Finite Group Databasebeta

← C2×#10595077 #11902420

Subgroups — C2×#10595077 #11902420

Order 1152.

4245 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C22×D3×#67C211yesmaximal, characteristic, complemented
3C2×C3×#929C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic, complemented
8#10595077C2116yesmaximal, direct product factor
9C2×#63923C211yesmaximal, characteristic, complemented
10C2×#63921C211yesmaximal, characteristic, complemented
11C2×#63913C211yesmaximal, characteristic, complemented
12C2×#63912C211yesmaximal, characteristic, complemented
13C2×#63910C211yesmaximal, characteristic, complemented
14C2×#63896C211yesmaximal, characteristic, complemented
15C2×#63881C211yesmaximal, characteristic, complemented
16C2×#63853C211yesmaximal, characteristic, complemented
17C2×#5654—31nomaximal
18C2×#5490—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic, complemented
24C2×#3828—28no—
25C2×#3828C2218yescomplemented
26C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
27C22×C4×C3⋊D3C2211yescharacteristic, complemented
28C22×C4×C3⋊D3C2211yescharacteristic, complemented
29C22×#634C2211yescharacteristic, complemented
30C22×C3×#67C2211yescharacteristic
31C23×C3×Dic3C2211yescharacteristic, complemented
32C2×D3×#67—28no—
33C2×D3×#67C2218yescomplemented
34C22×#626C2211yescharacteristic
35C22×#626C2211yescharacteristic
36C22×#626C2211yescharacteristic, complemented
37C22×#626C2211yescharacteristic, complemented
38C22×#625C2211yescharacteristic
39C22×#624C2211yescharacteristic, complemented
40C22×D3×Dic3C2211yescharacteristic
41C2×C3×#217C2211yescharacteristic, complemented
42C3×#929C2218yescomplemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2218yescomplemented
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52#63978C2218yescomplemented
53#63977C2218yescomplemented
54C2×#3724C2211yescharacteristic, complemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×#3722C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×Dic32C2211yescharacteristic, complemented
62#63952C2218yescomplemented
63#63923C2218yescomplemented
64#63921C2218yescomplemented
65#63913C2218yescomplemented
66#63912C2218yescomplemented
67#63910C2218yescomplemented
68#63896C2218yescomplemented
69#63881C2218yescomplemented
70#63853C2218yescomplemented
71C23×#67—31no—
72C22×D3×D4—31no—
73C22×#235—31no—
74C22×#235—31no—
75C22×#235—61no—
76C2×C3×#123—31no—
77C22×C3×C22⋊C4—31no—
78C2×#953—31no—
79C2×#939—31no—
80C2×#930—31no—
81C2×#929D311yescharacteristic, complemented
82C2×C4×#67—31no—
83C22×(C2×D3)⋊C4D311yescharacteristic, complemented
84#5654—316no—
85C2×#896—31no—
86C2×#895—31no—
87C2×#894—31no—
88C2×#893—31no—
89C2×#885—31no—
90C2×#885—31no—
91#5490—316no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#883—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—31no—
99C2×#67⋊C4—31no—
100C2×#67⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×D3×C22⋊C4—31no—
103C2×#878—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3—24no—
108C23×C3×D3—24no—
109C23×C3×D3—42no—
