Finite Group Databasebeta

← C2×#10595068 #11902419

Subgroups — C2×#10595068 #11902419

Order 1152.

4137 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×#3811C211yesmaximal, characteristic, complemented
3C22×#3752C211yesmaximal, characteristic, complemented
4C2×C3×#929C211yesmaximal, characteristic, complemented
5C2×#63981C211yesmaximal, characteristic, complemented
6C2×#63980C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
8#10595068C2116yesmaximal, direct product factor
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63907C211yesmaximal, characteristic, complemented
12C2×#63906C211yesmaximal, characteristic, complemented
13C2×#63904C211yesmaximal, characteristic, complemented
14C2×#63888C211yesmaximal, characteristic, complemented
15C2×#63886C211yesmaximal, characteristic, complemented
16C2×#63850C211yesmaximal, characteristic, complemented
17C2×#5829—31nomaximal
18C2×#5654—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic, complemented
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic, complemented
26C2×C3×#235—28no—
27C2×C3×#235C2218yescomplemented
28C22×C3×D12C2211yescharacteristic, complemented
29C22×C3×C4×D3C2211yescharacteristic, complemented
30C22×C3×C4×D3C2211yescharacteristic, complemented
31C22×C3×Dic6C2211yescharacteristic, complemented
32C2×#3811—28no—
33C2×#3811C2218yescomplemented
34C22×#626C2211yescharacteristic
35C22×#626C2211yescharacteristic
36C22×#626C2211yescharacteristic
37C22×#626C2211yescharacteristic, complemented
38C22×#625C2211yescharacteristic, complemented
39C22×#624C2211yescharacteristic
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43C2×#3752C2218yescomplemented
44C2×#3752C2211yescharacteristic, complemented
45C2×#3752C2211yescharacteristic, complemented
46C2×C3×#217C2211yescharacteristic, complemented
47C3×#929C2218yescomplemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52#63981C2218yescomplemented
53#63980C2218yescomplemented
54#67⋊Dic3C2218yescomplemented
55C2×#3724C2211yescharacteristic, complemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×Dic32C2211yescharacteristic, complemented
63#63922C2218yescomplemented
64D3×(C2×D3)⋊C4C2218yescomplemented
65#63907C2218yescomplemented
66#63906C2218yescomplemented
67#63904C2218yescomplemented
68#63888C2218yescomplemented
69#63886C2218yescomplemented
70#63850C2218yescomplemented
71C22×C3×#41—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C22×#235D311yescharacteristic, complemented
75C2×C3×#123—31no—
76#5829—316no—
77C2×#947—31no—
78C2×#946—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#939—31no—
82C2×#937—31no—
83C2×#937—31no—
84C2×D4×Dic3—31no—
85C2×#930—31no—
86C2×#929—31no—
87C2×#929D311yescharacteristic, complemented
88C2×C4×#67—31no—
89C22×(C2×D3)⋊C4—31no—
90C22×(C2×D3)⋊C4—31no—
91C22×(C2×D3)⋊C4—31no—
92C22×(C2×D3)⋊C4—61no—
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
105C23×C3⋊D3—24no—
106C23×C3⋊D3—24no—
107C23×C3⋊D3—42no—
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2314yes—
110C23×C3⋊D3C2311yescharacteristic
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C22×C32×C4—24no—
119C22×C32×C4C2311yescharacteristic
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2314yescomplemented
122C22×C3⋊Dic3—42no—
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2314yescomplemented
126C2×C3×#67—24no—
