Finite Group Databasebeta

← C2×#10595281 #11900959

Subgroups — C2×#10595281 #11900959

Order 1152.

4299 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic, complemented
2C22×D3×#67C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic, complemented
4C2×C3×#938C211yesmaximal, characteristic, complemented
5C2×C3×#937C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63977C211yesmaximal, characteristic, complemented
8C2×#63975C211yesmaximal, characteristic, complemented
9C2×#63971C211yesmaximal, characteristic, complemented
10C2×#63970C211yesmaximal, characteristic, complemented
11C2×#63969C211yesmaximal, characteristic, complemented
12#10595281C2116yesmaximal, direct product factor
13C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14C2×#63906C211yesmaximal, characteristic, complemented
15C2×#63890C211yesmaximal, characteristic, complemented
16C2×#63854C211yesmaximal, characteristic, complemented
17C2×#5605—31nomaximal
18C2×#5589—31nomaximal
19C24×C3⋊D3C2211yescharacteristic, complemented
20C24×C3×D3C2211yescharacteristic, complemented
21C23×D32C2211yescharacteristic
22C22×C32×D4C2211yescharacteristic, complemented
23C22×#638C2211yescharacteristic
24C22×#638C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic, complemented
27C22×C3×#67C2211yescharacteristic, complemented
28C22×C3×#67C2211yescharacteristic, complemented
29C22×C3×C4×D3C2211yescharacteristic, complemented
30C2×#3811—28no—
31C2×#3811C2218yescomplemented
32C2×D3×#67—28no—
33C2×D3×#67C2218yescomplemented
34C22×#626C2211yescharacteristic
35C22×#626C2211yescharacteristic
36C22×#626C2211yescharacteristic, complemented
37C22×#626C2211yescharacteristic, complemented
38C22×#625C2211yescharacteristic, complemented
39C22×#624C2211yescharacteristic, complemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C22×D3×Dic3C2211yescharacteristic, complemented
42C2×#3757C2211yescharacteristic, complemented
43#64146C2218yescomplemented
44C2×#3752C2211yescharacteristic, complemented
45C2×#3752C2211yescharacteristic, complemented
46C2×C3×#217C2211yescharacteristic, complemented
47C2×C3×#217C2211yescharacteristic, complemented
48C2×C3×#217C2211yescharacteristic, complemented
49C3×#938C2218yescomplemented
50C3×#937C2218yescomplemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
53C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
54#63981C2218yescomplemented
55#63977C2218yescomplemented
56#63975C2218yescomplemented
57#63971C2218yescomplemented
58#63970C2218yescomplemented
59#63969C2218yescomplemented
60C2×#3724C2211yescharacteristic, complemented
61C2×Dic3⋊Dic3C2211yescharacteristic, complemented
62C2×Dic3⋊Dic3C2211yescharacteristic, complemented
63C2×#3722C2211yescharacteristic, complemented
64C2×#3722C2211yescharacteristic, complemented
65C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
66C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
67D3×(C2×D3)⋊C4C2218yescomplemented
68#63906C2218yescomplemented
69#63890C2218yescomplemented
70#63854C2218yescomplemented
71C23×#67—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C22×D3×D4—31no—
75C2×C3×#121—31no—
76C2×C3×#120—31no—
77C2×#953—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#938—31no—
81C2×#938D311yescharacteristic, complemented
82C2×#937—31no—
83C2×#937—31no—
84C2×#937—31no—
85C2×#937—61no—
86C2×#937D311yescharacteristic, complemented
87C2×#935—31no—
88C2×#930—31no—
89C22×(C2×D3)⋊C4—31no—
90#5605—316no—
91#5589—316no—
92C2×#894—31no—