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2314yes—
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
122C2×#638—24no—
123C2×#638D418yescomplemented
124C2×#638C2314yes—
125C2×#638C2314yescomplemented
126C22×C3⋊Dic3C2311yescharacteristic
127C22×C3⋊Dic3C2311yescharacteristic
128#3828—232no—
129C2×C4⋊(C3⋊D3)—24no—
130C2×C4⋊(C3⋊D3)C2314yescomplemented
131C2×C4×C3⋊D3—24no—
132C2×C4×C3⋊D3—24no—
133C2×C4×C3⋊D3C2314yescomplemented
134C2×C4×C3⋊D3C2314yescomplemented
135C2×#634—24no—
136C2×#634C2314yescomplemented
137C2×C3×#67—24no—
138C2×C3×#67C2314yes—
139C22×C3×Dic3—42no—
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2311yescharacteristic
145C22×C3×Dic3C2314yescomplemented
146D3×#67—232no—
147C2×#626—24no—
148C2×#626—24no—
149C2×#626—42no—
150C2×#626—42no—
151C2×#626C2314yes—
152C2×#626C2314yes—
153C2×#626C2314yescomplemented
154C2×#626C2314yescomplemented
155C2×#625—24no—
156C2×#625C2314yes—
157C2×#624—42no—
158C2×#624C2314yescomplemented
159C2×D3×Dic3—24no—
160C2×D3×Dic3C2314yes—
161C3×#217C2314yescomplemented
162C3×(C2×D3)⋊C4C2314yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×(C2×D3)⋊C4C2314yescomplemented
165C3×(C2×D3)⋊C4C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×Dic3⋊C4C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170#3724C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yescomplemented
173#3722C2314yescomplemented
174(C2×D3)⋊Dic3C2314yes—
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—31no—
184C23×C3×C4—21no—
185C23×C3×C4—31no—
186C23×C3×C4C2×D311yescharacteristic, complemented
187C23×C3×C4C2×D311yescharacteristic, complemented
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—38no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—61no—
200C22×#67—61no—
201C22×#67—68no—
202C22×#67C2×D311yescharacteristic
203C23×Dic3—31no—
204C23×Dic3C2×D311yescharacteristic, complemented
205C2×D3×D4—38no—
206C2×D3×D4—68no—
207C2×#235—38no—
208C2×#235—38no—
209C2×#235—68no—
210C2×#235—68no—
211C2×#235—68no—
212C2×#235—616no—
213C22×D12—31no—
214C22×D12—31no—
215C22×D12—31no—
216C22×D12—31no—
217C22×D12—31no—
218C22×D12—31no—
219C22×D12—61no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3—31no—
225C22×C4×D3—31no—
226C22×C4×D3—31no—
227C22×C4×D3—61no—
228C22×C4×D3—61no—
229C22×Dic6—31no—
230C22×Dic6—31no—
231C22×Dic6—61no—
232C3×#123—38no—
233C2×C3×C4⋊C4—31no—
234C2×C3×C4⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4—31no—
237C2×C3×C22⋊C4—31no—
238C2×C3×C22⋊C4—31no—
239C2×C3×C22⋊C4—31no—
240C2×C3×C22⋊C4—31no—
241C2×C3×C22⋊C4—31no—
242C2×C3×C22⋊C4—38no—
243#953—38no—
244C2×#217—31no—
245C2×#217—31no—
246C2×#217—31no—
247C2×#217C2×D311yescharacteristic, complemented
248#939—38no—
249#930—38no—
250#929C2×D318yescomplemented
251C4×#67—38no—
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)⋊C4C2×D311yescharacteristic
260C2×(C2×D3)⋊C4C2×D311yescharacteristic
261C2×(C2×D3)⋊C4C2×D318yescomplemented
262C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
266C2×C4⋊Dic3—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4C2×D311yescharacteristic, complemented