127C2×C3×#67—24no—
128C2×C3×#67D418yescomplemented
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C2×C3×#67C2314yescomplemented
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C3×#235—232no—
138C2×C3×D12—24no—
139C2×C3×D12C2314yescomplemented
140C2×C3×C4×D3—24no—
141C2×C3×C4×D3—24no—
142C2×C3×C4×D3C2314yescomplemented
143C2×C3×C4×D3C2314yescomplemented
144C2×C3×Dic6—24no—
145C2×C3×Dic6C2314yescomplemented
146#3811—232no—
147C2×#626—24no—
148C2×#626—24no—
149C2×#626—24no—
150C2×#626—42no—
151C2×#626C2314yes—
152C2×#626C2314yes—
153C2×#626C2314yes—
154C2×#626C2314yescomplemented
155C2×#625—42no—
156C2×#625C2314yescomplemented
157C2×#624—24no—
158C2×#624C2314yes—
159C2×D3×Dic3—42no—
160C2×D3×Dic3C2314yescomplemented
161#3752C2314yes—
162#3752C2314yes—
163#3752C2314yescomplemented
164#3752C2314yescomplemented
165C3×#217C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×Dic3⋊C4C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170#3724C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yes—
173#3722C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C24×D3—61no—
184C2×C3×#41—38no—
185C2×C3×#41—68no—
186C22×C3×Q8—31no—
187C22×C3×D4—31no—
188C22×C3×D4—31no—
189C22×C3×D4—31no—
190C22×C3×D4—31no—
191C23×C3×C4—21no—
192C23×C3×C4—31no—
193C23×C3×C4—31no—
194C23×C3×C4C2×D311yescharacteristic, complemented
195C23×C3×C4C2×D311yescharacteristic, complemented
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic
204C22×#67C2×D311yescharacteristic, complemented
205C23×Dic3—31no—
206C23×Dic3—31no—
207C23×Dic3—31no—
208C23×Dic3—61no—
209C2×D3×D4—38no—
210C2×D3×D4—38no—
211C2×D3×D4—68no—
212C2×D3×D4—68no—
213C2×#235—28no—
214C2×#235C2×D318yescomplemented
215C22×D12—31no—
216C22×D12—31no—
217C22×D12—31no—
218C22×D12—31no—
219C22×D12C2×D311yescharacteristic, complemented
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3C2×D311yescharacteristic, complemented
224C22×C4×D3C2×D311yescharacteristic, complemented
225C22×Dic6C2×D311yescharacteristic, complemented
226C3×#123—38no—
227C2×C3×C4⋊C4—31no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×#217—31no—
233C2×#217—31no—
234C2×#217—31no—
235C2×#217C2×D311yescharacteristic, complemented
236#947—38no—
237#946—38no—
238#939—38no—
239#939—38no—
240#939—38no—
241#937—38no—
242#937—38no—
243D4×Dic3—38no—
244#930—38no—
245#929—38no—
246#929C2×D318yescomplemented
247C4×#67—38no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—31no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—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—38no—
266C2×(C2×D3)⋊C4—61no—
267C2×(C2×D3)⋊C4—61no—
268C2×(C2×D3)⋊C4—61no—
269C2×(C2×D3)⋊C4—61no—
270C2×(C2×D3)⋊C4—68no—
271C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
272C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
273C2×C4⋊Dic3—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—31no—
276C2×Dic3⋊C4—31no—
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×C32C2×D414yes—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—28no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—28no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—44no—
304C22×C3⋊D3—416no—
305C22×C3⋊D3#4114yescomplemented
306C22×C3⋊D3C2412yes—
307C22×C3⋊D3C2412yes—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3C2×D414yes—
317C22×C3×D3C2412yes—