93C2×#894—31no—
94C2×#886—31no—
95C2×#884—31no—
96C2×#884—31no—
97C2×#883—31no—
98C2×#883—31no—
99C2×#883—31no—
100C2×#883—31no—
101C2×#882—31no—
102C2×#882—31no—
103C2×D3×C22⋊C4—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3—24no—
107C23×C3⋊D3—42no—
108C23×C3⋊D3—42no—
109C23×C3⋊D3C2311yescharacteristic
110C23×C3⋊D3C2311yescharacteristic
111C23×C3⋊D3C2314yescomplemented
112C23×C3×D3—24no—
113C23×C3×D3—42no—
114C23×C3×D3—42no—
115C23×C3×D3C2311yescharacteristic
116C23×C3×D3C2311yescharacteristic
117C23×C3×D3C2311yescharacteristic
118C23×C3×D3C2314yescomplemented
119C22×D32—42no—
120C22×D32—42no—
121C22×D32D418yescomplemented
122C22×D32C2314yes—
123C2×C32×D4—42no—
124C2×C32×D4C2314yescomplemented
125C22×C32×C4C2311yescharacteristic
126C2×#638—24no—
127C2×#638—42no—
128C2×#638C2314yes—
129C2×#638C2314yescomplemented
130C22×C3⋊Dic3C2311yescharacteristic
131C22×C3⋊Dic3C2311yescharacteristic
132C2×C3×#67—24no—
133C2×C3×#67—24no—
134C2×C3×#67—24no—
135C2×C3×#67—42no—
136C2×C3×#67C2314yes—
137C2×C3×#67C2314yescomplemented
138C2×C3×#67C2314yescomplemented
139C2×C3×#67C2314yescomplemented
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2311yescharacteristic
145C2×C3×C4×D3—42no—
146C2×C3×C4×D3C2314yescomplemented
147#3811—232no—
148D3×#67—232no—
149C2×#626—24no—
150C2×#626—24no—
151C2×#626—24no—
152C2×#626—42no—
153C2×#626C2314yes—
154C2×#626C2314yes—
155C2×#626C2314yescomplemented
156C2×#626C2314yescomplemented
157C2×#625—24no—
158C2×#625C2314yescomplemented
159C2×#624—24no—
160C2×#624C2314yescomplemented
161C2×D3×Dic3—24no—
162C2×D3×Dic3—42no—
163C2×D3×Dic3C2314yescomplemented
164C2×D3×Dic3C2314yescomplemented
165#3757C2314yescomplemented
166#3752C2314yescomplemented
167#3752C2314yescomplemented
168C3×#217C2314yescomplemented
169C3×#217C2314yescomplemented
170C3×#217C2314yescomplemented
171C3×(C2×D3)⋊C4C2314yescomplemented
172C3×(C2×D3)⋊C4C2314yescomplemented
173C3×C4⋊Dic3C2314yescomplemented
174#3724C2314yescomplemented
175Dic3⋊Dic3C2314yescomplemented
176Dic3⋊Dic3C2314yescomplemented
177#3722C2314yescomplemented
178#3722C2314yescomplemented
179(C2×D3)⋊Dic3C2314yescomplemented
180(C2×D3)⋊Dic3C2314yescomplemented
181C2×#534—91noSylow
182C25×C3—31no—
183C24×D3—31no—
184C24×D3—31no—
185C24×D3—31no—
186C24×D3—31no—
187C24×D3—61no—
188C24×D3C2×D311yescharacteristic, complemented
189C22×C3×D4—21no—
190C22×C3×D4—31no—
191C22×C3×D4—31no—
192C22×C3×D4—31no—
193C22×C3×D4—31no—
194C22×C3×D4C2×D311yescharacteristic, complemented
195C22×C3×D4C2×D311yescharacteristic, complemented
196C23×C3×C4—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—31no—
203C22×#67—38no—
204C22×#67—31no—
205C22×#67—31no—
206C22×#67—31no—
207C22×#67—31no—
208C22×#67—61no—
209C22×#67—61no—
210C22×#67—68no—
211C22×#67C2×D311yescharacteristic
212C22×#67C2×D311yescharacteristic, complemented
213C22×#67C2×D311yescharacteristic, complemented
214C22×#67C2×D311yescharacteristic, complemented
215C23×Dic3—31no—
216C23×Dic3—31no—
217C2×D3×D4—38no—
218C2×D3×D4—38no—
219C2×D3×D4—38no—
220C2×D3×D4—68no—
221C2×D3×D4—68no—
222C2×D3×D4—68no—
223C22×D12—31no—
224C22×D12—31no—
225C22×D12—31no—
226C22×D12—31no—
227C22×C4×D3—31no—
228C22×C4×D3—31no—
229C22×C4×D3—31no—
230C22×C4×D3—31no—
231C22×C4×D3C2×D311yescharacteristic, complemented
232C3×#121—38no—
233C3×#120—38no—
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—
240#953—38no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—31no—
244C2×#217—31no—
245C2×#217—61no—