271C2×Dic3⋊C4C2×D311yescharacteristic, complemented
272C2×C4×Dic3—31no—
273C2×C4×Dic3—31no—
274#896—38no—
275#895—38no—
276#894—38no—
277#893—38no—
278#885—38no—
279#885—38no—
280#884—38no—
281#884—38no—
282#884—38no—
283#883—38no—
284#882—38no—
285#882—38no—
286#882—38no—
287#67⋊C4—38no—
288#67⋊C4—38no—
289D3×C22⋊C4—38no—
290D3×C22⋊C4—38no—
291#878—38no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32C2×D414yes—
295C23×C32C2412yes—
296C23×C32C2411yescharacteristic
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3C2×D414yes—
303C22×C3⋊D3C2412yes—
304C22×C3⋊D3C2412yes—
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—22no—
313C22×C3×D3—22no—
314C22×C3×D3—28no—
315C22×C3×D3—44no—
316C22×C3×D3—416no—
317C22×C3×D3#4114yescomplemented
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C22×C3×D3C2412yes—
321C2×D32—28no—
322C2×D32—28no—
323C2×D32—44no—
324C2×D32—416no—
325C2×C32×C4—22no—
326C2×C32×C4—22no—
327C2×C32×C4—28no—
328C2×C32×C4C2412yes—
329C2×C32×C4C2412yes—
330#638—28no—
331#638C2×D4116yescomplemented
332C2×C3⋊Dic3—22no—
333C2×C3⋊Dic3C2×D414yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C4⋊(C3⋊D3)—28no—
337C4×C3⋊D3—28no—
338C4×C3⋊D3—28no—
339#634—28no—
340C3×#67—28no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—22no—
344C2×C3×Dic3—22no—
345C2×C3×Dic3—22no—
346C2×C3×Dic3—44no—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352#626—28no—
353#626—28no—
354#626—44no—
355#626—44no—
356#625—28no—
357#624—44no—
358D3×Dic3—28no—
359C22×#41—91no—
360C23×D4—91no—
361#546—916no—
362C2×#124—91no—
363C2×#123—31no—
364C2×#123—91no—
365C2×C22⋊Q8—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#121—91no—
369C2×#120—91no—
370C2×#120—91no—
371C2×C4×D4—91no—
372C2×C4×D4—91no—
373C22×C22⋊C4—31no—
374C22×C22⋊C4—91no—
375C24×C3—21no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—31no—
379C24×C3—34no—
380C24×C3—64no—
381C24×C3—64no—
382C24×C3—122no—
383C24×C3C22×D311yescharacteristic
384C24×C3C22×D311yescharacteristic
385C23×D3—24no—
386C23×D3—24no—
387C23×D3—31no—
388C23×D3—31no—
389C23×D3—31no—
390C23×D3—31no—
391C23×D3—34no—
392C23×D3—34no—
393C23×D3—42no—
394C23×D3—61no—
395C23×D3—61no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—122no—
401C23×D3—122no—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C23×D3C22×D314yes—
405C23×D3C22×D311yescharacteristic
406C2×C3×D4—34no—
407C2×C3×D4—64no—
408C22×C3×C4—28no—
409C22×C3×C4—24no—
410C22×C3×C4—24no—
411C22×C3×C4—21no—
412C22×C3×C4—21no—
413C22×C3×C4—24no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—31no—
418C22×C3×C4—31no—
419C22×C3×C4—34no—
420C22×C3×C4—122no—
421C22×C3×C4C22×D311yescharacteristic
422C22×C3×C4C22×D311yescharacteristic
423C22×C3×C4C22×D311yescharacteristic
424C22×C3×C4C22×D311yescharacteristic
425C22×C3×C4C22×D314yescomplemented
426C22×C3×C4C22×D314yescomplemented
427C2×#67—24no—
428C2×#67—38no—
429C2×#67—38no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—68no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—632no—