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—28no—
321C2×D32—28no—
322C2×D32—44no—
323C2×D32—416no—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4—28no—
327C2×C32×C4C2412yes—
328C2×C32×C4C2412yes—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—44no—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C3×#67—28no—
335C3×#67—28no—
336C3×#67C2×D4116yescomplemented
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3C2×D414yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C3×D12—28no—
348C3×C4×D3—28no—
349C3×C4×D3—28no—
350C3×Dic6—28no—
351#626—28no—
352#626—28no—
353#626—28no—
354#626—44no—
355#625—44no—
356#624—28no—
357D3×Dic3—44no—
358C22×#41—31no—
359C23×D4—91no—
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—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—34no—
385C23×D3—34no—
386C23×D3—34no—
387C23×D3—34no—
388C23×D3—61no—
389C23×D3—61no—
390C23×D3—64no—
391C23×D3—64no—
392C23×D3—64no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—68no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—124no—
401C23×D3—122no—
402C23×D3—122no—
403C23×D3—122no—
404C23×D3—122no—
405C23×D3—124no—
406C23×D3C22×D311yescharacteristic
407C23×D3C22×D311yescharacteristic
408C23×D3C22×D311yescharacteristic
409C3×#41—632no—
410C2×C3×Q8—34no—
411C2×C3×Q8—64no—
412C2×C3×D4—38no—
413C2×C3×D4—34no—
414C2×C3×D4—34no—
415C2×C3×D4—34no—
416C2×C3×D4—34no—
417C2×C3×D4—64no—
418C2×C3×D4—64no—
419C2×C3×D4—64no—
420C22×C3×C4—24no—
421C22×C3×C4—24no—
422C22×C3×C4—21no—
423C22×C3×C4—21no—
424C22×C3×C4—24no—
425C22×C3×C4—31no—
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—31no—
429C22×C3×C4—31no—
430C22×C3×C4—34no—
431C22×C3×C4—34no—
432C22×C3×C4—44no—
433C22×C3×C4—64no—
434C22×C3×C4—64no—
435C22×C3×C4C22×D311yescharacteristic
436C22×C3×C4C22×D311yescharacteristic
437C22×C3×C4C22×D311yescharacteristic
438C22×C3×C4C22×D311yescharacteristic
439C22×C3×C4C22×D314yescomplemented
440C22×C3×C4C22×D314yescomplemented
441C2×#67—24no—
442C2×#67—24no—
443C2×#67—34no—
444C2×#67—34no—
445C2×#67—34no—
446C2×#67—34no—
447C2×#67—34no—
448C2×#67—34no—
449C2×#67—64no—
450C2×#67—64no—
451C2×#67—64no—
452C2×#67—122no—
453C2×#67—122no—
454C2×#67—122no—
455C2×#67#6718yescomplemented
456C2×#67C22×D314yes—
457C2×#67C22×D314yes—
458C2×#67C22×D314yescomplemented
459C22×Dic3—31no—
460C22×Dic3—31no—
461C22×Dic3—31no—
462C22×Dic3—31no—
463C22×Dic3—34no—
464C22×Dic3—34no—
465C22×Dic3—34no—
466C22×Dic3—61no—
467C22×Dic3—61no—
468C22×Dic3—64no—
469C22×Dic3—122no—
470C22×Dic3—122no—
471C22×Dic3—122no—
472C22×Dic3—124no—
473C22×Dic3C22×D311yescharacteristic
474C22×Dic3C22×D311yescharacteristic
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D311yescharacteristic
477C22×Dic3C22×D311yescharacteristic
478D3×D4—632no—
479D3×D4—632no—
480#235—232no—
481C2×D12—24no—
482C2×D12—34no—
483C2×D12—34no—
484C2×D12—34no—
485C2×D12—34no—
486C2×D12—64no—
487C2×D12—64no—
488C2×D12—64no—
489C2×D12—122no—
490C2×D12C22×D314yescomplemented
491C2×C4×D3—24no—
492C2×C4×D3—24no—
493C2×C4×D3—34no—
494C2×C4×D3—34no—
495C2×C4×D3—34no—
496C2×C4×D3—64no—
497C2×C4×D3—64no—
498C2×C4×D3—122no—
499C2×C4×D3C22×D314yescomplemented
500C2×C4×D3C22×D314yescomplemented
501C2×Dic6—24no—
502C2×Dic6C22×D314yescomplemented
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#217C22×D314yescomplemented