246C2×#217C2×D311yescharacteristic, complemented
247C2×#217C2×D311yescharacteristic, complemented
248C2×#217C2×D311yescharacteristic, complemented
249#939—38no—
250#939—38no—
251#938—38no—
252#938C2×D318yescomplemented
253#937—38no—
254#937—38no—
255#937—38no—
256#937—68no—
257#937C2×D318yescomplemented
258#935—38no—
259#930—38no—
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—31no—
267C2×(C2×D3)⋊C4—31no—
268C2×(C2×D3)⋊C4—31no—
269C2×(C2×D3)⋊C4—31no—
270C2×(C2×D3)⋊C4—38no—
271C2×(C2×D3)⋊C4—61no—
272C2×(C2×D3)⋊C4—61no—
273C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
274C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
275C2×C4⋊Dic3—31no—
276C2×C4⋊Dic3—31no—
277C2×C4⋊Dic3C2×D311yescharacteristic, complemented
278C2×Dic3⋊C4—31no—
279C2×Dic3⋊C4—31no—
280C2×Dic3⋊C4—31no—
281C2×Dic3⋊C4—31no—
282#894—38no—
283#894—38no—
284#886—38no—
285#884—38no—
286#884—38no—
287#883—38no—
288#883—38no—
289#883—38no—
290#883—38no—
291#882—38no—
292#882—38no—
293D3×C22⋊C4—38no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32—22no—
298C23×C32—22no—
299C23×C32—22no—
300C23×C32C2412yes—
301C23×C32C2412yes—
302C23×C32C2411yescharacteristic
303C22×C3⋊D3—22no—
304C22×C3⋊D3—22no—
305C22×C3⋊D3—22no—
306C22×C3⋊D3—22no—
307C22×C3⋊D3—22no—
308C22×C3⋊D3—28no—
309C22×C3⋊D3—44no—
310C22×C3⋊D3—44no—
311C22×C3⋊D3—416no—
312C22×C3⋊D3C2×D414yes—
313C22×C3⋊D3C2412yes—
314C22×C3⋊D3C2412yes—
315C22×C3×D3—22no—
316C22×C3×D3—22no—
317C22×C3×D3—22no—
318C22×C3×D3—22no—
319C22×C3×D3—22no—
320C22×C3×D3—22no—
321C22×C3×D3—22no—
322C22×C3×D3—28no—
323C22×C3×D3—44no—
324C22×C3×D3—44no—
325C22×C3×D3—416no—
326C22×C3×D3C2×D414yes—
327C22×C3×D3C2×D414yes—
328C22×C3×D3C2412yes—
329C22×C3×D3C2412yes—
330C22×C3×D3C2412yes—
331C2×D32—416no—
332C2×D32—44no—
333C2×D32—44no—
334C2×D32C2×D4116yescomplemented
335C32×D4—44no—
336C2×C32×C4—22no—
337C2×C32×C4C2412yes—
338#638—28no—
339#638—44no—
340C2×C3⋊Dic3—22no—
341C2×C3⋊Dic3—22no—
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2412yes—
344C3×#67—28no—
345C3×#67—28no—
346C3×#67—28no—
347C3×#67—44no—
348C2×C3×Dic3—22no—
349C2×C3×Dic3—22no—
350C2×C3×Dic3—22no—
351C2×C3×Dic3—22no—
352C2×C3×Dic3—22no—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2412yes—
357C2×C3×Dic3C2412yes—
358C3×C4×D3—44no—
359#626—28no—
360#626—28no—
361#626—28no—
362#626—44no—
363#625—28no—
364#624—28no—
365D3×Dic3—28no—
366D3×Dic3—44no—
367C23×D4—91no—
368C23×D4—91no—
369#534—916no—
370C2×#123—91no—
371C2×#123—91no—
372C2×#123—91no—
373C2×#123—91no—
374C2×#121—31no—
375C2×#121—91no—
376C2×#121—91no—
377C2×#121—91no—
378C2×#120—31no—
379C2×#120—91no—
380C2×#120—91no—
381C2×#120—91no—
382C22×C22⋊C4—91no—
383C24×C3—21no—
384C24×C3—21no—
385C24×C3—31no—
386C24×C3—31no—
387C24×C3—31no—
388C24×C3—34no—
389C24×C3—64no—
390C24×C3—122no—
391C24×C3—122no—
392C24×C3C22×D311yescharacteristic
393C24×C3C22×D311yescharacteristic
394C24×C3C22×D311yescharacteristic
395C24×C3C22×D311yescharacteristic
396C23×D3—24no—
397C23×D3—31no—
398C23×D3—31no—
399C23×D3—38no—
400C23×D3—38no—
401C23×D3—34no—
402C23×D3—34no—
403C23×D3—31no—
404C23×D3—31no—
405C23×D3—34no—
406C23×D3—34no—
407C23×D3—42no—
408C23×D3—42no—
409C23×D3—61no—
410C23×D3—61no—
411C23×D3—64no—
412C23×D3—64no—
413C23×D3—64no—
414C23×D3—124no—
415C23×D3—122no—
416C23×D3—122no—
417C23×D3—122no—
418C23×D3—122no—
419C23×D3—122no—
420C23×D3—122no—
421C23×D3—122no—
422C23×D3—122no—
423C23×D3—124no—
424C23×D3—124no—
425C23×D3C22×D311yescharacteristic
