Finite Group Databasebeta

← C2×#10595163 #11902442

Subgroups — C2×#10595163 #11902442

Order 1152.

4481 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×C3×#939C211yesmaximal, characteristic, complemented
4C2×C3×#935C211yesmaximal, characteristic, complemented
5C2×#63981C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63974C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9C22×#3722C211yesmaximal, characteristic, complemented
10C2×#63953C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595163C2116yesmaximal, direct product factor
13C2×#63910C211yesmaximal, characteristic, complemented
14C2×#63897C211yesmaximal, characteristic, complemented
15C2×#63881C211yesmaximal, characteristic, complemented
16C2×#63865C211yesmaximal, characteristic, complemented
17C2×#5654—31nomaximal
18C2×#5610—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C24×C3⋊D3C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic
24C2×D4×C3⋊D3—28no—
25C2×D4×C3⋊D3C2218yescomplemented
26C22×C4⋊(C3⋊D3)C2211yescharacteristic
27C22×C4×C3⋊D3C2211yescharacteristic
28C22×C3×#67C2211yescharacteristic, complemented
29C22×C3×#67C2211yescharacteristic, complemented
30C23×C3×Dic3C2211yescharacteristic, complemented
31C23×C3×Dic3C2211yescharacteristic, complemented
32C22×#627C2211yescharacteristic, complemented
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic, complemented
35C22×#626C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic, complemented
37C22×#624C2211yescharacteristic, complemented
38C2×#3804—28no—
39C2×#3804C2218yescomplemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×C3×#217C2211yescharacteristic, complemented
42C2×C3×#217C2211yescharacteristic, complemented
43C2×C3×#217C2211yescharacteristic, complemented
44C2×C3×#217C2211yescharacteristic, complemented
45C3×#939C2218yescomplemented
46C3×#935C2218yescomplemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51#63981C2218yescomplemented
52#63981C2218yescomplemented
53#63974C2218yescomplemented
54#63971C2218yescomplemented
55C2×#3724C2211yescharacteristic, complemented
56C2×#3722C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic
59C2×#3722C2218yescomplemented
60C2×#3722C2211yescharacteristic, complemented
61C2×#3722C2211yescharacteristic, complemented
62C2×#3722C2211yescharacteristic, complemented
63C2×#3722C2211yescharacteristic, complemented
64C2×Dic32C2211yescharacteristic, complemented
65#63953C2218yescomplemented
66#63952C2218yescomplemented
67#63910C2218yescomplemented
68#63897C2218yescomplemented
69#63881C2218yescomplemented
70#63865C2218yescomplemented
71C22×#237—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C22×D3×D4—61no—
75C22×#235—31no—
76C2×C3×#123—31no—
77C2×C3×#121—31no—
78C2×#939—31no—
79C2×#939D311yescharacteristic, complemented
80C2×#937—31no—
81C2×#937—31no—
82C2×#935D311yescharacteristic, complemented
83C2×C4×#67—31no—
84C22×(C2×D3)⋊C4—31no—
85C22×(C2×D3)⋊C4—31no—
86#5654—316no—
87#5610—316no—
88C2×#896—31no—
89C2×#896—31no—
90C2×#895—31no—
91C2×#894—31no—
92C2×#894—31no—
93C2×#893—31no—
94C2×#885—31no—
95C2×#885—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#882—31no—
99C2×#882—31no—
100C2×#67⋊C4—31no—
101C2×#67⋊C4—31no—
