Finite Group Databasebeta

← C2×#10594662 #11910197

Subgroups — C2×#10594662 #11910197

Order 1152.

2811 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64107C211yesmaximal, characteristic, complemented
2C2×C3×#895C211yesmaximal, characteristic, complemented
3C2×C3×#894C211yesmaximal, characteristic, complemented
4C2×#63922C211yesmaximal, characteristic, complemented
5C2×#63922C211yesmaximal, characteristic, complemented
6C2×#63922C211yesmaximal, characteristic, complemented
7C2×#63914C211yesmaximal, characteristic, complemented
8C2×#63908C211yesmaximal, characteristic, complemented
9C2×#63906C211yesmaximal, characteristic, complemented
10C2×#63906C211yesmaximal, characteristic, complemented
11C2×#63905C211yesmaximal, characteristic, complemented
12C2×#63891C211yesmaximal, characteristic, complemented
13C2×#63886C211yesmaximal, characteristic, complemented
14C2×#63885C211yesmaximal, characteristic, complemented
15C2×#63862C211yesmaximal, characteristic, complemented
16#10594662C2116yesmaximal, direct product factor
17C2×#5666—31nomaximal
18C2×#5620—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic, complemented
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C22×#625C2211yescharacteristic
32C22×#625C2211yescharacteristic, complemented
33C22×#625C2211yescharacteristic, complemented
34C22×D3×Dic3C2211yescharacteristic, complemented
35C2×C32×C4⋊C4C2211yescharacteristic, complemented
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×#3752C2211yescharacteristic
39C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40C2×#3750C2211yescharacteristic, complemented
41C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
42#64107C2218yescomplemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C3×#895C2218yescomplemented
50C3×#894C2218yescomplemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57#63922C2218yescomplemented
58#63922C2218yescomplemented
59#63922C2218yescomplemented
60#63914C2218yescomplemented
61#63908C2218yescomplemented
62#63906C2218yescomplemented
63#63906C2218yescomplemented
64#63905C2218yescomplemented
65#63891C2218yescomplemented
66#63886C2218yescomplemented
67#63885C2218yescomplemented
68#63862C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#121—31no—
71C2×#940—31no—
72C2×#940—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#938—31no—
76C2×#937—31no—
77C2×#937—31no—
78C2×#937—31no—
79C2×#930—31no—
80C2×#930—31no—
81C2×#930—31no—
82C2×#929—31no—
83#5666—316no—
84#5620—316no—
85C2×#898—31no—
86C2×#898—31no—
87C2×#898—31no—
88C2×#898—61no—
89C2×#895—31no—
90C2×#895D311yescharacteristic, complemented
91C2×#894D311yescharacteristic, complemented
92C2×#886—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#883—31no—
97C2×#883—31no—
98C2×#882—31no—
99C2×#882—31no—
100C2×#882—31no—
101C2×#879—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C22×D32—42no—
109C22×D32—42no—
110C22×D32—42no—
111C22×D32C2314yes—
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×D12—42no—