426C23×D3C22×D311yescharacteristic
427C23×D3C22×D311yescharacteristic
428C23×D3C22×D314yescomplemented
429C2×C3×D4—24no—
430C2×C3×D4—34no—
431C2×C3×D4—34no—
432C2×C3×D4—34no—
433C2×C3×D4—34no—
434C2×C3×D4—42no—
435C2×C3×D4—42no—
436C2×C3×D4—44no—
437C2×C3×D4—64no—
438C2×C3×D4—64no—
439C2×C3×D4—64no—
440C2×C3×D4—122no—
441C2×C3×D4C22×D314yescomplemented
442C2×C3×D4C22×D314yescomplemented
443C22×C3×C4—21no—
444C22×C3×C4—31no—
445C22×C3×C4—31no—
446C22×C3×C4—31no—
447C22×C3×C4—31no—
448C22×C3×C4—31no—
449C22×C3×C4—34no—
450C22×C3×C4—122no—
451C22×C3×C4C22×D311yescharacteristic
452C22×C3×C4C22×D311yescharacteristic
453C2×#67—24no—
454C2×#67—24no—
455C2×#67—24no—
456C2×#67—34no—
457C2×#67—34no—
458C2×#67—34no—
459C2×#67—34no—
460C2×#67—34no—
461C2×#67—34no—
462C2×#67—34no—
463C2×#67—34no—
464C2×#67—34no—
465C2×#67—34no—
466C2×#67—42no—
467C2×#67—64no—
468C2×#67—64no—
469C2×#67—64no—
470C2×#67—64no—
471C2×#67—64no—
472C2×#67—632no—
473C2×#67—64no—
474C2×#67—64no—
475C2×#67—64no—
476C2×#67—64no—
477C2×#67—124no—
478C2×#67—122no—
479C2×#67—122no—
480C2×#67—122no—
481C2×#67—124no—
482C2×#67C22×D314yes—
483C2×#67C22×D314yescomplemented
484C2×#67C22×D314yescomplemented
485C2×#67C22×D314yescomplemented
486C22×Dic3—31no—
487C22×Dic3—31no—
488C22×Dic3—31no—
489C22×Dic3—31no—
490C22×Dic3—34no—
491C22×Dic3—34no—
492C22×Dic3—61no—
493C22×Dic3—61no—
494C22×Dic3—64no—
495C22×Dic3—122no—
496C22×Dic3C22×D311yescharacteristic
497C22×Dic3C22×D311yescharacteristic
498C22×Dic3C22×D311yescharacteristic
499C22×Dic3C22×D311yescharacteristic
500C22×Dic3C22×D311yescharacteristic
501D3×D4—632no—
502D3×D4—632no—
503D3×D4—632no—
504C2×D12—34no—
505C2×D12—34no—
506C2×D12—34no—
507C2×D12—34no—
508C2×D12—64no—
509C2×D12—64no—
510C2×D12—64no—
511C2×D12—122no—
512C2×C4×D3—34no—
513C2×C4×D3—34no—
514C2×C4×D3—34no—
515C2×C4×D3—34no—
516C2×C4×D3—42no—
517C2×C4×D3—64no—
518C2×C4×D3—64no—
519C2×C4×D3—64no—
520C2×C4×D3—122no—
521C2×C4×D3C22×D314yescomplemented
522C3×C4⋊C4—34no—
523C3×C22⋊C4—34no—
524C3×C22⋊C4—34no—
525C3×C22⋊C4—34no—
526C3×C22⋊C4—34no—
527C3×C22⋊C4—34no—
528#217—34no—
529#217—34no—
530#217—34no—
531#217—34no—
532#217—64no—
533#217C22×D314yescomplemented
534#217C22×D314yescomplemented
535#217C22×D314yescomplemented
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)⋊C4—34no—
542(C2×D3)⋊C4—34no—
543(C2×D3)⋊C4—34no—
544(C2×D3)⋊C4—34no—
545(C2×D3)⋊C4—34no—
546(C2×D3)⋊C4—64no—
547(C2×D3)⋊C4—64no—
548(C2×D3)⋊C4C22×D314yescomplemented
549(C2×D3)⋊C4C22×D314yescomplemented
550C4⋊Dic3—34no—
551C4⋊Dic3—34no—
552C4⋊Dic3C22×D314yescomplemented
553Dic3⋊C4—34no—
554Dic3⋊C4—34no—
555Dic3⋊C4—34no—
556Dic3⋊C4—34no—
557C22×C32—22no—
558C22×C32—22no—
559C22×C32—22no—
560C22×C32—22no—
561C22×C32—22no—
562C22×C32—22no—
563C22×C32—44no—
564C22×C32—44no—
565C22×C32C22×D412yes—
566C22×C32H(5,𝔽2)12yes—
567C22×C32H(5,𝔽2)12yes—
568C22×C32C2511yescharacteristic
569C2×C3⋊D3—22no—
570C2×C3⋊D3—28no—
571C2×C3⋊D3—22no—
572C2×C3⋊D3—22no—
573C2×C3⋊D3—22no—
574C2×C3⋊D3—22no—
575C2×C3⋊D3—416no—
576C2×C3⋊D3—44no—
577C2×C3⋊D3C22×D414yes—
578C2×C3×D3—28no—
579C2×C3×D3—28no—
580C2×C3×D3—22no—
581C2×C3×D3—22no—
582C2×C3×D3—22no—
583C2×C3×D3—22no—
584C2×C3×D3—22no—
585C2×C3×D3—22no—
586C2×C3×D3—22no—
587C2×C3×D3—416no—
588C2×C3×D3—44no—
589C2×C3×D3C22×D414yes—
590C2×C3×D3C22×D414yes—
591D32—416no—
592C32×C4—22no—
593C3⋊Dic3—22no—
594C3⋊Dic3—22no—
595C3×Dic3—22no—
596C3×Dic3—22no—
597C3×Dic3—22no—
598C3×Dic3—22no—
599C3×Dic3—22no—
600C25—31no—
601C25—91no—