102C2×D3×C22⋊C4—31no—
103C2×D3×C22⋊C4—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3—24no—
107C23×C3⋊D3—24no—
108C23×C3⋊D3—24no—
109C23×C3⋊D3—24no—
110C23×C3⋊D3—42no—
111C23×C3⋊D3—42no—
112C23×C3⋊D3C2311yescharacteristic
113C23×C3⋊D3C2314yes—
114C23×C3⋊D3C2314yes—
115C23×C3⋊D3C2311yescharacteristic
116C23×C3⋊D3C2311yescharacteristic
117C23×C3×D3C2311yescharacteristic
118C2×C32×D4—24no—
119C2×C32×D4C2314yes—
120C22×C32×C4C2311yescharacteristic
121C2×#638—24no—
122C2×#638D418yescomplemented
123C2×#638C2314yes—
124C2×#638C2314yes—
125C22×C3⋊Dic3C2311yescharacteristic
126D4×C3⋊D3—232no—
127C2×C4⋊(C3⋊D3)—24no—
128C2×C4⋊(C3⋊D3)C2314yes—
129C2×C4×C3⋊D3—24no—
130C2×C4×C3⋊D3C2314yes—
131C2×C3×#67—24no—
132C2×C3×#67—42no—
133C2×C3×#67C2314yescomplemented
134C2×C3×#67C2314yescomplemented
135C22×C3×Dic3—24no—
136C22×C3×Dic3—42no—
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2314yescomplemented
145C22×C3×Dic3C2314yescomplemented
146C2×#627—24no—
147C2×#627C2314yescomplemented
148C2×#626—24no—
149C2×#626—24no—
150C2×#626—42no—
151C2×#626C2314yes—
152C2×#626C2314yescomplemented
153C2×#626C2314yescomplemented
154C2×#624—24no—
155C2×#624—42no—
156C2×#624C2314yescomplemented
157C2×#624C2314yescomplemented
158#3804—232no—
159C2×D3×Dic3—24no—
160C2×D3×Dic3C2314yescomplemented
161C3×#217C2314yescomplemented
162C3×#217C2314yescomplemented
163C3×#217C2314yescomplemented
164C3×#217C2314yescomplemented
165C3×(C2×D3)⋊C4C2314yescomplemented
166C3×Dic3⋊C4C2314yescomplemented
167C3×Dic3⋊C4C2314yescomplemented
168C3×Dic3⋊C4C2314yescomplemented
169#3724C2314yescomplemented
170#3722C2314yes—
171#3722C2314yes—
172#3722C2314yes—
173#3722C2314yescomplemented
174#3722C2314yescomplemented
175#3722C2314yescomplemented
176#3722C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C24×D3—61no—
184C24×D3—61no—
185C22×C3×D4—21no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C22×C3×D4C2×D311yescharacteristic
189C22×C3×D4C2×D311yescharacteristic
190C23×C3×C4—31no—
191C23×C3×C4—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—61no—
200C22×#67—61no—
201C22×#67C2×D311yescharacteristic, complemented
202C22×#67C2×D311yescharacteristic, complemented
203C23×Dic3—31no—
204C23×Dic3C2×D311yescharacteristic, complemented
205C23×Dic3C2×D311yescharacteristic, complemented
206C2×#237—38no—
207C2×#237—68no—
208C2×D3×D4—38no—
209C2×D3×D4—38no—
210C2×D3×D4—68no—
211C2×D3×D4—68no—
212C2×D3×D4—68no—
213C2×D3×D4—616no—
214C2×#235—38no—
215C2×#235—68no—
216C22×D12—31no—
217C22×D12—31no—
218C22×D12—31no—
219C22×D12—31no—
220C22×D12—31no—
221C22×D12—61no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3—31no—
225C22×C4×D3—31no—
226C22×C4×D3—31no—
227C22×C4×D3—31no—
228C22×C4×D3—31no—
229C22×C4×D3—61no—
230C22×Dic6—31no—
231C22×Dic6—31no—
232C3×#123—38no—
233C3×#121—38no—
234C2×C3×C4⋊C4—31no—
235C2×C3×C4⋊C4—31no—
236C2×C3×C4⋊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×#217C2×D311yescharacteristic, complemented
243C2×#217C2×D311yescharacteristic, complemented
244C2×#217C2×D311yescharacteristic, complemented
245C2×#217C2×D311yescharacteristic, complemented
246#939—38no—
247#939C2×D318yescomplemented
248#937—38no—
249#937—38no—
