Finite Group Databasebeta

← C2×#10595302 #11900954

Subgroups — C2×#10595302 #11900954

Order 1152.

4181 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C22×D3×#67C211yesmaximal, characteristic, complemented
3C2×#64148C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C2×#63983C211yesmaximal, characteristic, complemented
6C2×#63980C211yesmaximal, characteristic, complemented
7C2×#63978C211yesmaximal, characteristic, complemented
8C2×#63977C211yesmaximal, characteristic, complemented
9C2×#63976C211yesmaximal, characteristic, complemented
10C2×#63969C211yesmaximal, characteristic, complemented
11C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
12#10595302C2116yesmaximal, direct product factor
13C2×#63922C211yesmaximal, characteristic, complemented
14C2×#63905C211yesmaximal, characteristic, complemented
15C2×#63884C211yesmaximal, characteristic, complemented
16C2×#63850C211yesmaximal, characteristic, complemented
17C2×#5804—31nomaximal
18C2×#5605—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C24×C3×D3C2211yescharacteristic, complemented
21C23×D32C2211yescharacteristic, complemented
22C22×C32×D4C2211yescharacteristic, complemented
23C22×#638C2211yescharacteristic, complemented
24C22×#638C2211yescharacteristic, complemented
25C23×C3⋊Dic3C2211yescharacteristic, complemented
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic, complemented
28C22×C3×#67C2211yescharacteristic, complemented
29C22×C3×#67C2211yescharacteristic, complemented
30C23×C3×Dic3C2211yescharacteristic, complemented
31C2×C3×D3×D4—28no—
32C2×C3×D3×D4C2218yescomplemented
33C22×C3×D12C2211yescharacteristic
34C22×C3×C4×D3C2211yescharacteristic, complemented
35C2×D3×#67—28no—
36C2×D3×#67C2218yescomplemented
37C22×#626C2211yescharacteristic
38C22×#626C2211yescharacteristic, complemented
39C22×#625C2211yescharacteristic
40C22×#625C2211yescharacteristic, complemented
41C22×D3×Dic3C2211yescharacteristic, complemented
42C2×#3757C2211yescharacteristic, complemented
43#64148C2218yescomplemented
44C2×#3752C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46C2×C3×#217C2211yescharacteristic, complemented
47C3×#939C2218yescomplemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
50#63983C2218yescomplemented
51#63980C2218yescomplemented
52#63978C2218yescomplemented
53#63977C2218yescomplemented
54#63976C2218yescomplemented
55#63969C2218yescomplemented
56C2×#3724C2211yescharacteristic, complemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
65C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
66C2×(C2×D3)⋊Dic3C2218yescomplemented
67#63922C2218yescomplemented
68#63905C2218yescomplemented