512(C2×D3)⋊C4—34no—
513(C2×D3)⋊C4—34no—
514(C2×D3)⋊C4—34no—
515(C2×D3)⋊C4—34no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
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—64no—
528(C2×D3)⋊C4—64no—
529(C2×D3)⋊C4—64no—
530(C2×D3)⋊C4—64no—
531(C2×D3)⋊C4C22×D314yescomplemented
532(C2×D3)⋊C4C22×D314yescomplemented
533C4⋊Dic3—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—34no—
536Dic3⋊C4—34no—
537Dic3⋊C4C22×D314yescomplemented
538Dic3⋊C4C22×D314yescomplemented
539C4×Dic3—34no—
540C4×Dic3—34no—
541C22×C32—28no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32C22×D414yes—
545C22×C32C22×D412yes—
546C22×C32C2×#4112yes—
547C22×C32H(5,𝔽2)12yes—
548C22×C32C2511yescharacteristic
549C2×C3⋊D3—22no—
550C2×C3⋊D3—28no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—22no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3—416no—
556C2×C3⋊D3—44no—
557C2×C3⋊D3C2×#4114yescomplemented
558C2×C3×D3—28no—
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—22no—
566C2×C3×D3—22no—
567C2×C3×D3—44no—
568C2×C3×D3—44no—
569C2×C3×D3C22×D414yes—
570D32—416no—
571C32×C4—22no—
572C32×C4—22no—
573C3⋊Dic3—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3C22×D414yes—
580C25—91no—
581C25—91no—
582C2×#41—38no—
583C2×#41—68no—
584C22×Q8—31no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—31no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—98no—
594C22×D4—91no—
595C22×D4—188no—
596C23×C4—31no—
597C23×C4—31no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601C23×C4D3211yescharacteristic, complemented
602#124—98no—
603#123—38no—
604#123—98no—
605C22⋊Q8—98no—
606#121—98no—
607#121—98no—
608#121—98no—
609#120—98no—
610#120—98no—
611C4×D4—98no—
612C4×D4—98no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4—91no—
616C2×C4⋊C4—91no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—98no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C22⋊C4—98no—
631C2×C42—91no—
632C23×C3—24no—
633C23×C3—24no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—21no—
640C23×C3—24no—
641C23×C3—34no—
642C23×C3—32no—
643C23×C3—32no—
644C23×C3—32no—
645C23×C3—62no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3D3×D414yes—
654C23×C3C2×#6714yes—
655C23×C3C23×D312yes—
656C23×C3C23×D312yes—
657C23×C3C23×D311yescharacteristic
658C23×C3C23×D311yescharacteristic
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—34no—
668C22×D3—34no—
669C22×D3—32no—
670C22×D3—32no—
671C22×D3—32no—
672C22×D3—32no—
673C22×D3—64no—
674C22×D3—62no—
675C22×D3—62no—
676C22×D3—68no—
677C22×D3—68no—
678C22×D3—68no—
679C22×D3—68no—
680C22×D3—68no—
681C22×D3—62no—
682C22×D3—62no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—616no—
686C22×D3—64no—
687C22×D3—62no—
688C22×D3—68no—
689C22×D3—62no—
690C22×D3—62no—
691C22×D3—62no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—68no—
695C22×D3—68no—
696C22×D3—122no—
697C22×D3—122no—
698C22×D3—122no—
699C22×D3—122no—
700C22×D3—128no—
701C22×D3—124no—
702C22×D3—124no—
703C22×D3—1216no—
704C22×D3—1216no—
705C22×D3—124no—
706C22×D3—124no—
707C22×D3—1216no—
708C22×D3—1216no—
709C22×D3—128no—
710C22×D3—1232no—
711C22×D3C2×#6714yes—
712C22×D3C23×D312yes—
713C22×D3C23×D312yes—
714C22×D3C23×D312yes—
715C3×Q8—68no—
716C3×D4—316no—
717C3×D4—68no—
718C3×D4—68no—
719C3×D4—68no—
720C2×C3×C4—22no—
721C2×C3×C4—22no—
