Finite Group Databasebeta

← C2×#10595148 #11902443

Subgroups — C2×#10595148 #11902443

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64148C211yesmaximal, characteristic, complemented
4C2×C3×#935C211yesmaximal, characteristic, complemented
5C2×#63977C211yesmaximal, characteristic, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C2×D3×#217C211yesmaximal, characteristic, complemented
9C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
10C2×#63959C211yesmaximal, characteristic, complemented
11C2×#63958C211yesmaximal, characteristic, complemented
12#10595148C2116yesmaximal, direct product factor
13C2×#63904C211yesmaximal, characteristic, complemented
14C2×#63886C211yesmaximal, characteristic, complemented
15C2×#63884C211yesmaximal, characteristic, complemented
16C2×#63851C211yesmaximal, characteristic, complemented
17C2×#5806—31nomaximal
18C2×#5654—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C24×C3×D3C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C22×#638C2211yescharacteristic, complemented
23C22×#638C2211yescharacteristic, complemented
24C23×C3⋊Dic3C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic, complemented
28C2×C3×D3×D4—28no—
29C2×C3×D3×D4C2218yescomplemented
30C22×C3×D12C2211yescharacteristic
31C22×C3×C4×D3C2211yescharacteristic
32C22×#627C2211yescharacteristic, complemented
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic, complemented
35C22×#626C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic, complemented
37C2×#3804—28no—
38C2×#3804C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic, complemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3757C2211yescharacteristic, complemented
42#64148C2218yescomplemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3750C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic, complemented
46C2×C3×#217C2211yescharacteristic, complemented
47C2×C3×#217C2211yescharacteristic, complemented
48C3×#935C2218yescomplemented
49C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51#63977C2218yescomplemented
52#63977C2218yescomplemented
53#67⋊Dic3C2218yescomplemented
54D3×#217C2218yescomplemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2218yescomplemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64#63959C2218yescomplemented
65#63958C2218yescomplemented
66C2×Dic32C2211yescharacteristic, complemented
67#63904C2218yescomplemented
68#63886C2218yescomplemented
69#63884C2218yescomplemented
70#63851C2218yescomplemented
71C23×C3×D4—31no—
72C22×#237—31no—
73C22×D3×D4D311yescharacteristic, complemented
74C22×#235—31no—
75C2×C3×#123—31no—
76C2×#953—31no—
77C2×#953—31no—
78C22×#217—31no—
79C22×#217—31no—
80#5806—316no—
81C2×#939—31no—
82C2×#939—31no—
83C2×#939—31no—
84C2×#939—61no—
85C2×#938—31no—
86C2×#936—31no—
87C2×#935—31no—
88C2×#935D311yescharacteristic, complemented
89C2×D4×Dic3—31no—
90C2×C4×#67—31no—
91C22×(C2×D3)⋊C4—31no—
92C2×#924—31no—
93#5654—316no—
94C2×#896—31no—
95C2×#895—31no—
96C2×#894—31no—
97C2×#893—31no—
98C2×#885—31no—
99C2×#884—31no—
100C2×#882—31no—
101C2×#882—31no—
102C2×#67⋊C4—31no—
103C2×D3×C22⋊C4—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3—24no—
108C23×C3×D3—24no—
109C23×C3×D3—24no—
110C23×C3×D3—24no—
111C23×C3×D3—42no—
112C23×C3×D3—42no—
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2314yes—
115C23×C3×D3C2314yes—
