—38no—
274#875—68no—
275C4×D12C2×D318yescomplemented
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#4114yes—
294C22×C3×D3C2412yes—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C2×D32—28no—
298C2×D32—44no—
299C2×D32—44no—
300C2×D32—416no—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4—22no—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3C2412yes—
310C2×C3⋊Dic3C2412yes—
311C4⋊(C3⋊D3)—44no—
312#634—44no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C3×D12—28no—
324C3×C4×D3—44no—
325C3×C4×D3—44no—
326#626—28no—
327#626—44no—
328#626—44no—
329#626—44no—
330#625—44no—
331#624—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—31no—
335C2×#126—91no—
336C2×#124—91no—
337C2×#124—91no—
338C2×#123—91no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#120—91no—
345C2×#120—91no—
346C2×C4×D4—31no—
347C2×C4×D4—91no—
348C22×C22⋊C4—91no—
349C24×C3—31no—
350C24×C3—31no—
351C24×C3—31no—
352C23×D3—31no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—34no—
357C23×D3—34no—
358C23×D3—61no—
359C23×D3—61no—
360C23×D3—64no—
361C23×D3—64no—
362C23×D3—122no—
363C23×D3—122no—
364C23×D3—122no—
365C23×D3—122no—
366C23×D3C22×D311yescharacteristic
367C23×D3C22×D311yescharacteristic
368C23×D3C22×D311yescharacteristic
369C2×C3×D4—34no—
370C2×C3×D4—64no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—21no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—34no—
380C22×C3×C4—34no—
381C22×C3×C4—122no—
382C22×C3×C4—122no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—64no—
396C2×#67—122no—
397C2×#67—122no—
398C2×#67—122no—
399C2×#67—122no—
400C2×#67—122no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—34no—
406C22×Dic3—61no—
407C22×Dic3—61no—
408C22×Dic3—122no—
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C2×D12—24no—
415C2×D12—34no—
416C2×D12—34no—
417C2×D12—34no—
418C2×D12—34no—
419C2×D12—34no—
420C2×D12—34no—
421C2×D12—64no—
422C2×D12—64no—
423C2×D12—122no—
424C2×D12—122no—
425C2×D12—124no—
426C2×D12—122no—
427C2×D12—122no—
428C2×D12—122no—
429C2×D12C22×D314yes—
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—34no—
433C2×C4×D3—42no—
434C2×C4×D3—42no—
435C2×C4×D3—122no—
436C2×C4×D3—122no—
437C2×C4×D3—122no—
438C2×C4×D3C22×D314yes—
439C2×C4×D3C22×D314yescomplemented
440C2×Dic6—34no—
441C2×Dic6—34no—
442C2×Dic6—64no—
443C2×Dic6—122no—
444C2×Dic6—122no—
445C2×Dic6—124no—
446C3×C4⋊C4—34no—
447C3×C4⋊C4—34no—
448C3×C4⋊C4—34no—
449C3×C4⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4—34no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C42—24no—
456C3×C42C22×D314yescomplemented
457C3×C42C22×D314yescomplemented
458#217—34no—
459#217—34no—
460#217—34no—
461(C2×D3)⋊C4—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—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—64no—
477(C2×D3)⋊C4—64no—
478(C2×D3)⋊C4—64no—
479(C2×D3)⋊C4—64no—
480(C2×D3)⋊C4C22×D314yes—
481(C2×D3)⋊C4C22×D314yes—
482(C2×D3)⋊C4C22×D314yes—
483(C2×D3)⋊C4C22×D314yes—
484(C2×D3)⋊C4C22×D314yescomplemented
485C4⋊Dic3—34no—
486C4⋊Dic3C22×D314yescomplemented
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4C22×D314yescomplemented
491Dic3⋊C4C22×D314yescomplemented
492Dic3⋊C4C22×D314yescomplemented
493C4×Dic3—34no—
494C4×Dic3—34no—
495C22×C32C2×#4112yes—
496C22×C32H(5,𝔽2)12yes—