722C2×C3×C4—28no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—28no—
726C2×C3×C4—22no—
727C2×C3×C4—22no—
728C2×C3×C4—34no—
729C2×C3×C4—32no—
730C2×C3×C4—32no—
731C2×C3×C4—32no—
732C2×C3×C4—32no—
733C2×C3×C4—32no—
734C2×C3×C4—42no—
735C2×C3×C4—42no—
736C2×C3×C4—48no—
737C2×C3×C4—68no—
738C2×C3×C4—68no—
739C2×C3×C4—62no—
740C2×C3×C4—62no—
741C2×C3×C4—62no—
742C2×C3×C4—62no—
743C2×C3×C4C23×D312yes—
744C2×C3×C4C23×D312yes—
745C2×C3×C4C23×D312yes—
746C2×C3×C4C23×D312yes—
747#67—28no—
748#67—28no—
749#67—68no—
750#67—68no—
751#67—68no—
752#67—124no—
753#67—124no—
754#67—124no—
755#67C2×#67116yescomplemented
756C2×Dic3—22no—
757C2×Dic3—22no—
758C2×Dic3—22no—
759C2×Dic3—22no—
760C2×Dic3—32no—
761C2×Dic3—32no—
762C2×Dic3—32no—
763C2×Dic3—32no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—62no—
768C2×Dic3—62no—
769C2×Dic3—62no—
770C2×Dic3—122no—
771C2×Dic3—122no—
772C2×Dic3—124no—
773C2×Dic3—124no—
774C2×Dic3—124no—
775C2×Dic3—128no—
776C2×Dic3C2×#6714yes—
777C2×Dic3C23×D312yes—
778C2×Dic3C23×D312yes—
779C2×Dic3C23×D312yes—
780C2×Dic3C23×D312yes—
781C2×Dic3C23×D312yes—
782D12—28no—
783D12—68no—
784D12—68no—
785D12—68no—
786D12—124no—
787C4×D3—28no—
788C4×D3—28no—
789C4×D3—68no—
790C4×D3—68no—
791C4×D3—124no—
792Dic6—28no—
793C2×C32—24no—
794C2×C32#54614yescomplemented
795C2×C32C23×D411yescharacteristic
796C2×C32C22×#4111yescharacteristic
797C2×C32C2×H(5,𝔽2)11yescharacteristic
798C3⋊D3—24no—
799C3⋊D3—42no—
800C3×D3—24no—
801C3×D3—42no—
802C3×D3—42no—
803C24—31no—
804C24—31no—
805C24—31no—
806C24—94no—
807C24—91no—
808C24—91no—
809C24—94no—
810C24—184no—
811C24—184no—
812C24—184no—
813C24—184no—
814C24—362no—
815C24—362no—
816C24C2×D3211yescharacteristic
817#41—632no—
818C2×Q8—34no—
819C2×Q8—64no—
820C2×D4—34no—
821C2×D4—38no—
822C2×D4—34no—
823C2×D4—34no—
824C2×D4—34no—
825C2×D4—64no—
826C2×D4—64no—
827C2×D4—64no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—94no—
831C2×D4—94no—
832C2×D4—94no—
833C2×D4—184no—
834C2×D4—184no—
835C2×D4—184no—
836C2×D4—1832no—
837C2×D4—362no—
838C2×D4—362no—
839C22×C4—24no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—31no—
844C22×C4—31no—
845C22×C4—34no—
846C22×C4—34no—
847C22×C4—64no—
848C22×C4—64no—
849C22×C4—94no—
850C22×C4—94no—
851C22×C4—91no—
852C22×C4—91no—
853C22×C4—94no—
854C22×C4—184no—
855C22×C4—362no—
856C22×C4—362no—
857C22×C4C2×D3211yescharacteristic
858C22×C4C2×D3211yescharacteristic
859C22×C4C2×D3214yescomplemented
860C4⋊C4—34no—
861C4⋊C4—34no—
862C4⋊C4—94no—
863C4⋊C4—94no—
864C22⋊C4—34no—
865C22⋊C4—34no—
866C22⋊C4—34no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C42—94no—
877C22×C3—24no—
878C22×C3—24no—
879C22×C3—216no—
880C22×C3—28no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—28no—
886C22×C3—22no—
887C22×C3—22no—
888C22×C3—24no—
889C22×C3—22no—
890C22×C3—21no—
891C22×C3—34no—
892C22×C3—68no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—124no—
902C22×C3—124no—
903C22×C3C2×D3×D414yes—
904C22×C3C2×D3×D412yes—
905C22×C3D3×#4112yes—
906C22×C3D3×#4112yes—
907C22×C3#100912yes—
908C22×C3#100912yes—
909C22×C3C22×#6714yes—
910C22×C3C22×#6712yes—
911C22×C3C24×D311yescharacteristic
912C22×C3C24×D311yescharacteristic
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—28no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—34no—
923C2×D3—34no—
924C2×D3—44no—
925C2×D3—44no—
926C2×D3—64no—