69#63884C2218yescomplemented
70#63850C2218yescomplemented
71C23×C3×D4—31no—
72C23×#67—31no—
73C22×D3×D4—31no—
74C22×D3×D4D311yescharacteristic, complemented
75C2×C3×#121—31no—
76C2×#953—31no—
77C2×#953—31no—
78C22×#217—31no—
79#5804—316no—
80C2×#939—31no—
81C2×#939—31no—
82C2×#939—31no—
83C2×#939—31no—
84C2×#939—31no—
85C2×#939—61no—
86C2×#939D311yescharacteristic, complemented
87C2×#937—31no—
88C2×#937—31no—
89C2×#937—31no—
90C2×#937—31no—
91C2×#935—31no—
92C2×#935—31no—
93C2×#930—31no—
94C2×#929—31no—
95C2×#929—31no—
96C22×(C2×D3)⋊C4—31no—
97#5605—316no—
98C2×#894—31no—
99C2×#894—31no—
100C2×#883—31no—
101C2×#883—31no—
102C2×#882—31no—
103C2×#882—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3—24no—
108C23×C3×D3—42no—
109C23×C3×D3—42no—
110C23×C3×D3—42no—
111C23×C3×D3—42no—
112C23×C3×D3D418yescomplemented
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2311yescharacteristic
115C23×C3×D3C2311yescharacteristic
116C23×C3×D3C2311yescharacteristic
117C23×C3×D3C2314yes—
118C23×C3×D3C2314yescomplemented
119C22×D32—24no—
120C22×D32—42no—
121C22×D32—42no—
122C22×D32C2314yescomplemented
123C2×C32×D4—24no—
124C2×C32×D4C2314yescomplemented
125C22×C32×C4C2311yescharacteristic
126C2×#638—24no—
127C2×#638—42no—
128C2×#638C2314yescomplemented
129C2×#638C2314yescomplemented
130C22×C3⋊Dic3—42no—
131C22×C3⋊Dic3C2311yescharacteristic
132C22×C3⋊Dic3C2311yescharacteristic
133C22×C3⋊Dic3C2311yescharacteristic
134C22×C3⋊Dic3C2314yescomplemented
135C2×C3×#67—24no—
136C2×C3×#67—24no—
137C2×C3×#67—24no—
138C2×C3×#67—42no—
139C2×C3×#67C2314yes—
140C2×C3×#67C2314yescomplemented
141C2×C3×#67C2314yescomplemented
142C2×C3×#67C2314yescomplemented
143C22×C3×Dic3—42no—
144C22×C3×Dic3C2311yescharacteristic
145C22×C3×Dic3C2311yescharacteristic
146C22×C3×Dic3C2311yescharacteristic
147C22×C3×Dic3C2311yescharacteristic
148C22×C3×Dic3C2314yescomplemented
149C3×D3×D4—232no—
150C2×C3×D12—24no—
151C2×C3×D12C2314yes—
152C2×C3×C4×D3—24no—
153C2×C3×C4×D3C2314yescomplemented
154D3×#67—232no—
155C2×#626—24no—
156C2×#626—42no—
157C2×#626C2314yes—
158C2×#626C2314yescomplemented
159C2×#625—24no—
160C2×#625—42no—
161C2×#625C2314yes—
162C2×#625C2314yescomplemented
163C2×D3×Dic3—24no—
164C2×D3×Dic3C2314yescomplemented
165#3757C2314yescomplemented
166#3752C2314yescomplemented
167#3750C2314yescomplemented
168C3×#217C2314yescomplemented
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171#3724C2314yescomplemented
172Dic3⋊Dic3C2314yescomplemented
173#3722C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178(C2×D3)⋊Dic3C2314yescomplemented
179(C2×D3)⋊Dic3C2314yescomplemented
180(C2×D3)⋊Dic3C2314yescomplemented
