Finite Group Databasebeta

← C2×#10594019 #11901307

Subgroups — C2×#10594019 #11901307

Order 1152.

2885 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×#876C211yesmaximal, characteristic, complemented
3C2×C3×#875C211yesmaximal, characteristic, complemented
4C2×#63923C211yesmaximal, characteristic, complemented
5C2×#63922C211yesmaximal, characteristic, complemented
6C2×#63921C211yesmaximal, characteristic, complemented
7C2×#63912C211yesmaximal, characteristic, complemented
8C2×#63910C211yesmaximal, characteristic, complemented
9C2×#63907C211yesmaximal, characteristic, complemented
10C2×#63891C211yesmaximal, characteristic, complemented
11C2×#63888C211yesmaximal, characteristic, complemented
12C2×#63886C211yesmaximal, characteristic, complemented
13C2×#63881C211yesmaximal, characteristic, complemented
14C2×#63861C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594019C2116yesmaximal, direct product factor
17C2×#5704—31nomaximal
18C2×#5678—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic, complemented
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic, complemented
29C22×#625C2211yescharacteristic
30C22×#624C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×C32×C42C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic, complemented
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C4×C4⋊(C3⋊D3)C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C3×#876C2218yescomplemented
48C3×#875C2218yescomplemented
49C2×#3724C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic, complemented
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic, complemented
57#63923C2218yescomplemented
58#63922C2218yescomplemented
59#63921C2218yescomplemented
60#63912C2218yescomplemented
61#63910C2218yescomplemented
62#63907C2218yescomplemented
63#63891C2218yescomplemented
64#63888C2218yescomplemented
65#63886C2218yescomplemented
66#63881C2218yescomplemented
67#63861C2218yescomplemented
68#63853C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#124—31no—
71C2×#947—31no—
72C2×#946—31no—
73C2×#939—31no—
74C2×#937—31no—
75#5704—316no—
76#5678—316no—
77C2×#898—31no—
78C2×#896—31no—
79C2×#895—31no—
80C2×#895—31no—
81C2×#894—31no—
82C2×#893—31no—
83C2×#886—31no—
84C2×#885—31no—
85C2×#884—31no—
86C2×#884—31no—
87C2×#884—31no—
88C2×#883—31no—
89C2×#883—31no—
90C2×#882—31no—
91C2×#882—31no—
92C2×#882—31no—
93C2×#67⋊C4—31no—
94C2×D3×C22⋊C4—31no—
95C2×D3×C22⋊C4—31no—
96C2×#879—31no—
97C2×#876D311yescharacteristic, complemented
98C2×#875D311yescharacteristic, complemented
99C2×C4×D12—31no—
100C2×C4×D12—31no—
101C2×C4×D12—61no—
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)—24no—
117C2×C4⋊(C3⋊D3)C2314yes—
118C2×C4×C3⋊D3—42no—
119C2×C4×C3⋊D3—42no—
120C2×C4×C3⋊D3C2314yes—
121C2×C4×C3⋊D3C2314yescomplemented
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C2×C3×D12—42no—
128C2×C3×D12C2314yes—
129C2×C3×Dic6—42no—
130C2×C3×Dic6C2314yescomplemented
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×#624C2314yes—
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yescomplemented
145C32×C42C2314yescomplemented
146#3752C2314yes—
147#3752C2314yescomplemented
148C4⋊(C3⋊Dic3)C2314yescomplemented
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yescomplemented
155C3×(C2×D3)⋊C4C2314yescomplemented
156C3×Dic3⋊C4C2314yescomplemented
157C3×Dic3⋊C4C2314yescomplemented
158C3×Dic3⋊C4C2314yescomplemented