927C2×D3—68no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—68no—
933C2×D3—64no—
934C2×D3—62no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—122no—
941C2×D3—122no—
942C2×D3—128no—
943C2×D3—122no—
944C2×D3—122no—
945C2×D3—1216no—
946C2×D3—1216no—
947C2×D3—1216no—
948C2×D3—1216no—
949C2×D3—1232no—
950C2×D3—128no—
951C2×D3—124no—
952C2×D3—124no—
953C2×D3C22×#6714yes—
954C3×C4—22no—
955C3×C4—22no—
956C3×C4—22no—
957C3×C4—22no—
958C3×C4—34no—
959C3×C4—42no—
960C3×C4—42no—
961C3×C4—62no—
962C3×C4—62no—
963C3×C4—62no—
964C3×C4—62no—
965Dic3—22no—
966Dic3—22no—
967Dic3—22no—
968Dic3—22no—
969Dic3—62no—
970Dic3—62no—
971Dic3—62no—
972Dic3—62no—
973Dic3—122no—
974Dic3—122no—
975Dic3C22×#6714yes—
976C32C2×#54611yescharacteristic, complemented, Sylow
977C23—22no—
978C23—22no—
979C23—34no—
980C23—32no—
981C23—32no—
982C23—32no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—94no—
992C23—92no—
993C23—92no—
994C23—188no—
995C23—188no—
996C23—188no—
997C23—182no—
998C23—182no—
999C23—182no—
1000C23—182no—
1001C23—188no—
1002C23—182no—
1003C23—364no—
1004C23—3616no—
1005C23—364no—
1006C23—3616no—
1007C23D3×#6714yes—
1008C23C22×D3212yes—
1009C23C22×D3211yescharacteristic
1010Q8—68no—
1011D4—316no—
1012D4—68no—
1013D4—68no—
1014D4—68no—
1015D4—188no—
1016D4—188no—
1017D4—188no—
1018D4—364no—
1019D4—364no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—28no—
1023C2×C4—34no—
1024C2×C4—32no—
1025C2×C4—32no—
1026C2×C4—32no—
1027C2×C4—32no—
1028C2×C4—32no—
1029C2×C4—68no—
1030C2×C4—68no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—92no—
1036C2×C4—92no—
1037C2×C4—188no—
1038C2×C4—182no—
1039C2×C4—182no—
1040C2×C4—364no—
1041C2×C4—364no—
1042C2×C4C22×D3212yes—
1043C2×C4C22×D3212yes—
1044C2×C3—28no—
1045C2×C3—24no—
1046C2×C3—24no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—24no—
1051C2×C3—64no—
1052C2×C3—122no—
1053C2×C3—122no—
1054C2×C3#565414yescomplemented
1055C2×C3#582914yescomplemented
1056C2×C3C22×D3×D411yescharacteristic
1057C2×C3C2×D3×#4111yescharacteristic
1058C2×C3C2×D3×#4111yescharacteristic
1059C2×C3C2×#100911yescharacteristic
1060C2×C3C2×#100911yescharacteristic
1061C2×C3C23×#6711yescharacteristic
1062D3—24no—
1063D3—42no—
1064D3—42no—
1065D3—64no—
1066D3—64no—
1067D3—124no—
1068D3—124no—
1069D3—122no—
1070D3—122no—
1071C22—22no—
1072C22—22no—
1073C22—28no—
1074C22—34no—
1075C22—62no—
1076C22—62no—
1077C22—68no—
1078C22—62no—
1079C22—62no—
1080C22—62no—
1081C22—62no—
1082C22—62no—
1083C22—62no—
1084C22—94no—
1085C22—124no—
1086C22—124no—
1087C22—182no—
1088C22—182no—
1089C22—188no—
1090C22—182no—
1091C22—182no—
1092C22—182no—
1093C22—3616no—
1094C22—3616no—
1095C22—364no—
1096C22#6430612yes—
1097C22#6430812yes—
1098C22C2×D3×#6714yes—
1099C22C2×D3×#6712yes—
1100C22C23×D3211yescharacteristic
1101C4—22no—
1102C4—22no—
1103C4—34no—
1104C4—62no—
1105C4—62no—
1106C4—62no—
1107C4—62no—
1108C4—182no—
1109C4—182no—
1110C3—21no—
1111C3C2×#565411yescharacteristic, complemented
1112C3C2×#582911yescharacteristic, complemented
1113C2—24no—
1114C2—64no—
1115C2—122no—
1116C2—122no—
1117C2—184no—
1118C2—362no—
1119C2#1059506814yesdirect product factor
1120C2C2×#6430611yescharacteristic
1121C2C2×#6430811yescharacteristic
1122C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C22×#3811C2semidirect
3. C22×#3752C2semidirect