250#935C2×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)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
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—38no—
267C2×(C2×D3)⋊C4—38no—
268C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—31no—
271C2×Dic3⋊C4C2×D311yescharacteristic, complemented
272C2×Dic3⋊C4C2×D311yescharacteristic, complemented
273C2×Dic3⋊C4C2×D311yescharacteristic, complemented
274C2×C4×Dic3—31no—
275C2×C4×Dic3—31no—
276#896—38no—
277#896—38no—
278#895—38no—
279#894—38no—
280#894—38no—
281#893—38no—
282#885—38no—
283#885—38no—
284#884—38no—
285#884—38no—
286#882—38no—
287#882—38no—
288#67⋊C4—38no—
289#67⋊C4—38no—
290D3×C22⋊C4—38no—
291D3×C22⋊C4—38no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32C2×D414yes—
298C23×C32C2412yes—
299C23×C32C2412yes—
300C23×C32C2411yescharacteristic
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—22no—
304C22×C3⋊D3—28no—
305C22×C3⋊D3—28no—
306C22×C3⋊D3—22no—
307C22×C3⋊D3—22no—
308C22×C3⋊D3—22no—
309C22×C3⋊D3—22no—
310C22×C3⋊D3—28no—
311C22×C3⋊D3—28no—
312C22×C3⋊D3—44no—
313C22×C3⋊D3—44no—
314C22×C3⋊D3—416no—
315C22×C3⋊D3—416no—
316C22×C3⋊D3C2×D414yes—
317C22×C3⋊D3#4114yescomplemented
318C22×C3⋊D3C2412yes—
319C22×C3⋊D3C2412yes—
320C22×C3⋊D3C2412yes—
321C22×C3×D3—22no—
322C22×C3×D3—22no—
323C22×C3×D3—22no—
324C22×C3×D3C2412yes—
325C32×D4—28no—
326C2×C32×C4—22no—
327C2×C32×C4C2412yes—
328#638—28no—
329#638C2×D4116yescomplemented
330C2×C3⋊Dic3C2×D414yes—
331C2×C3⋊Dic3C2412yes—
332C4⋊(C3⋊D3)—28no—
333C4×C3⋊D3—28no—
334C3×#67—28no—
335C3×#67—44no—
336C2×C3×Dic3—22no—
337C2×C3×Dic3—28no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—22no—
344C2×C3×Dic3—44no—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352#627—28no—
353#626—28no—
354#626—28no—
355#626—44no—
356#624—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—31no—
367C2×#121—91no—
368C2×#121—91no—
369C2×#120—91no—
370C2×#120—91no—
371C2×C4×D4—91no—
372C2×C4×D4—91no—
373C22×C22⋊C4—91no—
374C22×C22⋊C4—91no—
375C24×C3—21no—
376C24×C3—21no—
377C24×C3—31no—
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C24×C3C22×D311yescharacteristic
381C24×C3C22×D311yescharacteristic
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—31no—
385C23×D3—31no—
386C23×D3—31no—
387C23×D3—31no—
388C23×D3—34no—
389C23×D3—34no—
390C23×D3—34no—
391C23×D3—34no—
392C23×D3—61no—
393C23×D3—61no—
394C23×D3—61no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—64no—
401C23×D3—64no—
402C23×D3—64no—
403C23×D3—68no—
404C23×D3—68no—
405C23×D3—64no—
406C23×D3—64no—
407C23×D3—124no—
408C23×D3—124no—
409C23×D3—122no—
410C23×D3—122no—
411C23×D3—122no—
412C23×D3—122no—
413C23×D3—124no—
414C23×D3—124no—
415C23×D3C22×D311yescharacteristic
416C2×C3×D4—28no—
417C2×C3×D4—24no—
418C2×C3×D4—24no—
419C2×C3×D4—24no—
420C2×C3×D4—34no—
421C2×C3×D4—34no—
422C2×C3×D4—64no—
423C2×C3×D4—122no—
424C2×C3×D4C22×D314yes—
425C2×C3×D4C22×D314yes—
426C22×C3×C4—21no—
427C22×C3×C4—31no—
428C22×C3×C4—31no—
429C22×C3×C4—31no—
430C22×C3×C4—31no—
431C22×C3×C4—31no—
432C22×C3×C4—31no—
433C22×C3×C4—31no—
434C22×C3×C4—34no—
435C22×C3×C4—34no—
436C22×C3×C4—64no—
437C22×C3×C4—122no—
438C22×C3×C4C22×D311yescharacteristic
439C22×C3×C4C22×D311yescharacteristic
440C2×#67—24no—