181C2×#534—91noSylow
182C25×C3—31no—
183C25×C3—31no—
184C24×D3—31no—
185C24×D3—31no—
186C24×D3C2×D311yescharacteristic
187C24×D3C2×D311yescharacteristic, complemented
188C22×C3×D4—21no—
189C22×C3×D4—31no—
190C22×C3×D4—31no—
191C22×C3×D4—31no—
192C22×C3×D4—31no—
193C22×C3×D4—38no—
194C22×C3×D4—31no—
195C22×C3×D4—68no—
196C22×C3×D4C2×D311yescharacteristic, complemented
197C22×C3×D4C2×D311yescharacteristic, complemented
198C23×C3×C4—31no—
199C23×C3×C4—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—31no—
203C22×#67—31no—
204C22×#67—31no—
205C22×#67—31no—
206C22×#67—31no—
207C22×#67—31no—
208C22×#67—38no—
209C22×#67—31no—
210C22×#67—31no—
211C22×#67—61no—
212C22×#67—61no—
213C22×#67—68no—
214C22×#67C2×D311yescharacteristic
215C22×#67C2×D311yescharacteristic, complemented
216C22×#67C2×D311yescharacteristic, complemented
217C22×#67C2×D311yescharacteristic, complemented
218C23×Dic3—31no—
219C23×Dic3—31no—
220C23×Dic3—31no—
221C23×Dic3—61no—
222C23×Dic3C2×D311yescharacteristic, complemented
223C2×D3×D4—28no—
224C2×D3×D4—38no—
225C2×D3×D4—68no—
226C2×D3×D4C2×D318yescomplemented
227C22×D12—31no—
228C22×D12—31no—
229C22×D12C2×D311yescharacteristic
230C22×C4×D3—31no—
231C22×C4×D3C2×D311yescharacteristic, complemented
232C3×#121—38no—
233C2×C3×C4⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236#953—38no—
237#953—38no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—31no—
244C2×#217—31no—
245C2×#217—31no—
246C2×#217—31no—
247C2×#217—38no—
248C2×#217—61no—
249C2×#217C2×D311yescharacteristic, complemented
250#939—38no—
251#939—38no—
252#939—38no—
253#939—38no—
254#939—38no—
255#939—68no—
256#939C2×D318yescomplemented
257#937—38no—
258#937—38no—
259#937—38no—
260#937—38no—
261#935—38no—
262#935—38no—
263#930—38no—
264#929—38no—
265#929—38no—
266C2×(C2×D3)⋊C4—31no—
267C2×(C2×D3)⋊C4—31no—
268C2×(C2×D3)⋊C4—31no—
269C2×(C2×D3)⋊C4—31no—
270C2×(C2×D3)⋊C4—31no—
271C2×(C2×D3)⋊C4—31no—
272C2×(C2×D3)⋊C4—38no—
273C2×(C2×D3)⋊C4—31no—
274C2×(C2×D3)⋊C4—31no—
275C2×(C2×D3)⋊C4—31no—
276C2×(C2×D3)⋊C4—31no—
277C2×(C2×D3)⋊C4—31no—
278C2×(C2×D3)⋊C4—61no—
279C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
280C2×C4⋊Dic3—31no—
281C2×Dic3⋊C4—31no—
282C2×Dic3⋊C4—31no—
283C2×Dic3⋊C4—31no—
284C2×Dic3⋊C4—31no—
285C2×Dic3⋊C4—31no—
286C2×Dic3⋊C4—61no—
287C2×Dic3⋊C4C2×D311yescharacteristic, complemented
288#894—38no—
289#894—38no—
290#883—38no—
291#883—38no—
292#882—38no—
293#882—38no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32—22no—
298C23×C32—22no—
299C23×C32C2×D414yes—
300C23×C32C2412yes—
301C23×C32C2412yes—
302C23×C32C2411yescharacteristic
303C22×C3⋊D3—22no—