159#3724C2314yescomplemented
160Dic3⋊Dic3C2314yescomplemented
161#3722C2314yes—
162#3722C2314yescomplemented
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×Q8—31no—
171C22×C3×D4—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C23×Dic3—31no—
179C22×D12—31no—
180C22×D12—31no—
181C22×D12—31no—
182C22×D12—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×D12—61no—
186C22×D12C2×D311yescharacteristic
187C22×C4×D3—31no—
188C22×C4×D3—31no—
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—61no—
195C22×C4×D3—61no—
196C22×Dic6C2×D311yescharacteristic, complemented
197C3×#126—38no—
198C3×#124—38no—
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×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C42—21no—
210C2×C3×C42C2×D311yescharacteristic, complemented
211C2×C3×C42C2×D311yescharacteristic, complemented
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215#947—38no—
216#946—38no—
217#939—38no—
218#937—38no—
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—61no—
231C2×(C2×D3)⋊C4—61no—
232C2×(C2×D3)⋊C4C2×D311yescharacteristic
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, complemented
238C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
239C2×C4⋊Dic3—31no—
240C2×C4⋊Dic3—31no—
241C2×C4⋊Dic3—31no—
242C2×C4⋊Dic3—61no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4C2×D311yescharacteristic, complemented
247C2×Dic3⋊C4C2×D311yescharacteristic, complemented
248C2×Dic3⋊C4C2×D311yescharacteristic, complemented
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251#898—38no—
252#896—38no—
253#895—38no—
254#895—38no—
255#894—38no—
256#893—38no—
257#886—38no—
258#885—38no—
259#884—38no—
260#884—38no—
261#884—38no—
262#883—38no—
263#883—38no—
264#882—38no—
265#882—38no—
266#882—38no—
267#67⋊C4—38no—
268D3×C22⋊C4—38no—
269D3×C22⋊C4—38no—
270#879—38no—
271#876C2×D318yescomplemented
272#875C2×D318yescomplemented
273C4×D12—38no—
274C4×D12—38no—
275C4×D12—68no—
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#4114yes—
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×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)—28no—
312C4×C3⋊D3—44no—
313C4×C3⋊D3—44no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C3×D12—44no—
325C3×Dic6—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—31no—
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—91no—
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×Q8—34no—
370C2×C3×Q8—122no—
371C2×C3×D4—34no—
372C2×C3×D4—122no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C2×#67—34no—
388C2×#67—34no—
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—64no—
394C2×#67—122no—
395C2×#67—122no—
396C2×#67—122no—
397C2×#67—122no—
398C2×#67—122no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—34no—
404C22×Dic3—61no—
405C22×Dic3—61no—
406C22×Dic3—122no—
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C2×D12—34no—
413C2×D12—34no—
414C2×D12—34no—
415C2×D12—34no—
416C2×D12—34no—
417C2×D12—34no—
418C2×D12—42no—
419C2×D12—64no—
420C2×D12—64no—
421C2×D12—64no—
422C2×D12—68no—
423C2×D12—64no—
424C2×D12—122no—
425C2×D12—122no—
426C2×D12—122no—
427C2×D12C22×D314yes—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—34no—
435C2×C4×D3—64no—
436C2×C4×D3—64no—
437C2×C4×D3—122no—
438C2×C4×D3—122no—
439C2×C4×D3—122no—
440C2×C4×D3—122no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3—122no—
444C2×C4×D3—124no—
445C2×C4×D3—124no—