602C25—91no—
603C22×D4—31no—
604C22×D4—31no—
605C22×D4—31no—
606C22×D4—31no—
607C22×D4—91no—
608C22×D4—91no—
609C22×D4—91no—
610C22×D4—91no—
611C22×D4—98no—
612C22×D4—98no—
613C22×D4—91no—
614C22×D4—91no—
615C22×D4—91no—
616C22×D4—188no—
617C22×D4—188no—
618C22×D4D3211yescharacteristic, complemented
619C23×C4—31no—
620C23×C4—91no—
621C23×C4—91no—
622C23×C4—91no—
623#123—98no—
624#123—98no—
625#123—98no—
626#123—98no—
627#121—38no—
628#121—98no—
629#121—98no—
630#121—98no—
631#120—38no—
632#120—98no—
633#120—98no—
634#120—98no—
635C2×C4⋊C4—31no—
636C2×C4⋊C4—91no—
637C2×C4⋊C4—91no—
638C2×C4⋊C4—91no—
639C2×C22⋊C4—31no—
640C2×C22⋊C4—31no—
641C2×C22⋊C4—31no—
642C2×C22⋊C4—31no—
643C2×C22⋊C4—31no—
644C2×C22⋊C4—98no—
645C2×C22⋊C4—91no—
646C2×C22⋊C4—91no—
647C2×C22⋊C4—91no—
648C2×C22⋊C4—91no—
649C2×C22⋊C4—91no—
650C2×C22⋊C4—91no—
651C2×C22⋊C4—91no—
652C23×C3—24no—
653C23×C3—22no—
654C23×C3—22no—
655C23×C3—22no—
656C23×C3—22no—
657C23×C3—22no—
658C23×C3—22no—
659C23×C3—22no—
660C23×C3—22no—
661C23×C3—22no—
662C23×C3—22no—
663C23×C3—22no—
664C23×C3—22no—
665C23×C3—22no—
666C23×C3—22no—
667C23×C3—21no—
668C23×C3—34no—
669C23×C3—34no—
670C23×C3—32no—
671C23×C3—32no—
672C23×C3—32no—
673C23×C3—42no—
674C23×C3—42no—
675C23×C3—42no—
676C23×C3—42no—
677C23×C3—42no—
678C23×C3—68no—
679C23×C3—62no—
680C23×C3—62no—
681C23×C3—62no—
682C23×C3—62no—
683C23×C3—62no—
684C23×C3—62no—
685C23×C3—62no—
686C23×C3—124no—
687C23×C3—124no—
688C23×C3—1216no—
689C23×C3C23×D312yes—
690C23×C3C23×D312yes—
691C23×C3C23×D312yes—
692C23×C3C23×D312yes—
693C23×C3C23×D311yescharacteristic
694C23×C3C23×D311yescharacteristic
695C22×D3—22no—
696C22×D3—22no—
697C22×D3—22no—
698C22×D3—22no—
699C22×D3—22no—
700C22×D3—22no—
701C22×D3—22no—
702C22×D3—28no—
703C22×D3—34no—
704C22×D3—34no—
705C22×D3—32no—
706C22×D3—32no—
707C22×D3—316no—
708C22×D3—316no—
709C22×D3—32no—
710C22×D3—32no—
711C22×D3—44no—
712C22×D3—44no—
713C22×D3—416no—
714C22×D3—64no—
715C22×D3—62no—
716C22×D3—62no—
717C22×D3—68no—
718C22×D3—68no—
719C22×D3—62no—
720C22×D3—62no—
721C22×D3—62no—
722C22×D3—62no—
723C22×D3—64no—
724C22×D3—62no—
725C22×D3—62no—
726C22×D3—62no—
727C22×D3—62no—
728C22×D3—62no—
729C22×D3—62no—
730C22×D3—128no—
731C22×D3—122no—
732C22×D3—122no—
733C22×D3—122no—
734C22×D3—122no—
735C22×D3—124no—
736C22×D3—124no—
737C22×D3—124no—
738C22×D3—124no—
739C22×D3—1216no—
740C22×D3—1216no—
741C22×D3—124no—
742C22×D3—124no—
743C22×D3—124no—
744C22×D3—124no—
745C22×D3—128no—
746C22×D3—1216no—
747C22×D3—1216no—
748C22×D3—128no—
749C22×D3—1232no—
750C22×D3D3×D414yes—
751C22×D3D3×D414yes—
752C22×D3C23×D312yes—
753C22×D3C23×D312yes—
754C22×D3C23×D312yes—
755C3×D4—44no—
756C3×D4—44no—
757C3×D4—48no—
758C3×D4—68no—
759C3×D4—68no—
760C3×D4—68no—
761C3×D4—124no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—22no—
765C2×C3×C4—32no—
766C2×C3×C4—32no—
767C2×C3×C4—32no—
768C2×C3×C4—32no—
769C2×C3×C4—32no—
770C2×C3×C4—42no—
771C2×C3×C4—62no—
772C2×C3×C4—62no—
773C2×C3×C4—62no—
774C2×C3×C4—62no—
775C2×C3×C4—62no—
776C2×C3×C4—124no—
777C2×C3×C4C23×D312yes—
778C2×C3×C4C23×D312yes—
779#67—28no—
780#67—28no—
781#67—28no—
782#67—44no—
783#67—68no—
784#67—68no—
785#67—68no—
786#67—68no—
787#67—68no—
788#67—68no—
789#67—68no—
790#67—128no—
791#67—124no—
792#67—124no—
793#67—124no—
794#67—128no—
795C2×Dic3—22no—
796C2×Dic3—22no—
797C2×Dic3—22no—
798C2×Dic3—22no—
799C2×Dic3—22no—
800C2×Dic3—32no—
801C2×Dic3—32no—
802C2×Dic3—32no—
803C2×Dic3—32no—
804C2×Dic3—62no—