497C22×C32H(5,𝔽2)12yes—
498C22×C32C2511yescharacteristic
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—22no—
504C2×C3⋊D3—22no—
505C2×C3⋊D3—44no—
506C2×C3⋊D3—44no—
507C2×C3×D3—28no—
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—22no—
516C2×C3×D3—44no—
517C2×C3×D3—44no—
518C2×C3×D3C2×#4114yes—
519D32—416no—
520C32×C4—22no—
521C32×C4—22no—
522C32×C4—22no—
523C3⋊Dic3—22no—
524C3⋊Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C25—91no—
531C22×Q8—91no—
532C22×D4—31no—
533C22×D4—91no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C23×C4—31no—
540C23×C4—31no—
541C23×C4—91no—
542C23×C4—91no—
543#126—38no—
544#126—98no—
545#124—98no—
546#124—98no—
547#123—98no—
548#123—98no—
549C22⋊Q8—98no—
550#121—98no—
551#121—98no—
552#121—98no—
553#120—98no—
554#120—98no—
555C4×D4—38no—
556C4×D4—98no—
557C2×C4⋊C4—31no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—98no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C42—91no—
579C2×C42D3211yescharacteristic, complemented
580C23×C3—21no—
581C23×C3—34no—
582C23×C3—32no—
583C23×C3—32no—
584C23×C3—32no—
585C23×C3—62no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—62no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3—62no—
592C23×C3—62no—
593C23×C3C23×D311yescharacteristic
594C23×C3C23×D311yescharacteristic
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—32no—
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—32no—
607C22×D3—62no—
608C22×D3—62no—
609C22×D3—68no—
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—62no—
622C22×D3—68no—
623C22×D3—122no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—124no—
630C22×D3—124no—
631C22×D3—124no—
632C22×D3—124no—
633C22×D3—1216no—
634C22×D3—1216no—
635C22×D3#23514yes—
636C22×D3C23×D312yes—
637C22×D3C23×D312yes—
638C22×D3C23×D312yes—
639C3×D4—68no—
640C2×C3×C4—24no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—42no—
656C2×C3×C4—42no—
657C2×C3×C4—62no—
658C2×C3×C4—62no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—124no—
663C2×C3×C4—124no—
664C2×C3×C4C23×D312yes—
665C2×C3×C4C23×D312yes—
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669C2×C3×C4C23×D312yes—
670#67—68no—
671#67—124no—
672#67—124no—
673#67—124no—
674#67—124no—
675#67—124no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—62no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—122no—
692C2×Dic3—122no—
693C2×Dic3—124no—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D312yes—
699D12—28no—
700D12—68no—
701D12—124no—
702D12—124no—
703D12—128no—
704D12—124no—
705D12—124no—
706D12—124no—
707C4×D3—44no—
708C4×D3—44no—
709C4×D3—124no—
710C4×D3—124no—
711C4×D3—124no—
712Dic6—124no—
713Dic6—124no—
714Dic6—128no—
715C2×C32#53814yescomplemented
716C2×C32C22×#4111yescharacteristic
717C2×C32C2×H(5,𝔽2)11yescharacteristic
718C2×C32C2×H(5,𝔽2)11yescharacteristic
719C3⋊D3—42no—
720C3⋊D3—42no—
721C3×D3—24no—
722C3×D3—42no—
723C3×D3—42no—
724C24—31no—
725C24—31no—
726C24—31no—
727C24—94no—
728C24—91no—
729C24—91no—
730C24—184no—
731C24—362no—
732C24—362no—
733C2×Q8—94no—
734C2×Q8—362no—
735C2×D4—34no—
736C2×D4—64no—
737C2×D4—94no—
738C2×D4—94no—
739C2×D4—94no—
740C2×D4—94no—
741C2×D4—94no—
742C2×D4—94no—
743C2×D4—184no—
744C2×D4—362no—
745C2×D4—362no—
746C2×D4—362no—
747C2×D4—362no—