446C2×Dic6—42no—
447C2×Dic6C22×D314yescomplemented
448C3×C4⋊C4—34no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4—34no—
451C3×C22⋊C4—34no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C42—24no—
459C3×C42C22×D314yescomplemented
460C3×C42C22×D314yescomplemented
461#217—34no—
462#217—34no—
463#217—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—64no—
476(C2×D3)⋊C4—64no—
477(C2×D3)⋊C4C22×D314yes—
478(C2×D3)⋊C4C22×D314yes—
479(C2×D3)⋊C4C22×D314yes—
480(C2×D3)⋊C4C22×D314yes—
481(C2×D3)⋊C4C22×D314yes—
482(C2×D3)⋊C4C22×D314yescomplemented
483(C2×D3)⋊C4C22×D314yescomplemented
484C4⋊Dic3—34no—
485C4⋊Dic3—34no—
486C4⋊Dic3—34no—
487C4⋊Dic3—64no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4C22×D314yescomplemented
492Dic3⋊C4C22×D314yescomplemented
493Dic3⋊C4C22×D314yescomplemented
494C4×Dic3—34no—
495C4×Dic3—34no—
496C22×C32C2×#4112yes—
497C22×C32H(5,𝔽2)12yes—
498C22×C32H(5,𝔽2)12yes—
499C22×C32C2511yescharacteristic
500C2×C3⋊D3—22no—
501C2×C3⋊D3—28no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—22no—
504C2×C3⋊D3—22no—
505C2×C3⋊D3—22no—
506C2×C3⋊D3—44no—
507C2×C3⋊D3C2×#4114yes—
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—22no—
517C2×C3×D3—44no—
518C2×C3×D3—44no—
519C2×C3×D3—44no—
520D32—416no—
521C32×C4—22no—
522C32×C4—22no—
523C32×C4—22no—
524C3⋊Dic3—22no—
525C3⋊Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C25—91no—
532C22×Q8—31no—
533C22×D4—31no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C23×C4—91no—
541C23×C4—91no—
542C23×C4—91no—
543C23×C4—91no—
544#126—38no—
545#126—98no—
546#124—38no—
547#124—98no—
548#123—98no—
549#123—98no—
550C22⋊Q8—98no—
551#121—98no—
552#121—98no—
553#121—98no—
554#120—98no—
555#120—98no—
556C4×D4—98no—
557C4×D4—98no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—98no—
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×C22⋊C4—91no—
579C2×C42—91no—
580C2×C42D3211yescharacteristic, complemented
581C23×C3—21no—
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×C3—62no—
594C23×C3C23×D311yescharacteristic
595C23×C3C23×D311yescharacteristic
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—34no—
606C22×D3—34no—
607C22×D3—32no—
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—32no—
611C22×D3—64no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—68no—
615C22×D3—68no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—64no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3—124no—
632C22×D3—124no—
633C22×D3—124no—
634C22×D3—124no—
635C22×D3—1216no—
636C22×D3—1216no—
637C22×D3C23×D312yes—
638C22×D3C23×D312yes—
639C22×D3C23×D312yes—
640C3×Q8—124no—
641C3×D4—124no—
642C2×C3×C4—24no—
643C2×C3×C4—24no—
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—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—42no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
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—44no—
700D12—68no—
701D12—68no—
702D12—616no—
703D12—68no—
704D12—124no—
705D12—124no—
706D12—124no—
707C4×D3—124no—
708C4×D3—124no—
709C4×D3—124no—
710C4×D3—124no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3—128no—
715C4×D3—128no—
716Dic6—44no—
717C2×C32#53814yescomplemented
718C2×C32C22×#4111yescharacteristic
719C2×C32C2×H(5,𝔽2)11yescharacteristic
720C2×C32C2×H(5,𝔽2)11yescharacteristic
721C3⋊D3—24no—
722C3⋊D3—42no—
723C3×D3—42no—
724C3×D3—42no—
725C3×D3—42no—
726C24—31no—
727C24—31no—
728C24—31no—