441C2×#67—38no—
442C2×#67—38no—
443C2×#67—34no—
444C2×#67—34no—
445C2×#67—34no—
446C2×#67—34no—
447C2×#67—34no—
448C2×#67—34no—
449C2×#67—34no—
450C2×#67—42no—
451C2×#67—68no—
452C2×#67—64no—
453C2×#67—64no—
454C2×#67—64no—
455C2×#67—64no—
456C2×#67—64no—
457C2×#67—64no—
458C2×#67—68no—
459C2×#67—122no—
460C2×#67C22×D314yescomplemented
461C2×#67C22×D314yescomplemented
462C22×Dic3—24no—
463C22×Dic3—31no—
464C22×Dic3—31no—
465C22×Dic3—34no—
466C22×Dic3—42no—
467C22×Dic3—61no—
468C22×Dic3—64no—
469C22×Dic3C22×D311yescharacteristic
470C22×Dic3C22×D311yescharacteristic
471C22×Dic3C22×D311yescharacteristic
472C22×Dic3C22×D311yescharacteristic
473C22×Dic3C22×D311yescharacteristic
474C22×Dic3C22×D311yescharacteristic
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D314yescomplemented
477C22×Dic3C22×D314yescomplemented
478#237—632no—
479D3×D4—632no—
480D3×D4—632no—
481D3×D4—664no—
482#235—632no—
483C2×D12—34no—
484C2×D12—34no—
485C2×D12—34no—
486C2×D12—34no—
487C2×D12—34no—
488C2×D12—64no—
489C2×D12—64no—
490C2×D12—64no—
491C2×D12—68no—
492C2×D12—64no—
493C2×D12—64no—
494C2×D12—122no—
495C2×C4×D3—34no—
496C2×C4×D3—34no—
497C2×C4×D3—34no—
498C2×C4×D3—34no—
499C2×C4×D3—34no—
500C2×C4×D3—34no—
501C2×C4×D3—34no—
502C2×C4×D3—64no—
503C2×C4×D3—64no—
504C2×C4×D3—64no—
505C2×C4×D3—64no—
506C2×C4×D3—64no—
507C2×C4×D3—64no—
508C2×C4×D3—68no—
509C2×C4×D3—122no—
510C2×C4×D3—122no—
511C2×Dic6—34no—
512C2×Dic6—34no—
513C2×Dic6—64no—
514C2×Dic6—64no—
515C3×C4⋊C4—34no—
516C3×C4⋊C4—34no—
517C3×C4⋊C4—34no—
518C3×C22⋊C4—34no—
519C3×C22⋊C4—34no—
520C3×C22⋊C4—34no—
521C3×C22⋊C4—34no—
522C3×C22⋊C4—34no—
523#217C22×D314yescomplemented
524#217C22×D314yescomplemented
525#217C22×D314yescomplemented
526#217C22×D314yescomplemented
527(C2×D3)⋊C4—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—34no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—34no—
534(C2×D3)⋊C4—34no—
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—34no—
540(C2×D3)⋊C4—34no—
541(C2×D3)⋊C4C22×D314yescomplemented
542Dic3⋊C4—34no—
543Dic3⋊C4—34no—
544Dic3⋊C4C22×D314yescomplemented
545Dic3⋊C4C22×D314yescomplemented
546Dic3⋊C4C22×D314yescomplemented
547C4×Dic3—34no—
548C4×Dic3—34no—
549C22×C32—22no—
550C22×C32—28no—
551C22×C32—22no—
552C22×C32—22no—
553C22×C32—22no—
554C22×C32—22no—
555C22×C32—44no—
556C22×C32C22×D414yes—
557C22×C32C22×D412yes—
558C22×C32C2×#4112yes—
559C22×C32H(5,𝔽2)12yes—
560C22×C32C2511yescharacteristic
561C2×C3⋊D3—28no—
562C2×C3⋊D3—22no—
563C2×C3⋊D3—22no—
564C2×C3⋊D3—22no—
565C2×C3⋊D3—28no—
566C2×C3⋊D3—22no—
567C2×C3⋊D3—22no—
568C2×C3⋊D3—22no—
569C2×C3⋊D3—22no—
570C2×C3⋊D3—416no—
571C2×C3⋊D3—416no—
572C2×C3⋊D3—44no—
573C2×C3⋊D3C22×D414yes—
574C2×C3⋊D3C2×#4114yescomplemented
575C2×C3×D3—22no—
576C2×C3×D3—22no—
577C2×C3×D3—22no—
578C2×C3×D3—44no—
579C32×C4—22no—
580C3⋊Dic3C22×D414yes—
581C3×Dic3—22no—
582C3×Dic3—22no—
583C3×Dic3—22no—
584C3×Dic3—22no—
585C3×Dic3—22no—
586C3×Dic3—22no—
587C3×Dic3—22no—
588C25—91no—
589C25—91no—
590C2×#41—98no—
591C2×#41—188no—
592C22×Q8—91no—
593C22×D4—31no—
594C22×D4—31no—
595C22×D4—91no—
596C22×D4—91no—
597C22×D4—91no—
598C22×D4—91no—
599C22×D4—91no—
600C22×D4—98no—
601C22×D4—91no—
602C22×D4—188no—
603C22×D4D3211yescharacteristic