304C22×C3⋊D3—22no—
305C22×C3⋊D3—22no—
306C22×C3⋊D3C2412yes—
307C22×C3×D3—22no—
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×D3—22no—
317C22×C3×D3—28no—
318C22×C3×D3—416no—
319C22×C3×D3—44no—
320C22×C3×D3—44no—
321C22×C3×D3—44no—
322C22×C3×D3—44no—
323C22×C3×D3—416no—
324C22×C3×D3C2×D414yes—
325C22×C3×D3C2×D414yes—
326C22×C3×D3C2×D4116yescomplemented
327C22×C3×D3C2412yes—
328C22×C3×D3C2412yes—
329C22×C3×D3C2412yes—
330C22×C3×D3C2412yes—
331C2×D32—28no—
332C2×D32—44no—
333C2×D32—44no—
334C2×D32—416no—
335C32×D4—28no—
336C2×C32×C4—22no—
337C2×C32×C4C2412yes—
338#638—28no—
339#638—44no—
340C2×C3⋊Dic3—22no—
341C2×C3⋊Dic3—22no—
342C2×C3⋊Dic3—22no—
343C2×C3⋊Dic3—44no—
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2412yes—
346C2×C3⋊Dic3C2412yes—
347C3×#67—28no—
348C3×#67—28no—
349C3×#67—28no—
350C3×#67—44no—
351C2×C3×Dic3—22no—
352C2×C3×Dic3—22no—
353C2×C3×Dic3—22no—
354C2×C3×Dic3—22no—
355C2×C3×Dic3—44no—
356C2×C3×Dic3C2412yes—
357C2×C3×Dic3C2412yes—
358C2×C3×Dic3C2412yes—
359C2×C3×Dic3C2412yes—
360C3×D12—28no—
361C3×C4×D3—28no—
362#626—28no—
363#626—44no—
364#625—28no—
365#625—44no—
366D3×Dic3—28no—
367C23×D4—31no—
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—91no—
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—38no—
388C24×C3—34no—
389C24×C3—31no—
390C24×C3—31no—
391C24×C3—34no—
392C24×C3—64no—
393C24×C3—122no—
394C24×C3—122no—
395C24×C3—122no—
396C24×C3—122no—
397C24×C3C22×D311yescharacteristic
398C24×C3C22×D311yescharacteristic
399C24×C3C22×D311yescharacteristic
400C24×C3C22×D311yescharacteristic
401C23×D3—24no—
402C23×D3—31no—
403C23×D3—31no—
404C23×D3—34no—
405C23×D3—34no—
406C23×D3—42no—
407C23×D3—42no—
408C23×D3—42no—
409C23×D3—42no—
410C23×D3—61no—
411C23×D3—64no—
412C23×D3—64no—
413C23×D3—122no—
414C23×D3—122no—
415C23×D3—122no—
416C23×D3—122no—
417C23×D3#6718yescomplemented
418C23×D3C22×D311yescharacteristic
419C23×D3C22×D311yescharacteristic
420C23×D3C22×D311yescharacteristic
421C23×D3C22×D311yescharacteristic
422C23×D3C22×D314yes—
423C23×D3C22×D314yescomplemented
424C2×C3×D4—24no—
425C2×C3×D4—24no—
426C2×C3×D4—24no—
427C2×C3×D4—34no—
428C2×C3×D4—34no—
429C2×C3×D4—34no—
430C2×C3×D4—34no—
431C2×C3×D4—34no—
432C2×C3×D4—44no—
433C2×C3×D4—64no—
434C2×C3×D4—632no—
435C2×C3×D4—64no—
436C2×C3×D4—64no—
437C2×C3×D4—64no—
438C2×C3×D4—122no—
439C2×C3×D4C22×D314yescomplemented
440C2×C3×D4C22×D314yescomplemented
441C22×C3×C4—21no—
442C22×C3×C4—31no—
443C22×C3×C4—31no—
444C22×C3×C4—31no—
445C22×C3×C4—31no—
446C22×C3×C4—34no—
447C22×C3×C4—34no—
448C22×C3×C4—64no—
449C22×C3×C4—122no—
450C22×C3×C4C22×D311yescharacteristic
451C22×C3×C4C22×D311yescharacteristic