448C2×#67—68no—
449C2×#67—64no—
450C2×#67—64no—
451C2×#67—122no—
452C2×#67—122no—
453C2×#67C22×D314yes—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—34no—
459C22×Dic3—42no—
460C22×Dic3—61no—
461C22×Dic3—61no—
462C22×Dic3—64no—
463C22×Dic3C22×D311yescharacteristic
464C22×Dic3C22×D311yescharacteristic
465C22×Dic3C22×D311yescharacteristic
466C22×Dic3C22×D311yescharacteristic
467C22×Dic3C22×D311yescharacteristic
468C22×Dic3C22×D314yescomplemented
469D3×D4—632no—
470#235—632no—
471#235—632no—
472#235—664no—
473C2×D12—34no—
474C2×D12—34no—
475C2×D12—34no—
476C2×D12—34no—
477C2×D12—34no—
478C2×D12—34no—
479C2×D12—64no—
480C2×D12—64no—
481C2×D12—64no—
482C2×D12—68no—
483C2×D12—64no—
484C2×D12—64no—
485C2×D12—122no—
486C2×D12—122no—
487C2×C4×D3—34no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
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—64no—
498C2×C4×D3—64no—
499C2×C4×D3—64no—
500C2×C4×D3—64no—
501C2×C4×D3—68no—
502C2×C4×D3—68no—
503C2×C4×D3—122no—
504C2×C4×D3—122no—
505C2×Dic6—34no—
506C2×Dic6—34no—
507C2×Dic6—64no—
508C2×Dic6—64no—
509C2×Dic6—64no—
510C2×Dic6—68no—
511C3×C4⋊C4—34no—
512C3×C4⋊C4—34no—
513C3×C22⋊C4—34no—
514C3×C22⋊C4—34no—
515C3×C22⋊C4—34no—
516C3×C22⋊C4—34no—
517C3×C22⋊C4—34no—
518C3×C22⋊C4—34no—
519C3×C22⋊C4—34no—
520#217—34no—
521#217—34no—
522#217—34no—
523#217C22×D314yescomplemented
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—34no—
531(C2×D3)⋊C4C22×D314yes—
532(C2×D3)⋊C4C22×D314yes—
533(C2×D3)⋊C4C22×D314yescomplemented
534(C2×D3)⋊C4C22×D314yescomplemented
535(C2×D3)⋊C4C22×D314yescomplemented
536(C2×D3)⋊C4C22×D314yescomplemented
537C4⋊Dic3—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4—34no—
540Dic3⋊C4—34no—
541Dic3⋊C4C22×D314yescomplemented
542Dic3⋊C4C22×D314yescomplemented
543C4×Dic3—34no—
544C4×Dic3—34no—
545C22×C32—28no—
546C22×C32—22no—
547C22×C32—22no—
548C22×C32C22×D414yes—
549C22×C32C22×D412yes—
550C22×C32C2×#4112yes—
551C22×C32H(5,𝔽2)12yes—
552C22×C32C2511yescharacteristic
553C2×C3⋊D3—22no—
554C2×C3⋊D3—28no—
555C2×C3⋊D3—22no—
556C2×C3⋊D3—22no—
557C2×C3⋊D3—22no—
558C2×C3⋊D3—22no—
559C2×C3⋊D3—44no—
560C2×C3⋊D3C22×D414yes—
561C2×C3×D3—28no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—22no—
568C2×C3×D3—22no—
569C2×C3×D3—22no—
570C2×C3×D3—416no—
571C2×C3×D3—44no—
572C2×C3×D3—44no—
573C2×C3×D3C2×#4114yescomplemented
574D32—416no—
575C32×C4—22no—
576C32×C4—22no—
577C3⋊Dic3—22no—
578C3⋊Dic3C22×D414yes—
579C3×Dic3—22no—
580C3×Dic3—22no—
581C3×Dic3—22no—
582C3×Dic3—22no—
583C3×Dic3—22no—
584C25—31no—
585C25—91no—
586C2×#41—98no—
587C2×#41—188no—
588C22×Q8—91no—
589C22×D4—31no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—91no—
594C22×D4—98no—
595C22×D4—91no—
596C22×D4—91no—
597C22×D4—91no—
598C22×D4—91no—
599C22×D4—188no—
600C23×C4—31no—
601C23×C4—91no—
602C23×C4—91no—
603C23×C4—91no—
604C23×C4—91no—
605C23×C4D3211yescharacteristic, complemented
606#124—98no—
607#123—38no—
608#123—98no—
609C22⋊Q8—98no—
610#121—98no—
611#121—98no—
612#121—98no—
613#120—98no—
614#120—98no—