604C23×C4—31no—
605C23×C4—31no—
606C23×C4—91no—
607C23×C4—91no—
608C23×C4—91no—
609C23×C4—91no—
610#124—98no—
611#123—38no—
612#123—98no—
613C22⋊Q8—98no—
614#121—38no—
615#121—98no—
616#121—98no—
617#120—98no—
618#120—98no—
619C4×D4—98no—
620C4×D4—98no—
621C2×C4⋊C4—31no—
622C2×C4⋊C4—31no—
623C2×C4⋊C4—31no—
624C2×C4⋊C4—91no—
625C2×C22⋊C4—31no—
626C2×C22⋊C4—31no—
627C2×C22⋊C4—31no—
628C2×C22⋊C4—31no—
629C2×C22⋊C4—31no—
630C2×C22⋊C4—98no—
631C2×C22⋊C4—91no—
632C2×C22⋊C4—91no—
633C2×C22⋊C4—91no—
634C2×C22⋊C4—91no—
635C2×C22⋊C4—91no—
636C2×C22⋊C4—98no—
637C2×C22⋊C4—91no—
638C2×C22⋊C4—91no—
639C2×C42—91no—
640C23×C3—22no—
641C23×C3—22no—
642C23×C3—22no—
643C23×C3—22no—
644C23×C3—24no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—22no—
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—22no—
651C23×C3—22no—
652C23×C3—22no—
653C23×C3—21no—
654C23×C3—24no—
655C23×C3—32no—
656C23×C3—42no—
657C23×C3—42no—
658C23×C3—42no—
659C23×C3—42no—
660C23×C3—62no—
661C23×C3—62no—
662C23×C3—62no—
663C23×C3D3×D414yes—
664C23×C3D3×D414yes—
665C23×C3C23×D312yes—
666C23×C3C23×D312yes—
667C23×C3C23×D312yes—
668C23×C3C23×D312yes—
669C23×C3C23×D311yescharacteristic
670C23×C3C23×D311yescharacteristic
671C22×D3—22no—
672C22×D3—22no—
673C22×D3—22no—
674C22×D3—34no—
675C22×D3—34no—
676C22×D3—34no—
677C22×D3—34no—
678C22×D3—32no—
679C22×D3—32no—
680C22×D3—32no—
681C22×D3—32no—
682C22×D3—32no—
683C22×D3—32no—
684C22×D3—64no—
685C22×D3—62no—
686C22×D3—64no—
687C22×D3—62no—
688C22×D3—62no—
689C22×D3—68no—
690C22×D3—68no—
691C22×D3—68no—
692C22×D3—68no—
693C22×D3—68no—
694C22×D3—68no—
695C22×D3—64no—
696C22×D3—64no—
697C22×D3—62no—
698C22×D3—62no—
699C22×D3—62no—
700C22×D3—62no—
701C22×D3—62no—
702C22×D3—62no—
703C22×D3—62no—
704C22×D3—62no—
705C22×D3—64no—
706C22×D3—616no—
707C22×D3—616no—
708C22×D3—62no—
709C22×D3—62no—
710C22×D3—68no—
711C22×D3—68no—
712C22×D3—62no—
713C22×D3—62no—
714C22×D3—62no—
715C22×D3—62no—
716C22×D3—128no—
717C22×D3—128no—
718C22×D3—122no—
719C22×D3—122no—
720C22×D3—122no—
721C22×D3—122no—
722C22×D3—124no—
723C22×D3—124no—
724C22×D3—124no—
725C22×D3—124no—
726C22×D3—1216no—
727C22×D3—1216no—
728C22×D3—1216no—
729C22×D3—1216no—
730C22×D3—128no—
731C22×D3—128no—
732C22×D3—1232no—
733C22×D3—1232no—
734C22×D3C23×D312yes—
735C3×D4—216no—
736C3×D4—28no—
737C3×D4—28no—
738C3×D4—68no—
739C3×D4—124no—
740C2×C3×C4—24no—
741C2×C3×C4—22no—
742C2×C3×C4—22no—
743C2×C3×C4—22no—
744C2×C3×C4—32no—
745C2×C3×C4—32no—
746C2×C3×C4—32no—
747C2×C3×C4—32no—
748C2×C3×C4—32no—
749C2×C3×C4—32no—
750C2×C3×C4—32no—
751C2×C3×C4—62no—
752C2×C3×C4—62no—
753C2×C3×C4—62no—
754C2×C3×C4—68no—
755C2×C3×C4—62no—
756C2×C3×C4—62no—
757C2×C3×C4—62no—
758C2×C3×C4—62no—
759C2×C3×C4—124no—
760C2×C3×C4C23×D312yes—
761C2×C3×C4C23×D312yes—
762#67—28no—
763#67—316no—
764#67—316no—
765#67—44no—
766#67—616no—
767#67—68no—
768#67—68no—
769#67—68no—
770#67—68no—
771#67—616no—
772#67—124no—
773C2×Dic3—22no—
774C2×Dic3—22no—
775C2×Dic3—22no—
776C2×Dic3—28no—
777C2×Dic3—22no—
778C2×Dic3—22no—
779C2×Dic3—22no—
780C2×Dic3—22no—
781C2×Dic3—34no—
782C2×Dic3—34no—
783C2×Dic3—32no—
784C2×Dic3—32no—
785C2×Dic3—44no—
786C2×Dic3—64no—
787C2×Dic3—62no—
788C2×Dic3—68no—