122C2×C3×D12—42no—
123C2×C3×D12—42no—
124C2×C3×D12—42no—
125C2×C3×D12C2314yes—
126C2×C3×D12C2314yes—
127C2×C3×D12C2314yes—
128C2×C3×D12C2314yescomplemented
129C2×C3×C4×D3—42no—
130C2×C3×C4×D3—42no—
131C2×C3×C4×D3C2314yescomplemented
132C2×C3×C4×D3C2314yescomplemented
133C2×#626—42no—
134C2×#626—42no—
135C2×#626—42no—
136C2×#626C2314yes—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#625—42no—
140C2×#625—42no—
141C2×#625—42no—
142C2×#625—42no—
143C2×#625—42no—
144C2×#625C2314yes—
145C2×#625C2314yes—
146C2×#625C2314yes—
147C2×#625C2314yescomplemented
148C2×#625C2314yescomplemented
149C2×D3×Dic3—42no—
150C2×D3×Dic3C2314yescomplemented
151C32×C4⋊C4C2314yescomplemented
152#3752C2314yes—
153#3752C2314yes—
154#3752C2314yes—
155C4⋊(C3⋊Dic3)C2314yescomplemented
156#3750C2314yescomplemented
157C4×C3⋊Dic3C2314yescomplemented
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2314yescomplemented
162C3×(C2×D3)⋊C4C2314yescomplemented
163C3×Dic3⋊C4C2314yescomplemented
164Dic3⋊Dic3C2314yescomplemented
165Dic3⋊Dic3C2314yescomplemented
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2314yescomplemented
170C2×#560—91noSylow
171C24×D3—31no—
172C24×D3—31no—
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C23×C3×C4—31no—
178C23×C3×C4—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C23×Dic3—31no—
193C22×D12—31no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12C2×D311yescharacteristic
197C22×D12C2×D311yescharacteristic
198C22×D12C2×D311yescharacteristic
199C22×D12C2×D311yescharacteristic, complemented
200C22×C4×D3—31no—
201C22×C4×D3C2×D311yescharacteristic, complemented
202C22×C4×D3C2×D311yescharacteristic, complemented
203C3×#123—38no—
204C3×#121—38no—
205C2×C3×C4⋊C4—21no—
206C2×C3×C4⋊C4—31no—
207C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
208C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
209C2×C3×C22⋊C4—31no—
210C2×C3×C22⋊C4—31no—
211C2×C3×C22⋊C4—31no—
212C2×C3×C22⋊C4—31no—
213C2×C3×C22⋊C4—31no—
214C2×#217—31no—
215C2×#217—31no—
216C2×#217—31no—
217C2×#217—31no—
218#940—38no—
219#940—38no—
220#939—38no—
221#939—38no—
222#938—38no—
223#937—38no—
224#937—38no—
225#937—38no—
226#930—38no—
227#930—38no—
228#930—38no—
229#929—38no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—61no—
241C2×(C2×D3)⋊C4—61no—
242C2×(C2×D3)⋊C4—61no—
243C2×(C2×D3)⋊C4C2×D311yescharacteristic
244C2×(C2×D3)⋊C4C2×D311yescharacteristic
245C2×(C2×D3)⋊C4C2×D311yescharacteristic
246C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
247C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
248C2×C4⋊Dic3—31no—
249C2×C4⋊Dic3—31no—
250C2×C4⋊Dic3—31no—
251C2×C4⋊Dic3—31no—
252C2×C4⋊Dic3—61no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—61no—
258C2×Dic3⋊C4C2×D311yescharacteristic, complemented
259C2×C4×Dic3—31no—
260C2×C4×Dic3—31no—
261C2×C4×Dic3—61no—
262#898—38no—
263#898—38no—
264#898—38no—
265#898—68no—
266#895—38no—
267#895C2×D318yescomplemented
268#894C2×D318yescomplemented