805C2×Dic3—62no—
806C2×Dic3—68no—
807C2×Dic3—62no—
808C2×Dic3—62no—
809C2×Dic3—62no—
810C2×Dic3—62no—
811C2×Dic3—122no—
812C2×Dic3—122no—
813C2×Dic3—124no—
814C2×Dic3C23×D312yes—
815C2×Dic3C23×D312yes—
816C2×Dic3C23×D312yes—
817C2×Dic3C23×D312yes—
818C2×Dic3C23×D312yes—
819D12—68no—
820D12—68no—
821D12—68no—
822D12—124no—
823C4×D3—44no—
824C4×D3—68no—
825C4×D3—68no—
826C4×D3—68no—
827C4×D3—124no—
828C2×C32—42no—
829C2×C32—42no—
830C2×C32#53414yescomplemented
831C2×C32C23×D411yescharacteristic
832C2×C32C2×H(5,𝔽2)11yescharacteristic
833C2×C32C2×H(5,𝔽2)11yescharacteristic
834C3⋊D3—24no—
835C3⋊D3—42no—
836C3×D3—24no—
837C3×D3—24no—
838C3×D3—42no—
839C24—31no—
840C24—31no—
841C24—31no—
842C24—34no—
843C24—64no—
844C24—94no—
845C24—98no—
846C24—91no—
847C24—91no—
848C24—94no—
849C24—122no—
850C24—122no—
851C24—184no—
852C24—362no—
853C24—362no—
854C24—362no—
855C24—362no—
856C24C2×D3211yescharacteristic
857C24C2×D3211yescharacteristic
858C2×D4—34no—
859C2×D4—34no—
860C2×D4—34no—
861C2×D4—34no—
862C2×D4—42no—
863C2×D4—64no—
864C2×D4—64no—
865C2×D4—64no—
866C2×D4—94no—
867C2×D4—94no—
868C2×D4—94no—
869C2×D4—94no—
870C2×D4—94no—
871C2×D4—94no—
872C2×D4—94no—
873C2×D4—122no—
874C2×D4—184no—
875C2×D4—184no—
876C2×D4—184no—
877C2×D4—1832no—
878C2×D4—1832no—
879C2×D4—184no—
880C2×D4—184no—
881C2×D4—362no—
882C2×D4—362no—
883C2×D4C2×D3214yescomplemented
884C22×C4—31no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—31no—
888C22×C4—31no—
889C22×C4—34no—
890C22×C4—94no—
891C22×C4—94no—
892C22×C4—94no—
893C22×C4—91no—
894C22×C4—91no—
895C22×C4—122no—
896C22×C4—184no—
897C22×C4—184no—
898C22×C4—362no—
899C22×C4C2×D3211yescharacteristic
900C4⋊C4—34no—
901C4⋊C4—94no—
902C4⋊C4—94no—
903C4⋊C4—94no—
904C22⋊C4—34no—
905C22⋊C4—34no—
906C22⋊C4—34no—
907C22⋊C4—34no—
908C22⋊C4—34no—
909C22⋊C4—94no—
910C22⋊C4—94no—
911C22⋊C4—94no—
912C22⋊C4—94no—
913C22⋊C4—94no—
914C22⋊C4—94no—
915C22⋊C4—94no—
916C22×C3—24no—
917C22×C3—22no—
918C22×C3—22no—
919C22×C3—22no—
920C22×C3—22no—
921C22×C3—22no—
922C22×C3—22no—
923C22×C3—22no—
924C22×C3—22no—
925C22×C3—22no—
926C22×C3—22no—
927C22×C3—22no—
928C22×C3—22no—
929C22×C3—22no—
930C22×C3—22no—
931C22×C3—22no—
932C22×C3—21no—
933C22×C3—34no—
934C22×C3—34no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3—42no—
938C22×C3—42no—
939C22×C3—42no—
940C22×C3—48no—
941C22×C3—44no—
942C22×C3—44no—
943C22×C3—44no—
944C22×C3—44no—
945C22×C3—62no—
946C22×C3—62no—
947C22×C3—62no—
948C22×C3—62no—
949C22×C3—68no—
950C22×C3—68no—
951C22×C3—62no—
952C22×C3—62no—
953C22×C3—62no—
954C22×C3—84no—
955C22×C3—1216no—
956C22×C3—124no—
957C22×C3C2×D3×D412yes—
958C22×C3C2×D3×D412yes—
959C22×C3#100412yes—
960C22×C3#100412yes—
961C22×C3#100412yes—
962C22×C3#100912yes—
963C22×C3C24×D311yescharacteristic
964C22×C3C24×D311yescharacteristic
965C2×D3—22no—
966C2×D3—22no—
967C2×D3—22no—
968C2×D3—22no—
969C2×D3—28no—
970C2×D3—28no—
971C2×D3—22no—
972C2×D3—22no—
973C2×D3—22no—
974C2×D3—34no—
975C2×D3—34no—
976C2×D3—416no—
977C2×D3—44no—
978C2×D3—64no—
979C2×D3—62no—
980C2×D3—62no—
981C2×D3—62no—
982C2×D3—62no—
983C2×D3—68no—
984C2×D3—68no—
985C2×D3—64no—
986C2×D3—62no—
987C2×D3—62no—
988C2×D3—62no—
989C2×D3—62no—
990C2×D3—62no—
991C2×D3—62no—
992C2×D3—122no—
993C2×D3—122no—
994C2×D3—128no—
995C2×D3—122no—
996C2×D3—122no—
997C2×D3—1216no—
998C2×D3—1216no—
999C2×D3—1216no—
1000C2×D3—1216no—
1001C2×D3—128no—
1002C2×D3—1232no—
1003C2×D3—124no—
1004C2×D3—124no—
1005C2×D3C2×D3×D414yes—
1006C2×D3C2×D3×D414yes—