116C23×C3×D3C2311yescharacteristic
117C23×C3×D3C2311yescharacteristic
118C2×C32×D4—24no—
119C2×C32×D4C2314yes—
120C22×C32×C4C2311yescharacteristic
121C2×#638—24no—
122C2×#638—42no—
123C2×#638C2314yescomplemented
124C2×#638C2314yescomplemented
125C22×C3⋊Dic3—42no—
126C22×C3⋊Dic3C2311yescharacteristic
127C22×C3⋊Dic3C2311yescharacteristic
128C22×C3⋊Dic3C2311yescharacteristic
129C22×C3⋊Dic3C2314yescomplemented
130C2×C3×#67—24no—
131C2×C3×#67D418yescomplemented
132C2×C3×#67C2314yes—
133C2×C3×#67C2314yes—
134C22×C3×Dic3—24no—
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2314yescomplemented
141C3×D3×D4—232no—
142C2×C3×D12—24no—
143C2×C3×D12C2314yes—
144C2×C3×C4×D3—24no—
145C2×C3×C4×D3C2314yes—
146C2×#627—24no—
147C2×#627C2314yescomplemented
148C2×#626—24no—
149C2×#626—24no—
150C2×#626—42no—
151C2×#626C2314yes—
152C2×#626C2314yescomplemented
153C2×#626C2314yescomplemented
154C2×#624—24no—
155C2×#624C2314yescomplemented
156#3804—232no—
157C2×D3×Dic3—24no—
158C2×D3×Dic3—42no—
159C2×D3×Dic3C2314yescomplemented
160C2×D3×Dic3C2314yescomplemented
161#3757C2314yescomplemented
162#3752C2314yescomplemented
163#3750C2314yescomplemented
164C3×#217C2314yescomplemented
165C3×#217C2314yescomplemented
166C3×#217C2314yescomplemented
167C3×Dic3⋊C4C2314yescomplemented
168C3×Dic3⋊C4C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170(C2×D3)⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C25×C3—31no—
181C24×D3C2×D311yescharacteristic
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—21no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—38no—
187C22×C3×D4—31no—
188C22×C3×D4—68no—
189C22×C3×D4C2×D311yescharacteristic
190C22×C3×D4C2×D311yescharacteristic
191C23×C3×C4—31no—
192C23×C3×C4—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—61no—
201C22×#67—61no—
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic
204C23×Dic3—31no—
205C23×Dic3—31no—
206C23×Dic3—31no—
207C23×Dic3—31no—
208C23×Dic3—61no—
209C23×Dic3C2×D311yescharacteristic, complemented
210C2×#237—38no—
211C2×#237—68no—
212C2×D3×D4—28no—
213C2×D3×D4C2×D318yescomplemented
214C2×#235—38no—
215C2×#235—68no—
216C22×D12—31no—
217C22×D12—31no—
218C22×D12—31no—
219C22×D12C2×D311yescharacteristic
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3C2×D311yescharacteristic
225C22×Dic6—31no—
226C22×Dic6—31no—
227C3×#123—38no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233#953—38no—
234#953—38no—
235C2×#217—31no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—31no—
244C2×#217—38no—
245C2×#217—38no—
246C2×#217—61no—
247C2×#217C2×D311yescharacteristic, complemented
248C2×#217C2×D311yescharacteristic, complemented
249C2×#217C2×D311yescharacteristic, complemented
250#939—38no—
251#939—38no—
252#939—38no—
253#939—68no—
254#938—38no—
255#936—38no—
256#935—38no—
257#935C2×D318yescomplemented
258D4×Dic3—38no—
259C4×#67—38no—
260C2×(C2×D3)⋊C4—38no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—31no—
264C2×(C2×D3)⋊C4—31no—
265C2×(C2×D3)⋊C4—31no—
266C2×(C2×D3)⋊C4—31no—
267C2×(C2×D3)⋊C4—31no—
268C2×(C2×D3)⋊C4—31no—
269C2×(C2×D3)⋊C4—31no—
270C2×(C2×D3)⋊C4—61no—
271C2×C4⋊Dic3—31no—
272#924—38no—
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—31no—
276C2×Dic3⋊C4—61no—
277C2×Dic3⋊C4C2×D311yescharacteristic, complemented
278C2×Dic3⋊C4C2×D311yescharacteristic, complemented
279C2×C4×Dic3—31no—
280C2×C4×Dic3—31no—