269#886—38no—
270#884—38no—
271#884—38no—
272#884—38no—
273#883—38no—
274#883—38no—
275#882—38no—
276#882—38no—
277#882—38no—
278#879—38no—
279C23×C32C2411yescharacteristic
280C22×C3⋊D3—22no—
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3C2412yes—
284C22×C3×D3—22no—
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×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3C2412yes—
300C22×C3×D3C2412yes—
301C22×C3×D3C2412yes—
302C22×C3×D3C2412yes—
303C22×C3×D3C2412yes—
304C2×D32—44no—
305C2×D32—44no—
306C2×D32—44no—
307C2×D32—416no—
308C2×C32×C4—22no—
309C2×C32×C4—22no—
310C2×C32×C4—22no—
311C2×C32×C4C2412yes—
312C2×C32×C4C2412yes—
313C2×C32×C4C2412yes—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3—22no—
317C2×C3⋊Dic3C2412yes—
318C2×C3⋊Dic3C2412yes—
319C2×C3⋊Dic3C2412yes—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C3×D12—44no—
327C3×D12—44no—
328C3×D12—44no—
329C3×D12—44no—
330C3×C4×D3—44no—
331C3×C4×D3—44no—
332#626—44no—
333#626—44no—
334#626—44no—
335#625—44no—
336#625—44no—
337#625—44no—
338#625—44no—
339#625—44no—
340D3×Dic3—44no—
341#560—916no—
342C2×#127—91no—
343C2×#126—91no—
344C2×#126—91no—
345C2×#123—31no—
346C2×#123—91no—
347C2×#123—91no—
348C2×#121—31no—
349C2×#121—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×#121—91no—
353C2×#121—91no—
354C2×#120—91no—
355C2×#120—91no—
356C2×#120—91no—
357C24×C3—31no—
358C24×C3—31no—
359C24×C3—31no—
360C24×C3—31no—
361C24×C3—31no—
362C23×D3—31no—
363C23×D3—31no—
364C23×D3—34no—
365C23×D3—34no—
366C23×D3—61no—
367C23×D3—122no—
368C23×D3—122no—
369C23×D3—122no—
370C23×D3—122no—
371C23×D3—122no—
372C23×D3—122no—
373C23×D3C22×D311yescharacteristic
374C23×D3C22×D311yescharacteristic
375C23×D3C22×D311yescharacteristic
376C23×D3C22×D311yescharacteristic
377C23×D3C22×D311yescharacteristic
378C2×C3×D4—34no—
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—122no—
383C2×C3×D4—122no—
384C2×C3×D4—122no—
385C2×C3×D4—122no—
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—34no—
393C22×C3×C4—34no—
394C22×C3×C4—122no—
395C22×C3×C4—122no—
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C22×C3×C4C22×D311yescharacteristic
401C22×C3×C4C22×D311yescharacteristic
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—122no—
416C2×#67—122no—
417C2×#67—122no—
418C2×#67—122no—
419C2×#67—122no—
420C2×#67—122no—
421C2×#67—122no—
422C2×#67—122no—
423C2×#67—122no—
424C2×#67—122no—
425C2×#67—122no—
426C2×#67—122no—
427C2×#67—122no—
428C22×Dic3—31no—
429C22×Dic3—31no—
430C22×Dic3—31no—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—34no—
435C22×Dic3—61no—
436C22×Dic3—61no—
437C22×Dic3—61no—
438C22×Dic3—122no—
439C22×Dic3C22×D311yescharacteristic
440C22×Dic3C22×D311yescharacteristic
441C22×Dic3C22×D311yescharacteristic
442C2×D12—34no—
443C2×D12—34no—
444C2×D12—34no—
445C2×D12—42no—
446C2×D12—42no—
447C2×D12—42no—
448C2×D12—42no—
449C2×D12—122no—
450C2×D12—122no—
451C2×D12—122no—
452C2×D12C22×D314yes—
453C2×D12C22×D314yes—
454C2×D12C22×D314yes—