789C2×Dic3C23×D312yes—
790C2×Dic3C23×D312yes—
791C2×Dic3C23×D312yes—
792C2×Dic3C23×D312yes—
793C2×Dic3C23×D312yes—
794C2×Dic3C23×D312yes—
795C2×Dic3C23×D312yes—
796D12—68no—
797D12—68no—
798D12—616no—
799D12—68no—
800D12—68no—
801D12—124no—
802C4×D3—68no—
803C4×D3—68no—
804C4×D3—68no—
805C4×D3—68no—
806C4×D3—68no—
807C4×D3—616no—
808C4×D3—124no—
809C4×D3—124no—
810Dic6—68no—
811Dic6—68no—
812C2×C32—24no—
813C2×C32—42no—
814C2×C32#54614yescomplemented
815C2×C32C23×D411yescharacteristic
816C2×C32C22×#4111yescharacteristic
817C2×C32C2×H(5,𝔽2)11yescharacteristic
818C3⋊D3—24no—
819C3⋊D3—24no—
820C3⋊D3—42no—
821C3×D3—42no—
822C24—31no—
823C24—91no—
824C24—91no—
825C24—91no—
826C24—94no—
827C24—94no—
828C24—184no—
829C24—184no—
830C24—184no—
831C24—184no—
832C24—362no—
833C24—362no—
834C24C2×D3211yescharacteristic
835C24C2×D3211yescharacteristic
836#41—1832no—
837C2×Q8—94no—
838C2×Q8—184no—
839C2×D4—24no—
840C2×D4—34no—
841C2×D4—34no—
842C2×D4—64no—
843C2×D4—94no—
844C2×D4—94no—
845C2×D4—94no—
846C2×D4—94no—
847C2×D4—98no—
848C2×D4—94no—
849C2×D4—94no—
850C2×D4—122no—
851C2×D4—184no—
852C2×D4—184no—
853C2×D4—184no—
854C2×D4—184no—
855C2×D4—1832no—
856C2×D4—362no—
857C2×D4C2×D3214yes—
858C22×C4—34no—
859C22×C4—31no—
860C22×C4—31no—
861C22×C4—31no—
862C22×C4—31no—
863C22×C4—31no—
864C22×C4—31no—
865C22×C4—31no—
866C22×C4—34no—
867C22×C4—64no—
868C22×C4—94no—
869C22×C4—94no—
870C22×C4—94no—
871C22×C4—91no—
872C22×C4—94no—
873C22×C4—122no—
874C22×C4—184no—
875C22×C4—184no—
876C22×C4—184no—
877C22×C4—362no—
878C22×C4C2×D3211yescharacteristic
879C4⋊C4—34no—
880C4⋊C4—34no—
881C4⋊C4—34no—
882C4⋊C4—94no—
883C22⋊C4—34no—
884C22⋊C4—34no—
885C22⋊C4—34no—
886C22⋊C4—34no—
887C22⋊C4—34no—
888C22⋊C4—94no—
889C22⋊C4—94no—
890C22⋊C4—94no—
891C22⋊C4—94no—
892C22⋊C4—94no—
893C22⋊C4—94no—
894C22⋊C4—94no—
895C42—94no—
896C22×C3—28no—
897C22×C3—22no—
898C22×C3—22no—
899C22×C3—22no—
900C22×C3—22no—
901C22×C3—28no—
902C22×C3—24no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—22no—
907C22×C3—22no—
908C22×C3—22no—
909C22×C3—22no—
910C22×C3—22no—
911C22×C3—22no—
912C22×C3—24no—
913C22×C3—21no—
914C22×C3—42no—
915C22×C3—42no—
916C22×C3—48no—
917C22×C3—42no—
918C22×C3—42no—
919C22×C3—48no—
920C22×C3—44no—
921C22×C3—44no—
922C22×C3—62no—
923C22×C3—62no—
924C22×C3—62no—
925C22×C3—124no—
926C22×C3C2×D3×D414yes—
927C22×C3C2×D3×D414yes—
928C22×C3C2×D3×D412yes—
929C22×C3C2×D3×D412yes—
930C22×C3#100412yes—
931C22×C3D3×#4112yes—
932C22×C3D3×#4112yes—
933C22×C3#100912yes—
934C22×C3C24×D311yescharacteristic
935C22×C3C24×D311yescharacteristic
936C2×D3—22no—
937C2×D3—22no—
938C2×D3—22no—
939C2×D3—34no—
940C2×D3—34no—
941C2×D3—34no—
942C2×D3—34no—
943C2×D3—44no—
944C2×D3—64no—
945C2×D3—64no—
946C2×D3—64no—
947C2×D3—64no—
948C2×D3—616no—
949C2×D3—68no—
950C2×D3—68no—
951C2×D3—62no—
952C2×D3—62no—
953C2×D3—62no—
954C2×D3—62no—
955C2×D3—62no—
956C2×D3—62no—
957C2×D3—62no—
958C2×D3—62no—
959C2×D3—68no—
960C2×D3—68no—
961C2×D3—64no—
962C2×D3—62no—
963C2×D3—62no—
964C2×D3—62no—
965C2×D3—62no—
966C2×D3—62no—
967C2×D3—62no—
968C2×D3—122no—
969C2×D3—122no—
970C2×D3—128no—
971C2×D3—122no—
972C2×D3—122no—
973C2×D3—1216no—
974C2×D3—1216no—
975C2×D3—1216no—
976C2×D3—1216no—