1007C3×C4—22no—
1008C3×C4—22no—
1009C3×C4—42no—
1010C3×C4—62no—
1011C3×C4—62no—
1012C3×C4—62no—
1013C3×C4—62no—
1014C3×C4—62no—
1015Dic3—22no—
1016Dic3—22no—
1017Dic3—22no—
1018Dic3—22no—
1019Dic3—22no—
1020Dic3—62no—
1021Dic3—62no—
1022Dic3—62no—
1023Dic3—62no—
1024Dic3—122no—
1025Dic3—122no—
1026C32C2×#53411yescharacteristic, complemented, Sylow
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—34no—
1034C23—34no—
1035C23—32no—
1036C23—32no—
1037C23—32no—
1038C23—68no—
1039C23—62no—
1040C23—62no—
1041C23—62no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—916no—
1047C23—94no—
1048C23—92no—
1049C23—92no—
1050C23—124no—
1051C23—124no—
1052C23—1216no—
1053C23—188no—
1054C23—182no—
1055C23—182no—
1056C23—182no—
1057C23—182no—
1058C23—182no—
1059C23—364no—
1060C23—364no—
1061C23—3616no—
1062C23—364no—
1063C23—364no—
1064C23—3616no—
1065C23C22×D3212yes—
1066C23C22×D3212yes—
1067C23C22×D3211yescharacteristic
1068D4—44no—
1069D4—68no—
1070D4—68no—
1071D4—68no—
1072D4—124no—
1073D4—188no—
1074D4—188no—
1075D4—188no—
1076D4—188no—
1077D4—188no—
1078D4—364no—
1079D4—364no—
1080C2×C4—22no—
1081C2×C4—32no—
1082C2×C4—32no—
1083C2×C4—32no—
1084C2×C4—32no—
1085C2×C4—32no—
1086C2×C4—62no—
1087C2×C4—62no—
1088C2×C4—62no—
1089C2×C4—62no—
1090C2×C4—62no—
1091C2×C4—92no—
1092C2×C4—92no—
1093C2×C4—124no—
1094C2×C4—188no—
1095C2×C4—188no—
1096C2×C4—182no—
1097C2×C4—182no—
1098C2×C4—364no—
1099C2×C4C22×D3212yes—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—24no—
1104C2×C3—44no—
1105C2×C3—42no—
1106C2×C3—42no—
1107C2×C3—42no—
1108C2×C3—42no—
1109C2×C3—64no—
1110C2×C3—64no—
1111C2×C3—82no—
1112C2×C3—122no—
1113C2×C3#558914yescomplemented
1114C2×C3#560514yescomplemented
1115C2×C3C22×D3×D411yescharacteristic
1116C2×C3C22×D3×D411yescharacteristic
1117C2×C3C2×#100411yescharacteristic
1118C2×C3C2×#100411yescharacteristic
1119C2×C3C2×#100411yescharacteristic
1120C2×C3C2×#100911yescharacteristic
1121D3—24no—
1122D3—24no—
1123D3—42no—
1124D3—64no—
1125D3—64no—
1126D3—124no—
1127D3—124no—
1128D3—122no—
1129D3—122no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—22no—
1135C22—22no—
1136C22—34no—
1137C22—34no—
1138C22—44no—
1139C22—44no—
1140C22—62no—
1141C22—62no—
1142C22—62no—
1143C22—62no—
1144C22—68no—
1145C22—68no—
1146C22—62no—
1147C22—62no—
1148C22—62no—
1149C22—94no—
1150C22—1216no—
1151C22—124no—
1152C22—182no—
1153C22—182no—
1154C22—188no—
1155C22—182no—
1156C22—182no—
1157C22—182no—
1158C22—3616no—
1159C22—3616no—
1160C22—364no—
1161C22D32×D412yes—
1162C22#6431412yes—
1163C22#6433012yes—
1164C22C23×D3211yescharacteristic
1165C4—22no—
1166C4—62no—
1167C4—62no—
1168C4—62no—
1169C4—62no—
1170C4—62no—
1171C4—182no—
1172C4—182no—
1173C3—21no—
1174C3C2×#558911yescharacteristic, complemented
1175C3C2×#560511yescharacteristic, complemented
1176C2—42no—
1177C2—42no—
1178C2—64no—
1179C2—64no—
1180C2—122no—
1181C2—184no—
1182C2—362no—
1183C2#1059528114yesdirect product factor
1184C2C2×D32×D411yescharacteristic
1185C2C2×#6431411yescharacteristic
1186C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3811C2semidirect
2. C22×D3×#67C2semidirect
3. C2×#64146C2semidirect
4. C2×C3×#938C2semidirect
5. C2×C3×#937C2semidirect
6. C2×#63981C2semidirect
7. C2×#63977C2semidirect
8. C2×#63975C2semidirect
9. C2×#63971C2semidirect
10. C2×#63970C2semidirect
11. C2×#63969C2semidirect
12. #10595281C2direct (N × H)
13. C2×D3×(C2×D3)⋊C4C2semidirect
14. C2×#63906C2semidirect
15. C2×#63890C2semidirect
16. C2×#63854C2semidirect