455C2×D12C22×D314yescomplemented
456C2×C4×D3—34no—
457C2×C4×D3—42no—
458C2×C4×D3—42no—
459C2×C4×D3—122no—
460C2×C4×D3C22×D314yescomplemented
461C2×C4×D3C22×D314yescomplemented
462C3×C4⋊C4—24no—
463C3×C4⋊C4—34no—
464C3×C4⋊C4C22×D314yescomplemented
465C3×C4⋊C4C22×D314yescomplemented
466C3×C22⋊C4—34no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—34no—
471#217—34no—
472#217—34no—
473#217—34no—
474#217—34no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—64no—
486(C2×D3)⋊C4—64no—
487(C2×D3)⋊C4—64no—
488(C2×D3)⋊C4C22×D314yes—
489(C2×D3)⋊C4C22×D314yes—
490(C2×D3)⋊C4C22×D314yes—
491(C2×D3)⋊C4C22×D314yescomplemented
492(C2×D3)⋊C4C22×D314yescomplemented
493C4⋊Dic3—34no—
494C4⋊Dic3—34no—
495C4⋊Dic3—34no—
496C4⋊Dic3—34no—
497C4⋊Dic3—64no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—64no—
503Dic3⋊C4C22×D314yescomplemented
504C4×Dic3—34no—
505C4×Dic3—34no—
506C4×Dic3—64no—
507C22×C32H(5,𝔽2)12yes—
508C22×C32H(5,𝔽2)12yes—
509C22×C32H(5,𝔽2)12yes—
510C22×C32C2511yescharacteristic
511C2×C3⋊D3—22no—
512C2×C3⋊D3—22no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—44no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—22no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—44no—
531C2×C3×D3—44no—
532C2×C3×D3—44no—
533C2×C3×D3—44no—
534C2×C3×D3—44no—
535D32—416no—
536C32×C4—22no—
537C32×C4—22no—
538C32×C4—22no—
539C3⋊Dic3—22no—
540C3⋊Dic3—22no—
541C3⋊Dic3—22no—
542C3×Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C25—91no—
546C22×D4—31no—
547C22×D4—31no—
548C22×D4—31no—
549C22×D4—31no—
550C22×D4—91no—
551C22×D4—91no—
552C22×D4—91no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C23×C4—31no—
559C23×C4—31no—
560C23×C4—91no—
561#127—98no—
562#126—98no—
563#126—98no—
564#123—38no—
565#123—98no—
566#123—98no—
567#121—38no—
568#121—98no—
569#121—98no—
570#121—98no—
571#121—98no—
572#121—98no—
573#120—98no—
574#120—98no—
575#120—98no—
576C2×C4⋊C4—31no—
577C2×C4⋊C4—91no—
578C2×C4⋊C4—91no—
579C2×C4⋊C4—91no—
580C2×C4⋊C4—91no—
581C2×C4⋊C4D3211yescharacteristic, complemented
582C2×C22⋊C4—31no—
583C2×C22⋊C4—31no—
584C2×C22⋊C4—31no—
585C2×C22⋊C4—31no—
586C2×C22⋊C4—31no—
587C2×C22⋊C4—91no—
588C2×C22⋊C4—91no—
589C2×C22⋊C4—91no—
590C2×C22⋊C4—91no—
591C2×C22⋊C4—91no—
592C2×C22⋊C4—91no—
593C2×C22⋊C4—91no—
594C2×C42—91no—
595C23×C3—21no—
596C23×C3—32no—
597C23×C3—32no—
598C23×C3—32no—
599C23×C3—32no—
600C23×C3—32no—
601C23×C3—62no—
602C23×C3—62no—
603C23×C3—62no—
604C23×C3—62no—
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3—62no—
610C23×C3—62no—
611C23×C3—62no—
612C23×C3—62no—
613C23×C3—62no—
614C23×C3—62no—
615C23×C3—62no—
616C23×C3C23×D311yescharacteristic
617C23×C3C23×D311yescharacteristic
618C22×D3—22no—
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—22no—
624C22×D3—22no—
625C22×D3—22no—
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—32no—
634C22×D3—32no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—62no—
641C22×D3—62no—
642C22×D3—122no—
643C22×D3—122no—
