Finite Group Databasebeta

← C2×#10594657 #11901304

Subgroups — C2×#10594657 #11901304

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×#64102C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#894C211yesmaximal, characteristic, complemented
4C2×#63923C211yesmaximal, characteristic, complemented
5C2×#63922C211yesmaximal, characteristic, complemented
6C2×#63921C211yesmaximal, characteristic, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×#63915C211yesmaximal, characteristic, complemented
9C2×#63910C211yesmaximal, characteristic, complemented
10C2×#63906C211yesmaximal, characteristic, complemented
11C2×C4×#626C211yesmaximal, characteristic, complemented
12C2×#63895C211yesmaximal, characteristic, complemented
13C2×#63862C211yesmaximal, characteristic, complemented
14C2×#63853C211yesmaximal, characteristic, complemented
15C2×#63852C211yesmaximal, characteristic, complemented
16#10594657C2116yesmaximal, direct product factor
17C2×#5704—31nomaximal
18C2×#5657—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C22×#627C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic, complemented
30C22×#625C2211yescharacteristic
31C22×#624C2211yescharacteristic
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic, complemented
35C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
36#64102C2218yescomplemented
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×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×C4×Dic3C2211yescharacteristic, complemented
47C3×#898C2218yescomplemented
48C3×#894C2218yescomplemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic, complemented
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57#63923C2218yescomplemented
58#63922C2218yescomplemented
59#63921C2218yescomplemented
60#63916C2218yescomplemented
61#63915C2218yescomplemented
62#63910C2218yescomplemented
63#63906C2218yescomplemented
64C4×#626C2218yescomplemented
65#63895C2218yescomplemented
66#63862C2218yescomplemented
67#63853C2218yescomplemented
68#63852C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#123—31no—
71C2×#938—31no—
72C2×#937—31no—
73C2×#930—31no—
74C2×C4×#67—31no—
75#5704—316no—
76#5657—316no—
77C2×#898—31no—
78C2×#898D311yescharacteristic, complemented
79C2×#897—31no—
80C2×#896—31no—
81C2×#895—31no—
82C2×#895—31no—
83C2×#894—31no—
84C2×#894D311yescharacteristic, complemented
85C2×#893—31no—
86C2×#893—31no—
87C2×#893—61no—
88C2×#885—31no—
89C2×#885—31no—
90C2×#885—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#882—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×D3×C22⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×#879—31no—
100C2×#875—31no—
101C2×C4×D12—31no—
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×C4×D3—42no—
130C2×C3×C4×D3C2314yescomplemented
131C2×#627—42no—
132C2×#627C2314yescomplemented
133C2×#626—24no—
134C2×#626—42no—
135C2×#626—42no—
136C2×#626—42no—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#626C2314yes—
140C2×#626C2314yescomplemented
141C2×#625—42no—
142C2×#625C2314yes—
143C2×#624—42no—
144C2×#624C2314yes—
145C32×C4⋊C4C2314yescomplemented
146#3752C2314yes—
147#3752C2314yescomplemented
148C4×C3⋊Dic3C2314yescomplemented
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×C4⋊Dic3C2314yescomplemented
156C3×Dic3⋊C4C2314yescomplemented
157C3×Dic3⋊C4C2314yescomplemented
158C3×C4×Dic3C2314yescomplemented
159Dic3⋊Dic3C2314yescomplemented
160Dic3⋊Dic3C2314yescomplemented
161#3722C2314yes—
162#3722C2314yescomplemented
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×D4—31no—
171C23×C3×C4—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×D12—31no—
179C22×D12—31no—
180C22×D12—31no—
181C22×D12—31no—
182C22×D12—31no—
183C22×D12—31no—
184C22×D12—61no—
185C22×D12C2×D311yescharacteristic
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3—31no—
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—61no—
193C22×C4×D3—61no—
194C22×C4×D3C2×D311yescharacteristic, complemented
195C22×Dic6—31no—
196C22×Dic6—31no—
197C3×#126—38no—
198C3×#123—38no—
199C2×C3×C4⋊C4—21no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
204C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4—31no—
210C2×C3×C22⋊C4—31no—
211C2×C3×C42—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217—31no—
216#938—38no—
217#937—38no—
218#930—38no—