281#896—38no—
282#895—38no—
283#894—38no—
284#893—38no—
285#885—38no—
286#884—38no—
287#882—38no—
288#882—38no—
289#67⋊C4—38no—
290D3×C22⋊C4—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32C2×D414yes—
297C23×C32C2412yes—
298C23×C32C2412yes—
299C23×C32C2411yescharacteristic
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3C2412yes—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—28no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—28no—
313C22×C3×D3—28no—
314C22×C3×D3—28no—
315C22×C3×D3—44no—
316C22×C3×D3—44no—
317C22×C3×D3—416no—
318C22×C3×D3—416no—
319C22×C3×D3C2×D414yes—
320C22×C3×D3#4114yescomplemented
321C22×C3×D3C2412yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
324C32×D4—28no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327#638—28no—
328#638—44no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3—44no—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C3×#67—28no—
337C3×#67C2×D4116yescomplemented
338C2×C3×Dic3—22no—
339C2×C3×Dic3—28no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3C2×D414yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C3×D12—28no—
350C3×C4×D3—28no—
351#627—28no—
352#626—28no—
353#626—28no—
354#626—44no—
355#624—28no—
356D3×Dic3—28no—
357D3×Dic3—44no—
358C22×#41—91no—
359C23×D4—31no—
360#546—916no—
361C2×#124—91no—
362C2×#123—31no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—21no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—31no—
379C24×C3—34no—
380C24×C3—34no—
381C24×C3—64no—
382C24×C3—64no—
383C24×C3—64no—
384C24×C3—64no—
385C24×C3—122no—
386C24×C3—122no—
387C24×C3C22×D311yescharacteristic
388C24×C3C22×D311yescharacteristic
389C24×C3C22×D311yescharacteristic
390C24×C3C22×D311yescharacteristic
391C23×D3—24no—
392C23×D3—24no—
393C23×D3—24no—
394C23×D3—24no—
395C23×D3—31no—
396C23×D3—31no—
397C23×D3—42no—
398C23×D3—42no—
399C23×D3—61no—
400C23×D3C22×D311yescharacteristic
401C23×D3C22×D314yes—
402C23×D3C22×D314yes—
403C23×D3C22×D311yescharacteristic
404C23×D3C22×D311yescharacteristic
405C2×C3×D4—24no—
406C2×C3×D4—24no—
407C2×C3×D4—24no—
408C2×C3×D4—38no—
409C2×C3×D4—34no—
410C2×C3×D4—34no—
411C2×C3×D4—34no—
412C2×C3×D4—44no—
413C2×C3×D4—64no—
414C2×C3×D4—64no—
415C2×C3×D4—632no—
416C2×C3×D4C22×D314yes—
417C2×C3×D4C22×D314yes—
418C22×C3×C4—21no—
419C22×C3×C4—31no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—34no—
425C22×C3×C4—34no—
426C22×C3×C4—64no—
427C22×C3×C4—64no—
428C22×C3×C4C22×D311yescharacteristic
429C22×C3×C4C22×D311yescharacteristic
430C2×#67—24no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—64no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—124no—
445C2×#67—122no—
446C2×#67—122no—
447C2×#67—122no—
448C2×#67—124no—
449C2×#67#6718yescomplemented
450C2×#67C22×D314yes—
451C2×#67C22×D314yes—
452C22×Dic3—24no—
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—34no—
460C22×Dic3—34no—
461C22×Dic3—34no—
462C22×Dic3—34no—
463C22×Dic3—61no—
464C22×Dic3—61no—
465C22×Dic3—61no—
466C22×Dic3—64no—
467C22×Dic3—64no—
468C22×Dic3—122no—
469C22×Dic3—122no—
470C22×Dic3—122no—
471C22×Dic3—124no—
472C22×Dic3C22×D311yescharacteristic
473C22×Dic3C22×D311yescharacteristic
474C22×Dic3C22×D311yescharacteristic
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D311yescharacteristic
477C22×Dic3C22×D314yescomplemented
478#237—632no—
479D3×D4—232no—
480#235—632no—
481C2×D12—24no—