977C2×D3—1232no—
978C2×D3—1232no—
979C2×D3—128no—
980C2×D3—124no—
981C2×D3—124no—
982C3×C4—24no—
983C3×C4—22no—
984C3×C4—22no—
985C3×C4—62no—
986C3×C4—62no—
987C3×C4—62no—
988C3×C4—62no—
989C3×C4—62no—
990C3×C4—62no—
991C3×C4—62no—
992Dic3—22no—
993Dic3—22no—
994Dic3—22no—
995Dic3—22no—
996Dic3—22no—
997Dic3—22no—
998Dic3—22no—
999Dic3—34no—
1000Dic3—34no—
1001Dic3—64no—
1002C32C2×#54611yescharacteristic, complemented, Sylow
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—32no—
1009C23—62no—
1010C23—62no—
1011C23—62no—
1012C23—94no—
1013C23—94no—
1014C23—92no—
1015C23—92no—
1016C23—92no—
1017C23—188no—
1018C23—188no—
1019C23—188no—
1020C23—182no—
1021C23—182no—
1022C23—182no—
1023C23—182no—
1024C23—182no—
1025C23—182no—
1026C23—188no—
1027C23—182no—
1028C23—364no—
1029C23—364no—
1030C23—3616no—
1031C23—3616no—
1032C23#381114yes—
1033C23C22×D3212yes—
1034C23C22×D3212yes—
1035C23C22×D3211yescharacteristic
1036Q8—188no—
1037D4—28no—
1038D4—68no—
1039D4—916no—
1040D4—124no—
1041D4—188no—
1042D4—188no—
1043D4—188no—
1044D4—188no—
1045D4—364no—
1046C2×C4—22no—
1047C2×C4—32no—
1048C2×C4—32no—
1049C2×C4—32no—
1050C2×C4—32no—
1051C2×C4—32no—
1052C2×C4—32no—
1053C2×C4—32no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—62no—
1058C2×C4—62no—
1059C2×C4—62no—
1060C2×C4—68no—
1061C2×C4—62no—
1062C2×C4—94no—
1063C2×C4—92no—
1064C2×C4—124no—
1065C2×C4—188no—
1066C2×C4—188no—
1067C2×C4—188no—
1068C2×C4—364no—
1069C2×C4C22×D3212yes—
1070C2×C3—24no—
1071C2×C3—24no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—24no—
1075C2×C3—21no—
1076C2×C3—44no—
1077C2×C3—44no—
1078C2×C3—42no—
1079C2×C3—42no—
1080C2×C3—122no—
1081C2×C3#561014yescomplemented
1082C2×C3#565414yescomplemented
1083C2×C3C22×D3×D411yescharacteristic
1084C2×C3C22×D3×D411yescharacteristic
1085C2×C3C2×#100411yescharacteristic
1086C2×C3C2×D3×#4111yescharacteristic
1087C2×C3C2×D3×#4111yescharacteristic
1088C2×C3C2×#100911yescharacteristic
1089D3—42no—
1090D3—68no—
1091D3—64no—
1092D3—64no—
1093D3—64no—
1094D3—64no—
1095D3—124no—
1096D3—124no—
1097D3—122no—
1098D3—122no—
1099C22—22no—
1100C22—22no—
1101C22—28no—
1102C22—22no—
1103C22—22no—
1104C22—22no—
1105C22—44no—
1106C22—62no—
1107C22—62no—
1108C22—62no—
1109C22—94no—
1110C22—94no—
1111C22—124no—
1112C22—182no—
1113C22—182no—
1114C22—182no—
1115C22—188no—
1116C22—188no—
1117C22—182no—
1118C22—182no—
1119C22—182no—
1120C22—182no—
1121C22—3616no—
1122C22—3616no—
1123C22—364no—
1124C22#6431212yes—
1125C22#6431412yes—
1126C22C2×#381114yes—
1127C22C2×#381112yes—
1128C22C23×D3211yescharacteristic
1129C4—22no—
1130C4—62no—
1131C4—62no—
1132C4—62no—
1133C4—62no—
1134C4—62no—
1135C4—62no—
1136C4—62no—
1137C4—94no—
1138C3—21no—
1139C3C2×#561011yescharacteristic, complemented
1140C3C2×#565411yescharacteristic, complemented
1141C2—24no—
1142C2—42no—
1143C2—122no—
1144C2—184no—
1145C2—184no—
1146C2—362no—
1147C2#1059516314yesdirect product factor
1148C2C2×#6431211yescharacteristic
1149C2C2×#6431411yescharacteristic
1150C2C22×#381111yescharacteristic
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×D4×C3⋊D3C2semidirect
2. C22×#3804C2semidirect
3. C2×C3×#939C2semidirect
4. C2×C3×#935C2semidirect
5. C2×#63981C2semidirect