219C4×#67—38no—
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—61no—
233C2×(C2×D3)⋊C4—61no—
234C2×(C2×D3)⋊C4C2×D311yescharacteristic
235C2×(C2×D3)⋊C4C2×D311yescharacteristic
236C2×(C2×D3)⋊C4C2×D311yescharacteristic
237C2×(C2×D3)⋊C4C2×D311yescharacteristic
238C2×(C2×D3)⋊C4C2×D311yescharacteristic
239C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
240C2×C4⋊Dic3—31no—
241C2×C4⋊Dic3—31no—
242C2×C4⋊Dic3C2×D311yescharacteristic, complemented
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4C2×D311yescharacteristic, complemented
246C2×Dic3⋊C4C2×D311yescharacteristic, complemented
247C2×C4×Dic3—31no—
248C2×C4×Dic3—31no—
249C2×C4×Dic3—61no—
250C2×C4×Dic3C2×D311yescharacteristic, complemented
251#898—38no—
252#898C2×D318yescomplemented
253#897—38no—
254#896—38no—
255#895—38no—
256#895—38no—
257#894—38no—
258#894C2×D318yescomplemented
259#893—38no—
260#893—38no—
261#893—68no—
262#885—38no—
263#885—38no—
264#885—38no—
265#884—38no—
266#884—38no—
267#883—38no—
268#882—38no—
269#882—38no—
270#882—38no—
271D3×C22⋊C4—38no—
272D3×C22⋊C4—38no—
273#879—38no—
274#875—38no—
275C4×D12—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#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×C4×D3—44no—
326#627—44no—
327#626—28no—
328#626—44no—
329#626—44no—
330#626—44no—
331#625—44no—
332#624—44no—
333#538—916no—
334C2×#126—31no—
335C2×#126—91no—
336C2×#124—91no—
337C2×#124—91no—
338C2×#123—31no—
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×D4—34no—
370C2×C3×D4—122no—
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—122no—
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—61no—
404C22×Dic3—61no—
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C2×D12—34no—
411C2×D12—34no—
412C2×D12—34no—
413C2×D12—34no—
414C2×D12—34no—
415C2×D12—34no—
416C2×D12—42no—
417C2×D12—64no—
418C2×D12—64no—
419C2×D12—64no—
420C2×D12—68no—
421C2×D12—64no—
422C2×D12—122no—
423C2×D12—122no—
424C2×D12—122no—
425C2×D12C22×D314yes—
426C2×C4×D3—34no—
427C2×C4×D3—34no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—42no—
433C2×C4×D3—64no—
434C2×C4×D3—64no—
435C2×C4×D3—122no—
436C2×C4×D3—122no—
437C2×C4×D3—122no—
438C2×C4×D3—122no—
439C2×C4×D3—122no—
440C2×C4×D3—122no—
441C2×C4×D3—124no—
442C2×C4×D3—124no—
443C2×C4×D3C22×D314yescomplemented
444C2×Dic6—34no—
445C2×Dic6—34no—
446C2×Dic6—122no—
447C2×Dic6—122no—
448C3×C4⋊C4—24no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4—34no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4C22×D314yescomplemented
453C3×C4⋊C4C22×D314yescomplemented
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4—34no—
460C3×C42—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—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—34no—
477(C2×D3)⋊C4—64no—
478(C2×D3)⋊C4—64no—
479(C2×D3)⋊C4C22×D314yes—
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⋊Dic3—34no—
487C4⋊Dic3C22×D314yescomplemented
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4C22×D314yescomplemented
491Dic3⋊C4C22×D314yescomplemented
492C4×Dic3—34no—
493C4×Dic3—34no—
494C4×Dic3—64no—
495C4×Dic3C22×D314yescomplemented
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—91no—
533C22×D4—31no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C23×C4—31no—
541C23×C4—91no—
542C23×C4—91no—
543C23×C4—91no—
544#126—38no—
545#126—98no—
546#124—98no—
547#124—98no—
548#123—38no—
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⋊C4D3211yescharacteristic, complemented
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—98no—
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×C22⋊C4—91no—
579C2×C42—31no—
580C2×C42—91no—
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×D4—124no—
641C2×C3×C4—24no—
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—22no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—42no—
657C2×C3×C4—42no—
658C2×C3×C4—62no—
659C2×C3×C4—62no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
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—64no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—122no—
693C2×Dic3C23×D312yes—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698D12—44no—
699D12—68no—
700D12—68no—
701D12—616no—
702D12—68no—
703D12—124no—
704D12—124no—
705D12—124no—
706C4×D3—44no—
707C4×D3—124no—
708C4×D3—124no—
709C4×D3—124no—