748C2×D4—362no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—34no—
755C22×C4—34no—
756C22×C4—94no—
757C22×C4—94no—
758C22×C4—91no—
759C22×C4—91no—
760C22×C4—122no—
761C22×C4—122no—
762C22×C4—362no—
763C22×C4—362no—
764C22×C4C2×D3211yescharacteristic
765C22×C4C2×D3211yescharacteristic
766C22×C4C2×D3211yescharacteristic
767C4⋊C4—34no—
768C4⋊C4—34no—
769C4⋊C4—34no—
770C4⋊C4—34no—
771C4⋊C4—94no—
772C4⋊C4—94no—
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—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C42—94no—
788C42C2×D3214yescomplemented
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—21no—
793C22×C3—34no—
794C22×C3—68no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—124no—
804C22×C3—124no—
805C22×C3C2×#23512yes—
806C22×C3#100412yes—
807C22×C3D3×#4112yes—
808C22×C3#100912yes—
809C22×C3#100912yes—
810C22×C3#100912yes—
811C22×C3C24×D311yescharacteristic
812C22×C3C24×D311yescharacteristic
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—28no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—22no—
822C2×D3—44no—
823C2×D3—44no—
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—62no—
835C2×D3—62no—
836C2×D3—122no—
837C2×D3—122no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—1216no—
843C2×D3—1216no—
844C2×D3—124no—
845C2×D3—124no—
846C2×D3—124no—
847C2×D3—124no—
848C2×D3—244no—
849C2×D3—244no—
850C2×D3C2×#23514yes—
851C3×C4—24no—
852C3×C4—22no—
853C3×C4—22no—
854C3×C4—22no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—22no—
858C3×C4—42no—
859C3×C4—42no—
860C3×C4—62no—
861C3×C4—62no—
862C3×C4—62no—
863C3×C4—62no—
864C3×C4—62no—
865Dic3—22no—
866Dic3—22no—
867Dic3—22no—
868Dic3—22no—
869Dic3—22no—
870Dic3—62no—
871Dic3—62no—
872Dic3—62no—
873Dic3—62no—
874Dic3—122no—
875Dic3—122no—
876C32C2×#53811yescharacteristic, complemented, Sylow
877C23—34no—
878C23—32no—
879C23—32no—
880C23—32no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—92no—
890C23—92no—
891C23—188no—
892C23—182no—
893C23—182no—
894C23—182no—
895C23—182no—
896C23—182no—
897C23—182no—
898C23—364no—
899C23—364no—
900C23—3616no—
901C23C22×D3211yescharacteristic
902Q8—364no—
903D4—68no—
904D4—188no—
905D4—364no—
906D4—364no—
907D4—364no—
908D4—364no—
909D4—364no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—32no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—92no—
924C2×C4—92no—
925C2×C4—124no—
926C2×C4—124no—
927C2×C4—182no—
928C2×C4—182no—
929C2×C4—364no—
930C2×C4—364no—
931C2×C4C22×D3212yes—
932C2×C4C22×D3212yes—
933C2×C4C22×D3212yes—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—24no—
938C2×C3—64no—
939C2×C3—122no—
940C2×C3—122no—
941C2×C3#556014yescomplemented
942C2×C3#570414yescomplemented
943C2×C3C22×#23511yescharacteristic
944C2×C3C2×#100411yescharacteristic
945C2×C3C2×D3×#4111yescharacteristic
946C2×C3C2×#100911yescharacteristic
947C2×C3C2×#100911yescharacteristic
948C2×C3C2×#100911yescharacteristic
949D3—24no—
950D3—42no—
951D3—42no—
952D3—122no—
953D3—122no—
954D3—122no—
955D3—122no—
956D3—242no—
957D3—242no—
958C22—34no—
959C22—62no—
960C22—62no—
961C22—68no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—124no—
969C22—124no—
970C22—182no—
971C22—182no—
972C22—182no—
973C22—182no—
974C22—182no—
975C22—182no—
976C22—3616no—
977C22—364no—
978C22—364no—