482C2×D12—34no—
483C2×D12—34no—
484C2×D12—34no—
485C2×D12—64no—
486C2×D12—64no—
487C2×D12—122no—
488C2×D12C22×D314yes—
489C2×C4×D3—24no—
490C2×C4×D3—34no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—34no—
494C2×C4×D3—64no—
495C2×C4×D3—64no—
496C2×C4×D3—64no—
497C2×C4×D3—122no—
498C2×C4×D3C22×D314yes—
499C2×Dic6—34no—
500C2×Dic6—34no—
501C2×Dic6—64no—
502C2×Dic6—64no—
503C3×C4⋊C4—34no—
504C3×C4⋊C4—34no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508#217—34no—
509#217—34no—
510#217—34no—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516#217—34no—
517#217—64no—
518#217C22×D314yescomplemented
519#217C22×D314yescomplemented
520#217C22×D314yescomplemented
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—64no—
531C4⋊Dic3—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—64no—
536Dic3⋊C4C22×D314yescomplemented
537Dic3⋊C4C22×D314yescomplemented
538C4×Dic3—34no—
539C4×Dic3—34no—
540C22×C32—28no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—22no—
546C22×C32—44no—
547C22×C32C22×D414yes—
548C22×C32C22×D412yes—
549C22×C32C2×#4112yes—
550C22×C32H(5,𝔽2)12yes—
551C22×C32C2511yescharacteristic
552C2×C3⋊D3—22no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3—44no—
556C2×C3×D3—28no—
557C2×C3×D3—28no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3—416no—
566C2×C3×D3—416no—
567C2×C3×D3—44no—
568C2×C3×D3C22×D414yes—
569C2×C3×D3C2×#4114yescomplemented
570C32×C4—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3⋊Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3C22×D414yes—
579C25—31no—
580C25—31no—
581C2×#41—98no—
582C2×#41—188no—
583C22×Q8—91no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—38no—
587C22×D4—31no—
588C22×D4—68no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—91no—
594C22×D4D3211yescharacteristic
595C23×C4—31no—
596C23×C4—31no—
597C23×C4—91no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601#124—98no—
602#123—38no—
603#123—98no—
604C22⋊Q8—98no—
605#121—98no—
606#121—98no—
607#121—98no—
608#120—98no—
609#120—98no—
610C4×D4—98no—
611C4×D4—98no—
612C2×C4⋊C4—31no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4—91no—
615C2×C4⋊C4—91no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—98no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—98no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C42—91no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—22no—
641C23×C3—22no—
642C23×C3—22no—
643C23×C3—21no—
644C23×C3—24no—
645C23×C3—34no—
646C23×C3—34no—
647C23×C3—32no—
648C23×C3—32no—
649C23×C3—32no—
650C23×C3—42no—
651C23×C3—42no—
652C23×C3—42no—
653C23×C3—42no—
654C23×C3—42no—
655C23×C3—68no—
656C23×C3—68no—
657C23×C3—68no—
658C23×C3—62no—
659C23×C3—62no—
660C23×C3—62no—
661C23×C3—62no—
662C23×C3—68no—
663C23×C3—62no—
664C23×C3—62no—
665C23×C3—62no—
666C23×C3—124no—
667C23×C3—124no—
668C23×C3—1216no—
669C23×C3—1216no—
670C23×C3D3×D414yes—
671C23×C3C2×#6714yes—
672C23×C3C23×D312yes—
673C23×C3C23×D312yes—
674C23×C3C23×D312yes—
675C23×C3C23×D312yes—
676C23×C3C23×D311yescharacteristic
677C23×C3C23×D311yescharacteristic
678C22×D3—22no—
679C22×D3—22no—
680C22×D3—22no—
681C22×D3—22no—
682C22×D3—22no—
683C22×D3—22no—
684C22×D3—22no—
685C22×D3—28no—
686C22×D3—28no—
687C22×D3—28no—
688C22×D3—28no—
689C22×D3—32no—
690C22×D3—32no—
691C22×D3—44no—
692C22×D3—44no—
693C22×D3—416no—
694C22×D3—416no—