452C2×#67—24no—
453C2×#67—24no—
454C2×#67—24no—
455C2×#67—34no—
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—42no—
466C2×#67—64no—
467C2×#67—64no—
468C2×#67—64no—
469C2×#67—632no—
470C2×#67—64no—
471C2×#67—64no—
472C2×#67—64no—
473C2×#67—64no—
474C2×#67—124no—
475C2×#67—122no—
476C2×#67—122no—
477C2×#67—122no—
478C2×#67—122no—
479C2×#67—122no—
480C2×#67—124no—
481C2×#67C22×D314yes—
482C2×#67C22×D314yescomplemented
483C2×#67C22×D314yescomplemented
484C2×#67C22×D314yescomplemented
485C22×Dic3—31no—
486C22×Dic3—31no—
487C22×Dic3—31no—
488C22×Dic3—31no—
489C22×Dic3—31no—
490C22×Dic3—31no—
491C22×Dic3—34no—
492C22×Dic3—34no—
493C22×Dic3—34no—
494C22×Dic3—42no—
495C22×Dic3—61no—
496C22×Dic3—61no—
497C22×Dic3—61no—
498C22×Dic3—64no—
499C22×Dic3—64no—
500C22×Dic3—122no—
501C22×Dic3—122no—
502C22×Dic3—124no—
503C22×Dic3C22×D311yescharacteristic
504C22×Dic3C22×D311yescharacteristic
505C22×Dic3C22×D311yescharacteristic
506C22×Dic3C22×D311yescharacteristic
507C22×Dic3C22×D314yescomplemented
508D3×D4—232no—
509D3×D4—632no—
510C2×D12—24no—
511C2×D12—34no—
512C2×D12—34no—
513C2×D12—64no—
514C2×D12—122no—
515C2×D12C22×D314yes—
516C2×C4×D3—24no—
517C2×C4×D3—34no—
518C2×C4×D3—64no—
519C2×C4×D3C22×D314yescomplemented
520C3×C4⋊C4—34no—
521C3×C22⋊C4—34no—
522C3×C22⋊C4—34no—
523#217—34no—
524#217—34no—
525#217—34no—
526#217—34no—
527#217—34no—
528#217—34no—
529#217—34no—
530#217—34no—
531#217—34no—
532#217—64no—
533#217C22×D314yescomplemented
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)⋊C4—34no—
542(C2×D3)⋊C4—34no—
543(C2×D3)⋊C4—34no—
544(C2×D3)⋊C4—34no—
545(C2×D3)⋊C4—64no—
546(C2×D3)⋊C4C22×D314yescomplemented
547C4⋊Dic3—34no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—34no—
551Dic3⋊C4—34no—
552Dic3⋊C4—34no—
553Dic3⋊C4—64no—
554Dic3⋊C4C22×D314yescomplemented
555C22×C32—28no—
556C22×C32—22no—
557C22×C32—22no—
558C22×C32—22no—
559C22×C32—22no—
560C22×C32—22no—
561C22×C32—44no—
562C22×C32C22×D414yes—
563C22×C32C22×D412yes—
564C22×C32H(5,𝔽2)12yes—
565C22×C32H(5,𝔽2)12yes—
566C22×C32C2511yescharacteristic
567C2×C3⋊D3—22no—
568C2×C3⋊D3—22no—
569C2×C3⋊D3—22no—
570C2×C3⋊D3—44no—
571C2×C3×D3—28no—
572C2×C3×D3—28no—
573C2×C3×D3—22no—
574C2×C3×D3—22no—
575C2×C3×D3—22no—
576C2×C3×D3—22no—
577C2×C3×D3—22no—
578C2×C3×D3—22no—
579C2×C3×D3—22no—
580C2×C3×D3—22no—
581C2×C3×D3—22no—
582C2×C3×D3—22no—
583C2×C3×D3—416no—
584C2×C3×D3—416no—
585C2×C3×D3—44no—
586C2×C3×D3—44no—
587C2×C3×D3C22×D414yes—
588C2×C3×D3C22×D414yes—
589D32—416no—
590C32×C4—22no—
591C3⋊Dic3—22no—
592C3⋊Dic3—22no—
593C3⋊Dic3—22no—
594C3×Dic3—22no—
595C3×Dic3—22no—
596C3×Dic3—22no—
597C3×Dic3—22no—