729C24—94no—
730C24—91no—
731C24—91no—
732C24—184no—
733C24—362no—
734C24—362no—
735C2×Q8—34no—
736C2×Q8—122no—
737C2×D4—34no—
738C2×D4—94no—
739C2×D4—94no—
740C2×D4—94no—
741C2×D4—94no—
742C2×D4—94no—
743C2×D4—94no—
744C2×D4—122no—
745C2×D4—184no—
746C2×D4—184no—
747C2×D4—362no—
748C2×D4—362no—
749C2×D4—362no—
750C2×D4—362no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—94no—
757C22×C4—94no—
758C22×C4—91no—
759C22×C4—91no—
760C22×C4—94no—
761C22×C4—94no—
762C22×C4—362no—
763C22×C4—362no—
764C22×C4—362no—
765C22×C4—362no—
766C22×C4C2×D3211yescharacteristic
767C22×C4C2×D3211yescharacteristic
768C22×C4C2×D3211yescharacteristic
769C4⋊C4—34no—
770C4⋊C4—34no—
771C4⋊C4—34no—
772C4⋊C4—94no—
773C4⋊C4—94no—
774C4⋊C4—94no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—34no—
778C22⋊C4—34no—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—34no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C42—94no—
790C42C2×D3214yescomplemented
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—21no—
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—62no—
804C22×C3—124no—
805C22×C3—124no—
806C22×C3—124no—
807C22×C3#100412yes—
808C22×C3D3×#4112yes—
809C22×C3D3×#4112yes—
810C22×C3#100912yes—
811C22×C3#100912yes—
812C22×C3#100912yes—
813C22×C3C24×D311yescharacteristic
814C22×C3C24×D311yescharacteristic
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—34no—
825C2×D3—34no—
826C2×D3—44no—
827C2×D3—44no—
828C2×D3—44no—
829C2×D3—64no—
830C2×D3—68no—
831C2×D3—62no—
832C2×D3—68no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—64no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—128no—
847C2×D3—122no—
848C2×D3—1216no—
849C2×D3—1216no—
850C2×D3—128no—
851C2×D3—124no—
852C2×D3—124no—
853C3×C4—24no—
854C3×C4—24no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—22no—
858C3×C4—22no—
859C3×C4—22no—
860C3×C4—22no—
861C3×C4—42no—
862C3×C4—62no—
863C3×C4—62no—
864C3×C4—62no—
865C3×C4—62no—
866C3×C4—62no—
867Dic3—22no—
868Dic3—22no—
869Dic3—22no—
870Dic3—22no—
871Dic3—22no—
872Dic3—62no—
873Dic3—62no—
874Dic3—62no—
875Dic3—62no—
876Dic3—122no—
877Dic3—122no—
878C32C2×#53811yescharacteristic, complemented, Sylow
879C23—32no—
880C23—32no—
881C23—32no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—94no—
892C23—92no—
893C23—92no—
894C23—188no—
895C23—182no—
896C23—182no—
897C23—182no—
898C23—182no—
899C23—182no—
900C23—364no—
901C23—364no—
902C23—3616no—
903C23C22×D3211yescharacteristic
904Q8—124no—
905D4—124no—
906D4—188no—
907D4—188no—
908D4—364no—
909D4—364no—
910D4—364no—
911D4—364no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—32no—
919C2×C4—32no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—92no—
926C2×C4—92no—
927C2×C4—182no—
928C2×C4—182no—
929C2×C4—364no—
930C2×C4—364no—
931C2×C4—364no—
932C2×C4—364no—
933C2×C4C22×D3212yes—
934C2×C4C22×D3212yes—
935C2×C4C22×D3212yes—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—24no—
940C2×C3—122no—
941C2×C3—122no—
942C2×C3—122no—
943C2×C3#567814yescomplemented
944C2×C3#570414yescomplemented
945C2×C3C2×#100411yescharacteristic
946C2×C3C2×D3×#4111yescharacteristic
947C2×C3C2×D3×#4111yescharacteristic
948C2×C3C2×#100911yescharacteristic
949C2×C3C2×#100911yescharacteristic
950C2×C3C2×#100911yescharacteristic
951D3—42no—
952D3—42no—
953D3—42no—
954D3—64no—
955D3—64no—
956D3—124no—
957D3—124no—
958D3—122no—
959D3—122no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—94no—