979C22D3×#23512yes—
980C22#6430712yes—
981C22#6430812yes—
982C22C23×D3211yescharacteristic
983C4—22no—
984C4—22no—
985C4—22no—
986C4—62no—
987C4—62no—
988C4—62no—
989C4—62no—
990C4—62no—
991C4—182no—
992C4—182no—
993C3—21no—
994C3C2×#556011yescharacteristic, complemented
995C3C2×#570411yescharacteristic, complemented
996C2—64no—
997C2—122no—
998C2—122no—
999C2—362no—
1000C2—362no—
1001C2#1059401314yesdirect product factor
1002C2C2×D3×#23511yescharacteristic
1003C2C2×#6430711yescharacteristic
1004C2C2×#6430811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64084C2semidirect
2. C2×C3×#876C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C2×#63923C2semidirect
5. C2×#63922C2semidirect
6. C2×D3×(C2×D3)⋊C4C2semidirect
7. C2×#63913C2semidirect
8. C2×#63910C2semidirect
9. C2×#63906C2semidirect
10. C2×#63904C2semidirect
11. C2×#63896C2semidirect
12. C2×#63886C2semidirect
13. C2×#63854C2semidirect
14. C2×#63850C2semidirect
15. C2×#63848C2semidirect
16. #10594013C2direct (N × H)
21. C22×#634C22semidirect
24. C22×C3×C4×D3C22semidirect
28. C22×#626C22semidirect
30. C22×#624C22semidirect
32. C2×C32×C42C22semidirect
35. C2×#3752C22semidirect
36. C2×#3752C22semidirect
37. #64084C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C3×#876C22semidirect
48. C3×C4×D12C22semidirect
49. C2×#3724C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
55. C2×(C2×D3)⋊Dic3C22semidirect
56. C2×Dic32C22semidirect
57. #63923C22semidirect
58. #63922C22semidirect
59. D3×(C2×D3)⋊C4C22semidirect
60. #63913C22semidirect
61. #63910C22semidirect
62. #63906C22semidirect
63. #63904C22semidirect
64. #63896C22semidirect
65. #63886C22semidirect
66. #63854C22semidirect
67. #63850C22semidirect
68. #63848C22semidirect
97. C2×#876D3semidirect
101. C2×C4×D12D3semidirect
119. C2×#634C23semidirect
130. C2×C3×C4×D3C23semidirect
138. C2×#626C23semidirect
142. C2×#624C23semidirect
145. C32×C42C23semidirect
148. #3752C23semidirect
149. #3752C23semidirect
154. C3×(C2×D3)⋊C4C23semidirect
155. C3×C4⋊Dic3C23semidirect
156. C3×Dic3⋊C4C23semidirect
157. C3×Dic3⋊C4C23semidirect
158. C3×Dic3⋊C4C23semidirect
159. #3724C23semidirect
160. Dic3⋊Dic3C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. Dic32C23semidirect
192. C22×C4×D3C2×D3semidirect
208. C2×C3×C42C2×D3semidirect
209. C2×C3×C42C2×D3semidirect
242. C2×(C2×D3)⋊C4C2×D3semidirect
244. C2×C4⋊Dic3C2×D3semidirect
248. C2×Dic3⋊C4C2×D3semidirect
249. C2×Dic3⋊C4C2×D3semidirect
250. C2×Dic3⋊C4C2×D3semidirect
271. #876C2×D3semidirect
275. C4×D12C2×D3semidirect
439. C2×C4×D3C22×D3semidirect
456. C3×C42C22×D3semidirect
457. C3×C42C22×D3semidirect
484. (C2×D3)⋊C4C22×D3semidirect
486. C4⋊Dic3C22×D3semidirect
490. Dic3⋊C4C22×D3semidirect
491. Dic3⋊C4C22×D3semidirect
492. Dic3⋊C4C22×D3semidirect
579. C2×C42D32semidirect
715. C2×C32#538semidirect
788. C42C2×D32semidirect
876. C32C2×#538semidirect
941. C2×C3#5560semidirect
942. C2×C3#5704semidirect
994. C3C2×#5560semidirect
995. C3C2×#5704semidirect
1001. C2#10594013direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640842
C2×C3×#8762
C2×C3×C4×D122
C2×#639232
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639132
C2×#639102
C2×#639062
C2×#639042
C2×#638962
C2×#638862
C2×#638542
C2×#638502
C2×#638482
#105940132
C2×#57043
C2×#55603