615C4×D4—98no—
616C4×D4—98no—
617C2×C4⋊C4—31no—
618C2×C4⋊C4—31no—
619C2×C4⋊C4—91no—
620C2×C4⋊C4—91no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—31no—
624C2×C22⋊C4—31no—
625C2×C22⋊C4—31no—
626C2×C22⋊C4—31no—
627C2×C22⋊C4—31no—
628C2×C22⋊C4—38no—
629C2×C22⋊C4—98no—
630C2×C22⋊C4—91no—
631C2×C22⋊C4—91no—
632C2×C22⋊C4—91no—
633C2×C22⋊C4—91no—
634C2×C22⋊C4—91no—
635C2×C42—91no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—22no—
641C23×C3—21no—
642C23×C3—24no—
643C23×C3—34no—
644C23×C3—32no—
645C23×C3—32no—
646C23×C3—32no—
647C23×C3—42no—
648C23×C3—42no—
649C23×C3—68no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—68no—
654C23×C3—62no—
655C23×C3—62no—
656C23×C3—62no—
657C23×C3—62no—
658C23×C3—62no—
659C23×C3—124no—
660C23×C3—1216no—
661C23×C3D3×D414yes—
662C23×C3D3×D414yes—
663C23×C3C23×D312yes—
664C23×C3C23×D312yes—
665C23×C3C23×D311yescharacteristic
666C23×C3C23×D311yescharacteristic
667C22×D3—22no—
668C22×D3—22no—
669C22×D3—22no—
670C22×D3—22no—
671C22×D3—28no—
672C22×D3—22no—
673C22×D3—22no—
674C22×D3—22no—
675C22×D3—22no—
676C22×D3—28no—
677C22×D3—34no—
678C22×D3—34no—
679C22×D3—32no—
680C22×D3—32no—
681C22×D3—32no—
682C22×D3—32no—
683C22×D3—44no—
684C22×D3—416no—
685C22×D3—64no—
686C22×D3—62no—
687C22×D3—62no—
688C22×D3—68no—
689C22×D3—68no—
690C22×D3—68no—
691C22×D3—62no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—64no—
696C22×D3—62no—
697C22×D3—62no—
698C22×D3—62no—
699C22×D3—62no—
700C22×D3—62no—
701C22×D3—62no—
702C22×D3—68no—
703C22×D3—122no—
704C22×D3—122no—
705C22×D3—122no—
706C22×D3—122no—
707C22×D3—124no—
708C22×D3—124no—
709C22×D3—1216no—
710C22×D3—1216no—
711C22×D3#23514yescomplemented
712C22×D3C23×D312yes—
713C22×D3C23×D312yes—
714C22×D3C23×D312yes—
715C3×D4—68no—
716C2×C3×C4—24no—
717C2×C3×C4—24no—
718C2×C3×C4—216no—
719C2×C3×C4—22no—
720C2×C3×C4—22no—
721C2×C3×C4—22no—
722C2×C3×C4—22no—
723C2×C3×C4—28no—
724C2×C3×C4—28no—
725C2×C3×C4—22no—
726C2×C3×C4—22no—
727C2×C3×C4—32no—
728C2×C3×C4—32no—
729C2×C3×C4—32no—
730C2×C3×C4—32no—
731C2×C3×C4—32no—
732C2×C3×C4—62no—
733C2×C3×C4—62no—
734C2×C3×C4—62no—
735C2×C3×C4—62no—
736C2×C3×C4—62no—
737C2×C3×C4—124no—
738C2×C3×C4C23×D312yes—
739C2×C3×C4C23×D312yes—
740C2×C3×C4C23×D312yes—
741C2×C3×C4C23×D312yes—
742#67—28no—
743#67—316no—
744#67—316no—
745#67—616no—
746#67—68no—
747#67—68no—
748#67—68no—
749#67—68no—
750#67—616no—
751#67—68no—
752#67—68no—
753#67—124no—
754#67—124no—
755C2×Dic3—22no—
756C2×Dic3—22no—
757C2×Dic3—22no—
758C2×Dic3—22no—
759C2×Dic3—22no—
760C2×Dic3—34no—
761C2×Dic3—34no—
762C2×Dic3—32no—
763C2×Dic3—32no—
764C2×Dic3—32no—
765C2×Dic3—32no—
766C2×Dic3—44no—
767C2×Dic3—64no—
768C2×Dic3—62no—
769C2×Dic3—62no—
770C2×Dic3—68no—
771C2×Dic3—64no—
772C2×Dic3—62no—
773C2×Dic3—62no—
774C2×Dic3C23×D312yes—
775C2×Dic3C23×D312yes—
776C2×Dic3C23×D312yes—
777C2×Dic3C23×D312yes—
778C2×Dic3C23×D312yes—
779D12—68no—
780D12—68no—
781D12—616no—
782D12—68no—
783D12—68no—
784D12—124no—
785D12—124no—
786C4×D3—68no—
787C4×D3—68no—
788C4×D3—68no—
789C4×D3—68no—
790C4×D3—68no—