19. C24×C3⋊D3C22semidirect
20. C24×C3×D3C22semidirect
22. C22×C32×D4C22semidirect
24. C22×#638C22semidirect
26. C22×C3×#67C22semidirect
27. C22×C3×#67C22semidirect
28. C22×C3×#67C22semidirect
29. C22×C3×C4×D3C22semidirect
31. C2×#3811C22semidirect
33. C2×D3×#67C22semidirect
36. C22×#626C22semidirect
37. C22×#626C22semidirect
38. C22×#625C22semidirect
39. C22×#624C22semidirect
40. C22×D3×Dic3C22semidirect
41. C22×D3×Dic3C22semidirect
42. C2×#3757C22semidirect
43. #64146C22semidirect
44. C2×#3752C22semidirect
45. C2×#3752C22semidirect
46. C2×C3×#217C22semidirect
47. C2×C3×#217C22semidirect
48. C2×C3×#217C22semidirect
49. C3×#938C22semidirect
50. C3×#937C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×(C2×D3)⋊C4C22semidirect
53. C2×C3×C4⋊Dic3C22semidirect
54. #63981C22semidirect
55. #63977C22semidirect
56. #63975C22semidirect
57. #63971C22semidirect
58. #63970C22semidirect
59. #63969C22semidirect
60. C2×#3724C22semidirect
61. C2×Dic3⋊Dic3C22semidirect
62. C2×Dic3⋊Dic3C22semidirect
63. C2×#3722C22semidirect
64. C2×#3722C22semidirect
65. C2×(C2×D3)⋊Dic3C22semidirect
66. C2×(C2×D3)⋊Dic3C22semidirect
67. D3×(C2×D3)⋊C4C22semidirect
68. #63906C22semidirect
69. #63890C22semidirect
70. #63854C22semidirect
81. C2×#938D3semidirect
86. C2×#937D3semidirect
111. C23×C3⋊D3C23semidirect
118. C23×C3×D3C23semidirect
121. C22×D32D4semidirect
124. C2×C32×D4C23semidirect
129. C2×#638C23semidirect
137. C2×C3×#67C23semidirect
138. C2×C3×#67C23semidirect
139. C2×C3×#67C23semidirect
146. C2×C3×C4×D3C23semidirect
155. C2×#626C23semidirect
156. C2×#626C23semidirect
158. C2×#625C23semidirect
160. C2×#624C23semidirect
163. C2×D3×Dic3C23semidirect
164. C2×D3×Dic3C23semidirect
165. #3757C23semidirect
166. #3752C23semidirect
167. #3752C23semidirect
168. C3×#217C23semidirect
169. C3×#217C23semidirect
170. C3×#217C23semidirect
171. C3×(C2×D3)⋊C4C23semidirect
172. C3×(C2×D3)⋊C4C23semidirect
173. C3×C4⋊Dic3C23semidirect
174. #3724C23semidirect
175. Dic3⋊Dic3C23semidirect
176. Dic3⋊Dic3C23semidirect
177. #3722C23semidirect
178. #3722C23semidirect
179. (C2×D3)⋊Dic3C23semidirect
180. (C2×D3)⋊Dic3C23semidirect
188. C24×D3C2×D3semidirect
194. C22×C3×D4C2×D3semidirect
195. C22×C3×D4C2×D3semidirect
212. C22×#67C2×D3semidirect
213. C22×#67C2×D3semidirect
214. C22×#67C2×D3semidirect
231. C22×C4×D3C2×D3semidirect
246. C2×#217C2×D3semidirect
247. C2×#217C2×D3semidirect
248. C2×#217C2×D3semidirect
252. #938C2×D3semidirect
257. #937C2×D3semidirect
273. C2×(C2×D3)⋊C4C2×D3semidirect
274. C2×(C2×D3)⋊C4C2×D3semidirect
277. C2×C4⋊Dic3C2×D3semidirect
334. C2×D32C2×D4semidirect
428. C23×D3C22×D3semidirect
441. C2×C3×D4C22×D3semidirect
442. C2×C3×D4C22×D3semidirect
483. C2×#67C22×D3semidirect
484. C2×#67C22×D3semidirect
485. C2×#67C22×D3semidirect
521. C2×C4×D3C22×D3semidirect
533. #217C22×D3semidirect
534. #217C22×D3semidirect
535. #217C22×D3semidirect
548. (C2×D3)⋊C4C22×D3semidirect
549. (C2×D3)⋊C4C22×D3semidirect
552. C4⋊Dic3C22×D3semidirect
618. C22×D4D32semidirect
830. C2×C32#534semidirect
883. C2×D4C2×D32semidirect
1026. C32C2×#534semidirect
1113. C2×C3#5589semidirect
1114. C2×C3#5605semidirect
1174. C3C2×#5589semidirect
1175. C3C2×#5605semidirect
1183. C2#10595281direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38112
C22×D3×#672
C2×#641462
C2×C3×#9382
C2×C3×#9372
C2×#639812
C2×#639772
C2×#639752
C2×#639712
C2×#639702
C2×#639692
#105952812
C2×D3×(C2×D3)⋊C42
C2×#639062
C2×#638902
C2×#638542
C2×#56053
C2×#55893