695C22×D3—62no—
696C22×D3—62no—
697C22×D3—62no—
698C22×D3—62no—
699C22×D3—62no—
700C22×D3—62no—
701C22×D3—62no—
702C22×D3—122no—
703C22×D3—122no—
704C22×D3—122no—
705C22×D3#23714yescomplemented
706C22×D3C2×#6714yes—
707C22×D3C23×D312yes—
708C22×D3C23×D312yes—
709C22×D3C23×D312yes—
710C3×D4—28no—
711C3×D4—28no—
712C3×D4—316no—
713C3×D4—48no—
714C3×D4—68no—
715C3×D4—68no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—34no—
720C2×C3×C4—32no—
721C2×C3×C4—32no—
722C2×C3×C4—32no—
723C2×C3×C4—32no—
724C2×C3×C4—32no—
725C2×C3×C4—42no—
726C2×C3×C4—68no—
727C2×C3×C4—62no—
728C2×C3×C4—62no—
729C2×C3×C4—62no—
730C2×C3×C4—62no—
731C2×C3×C4—68no—
732C2×C3×C4C23×D312yes—
733C2×C3×C4C23×D312yes—
734#67—28no—
735#67—68no—
736#67—68no—
737#67—68no—
738#67—68no—
739#67—128no—
740#67—124no—
741#67—124no—
742#67—124no—
743#67—128no—
744#67C2×#67116yescomplemented
745C2×Dic3—22no—
746C2×Dic3—22no—
747C2×Dic3—28no—
748C2×Dic3—22no—
749C2×Dic3—22no—
750C2×Dic3—32no—
751C2×Dic3—32no—
752C2×Dic3—32no—
753C2×Dic3—32no—
754C2×Dic3—32no—
755C2×Dic3—32no—
756C2×Dic3—62no—
757C2×Dic3—62no—
758C2×Dic3—62no—
759C2×Dic3—68no—
760C2×Dic3—64no—
761C2×Dic3—62no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—122no—
768C2×Dic3—122no—
769C2×Dic3—124no—
770C2×Dic3—124no—
771C2×Dic3—124no—
772C2×Dic3—128no—
773C2×Dic3C2×#6714yes—
774C2×Dic3C23×D312yes—
775C2×Dic3C23×D312yes—
776C2×Dic3C23×D312yes—
777C2×Dic3C23×D312yes—
778C2×Dic3C23×D312yes—
779D12—28no—
780D12—68no—
781D12—68no—
782D12—124no—
783C4×D3—28no—
784C4×D3—68no—
785C4×D3—68no—
786C4×D3—68no—
787C4×D3—124no—
788Dic6—68no—
789Dic6—68no—
790C2×C32—24no—
791C2×C32—42no—
792C2×C32#54614yescomplemented
793C2×C32C23×D411yescharacteristic
794C2×C32C22×#4111yescharacteristic
795C2×C32C2×H(5,𝔽2)11yescharacteristic
796C3⋊D3—42no—
797C3×D3—24no—
798C3×D3—24no—
799C3×D3—42no—
800C24—31no—
801C24—31no—
802C24—31no—
803C24—34no—
804C24—34no—
805C24—64no—
806C24—64no—
807C24—64no—
808C24—64no—
809C24—91no—
810C24—122no—
811C24—122no—
812C24C2×D3211yescharacteristic
813C24C2×D3211yescharacteristic
814#41—1832no—
815C2×Q8—94no—
816C2×Q8—184no—
817C2×D4—24no—
818C2×D4—34no—
819C2×D4—38no—
820C2×D4—34no—
821C2×D4—34no—
822C2×D4—64no—
823C2×D4—64no—
824C2×D4—632no—
825C2×D4—94no—
826C2×D4—94no—
827C2×D4—94no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—184no—
831C2×D4—184no—
832C2×D4—184no—
833C2×D4—362no—
834C2×D4—362no—
835C2×D4C2×D3214yes—
836C22×C4—31no—
837C22×C4—34no—
838C22×C4—31no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—34no—
843C22×C4—64no—
844C22×C4—64no—
845C22×C4—94no—
846C22×C4—94no—
847C22×C4—94no—
848C22×C4—91no—
849C22×C4—91no—
850C22×C4—91no—
851C22×C4—94no—
852C22×C4—184no—
853C22×C4—184no—
854C22×C4—362no—
855C22×C4—362no—
856C22×C4C2×D3211yescharacteristic
857C4⋊C4—34no—
858C4⋊C4—34no—
859C4⋊C4—94no—
860C4⋊C4—94no—
861C22⋊C4—34no—
862C22⋊C4—34no—
863C22⋊C4—34no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4—94no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C42—94no—
874C22×C3—28no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—28no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—24no—
890C22×C3—21no—
891C22×C3—34no—
892C22×C3—34no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—48no—
896C22×C3—42no—
897C22×C3—42no—
898C22×C3—42no—
899C22×C3—44no—
900C22×C3—44no—
901C22×C3—68no—
902C22×C3—68no—