644C22×D3—122no—
645C22×D3—124no—
646C22×D3—124no—
647C22×D3—124no—
648C22×D3—124no—
649C22×D3—124no—
650C22×D3—124no—
651C22×D3—1216no—
652C22×D3—1216no—
653C22×D3C23×D312yes—
654C22×D3C23×D312yes—
655C22×D3C23×D312yes—
656C22×D3C23×D312yes—
657C22×D3C23×D312yes—
658C3×D4—124no—
659C3×D4—124no—
660C3×D4—124no—
661C3×D4—124no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—32no—
672C2×C3×C4—32no—
673C2×C3×C4—32no—
674C2×C3×C4—42no—
675C2×C3×C4—42no—
676C2×C3×C4—42no—
677C2×C3×C4—62no—
678C2×C3×C4—62no—
679C2×C3×C4—62no—
680C2×C3×C4—124no—
681C2×C3×C4—124no—
682C2×C3×C4C23×D312yes—
683C2×C3×C4C23×D312yes—
684C2×C3×C4C23×D312yes—
685C2×C3×C4C23×D312yes—
686C2×C3×C4C23×D312yes—
687C2×C3×C4C23×D312yes—
688#67—124no—
689#67—124no—
690#67—124no—
691#67—124no—
692#67—124no—
693#67—124no—
694#67—124no—
695#67—124no—
696#67—124no—
697#67—124no—
698#67—124no—
699#67—124no—
700#67—124no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—22no—
704C2×Dic3—32no—
705C2×Dic3—32no—
706C2×Dic3—32no—
707C2×Dic3—32no—
708C2×Dic3—32no—
709C2×Dic3—32no—
710C2×Dic3—62no—
711C2×Dic3—62no—
712C2×Dic3—62no—
713C2×Dic3—62no—
714C2×Dic3—62no—
715C2×Dic3—62no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—62no—
719C2×Dic3—122no—
720C2×Dic3—122no—
721C2×Dic3—122no—
722C2×Dic3—124no—
723C2×Dic3C23×D312yes—
724C2×Dic3C23×D312yes—
725C2×Dic3C23×D312yes—
726D12—44no—
727D12—44no—
728D12—44no—
729D12—44no—
730D12—124no—
731D12—124no—
732D12—124no—
733C4×D3—44no—
734C4×D3—44no—
735C4×D3—124no—
736C2×C32#56014yescomplemented
737C2×C32C2×H(5,𝔽2)11yescharacteristic
738C2×C32C2×H(5,𝔽2)11yescharacteristic
739C2×C32C2×H(5,𝔽2)11yescharacteristic
740C3⋊D3—42no—
741C3×D3—42no—
742C3×D3—42no—
743C3×D3—42no—
744C3×D3—42no—
745C3×D3—42no—
746C24—31no—
747C24—31no—
748C24—31no—
749C24—31no—
750C24—31no—
751C24—94no—
752C24—91no—
753C24—362no—
754C24—362no—
755C24—362no—
756C2×D4—34no—
757C2×D4—34no—
758C2×D4—34no—
759C2×D4—34no—
760C2×D4—94no—
761C2×D4—94no—
762C2×D4—94no—
763C2×D4—94no—
764C2×D4—94no—
765C2×D4—94no—
766C2×D4—94no—
767C2×D4—94no—
768C2×D4—122no—
769C2×D4—122no—
770C2×D4—122no—
771C2×D4—122no—
772C2×D4—362no—
773C2×D4—362no—
774C2×D4—362no—
775C2×D4—362no—
776C2×D4—362no—
777C2×D4—362no—
778C2×D4—362no—
779C2×D4—362no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—34no—
784C22×C4—34no—
785C22×C4—94no—
786C22×C4—91no—
787C22×C4—91no—
788C22×C4—91no—
789C22×C4—122no—
790C22×C4—122no—
791C22×C4—362no—
792C22×C4C2×D3211yescharacteristic
793C22×C4C2×D3211yescharacteristic
794C22×C4C2×D3211yescharacteristic
795C4⋊C4—34no—
796C4⋊C4—94no—
797C4⋊C4—94no—
798C4⋊C4—94no—
799C4⋊C4—94no—
800C4⋊C4C2×D3214yescomplemented
801C22⋊C4—34no—
802C22⋊C4—34no—
803C22⋊C4—34no—
804C22⋊C4—34no—
805C22⋊C4—34no—
806C22⋊C4—94no—
807C22⋊C4—94no—
808C22⋊C4—94no—
809C22⋊C4—94no—
810C22⋊C4—94no—
811C22⋊C4—94no—
812C22⋊C4—94no—
813C42—94no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—21no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—124no—