598C25—31no—
599C25—31no—
600C25—91no—
601C22×D4—31no—
602C22×D4—31no—
603C22×D4—31no—
604C22×D4—31no—
605C22×D4—38no—
606C22×D4—31no—
607C22×D4—68no—
608C22×D4—91no—
609C22×D4—91no—
610C22×D4—98no—
611C22×D4—91no—
612C22×D4—91no—
613C22×D4—91no—
614C22×D4—91no—
615C22×D4—188no—
616C22×D4D3211yescharacteristic, complemented
617C23×C4—31no—
618C23×C4—31no—
619C23×C4—91no—
620C23×C4—91no—
621#123—98no—
622#123—98no—
623#123—98no—
624#123—98no—
625#121—38no—
626#121—98no—
627#121—98no—
628#121—98no—
629#120—98no—
630#120—98no—
631#120—98no—
632#120—98no—
633C2×C4⋊C4—31no—
634C2×C4⋊C4—91no—
635C2×C4⋊C4—91no—
636C2×C4⋊C4—91no—
637C2×C22⋊C4—31no—
638C2×C22⋊C4—31no—
639C2×C22⋊C4—91no—
640C2×C22⋊C4—91no—
641C2×C22⋊C4—91no—
642C2×C22⋊C4—91no—
643C2×C22⋊C4—91no—
644C2×C22⋊C4—98no—
645C2×C22⋊C4—91no—
646C2×C22⋊C4—91no—
647C2×C22⋊C4—91no—
648C2×C22⋊C4—91no—
649C2×C22⋊C4—91no—
650C23×C3—22no—
651C23×C3—22no—
652C23×C3—22no—
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—21no—
663C23×C3—24no—
664C23×C3—34no—
665C23×C3—34no—
666C23×C3—32no—
667C23×C3—32no—
668C23×C3—316no—
669C23×C3—32no—
670C23×C3—32no—
671C23×C3—42no—
672C23×C3—42no—
673C23×C3—42no—
674C23×C3—42no—
675C23×C3—42no—
676C23×C3—68no—
677C23×C3—62no—
678C23×C3—62no—
679C23×C3—62no—
680C23×C3—62no—
681C23×C3—62no—
682C23×C3—62no—
683C23×C3—62no—
684C23×C3—62no—
685C23×C3—62no—
686C23×C3—62no—
687C23×C3—124no—
688C23×C3—124no—
689C23×C3—1216no—
690C23×C3—124no—
691C23×C3—124no—
692C23×C3—1216no—
693C23×C3D3×D414yes—
694C23×C3C2×#6714yes—
695C23×C3C23×D312yes—
696C23×C3C23×D312yes—
697C23×C3C23×D312yes—
698C23×C3C23×D312yes—
699C23×C3C23×D311yescharacteristic
700C23×C3C23×D311yescharacteristic
701C22×D3—22no—
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—22no—
705C22×D3—22no—
706C22×D3—22no—
707C22×D3—22no—
708C22×D3—22no—
709C22×D3—22no—
710C22×D3—22no—
711C22×D3—28no—
712C22×D3—32no—
713C22×D3—32no—
714C22×D3—416no—
715C22×D3—44no—
716C22×D3—44no—
717C22×D3—44no—
718C22×D3—44no—
719C22×D3—416no—
720C22×D3—62no—
721C22×D3—68no—
722C22×D3—62no—
723C22×D3—62no—
724C22×D3—62no—
725C22×D3—62no—
726C22×D3—62no—
727C22×D3—62no—
728C22×D3—68no—
729C22×D3—122no—
730C22×D3—122no—
731C22×D3—122no—
732C22×D3—124no—
733C22×D3—124no—
734C22×D3—124no—
735C22×D3—124no—
736C22×D3—1216no—
737C22×D3—1216no—
738C22×D3C2×#6714yes—
739C22×D3C2×#6714yes—
740C22×D3C2×#67116yescomplemented
741C22×D3C23×D312yes—
742C22×D3C23×D312yes—
743C22×D3C23×D312yes—
744C22×D3C23×D312yes—
745C3×D4—28no—
746C3×D4—28no—
747C3×D4—48no—
748C3×D4—68no—
749C3×D4—68no—
750C3×D4—68no—
751C3×D4—68no—
752C3×D4—124no—
753C2×C3×C4—22no—
754C2×C3×C4—22no—