903C22×C3—62no—
904C22×C3—62no—
905C22×C3—62no—
906C22×C3—62no—
907C22×C3—62no—
908C22×C3—62no—
909C22×C3—62no—
910C22×C3—84no—
911C22×C3—1216no—
912C22×C3—1216no—
913C22×C3—124no—
914C22×C3C2×D3×D414yes—
915C22×C3C2×D3×D412yes—
916C22×C3C2×#23712yes—
917C22×C3#100412yes—
918C22×C3D3×#4112yes—
919C22×C3#100912yes—
920C22×C3C22×#6714yes—
921C22×C3C22×#6712yes—
922C22×C3C24×D311yescharacteristic
923C22×C3C24×D311yescharacteristic
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—22no—
928C2×D3—28no—
929C2×D3—28no—
930C2×D3—22no—
931C2×D3—22no—
932C2×D3—22no—
933C2×D3—416no—
934C2×D3—416no—
935C2×D3—44no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—62no—
942C2×D3—122no—
943C2×D3—122no—
944C2×D3—122no—
945C2×D3—124no—
946C2×D3—124no—
947C2×D3—244no—
948C2×D3C2×#23714yescomplemented
949C2×D3C22×#6714yes—
950C3×C4—22no—
951C3×C4—22no—
952C3×C4—34no—
953C3×C4—42no—
954C3×C4—62no—
955C3×C4—62no—
956C3×C4—62no—
957C3×C4—62no—
958Dic3—22no—
959Dic3—22no—
960Dic3—22no—
961Dic3—22no—
962Dic3—64no—
963Dic3—62no—
964Dic3—62no—
965Dic3—62no—
966Dic3—62no—
967Dic3—62no—
968Dic3—62no—
969Dic3—122no—
970Dic3—122no—
971Dic3C22×#6714yes—
972C32C2×#54611yescharacteristic, complemented, Sylow
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—34no—
979C23—34no—
980C23—32no—
981C23—32no—
982C23—32no—
983C23—68no—
984C23—68no—
985C23—68no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—68no—
993C23—62no—
994C23—92no—
995C23—124no—
996C23—124no—
997C23—1216no—
998C23—1216no—
999C23—182no—
1000C23—182no—
1001C23—182no—
1002C23D3×#6714yes—
1003C23C22×D3212yes—
1004C23C22×D3212yes—
1005C23C22×D3211yescharacteristic
1006Q8—188no—
1007D4—28no—
1008D4—316no—
1009D4—68no—
1010D4—68no—
1011D4—188no—
1012D4—188no—
1013D4—188no—
1014D4—364no—
1015D4—364no—
1016C2×C4—22no—
1017C2×C4—34no—
1018C2×C4—32no—
1019C2×C4—32no—
1020C2×C4—32no—
1021C2×C4—32no—
1022C2×C4—32no—
1023C2×C4—68no—
1024C2×C4—62no—
1025C2×C4—62no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—68no—
1029C2×C4—92no—
1030C2×C4—92no—
1031C2×C4—92no—
1032C2×C4—188no—
1033C2×C4—188no—
1034C2×C4—182no—
1035C2×C4—182no—
1036C2×C4—182no—
1037C2×C4—364no—
1038C2×C4—364no—
1039C2×C4C22×D3212yes—
1040C2×C3—24no—
1041C2×C3—24no—
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—24no—
1045C2×C3—21no—
1046C2×C3—44no—
1047C2×C3—42no—
1048C2×C3—42no—
1049C2×C3—64no—
1050C2×C3—64no—
1051C2×C3—82no—
1052C2×C3—122no—
1053C2×C3#565414yescomplemented
1054C2×C3#580614yescomplemented
1055C2×C3C22×D3×D411yescharacteristic
1056C2×C3C22×#23711yescharacteristic
1057C2×C3C2×#100411yescharacteristic
1058C2×C3C2×D3×#4111yescharacteristic
1059C2×C3C2×#100911yescharacteristic
1060C2×C3C23×#6711yescharacteristic
1061D3—24no—
1062D3—24no—
1063D3—42no—
1064D3—122no—
1065D3—122no—
1066D3—242no—
1067C22—22no—
1068C22—22no—
1069C22—28no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—34no—
1074C22—34no—
1075C22—44no—
1076C22—62no—
1077C22—62no—
1078C22—62no—
1079C22—68no—
1080C22—68no—
1081C22—62no—
1082C22—62no—
1083C22—62no—
1084C22—62no—
1085C22—1216no—
1086C22—1216no—
1087C22—124no—
1088C22—182no—
1089C22—182no—
1090C22—182no—
1091C22—364no—
1092C22D3×#23712yes—
1093C22#6431412yes—
1094C22C2×D3×#6714yes—
1095C22C2×D3×#6712yes—
1096C22C23×D3211yescharacteristic
1097C4—22no—
1098C4—34no—
1099C4—62no—
1100C4—62no—
1101C4—62no—
1102C4—62no—