834C22×C3—124no—
835C22×C3—124no—
836C22×C3—124no—
837C22×C3—124no—
838C22×C3#100412yes—
839C22×C3#100412yes—
840C22×C3#100412yes—
841C22×C3#100912yes—
842C22×C3#100912yes—
843C22×C3#100912yes—
844C22×C3C24×D311yescharacteristic
845C22×C3C24×D311yescharacteristic
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—22no—
858C2×D3—22no—
859C2×D3—22no—
860C2×D3—22no—
861C2×D3—44no—
862C2×D3—44no—
863C2×D3—44no—
864C2×D3—44no—
865C2×D3—44no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—62no—
872C2×D3—122no—
873C2×D3—122no—
874C2×D3—122no—
875C2×D3—1216no—
876C2×D3—1216no—
877C2×D3—124no—
878C2×D3—124no—
879C2×D3—244no—
880C3×C4—22no—
881C3×C4—22no—
882C3×C4—22no—
883C3×C4—22no—
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—42no—
887C3×C4—42no—
888C3×C4—42no—
889C3×C4—62no—
890C3×C4—62no—
891C3×C4—62no—
892Dic3—22no—
893Dic3—22no—
894Dic3—22no—
895Dic3—62no—
896Dic3—62no—
897Dic3—62no—
898Dic3—62no—
899Dic3—62no—
900Dic3—62no—
901Dic3—122no—
902Dic3—122no—
903Dic3—122no—
904C32C2×#56011yescharacteristic, complemented, Sylow
905C23—32no—
906C23—32no—
907C23—32no—
908C23—32no—
909C23—32no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—92no—
926C23—182no—
927C23—182no—
928C23—182no—
929C23—364no—
930C23—364no—
931C23—364no—
932C23—3616no—
933C23C22×D3211yescharacteristic
934D4—124no—
935D4—124no—
936D4—124no—
937D4—124no—
938D4—364no—
939D4—364no—
940D4—364no—
941D4—364no—
942D4—364no—
943D4—364no—
944D4—364no—
945D4—364no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—32no—
950C2×C4—32no—
951C2×C4—32no—
952C2×C4—62no—
953C2×C4—62no—
954C2×C4—62no—
955C2×C4—92no—
956C2×C4—92no—
957C2×C4—92no—
958C2×C4—124no—
959C2×C4—124no—
960C2×C4—182no—
961C2×C4—182no—
962C2×C4—182no—
963C2×C4—364no—
964C2×C4C22×D3212yes—
965C2×C4C22×D3212yes—
966C2×C4C22×D3212yes—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—24no—
971C2×C3—122no—
972C2×C3—122no—
973C2×C3—122no—
974C2×C3—122no—
975C2×C3—122no—
976C2×C3#562014yescomplemented
977C2×C3#566614yescomplemented
978C2×C3C2×#100411yescharacteristic
979C2×C3C2×#100411yescharacteristic
980C2×C3C2×#100411yescharacteristic
981C2×C3C2×#100911yescharacteristic
982C2×C3C2×#100911yescharacteristic
983C2×C3C2×#100911yescharacteristic
984D3—42no—
985D3—42no—
986D3—42no—
987D3—42no—
988D3—42no—
989D3—122no—
990D3—122no—
991D3—242no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—62no—
1002C22—62no—
1003C22—62no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—124no—
1008C22—124no—
1009C22—124no—
1010C22—124no—
1011C22—124no—
1012C22—182no—
1013C22—182no—
1014C22—182no—
1015C22—3616no—
1016C22—364no—
1017C22#6430712yes—
1018C22#6431312yes—
1019C22#6432012yes—
1020C22C23×D3211yescharacteristic
1021C4—22no—
1022C4—22no—
1023C4—22no—
1024C4—62no—
1025C4—62no—
1026C4—62no—
1027C4—182no—
1028C4—182no—
1029C4—182no—
1030C3—21no—
1031C3C2×#562011yescharacteristic, complemented
1032C3C2×#566611yescharacteristic, complemented
1033C2—122no—
1034C2—122no—