755C2×C3×C4—22no—
756C2×C3×C4—32no—
757C2×C3×C4—32no—
758C2×C3×C4—32no—
759C2×C3×C4—32no—
760C2×C3×C4—42no—
761C2×C3×C4—68no—
762C2×C3×C4—62no—
763C2×C3×C4—62no—
764C2×C3×C4—62no—
765C2×C3×C4—62no—
766C2×C3×C4—124no—
767C2×C3×C4C23×D312yes—
768C2×C3×C4C23×D312yes—
769#67—28no—
770#67—28no—
771#67—28no—
772#67—44no—
773#67—68no—
774#67—68no—
775#67—68no—
776#67—68no—
777#67—68no—
778#67—128no—
779#67—124no—
780#67—124no—
781#67—124no—
782#67—124no—
783#67—124no—
784#67—128no—
785C2×Dic3—22no—
786C2×Dic3—22no—
787C2×Dic3—22no—
788C2×Dic3—22no—
789C2×Dic3—32no—
790C2×Dic3—32no—
791C2×Dic3—32no—
792C2×Dic3—32no—
793C2×Dic3—32no—
794C2×Dic3—32no—
795C2×Dic3—44no—
796C2×Dic3—62no—
797C2×Dic3—62no—
798C2×Dic3—62no—
799C2×Dic3—68no—
800C2×Dic3—64no—
801C2×Dic3—62no—
802C2×Dic3—62no—
803C2×Dic3—62no—
804C2×Dic3—62no—
805C2×Dic3—62no—
806C2×Dic3—62no—
807C2×Dic3—122no—
808C2×Dic3—122no—
809C2×Dic3—124no—
810C2×Dic3—124no—
811C2×Dic3—128no—
812C2×Dic3C23×D312yes—
813C2×Dic3C23×D312yes—
814C2×Dic3C23×D312yes—
815C2×Dic3C23×D312yes—
816D12—28no—
817D12—68no—
818D12—124no—
819C4×D3—28no—
820C4×D3—68no—
821C2×C32—24no—
822C2×C32—42no—
823C2×C32#53414yescomplemented
824C2×C32C23×D411yescharacteristic
825C2×C32C2×H(5,𝔽2)11yescharacteristic
826C2×C32C2×H(5,𝔽2)11yescharacteristic
827C3⋊D3—42no—
828C3×D3—24no—
829C3×D3—24no—
830C3×D3—42no—
831C3×D3—42no—
832C24—31no—
833C24—31no—
834C24—34no—
835C24—38no—
836C24—31no—
837C24—31no—
838C24—34no—
839C24—64no—
840C24—94no—
841C24—91no—
842C24—122no—
843C24—122no—
844C24—122no—
845C24—122no—
846C24—184no—
847C24—362no—
848C24—362no—
849C24C2×D3211yescharacteristic
850C24C2×D3211yescharacteristic
851C2×D4—24no—
852C2×D4—34no—
853C2×D4—34no—
854C2×D4—34no—
855C2×D4—34no—
856C2×D4—34no—
857C2×D4—64no—
858C2×D4—632no—
859C2×D4—64no—
860C2×D4—64no—
861C2×D4—64no—
862C2×D4—94no—
863C2×D4—94no—
864C2×D4—94no—
865C2×D4—94no—
866C2×D4—94no—
867C2×D4—94no—
868C2×D4—122no—
869C2×D4—184no—
870C2×D4—1832no—
871C2×D4—184no—
872C2×D4—184no—
873C2×D4—362no—
874C2×D4—362no—
875C2×D4—362no—
876C2×D4C2×D3214yescomplemented
877C22×C4—31no—
878C22×C4—31no—
879C22×C4—31no—
880C22×C4—31no—
881C22×C4—34no—
882C22×C4—34no—
883C22×C4—64no—
884C22×C4—94no—
885C22×C4—91no—
886C22×C4—91no—
887C22×C4—91no—
888C22×C4—94no—
889C22×C4—122no—
890C22×C4—184no—
891C22×C4—362no—
892C22×C4C2×D3211yescharacteristic
893C4⋊C4—34no—
894C4⋊C4—94no—
895C4⋊C4—94no—
896C4⋊C4—94no—
897C22⋊C4—34no—
898C22⋊C4—34no—
899C22⋊C4—94no—
900C22⋊C4—94no—
901C22⋊C4—94no—
902C22⋊C4—94no—
903C22⋊C4—94no—
904C22⋊C4—94no—
905C22⋊C4—94no—
906C22⋊C4—94no—
907C22⋊C4—94no—
908C22⋊C4—94no—