6. C2×#63981C2semidirect
7. C2×#63974C2semidirect
8. C2×#63971C2semidirect
9. C22×#3722C2semidirect
10. C2×#63953C2semidirect
11. C2×#63952C2semidirect
12. #10595163C2direct (N × H)
13. C2×#63910C2semidirect
14. C2×#63897C2semidirect
15. C2×#63881C2semidirect
16. C2×#63865C2semidirect
25. C2×D4×C3⋊D3C22semidirect
28. C22×C3×#67C22semidirect
29. C22×C3×#67C22semidirect
30. C23×C3×Dic3C22semidirect
31. C23×C3×Dic3C22semidirect
32. C22×#627C22semidirect
34. C22×#626C22semidirect
35. C22×#626C22semidirect
36. C22×#624C22semidirect
37. C22×#624C22semidirect
39. C2×#3804C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×C3×#217C22semidirect
42. C2×C3×#217C22semidirect
43. C2×C3×#217C22semidirect
44. C2×C3×#217C22semidirect
45. C3×#939C22semidirect
46. C3×#935C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. #63981C22semidirect
52. #63981C22semidirect
53. #63974C22semidirect
54. #63971C22semidirect
55. C2×#3724C22semidirect
59. C2×#3722C22semidirect
60. C2×#3722C22semidirect
61. C2×#3722C22semidirect
62. C2×#3722C22semidirect
63. C2×#3722C22semidirect
64. C2×Dic32C22semidirect
65. #63953C22semidirect
66. #63952C22semidirect
67. #63910C22semidirect
68. #63897C22semidirect
69. #63881C22semidirect
70. #63865C22semidirect
79. C2×#939D3semidirect
82. C2×#935D3semidirect
122. C2×#638D4semidirect
133. C2×C3×#67C23semidirect
134. C2×C3×#67C23semidirect
144. C22×C3×Dic3C23semidirect
145. C22×C3×Dic3C23semidirect
147. C2×#627C23semidirect
152. C2×#626C23semidirect
153. C2×#626C23semidirect
156. C2×#624C23semidirect
157. C2×#624C23semidirect
160. C2×D3×Dic3C23semidirect
161. C3×#217C23semidirect
162. C3×#217C23semidirect
163. C3×#217C23semidirect
164. C3×#217C23semidirect
165. C3×(C2×D3)⋊C4C23semidirect
166. C3×Dic3⋊C4C23semidirect
167. C3×Dic3⋊C4C23semidirect
168. C3×Dic3⋊C4C23semidirect
169. #3724C23semidirect
173. #3722C23semidirect
174. #3722C23semidirect
175. #3722C23semidirect
176. #3722C23semidirect
177. Dic32C23semidirect
201. C22×#67C2×D3semidirect
202. C22×#67C2×D3semidirect
204. C23×Dic3C2×D3semidirect
205. C23×Dic3C2×D3semidirect
242. C2×#217C2×D3semidirect
243. C2×#217C2×D3semidirect
244. C2×#217C2×D3semidirect
245. C2×#217C2×D3semidirect
247. #939C2×D3semidirect
250. #935C2×D3semidirect
268. C2×(C2×D3)⋊C4C2×D3semidirect
271. C2×Dic3⋊C4C2×D3semidirect
272. C2×Dic3⋊C4C2×D3semidirect
273. C2×Dic3⋊C4C2×D3semidirect
317. C22×C3⋊D3#41semidirect
329. #638C2×D4semidirect
460. C2×#67C22×D3semidirect
461. C2×#67C22×D3semidirect
476. C22×Dic3C22×D3semidirect
477. C22×Dic3C22×D3semidirect
523. #217C22×D3semidirect
524. #217C22×D3semidirect
525. #217C22×D3semidirect
526. #217C22×D3semidirect
541. (C2×D3)⋊C4C22×D3semidirect
544. Dic3⋊C4C22×D3semidirect
545. Dic3⋊C4C22×D3semidirect
546. Dic3⋊C4C22×D3semidirect
574. C2×C3⋊D3C2×#41semidirect
814. C2×C32#546semidirect
1002. C32C2×#546semidirect
1081. C2×C3#5610semidirect
1082. C2×C3#5654semidirect
1139. C3C2×#5610semidirect
1140. C3C2×#5654semidirect
1147. C2#10595163direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C22×#38042
C2×C3×#9392
C2×C3×#9352
C2×#639812
C2×#639742
C2×#639712
C22×#37222
C2×#639532
C2×#639522
#105951632
C2×#639102
C2×#638972
C2×#638812
C2×#638652
C2×#56543
C2×#56103