4. C2×C3×#929C2semidirect
5. C2×#63981C2semidirect
6. C2×#63980C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. #10595068C2direct (N × H)
9. C2×#63922C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63907C2semidirect
12. C2×#63906C2semidirect
13. C2×#63904C2semidirect
14. C2×#63888C2semidirect
15. C2×#63886C2semidirect
16. C2×#63850C2semidirect
21. C23×C32×C4C22semidirect
22. C23×C3⋊Dic3C22semidirect
25. C22×C3×#67C22semidirect
27. C2×C3×#235C22semidirect
28. C22×C3×D12C22semidirect
29. C22×C3×C4×D3C22semidirect
30. C22×C3×C4×D3C22semidirect
31. C22×C3×Dic6C22semidirect
33. C2×#3811C22semidirect
37. C22×#626C22semidirect
38. C22×#625C22semidirect
40. C22×D3×Dic3C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. C2×#3752C22semidirect
46. C2×C3×#217C22semidirect
47. C3×#929C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. #63981C22semidirect
53. #63980C22semidirect
54. #67⋊Dic3C22semidirect
55. C2×#3724C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
58. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×Dic32C22semidirect
63. #63922C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63907C22semidirect
66. #63906C22semidirect
67. #63904C22semidirect
68. #63888C22semidirect
69. #63886C22semidirect
70. #63850C22semidirect
74. C22×#235D3semidirect
87. C2×#929D3semidirect
121. C22×C32×C4C23semidirect
125. C22×C3⋊Dic3C23semidirect
128. C2×C3×#67D4semidirect
131. C2×C3×#67C23semidirect
139. C2×C3×D12C23semidirect
142. C2×C3×C4×D3C23semidirect
143. C2×C3×C4×D3C23semidirect
145. C2×C3×Dic6C23semidirect
154. C2×#626C23semidirect
156. C2×#625C23semidirect
160. C2×D3×Dic3C23semidirect
163. #3752C23semidirect
164. #3752C23semidirect
165. C3×#217C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×Dic3⋊C4C23semidirect
169. C3×Dic3⋊C4C23semidirect
170. #3724C23semidirect
171. Dic3⋊Dic3C23semidirect
173. #3722C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
194. C23×C3×C4C2×D3semidirect
195. C23×C3×C4C2×D3semidirect
204. C22×#67C2×D3semidirect
214. C2×#235C2×D3semidirect
219. C22×D12C2×D3semidirect
223. C22×C4×D3C2×D3semidirect
224. C22×C4×D3C2×D3semidirect
225. C22×Dic6C2×D3semidirect
235. C2×#217C2×D3semidirect
246. #929C2×D3semidirect
271. C2×(C2×D3)⋊C4C2×D3semidirect
272. C2×(C2×D3)⋊C4C2×D3semidirect
277. C2×Dic3⋊C4C2×D3semidirect
278. C2×Dic3⋊C4C2×D3semidirect
305. C22×C3⋊D3#41semidirect
336. C3×#67C2×D4semidirect
439. C22×C3×C4C22×D3semidirect
440. C22×C3×C4C22×D3semidirect
455. C2×#67#67semidirect
458. C2×#67C22×D3semidirect
490. C2×D12C22×D3semidirect
499. C2×C4×D3C22×D3semidirect
500. C2×C4×D3C22×D3semidirect
502. C2×Dic6C22×D3semidirect
511. #217C22×D3semidirect
531. (C2×D3)⋊C4C22×D3semidirect
532. (C2×D3)⋊C4C22×D3semidirect
537. Dic3⋊C4C22×D3semidirect
538. Dic3⋊C4C22×D3semidirect
557. C2×C3⋊D3C2×#41semidirect
601. C23×C4D32semidirect
755. #67C2×#67semidirect
794. C2×C32#546semidirect
859. C22×C4C2×D32semidirect
976. C32C2×#546semidirect
1054. C2×C3#5654semidirect
1055. C2×C3#5829semidirect
1111. C3C2×#5654semidirect
1112. C3C2×#5829semidirect
1119. C2#10595068direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×#38112
C22×#37522
C2×C3×#9292
C2×#639812
C2×#639802
C2×#67⋊Dic32
#105950682
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639072
C2×#639062
C2×#639042
C2×#638882
C2×#638862
C2×#638502
C2×#58293
C2×#56543