970C22—124no—
971C22—124no—
972C22—124no—
973C22—182no—
974C22—182no—
975C22—188no—
976C22—182no—
977C22—182no—
978C22—182no—
979C22—3616no—
980C22—364no—
981C22#6430612yes—
982C22#6430712yes—
983C22#6430812yes—
984C22C23×D3211yescharacteristic
985C4—22no—
986C4—22no—
987C4—22no—
988C4—62no—
989C4—62no—
990C4—62no—
991C4—62no—
992C4—62no—
993C4—182no—
994C4—182no—
995C3—21no—
996C3C2×#567811yescharacteristic, complemented
997C3C2×#570411yescharacteristic, complemented
998C2—122no—
999C2—122no—
1000C2—122no—
1001C2—184no—
1002C2—362no—
1003C2#1059401914yesdirect product factor
1004C2C2×#6430611yescharacteristic
1005C2C2×#6430711yescharacteristic
1006C2C2×#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×C4×C4⋊(C3⋊D3)C2semidirect
2. C2×C3×#876C2semidirect
3. C2×C3×#875C2semidirect
4. C2×#63923C2semidirect
5. C2×#63922C2semidirect
6. C2×#63921C2semidirect
7. C2×#63912C2semidirect
8. C2×#63910C2semidirect
9. C2×#63907C2semidirect
10. C2×#63891C2semidirect
11. C2×#63888C2semidirect
12. C2×#63886C2semidirect
13. C2×#63881C2semidirect
14. C2×#63861C2semidirect
15. C2×#63853C2semidirect
16. #10594019C2direct (N × H)
22. C22×C4×C3⋊D3C22semidirect
24. C22×C3×Dic6C22semidirect
28. C22×#626C22semidirect
31. C22×D3×Dic3C22semidirect
32. C2×C32×C42C22semidirect
34. C2×#3752C22semidirect
35. C2×C4⋊(C3⋊Dic3)C22semidirect
36. C4×C4⋊(C3⋊D3)C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C3×#876C22semidirect
48. C3×#875C22semidirect
49. C2×#3724C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
52. C2×#3722C22semidirect
56. C2×Dic32C22semidirect
57. #63923C22semidirect
58. #63922C22semidirect
59. #63921C22semidirect
60. #63912C22semidirect
61. #63910C22semidirect
62. #63907C22semidirect
63. #63891C22semidirect
64. #63888C22semidirect
65. #63886C22semidirect
66. #63881C22semidirect
67. #63861C22semidirect
68. #63853C22semidirect
97. C2×#876D3semidirect
98. C2×#875D3semidirect
121. C2×C4×C3⋊D3C23semidirect
130. C2×C3×Dic6C23semidirect
138. C2×#626C23semidirect
144. C2×D3×Dic3C23semidirect
145. C32×C42C23semidirect
147. #3752C23semidirect
148. C4⋊(C3⋊Dic3)C23semidirect
154. C3×(C2×D3)⋊C4C23semidirect
155. C3×(C2×D3)⋊C4C23semidirect
156. C3×Dic3⋊C4C23semidirect
157. C3×Dic3⋊C4C23semidirect
158. C3×Dic3⋊C4C23semidirect
159. #3724C23semidirect
160. Dic3⋊Dic3C23semidirect
162. #3722C23semidirect
166. Dic32C23semidirect
196. C22×Dic6C2×D3semidirect
210. C2×C3×C42C2×D3semidirect
211. C2×C3×C42C2×D3semidirect
237. C2×(C2×D3)⋊C4C2×D3semidirect
238. C2×(C2×D3)⋊C4C2×D3semidirect
246. C2×Dic3⋊C4C2×D3semidirect
247. C2×Dic3⋊C4C2×D3semidirect
248. C2×Dic3⋊C4C2×D3semidirect
271. #876C2×D3semidirect
272. #875C2×D3semidirect
447. C2×Dic6C22×D3semidirect
459. C3×C42C22×D3semidirect
460. C3×C42C22×D3semidirect
482. (C2×D3)⋊C4C22×D3semidirect
483. (C2×D3)⋊C4C22×D3semidirect
491. Dic3⋊C4C22×D3semidirect
492. Dic3⋊C4C22×D3semidirect
493. Dic3⋊C4C22×D3semidirect
580. C2×C42D32semidirect
717. C2×C32#538semidirect
790. C42C2×D32semidirect
878. C32C2×#538semidirect
943. C2×C3#5678semidirect
944. C2×C3#5704semidirect
996. C3C2×#5678semidirect
997. C3C2×#5704semidirect
1003. C2#10594019direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8762
C2×C3×#8752
C2×#639232
C2×#639222
C2×#639212
C2×#639122
C2×#639102
C2×#639072
C2×#638912
C2×#638882
C2×#638862
C2×#638812
C2×#638612
C2×#638532
#105940192
C2×#57043
C2×#56783