1035C2—122no—
1036C2—122no—
1037C2—122no—
1038C2—362no—
1039C2#1059466214yesdirect product factor
1040C2C2×#6430711yescharacteristic
1041C2C2×#6431311yescharacteristic
1042C2C2×#6432011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#560
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×#64107C2semidirect
2. C2×C3×#895C2semidirect
3. C2×C3×#894C2semidirect
4. C2×#63922C2semidirect
5. C2×#63922C2semidirect
6. C2×#63922C2semidirect
7. C2×#63914C2semidirect
8. C2×#63908C2semidirect
9. C2×#63906C2semidirect
10. C2×#63906C2semidirect
11. C2×#63905C2semidirect
12. C2×#63891C2semidirect
13. C2×#63886C2semidirect
14. C2×#63885C2semidirect
15. C2×#63862C2semidirect
16. #10594662C2direct (N × H)
23. C22×C3×D12C22semidirect
24. C22×C3×C4×D3C22semidirect
25. C22×C3×C4×D3C22semidirect
32. C22×#625C22semidirect
33. C22×#625C22semidirect
34. C22×D3×Dic3C22semidirect
35. C2×C32×C4⋊C4C22semidirect
39. C2×C4⋊(C3⋊Dic3)C22semidirect
40. C2×#3750C22semidirect
41. C2×C4×C3⋊Dic3C22semidirect
42. #64107C22semidirect
46. C2×C3×(C2×D3)⋊C4C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. C3×#895C22semidirect
50. C3×#894C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. #63922C22semidirect
58. #63922C22semidirect
59. #63922C22semidirect
60. #63914C22semidirect
61. #63908C22semidirect
62. #63906C22semidirect
63. #63906C22semidirect
64. #63905C22semidirect
65. #63891C22semidirect
66. #63886C22semidirect
67. #63885C22semidirect
68. #63862C22semidirect
90. C2×#895D3semidirect
91. C2×#894D3semidirect
128. C2×C3×D12C23semidirect
131. C2×C3×C4×D3C23semidirect
132. C2×C3×C4×D3C23semidirect
147. C2×#625C23semidirect
148. C2×#625C23semidirect
150. C2×D3×Dic3C23semidirect
151. C32×C4⋊C4C23semidirect
155. C4⋊(C3⋊Dic3)C23semidirect
156. #3750C23semidirect
157. C4×C3⋊Dic3C23semidirect
161. C3×(C2×D3)⋊C4C23semidirect
162. C3×(C2×D3)⋊C4C23semidirect
163. C3×Dic3⋊C4C23semidirect
164. Dic3⋊Dic3C23semidirect
165. Dic3⋊Dic3C23semidirect
169. (C2×D3)⋊Dic3C23semidirect
199. C22×D12C2×D3semidirect
201. C22×C4×D3C2×D3semidirect
202. C22×C4×D3C2×D3semidirect
207. C2×C3×C4⋊C4C2×D3semidirect
208. C2×C3×C4⋊C4C2×D3semidirect
246. C2×(C2×D3)⋊C4C2×D3semidirect
247. C2×(C2×D3)⋊C4C2×D3semidirect
258. C2×Dic3⋊C4C2×D3semidirect
267. #895C2×D3semidirect
268. #894C2×D3semidirect
455. C2×D12C22×D3semidirect
460. C2×C4×D3C22×D3semidirect
461. C2×C4×D3C22×D3semidirect
464. C3×C4⋊C4C22×D3semidirect
465. C3×C4⋊C4C22×D3semidirect
491. (C2×D3)⋊C4C22×D3semidirect
492. (C2×D3)⋊C4C22×D3semidirect
503. Dic3⋊C4C22×D3semidirect
581. C2×C4⋊C4D32semidirect
736. C2×C32#560semidirect
800. C4⋊C4C2×D32semidirect
904. C32C2×#560semidirect
976. C2×C3#5620semidirect
977. C2×C3#5666semidirect
1031. C3C2×#5620semidirect
1032. C3C2×#5666semidirect
1039. C2#10594662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641072
C2×C3×#8952
C2×C3×#8942
C2×#639222
C2×#639142
C2×#639082
C2×#639062
C2×#639052
C2×#638912
C2×#638862
C2×#638852
C2×#638622
#105946622
C2×#56663
C2×#56203