791C4×D3—616no—
792C4×D3—616no—
793C4×D3—124no—
794C4×D3—124no—
795Dic6—68no—
796Dic6—68no—
797Dic6—616no—
798C2×C32—24no—
799C2×C32#54614yescomplemented
800C2×C32C23×D411yescharacteristic
801C2×C32C22×#4111yescharacteristic
802C2×C32C2×H(5,𝔽2)11yescharacteristic
803C3⋊D3—24no—
804C3⋊D3—42no—
805C3×D3—24no—
806C3×D3—42no—
807C3×D3—42no—
808C24—31no—
809C24—31no—
810C24—31no—
811C24—34no—
812C24—64no—
813C24—64no—
814C24—94no—
815C24—91no—
816C24—91no—
817C24—122no—
818C24—184no—
819C24—184no—
820C24—362no—
821C24C2×D3211yescharacteristic
822#41—1832no—
823C2×Q8—94no—
824C2×Q8—184no—
825C2×D4—34no—
826C2×D4—64no—
827C2×D4—94no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—94no—
831C2×D4—94no—
832C2×D4—98no—
833C2×D4—94no—
834C2×D4—94no—
835C2×D4—94no—
836C2×D4—184no—
837C2×D4—184no—
838C2×D4—184no—
839C2×D4—184no—
840C2×D4—1832no—
841C2×D4—184no—
842C2×D4—362no—
843C2×D4—362no—
844C22×C4—24no—
845C22×C4—31no—
846C22×C4—31no—
847C22×C4—31no—
848C22×C4—31no—
849C22×C4—31no—
850C22×C4—34no—
851C22×C4—94no—
852C22×C4—94no—
853C22×C4—91no—
854C22×C4—91no—
855C22×C4—94no—
856C22×C4—94no—
857C22×C4—122no—
858C22×C4—184no—
859C22×C4—184no—
860C22×C4—184no—
861C22×C4—362no—
862C22×C4C2×D3211yescharacteristic
863C22×C4C2×D3211yescharacteristic
864C22×C4C2×D3214yescomplemented
865C4⋊C4—34no—
866C4⋊C4—34no—
867C4⋊C4—94no—
868C4⋊C4—94no—
869C22⋊C4—34no—
870C22⋊C4—34no—
871C22⋊C4—34no—
872C22⋊C4—34no—
873C22⋊C4—34no—
874C22⋊C4—34no—
875C22⋊C4—34no—
876C22⋊C4—94no—
877C22⋊C4—94no—
878C22⋊C4—94no—
879C22⋊C4—94no—
880C22⋊C4—94no—
881C42—94no—
882C22×C3—28no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—28no—
888C22×C3—22no—
889C22×C3—22no—
890C22×C3—22no—
891C22×C3—24no—
892C22×C3—21no—
893C22×C3—34no—
894C22×C3—48no—
895C22×C3—42no—
896C22×C3—42no—
897C22×C3—68no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—62no—
903C22×C3—62no—
904C22×C3—62no—
905C22×C3—62no—
906C22×C3—1216no—
907C22×C3—124no—
908C22×C3—124no—
909C22×C3C2×#23512yes—
910C22×C3C2×D3×D414yes—
911C22×C3C2×D3×D414yes—
912C22×C3C2×D3×D412yes—
913C22×C3C2×D3×D412yes—
914C22×C3#100412yes—
915C22×C3D3×#4112yes—
916C22×C3#100912yes—
917C22×C3C24×D311yescharacteristic
918C22×C3C24×D311yescharacteristic
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—28no—
922C2×D3—22no—
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—22no—
928C2×D3—34no—
929C2×D3—34no—
930C2×D3—416no—
931C2×D3—44no—
932C2×D3—44no—
933C2×D3—64no—
934C2×D3—68no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—68no—
940C2×D3—64no—
941C2×D3—62no—
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—62no—
946C2×D3—62no—
947C2×D3—128no—
948C2×D3—122no—
949C2×D3—122no—
950C2×D3—122no—
951C2×D3—122no—
952C2×D3—1216no—
953C2×D3—1216no—
954C2×D3—128no—
955C2×D3—124no—
956C2×D3—124no—
957C2×D3C2×#23514yescomplemented
958C3×C4—24no—
959C3×C4—24no—
960C3×C4—22no—
961C3×C4—22no—
962C3×C4—22no—
963C3×C4—22no—
964C3×C4—62no—
965C3×C4—62no—
966C3×C4—62no—
967C3×C4—62no—
968C3×C4—62no—
969Dic3—22no—
970Dic3—22no—
971Dic3—22no—
972Dic3—22no—