710C4×D3—124no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—128no—
714C4×D3—128no—
715Dic6—124no—
716Dic6—124no—
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—94no—
736C2×Q8—362no—
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—34no—
757C22×C4—94no—
758C22×C4—91no—
759C22×C4—91no—
760C22×C4—94no—
761C22×C4—94no—
762C22×C4—122no—
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⋊C4C2×D3214yescomplemented
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—34no—
778C22⋊C4—34no—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C42—34no—
790C42—94no—
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—22no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—22no—
858C3×C4—22no—
859C3×C4—22no—
860C3×C4—42no—
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—64no—
873Dic3—62no—
874Dic3—62no—
875Dic3—62no—
876Dic3—62no—
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—364no—
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—124no—
928C2×C4—182no—
929C2×C4—182no—
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#565714yescomplemented
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#6431412yes—
983C22#6432012yes—
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×#565711yescharacteristic, complemented
997C3C2×#570411yescharacteristic, complemented
998C2—122no—
999C2—122no—
1000C2—122no—
1001C2—184no—
1002C2—362no—
1003C2#1059465714yesdirect product factor
1004C2C2×#6430611yescharacteristic
1005C2C2×#6431411yescharacteristic
1006C2C2×#6432011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#538
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×#64102C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#894C2semidirect
4. C2×#63923C2semidirect
5. C2×#63922C2semidirect
6. C2×#63921C2semidirect
7. C2×#63916C2semidirect
8. C2×#63915C2semidirect
9. C2×#63910C2semidirect
10. C2×#63906C2semidirect
11. C2×C4×#626C2semidirect
12. C2×#63895C2semidirect
13. C2×#63862C2semidirect
14. C2×#63853C2semidirect
15. C2×#63852C2semidirect
16. #10594657C2direct (N × H)
22. C22×C4×C3⋊D3C22semidirect
24. C22×C3×C4×D3C22semidirect
25. C22×#627C22semidirect
29. C22×#626C22semidirect
32. C2×C32×C4⋊C4C22semidirect
34. C2×#3752C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
36. #64102C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×C4×Dic3C22semidirect
47. C3×#898C22semidirect
48. C3×#894C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
52. C2×#3722C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. #63923C22semidirect
58. #63922C22semidirect
59. #63921C22semidirect
60. #63916C22semidirect
61. #63915C22semidirect
62. #63910C22semidirect
63. #63906C22semidirect
64. C4×#626C22semidirect
65. #63895C22semidirect
66. #63862C22semidirect
67. #63853C22semidirect
68. #63852C22semidirect
78. C2×#898D3semidirect
84. C2×#894D3semidirect
121. C2×C4×C3⋊D3C23semidirect
130. C2×C3×C4×D3C23semidirect
132. C2×#627C23semidirect
140. C2×#626C23semidirect
145. C32×C4⋊C4C23semidirect
147. #3752C23semidirect
148. C4×C3⋊Dic3C23semidirect
154. C3×(C2×D3)⋊C4C23semidirect
155. C3×C4⋊Dic3C23semidirect
156. C3×Dic3⋊C4C23semidirect
157. C3×Dic3⋊C4C23semidirect
158. C3×C4×Dic3C23semidirect
159. Dic3⋊Dic3C23semidirect
160. Dic3⋊Dic3C23semidirect
162. #3722C23semidirect
166. (C2×D3)⋊Dic3C23semidirect
194. C22×C4×D3C2×D3semidirect
203. C2×C3×C4⋊C4C2×D3semidirect
204. C2×C3×C4⋊C4C2×D3semidirect
239. C2×(C2×D3)⋊C4C2×D3semidirect
242. C2×C4⋊Dic3C2×D3semidirect
245. C2×Dic3⋊C4C2×D3semidirect
246. C2×Dic3⋊C4C2×D3semidirect
250. C2×C4×Dic3C2×D3semidirect
252. #898C2×D3semidirect
258. #894C2×D3semidirect
443. C2×C4×D3C22×D3semidirect
452. C3×C4⋊C4C22×D3semidirect
453. C3×C4⋊C4C22×D3semidirect
484. (C2×D3)⋊C4C22×D3semidirect
487. C4⋊Dic3C22×D3semidirect
490. Dic3⋊C4C22×D3semidirect
491. Dic3⋊C4C22×D3semidirect
495. C4×Dic3C22×D3semidirect
563. C2×C4⋊C4D32semidirect
717. C2×C32#538semidirect
774. C4⋊C4C2×D32semidirect
878. C32C2×#538semidirect
943. C2×C3#5657semidirect
944. C2×C3#5704semidirect
996. C3C2×#5657semidirect
997. C3C2×#5704semidirect
1003. C2#10594657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641022
C2×C3×#8982
C2×C3×#8942
C2×#639232
C2×#639222
C2×#639212
C2×#639162
C2×#639152
C2×#639102
C2×#639062
C2×C4×#6262
C2×#638952
C2×#638622
C2×#638532
C2×#638522
#105946572
C2×#57043
C2×#56573