1103C4—182no—
1104C4—182no—
1105C4—182no—
1106C3—21no—
1107C3C2×#565411yescharacteristic, complemented
1108C3C2×#580611yescharacteristic, complemented
1109C2—24no—
1110C2—42no—
1111C2—64no—
1112C2—64no—
1113C2—122no—
1114C2—362no—
1115C2#1059514814yesdirect product factor
1116C2C2×D3×#23711yescharacteristic
1117C2C2×#6431411yescharacteristic
1118C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C22×#3804C2semidirect
3. C2×#64148C2semidirect
4. C2×C3×#935C2semidirect
5. C2×#63977C2semidirect
6. C2×#63977C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. C2×D3×#217C2semidirect
9. C22×(C2×D3)⋊Dic3C2semidirect
10. C2×#63959C2semidirect
11. C2×#63958C2semidirect
12. #10595148C2direct (N × H)
13. C2×#63904C2semidirect
14. C2×#63886C2semidirect
15. C2×#63884C2semidirect
16. C2×#63851C2semidirect
22. C22×#638C22semidirect
23. C22×#638C22semidirect
24. C23×C3⋊Dic3C22semidirect
27. C23×C3×Dic3C22semidirect
29. C2×C3×D3×D4C22semidirect
32. C22×#627C22semidirect
34. C22×#626C22semidirect
35. C22×#626C22semidirect
36. C22×#624C22semidirect
38. C2×#3804C22semidirect
39. C22×D3×Dic3C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×#3757C22semidirect
42. #64148C22semidirect
43. C2×#3752C22semidirect
44. C2×#3750C22semidirect
45. C2×C3×#217C22semidirect
46. C2×C3×#217C22semidirect
47. C2×C3×#217C22semidirect
48. C3×#935C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. #63977C22semidirect
52. #63977C22semidirect
53. #67⋊Dic3C22semidirect
54. D3×#217C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63959C22semidirect
65. #63958C22semidirect
66. C2×Dic32C22semidirect
67. #63904C22semidirect
68. #63886C22semidirect
69. #63884C22semidirect
70. #63851C22semidirect
73. C22×D3×D4D3semidirect
88. C2×#935D3semidirect
123. C2×#638C23semidirect
124. C2×#638C23semidirect
129. C22×C3⋊Dic3C23semidirect
131. C2×C3×#67D4semidirect
140. C22×C3×Dic3C23semidirect
147. C2×#627C23semidirect
152. C2×#626C23semidirect
153. C2×#626C23semidirect
155. C2×#624C23semidirect
159. C2×D3×Dic3C23semidirect
160. C2×D3×Dic3C23semidirect
161. #3757C23semidirect
162. #3752C23semidirect
163. #3750C23semidirect
164. C3×#217C23semidirect
165. C3×#217C23semidirect
166. C3×#217C23semidirect
167. C3×Dic3⋊C4C23semidirect
168. C3×Dic3⋊C4C23semidirect
169. Dic3⋊Dic3C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
209. C23×Dic3C2×D3semidirect
213. C2×D3×D4C2×D3semidirect
247. C2×#217C2×D3semidirect
248. C2×#217C2×D3semidirect
249. C2×#217C2×D3semidirect
257. #935C2×D3semidirect
277. C2×Dic3⋊C4C2×D3semidirect
278. C2×Dic3⋊C4C2×D3semidirect
320. C22×C3×D3#41semidirect
337. C3×#67C2×D4semidirect
449. C2×#67#67semidirect
477. C22×Dic3C22×D3semidirect
518. #217C22×D3semidirect
519. #217C22×D3semidirect
520. #217C22×D3semidirect
536. Dic3⋊C4C22×D3semidirect
537. Dic3⋊C4C22×D3semidirect
569. C2×C3×D3C2×#41semidirect
705. C22×D3#237semidirect
744. #67C2×#67semidirect
792. C2×C32#546semidirect
948. C2×D3C2×#237semidirect
972. C32C2×#546semidirect
1053. C2×C3#5654semidirect
1054. C2×C3#5806semidirect
1107. C3C2×#5654semidirect
1108. C3C2×#5806semidirect
1115. C2#10595148direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C22×#38042
C2×#641482
C2×C3×#9352
C2×#639772
C2×#67⋊Dic32
C2×D3×#2172
C22×(C2×D3)⋊Dic32
C2×#639592
C2×#639582
#105951482
C2×#639042
C2×#638862
C2×#638842
C2×#638512
C2×#58063
C2×#56543