973Dic3—22no—
974Dic3—34no—
975Dic3—34no—
976Dic3—64no—
977Dic3—64no—
978Dic3—62no—
979Dic3—62no—
980C32C2×#54611yescharacteristic, complemented, Sylow
981C23—22no—
982C23—22no—
983C23—34no—
984C23—32no—
985C23—32no—
986C23—32no—
987C23—68no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—62no—
994C23—62no—
995C23—68no—
996C23—62no—
997C23—94no—
998C23—92no—
999C23—92no—
1000C23—124no—
1001C23—1216no—
1002C23—188no—
1003C23—188no—
1004C23—182no—
1005C23—182no—
1006C23—182no—
1007C23—182no—
1008C23—182no—
1009C23—364no—
1010C23—3616no—
1011C23#381114yes—
1012C23C22×D3212yes—
1013C23C22×D3211yescharacteristic
1014Q8—188no—
1015D4—68no—
1016D4—916no—
1017D4—188no—
1018D4—188no—
1019D4—188no—
1020D4—188no—
1021D4—188no—
1022D4—364no—
1023D4—364no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—28no—
1027C2×C4—32no—
1028C2×C4—32no—
1029C2×C4—32no—
1030C2×C4—32no—
1031C2×C4—32no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—94no—
1038C2×C4—92no—
1039C2×C4—92no—
1040C2×C4—124no—
1041C2×C4—188no—
1042C2×C4—188no—
1043C2×C4—188no—
1044C2×C4—182no—
1045C2×C4—364no—
1046C2×C4C22×D3212yes—
1047C2×C4C22×D3212yes—
1048C2×C3—24no—
1049C2×C3—24no—
1050C2×C3—24no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—44no—
1055C2×C3—64no—
1056C2×C3—122no—
1057C2×C3—122no—
1058C2×C3#549014yescomplemented
1059C2×C3#565414yescomplemented
1060C2×C3C22×#23511yescharacteristic
1061C2×C3C22×D3×D411yescharacteristic
1062C2×C3C22×D3×D411yescharacteristic
1063C2×C3C2×#100411yescharacteristic
1064C2×C3C2×D3×#4111yescharacteristic
1065C2×C3C2×#100911yescharacteristic
1066D3—24no—
1067D3—42no—
1068D3—42no—
1069D3—64no—
1070D3—64no—
1071D3—124no—
1072D3—124no—
1073D3—122no—
1074D3—122no—
1075C22—28no—
1076C22—22no—
1077C22—22no—
1078C22—34no—
1079C22—68no—
1080C22—62no—
1081C22—62no—
1082C22—62no—
1083C22—62no—
1084C22—62no—
1085C22—62no—
1086C22—62no—
1087C22—62no—
1088C22—94no—
1089C22—1216no—
1090C22—124no—
1091C22—124no—
1092C22—188no—
1093C22—182no—
1094C22—182no—
1095C22—182no—
1096C22—182no—
1097C22—182no—
1098C22—3616no—
1099C22—364no—
1100C22D3×#23512yes—
1101C22#6430712yes—
1102C22C2×#381114yes—
1103C22C2×#381112yes—
1104C22C23×D3211yescharacteristic
1105C4—22no—
1106C4—22no—
1107C4—62no—
1108C4—62no—
1109C4—62no—
1110C4—62no—
1111C4—62no—
1112C4—94no—
1113C4—182no—
1114C3—21no—
1115C3C2×#549011yescharacteristic, complemented
1116C3C2×#565411yescharacteristic, complemented
1117C2—24no—
1118C2—64no—
1119C2—122no—
1120C2—122no—
1121C2—184no—
1122C2—362no—
1123C2#1059507714yesdirect product factor
1124C2C2×D3×#23511yescharacteristic
1125C2C2×#6430711yescharacteristic
1126C2C22×#381111yescharacteristic
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×#3828C2semidirect
2. C22×D3×#67C2semidirect
3. C2×C3×#929C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C2×#63978C2semidirect
6. C2×#63977C2semidirect
7. C2×#63952C2semidirect
8. #10595077C2direct (N × H)
9. C2×#63923C2semidirect
10. C2×#63921C2semidirect
11. C2×#63913C2semidirect
12. C2×#63912C2semidirect
13. C2×#63910C2semidirect
14. C2×#63896C2semidirect
15. C2×#63881C2semidirect
16. C2×#63853C2semidirect
21. C23×C32×C4C22semidirect
23. C22×#638C22semidirect
25. C2×#3828C22semidirect
26. C22×C4⋊(C3⋊D3)C22semidirect
27. C22×C4×C3⋊D3C22semidirect
28. C22×C4×C3⋊D3C22semidirect
29. C22×#634C22semidirect
31. C23×C3×Dic3C22semidirect
33. C2×D3×#67C22semidirect
36. C22×#626C22semidirect
37. C22×#626C22semidirect
39. C22×#624C22semidirect
41. C2×C3×#217C22semidirect
42. C3×#929C22semidirect
45. C2×C3×(C2×D3)⋊C4C22semidirect
46. C2×C3×(C2×D3)⋊C4C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. #63978C22semidirect
53. #63977C22semidirect
54. C2×#3724C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
56. C2×#3722C22semidirect
57. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×Dic32C22semidirect
62. #63952C22semidirect
63. #63923C22semidirect
64. #63921C22semidirect
65. #63913C22semidirect
66. #63912C22semidirect
67. #63910C22semidirect
68. #63896C22semidirect
69. #63881C22semidirect
70. #63853C22semidirect
81. C2×#929D3semidirect
83. C22×(C2×D3)⋊C4D3semidirect
121. C22×C32×C4C23semidirect
123. C2×#638D4semidirect
125. C2×#638C23semidirect
130. C2×C4⋊(C3⋊D3)C23semidirect
133. C2×C4×C3⋊D3C23semidirect
134. C2×C4×C3⋊D3C23semidirect
136. C2×#634C23semidirect
145. C22×C3×Dic3C23semidirect
153. C2×#626C23semidirect
154. C2×#626C23semidirect
158. C2×#624C23semidirect
161. C3×#217C23semidirect
164. C3×(C2×D3)⋊C4C23semidirect
165. C3×(C2×D3)⋊C4C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×Dic3⋊C4C23semidirect
169. C3×Dic3⋊C4C23semidirect
170. #3724C23semidirect
171. Dic3⋊Dic3C23semidirect
172. #3722C23semidirect
173. #3722C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
186. C23×C3×C4C2×D3semidirect
187. C23×C3×C4C2×D3semidirect
204. C23×Dic3C2×D3semidirect
247. C2×#217C2×D3semidirect
250. #929C2×D3semidirect
261. C2×(C2×D3)⋊C4C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
263. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×(C2×D3)⋊C4C2×D3semidirect
265. C2×(C2×D3)⋊C4C2×D3semidirect
270. C2×Dic3⋊C4C2×D3semidirect
271. C2×Dic3⋊C4C2×D3semidirect
317. C22×C3×D3#41semidirect
331. #638C2×D4semidirect
425. C22×C3×C4C22×D3semidirect
426. C22×C3×C4C22×D3semidirect
468. C22×Dic3C22×D3semidirect
523. #217C22×D3semidirect
533. (C2×D3)⋊C4C22×D3semidirect
534. (C2×D3)⋊C4C22×D3semidirect
535. (C2×D3)⋊C4C22×D3semidirect
536. (C2×D3)⋊C4C22×D3semidirect
541. Dic3⋊C4C22×D3semidirect
542. Dic3⋊C4C22×D3semidirect
573. C2×C3×D3C2×#41semidirect
605. C23×C4D32semidirect
711. C22×D3#235semidirect
799. C2×C32#546semidirect
864. C22×C4C2×D32semidirect
957. C2×D3C2×#235semidirect
980. C32C2×#546semidirect
1058. C2×C3#5490semidirect
1059. C2×C3#5654semidirect
1115. C3C2×#5490semidirect
1116. C3C2×#5654semidirect
1123. C2#10595077direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×D3×#672
C2×C3×#9292
C22×C3×(C2×D3)⋊C42
C2×#639782
C2×#639772
C2×#639522
#105950772
C2×#639232
C2×#639212
C2×#639132
C2×#639122
C2×#639102
C2×#638962
C2×#638812
C2×#638532
C2×#56543
C2×#54903