909C22×C3—22no—
910C22×C3—22no—
911C22×C3—22no—
912C22×C3—22no—
913C22×C3—28no—
914C22×C3—28no—
915C22×C3—22no—
916C22×C3—22no—
917C22×C3—22no—
918C22×C3—22no—
919C22×C3—22no—
920C22×C3—22no—
921C22×C3—22no—
922C22×C3—22no—
923C22×C3—22no—
924C22×C3—24no—
925C22×C3—21no—
926C22×C3—34no—
927C22×C3—34no—
928C22×C3—42no—
929C22×C3—42no—
930C22×C3—48no—
931C22×C3—42no—
932C22×C3—42no—
933C22×C3—42no—
934C22×C3—44no—
935C22×C3—44no—
936C22×C3—62no—
937C22×C3—62no—
938C22×C3—62no—
939C22×C3—62no—
940C22×C3—68no—
941C22×C3—68no—
942C22×C3—62no—
943C22×C3—62no—
944C22×C3—62no—
945C22×C3—62no—
946C22×C3—62no—
947C22×C3—62no—
948C22×C3—84no—
949C22×C3—1216no—
950C22×C3—1216no—
951C22×C3—124no—
952C22×C3—124no—
953C22×C3C2×D3×D414yes—
954C22×C3C2×D3×D412yes—
955C22×C3#100412yes—
956C22×C3#100412yes—
957C22×C3#100412yes—
958C22×C3#100912yes—
959C22×C3C22×#6714yes—
960C22×C3C22×#6712yes—
961C22×C3C24×D311yescharacteristic
962C22×C3C24×D311yescharacteristic
963C2×D3—22no—
964C2×D3—22no—
965C2×D3—22no—
966C2×D3—22no—
967C2×D3—28no—
968C2×D3—28no—
969C2×D3—22no—
970C2×D3—22no—
971C2×D3—22no—
972C2×D3—22no—
973C2×D3—22no—
974C2×D3—22no—
975C2×D3—416no—
976C2×D3—416no—
977C2×D3—44no—
978C2×D3—44no—
979C2×D3—62no—
980C2×D3—62no—
981C2×D3—62no—
982C2×D3—62no—
983C2×D3—62no—
984C2×D3—62no—
985C2×D3—122no—
986C2×D3—122no—
987C2×D3—122no—
988C2×D3—1216no—
989C2×D3—1216no—
990C2×D3—124no—
991C2×D3—124no—
992C2×D3—244no—
993C2×D3C22×#6714yes—
994C2×D3C22×#6714yes—
995C3×C4—22no—
996C3×C4—22no—
997C3×C4—42no—
998C3×C4—62no—
999C3×C4—62no—
1000C3×C4—62no—
1001C3×C4—62no—
1002Dic3—22no—
1003Dic3—22no—
1004Dic3—22no—
1005Dic3—22no—
1006Dic3—64no—
1007Dic3—62no—
1008Dic3—62no—
1009Dic3—62no—
1010Dic3—62no—
1011Dic3—62no—
1012Dic3—62no—
1013Dic3—122no—
1014Dic3—122no—
1015C32C2×#53411yescharacteristic, complemented, Sylow
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—34no—
1022C23—34no—
1023C23—32no—
1024C23—32no—
1025C23—316no—
1026C23—32no—
1027C23—32no—
1028C23—68no—
1029C23—62no—
1030C23—62no—
1031C23—62no—
1032C23—62no—
1033C23—62no—
1034C23—62no—
1035C23—62no—
1036C23—62no—
1037C23—62no—
1038C23—62no—
1039C23—92no—
1040C23—124no—
1041C23—124no—
1042C23—1216no—
1043C23—124no—
1044C23—124no—
1045C23—1216no—
1046C23—188no—
1047C23—182no—
1048C23—182no—
1049C23—182no—
1050C23—364no—
1051C23—364no—
1052C23—3616no—
1053C23D3×#6714yes—
1054C23C22×D3212yes—
1055C23C22×D3212yes—
1056C23C22×D3211yescharacteristic
1057D4—28no—
1058D4—68no—
1059D4—68no—
1060D4—68no—
1061D4—68no—
1062D4—124no—
1063D4—188no—
1064D4—188no—
1065D4—188no—
1066D4—364no—
1067D4—364no—
1068D4—364no—
1069C2×C4—22no—
1070C2×C4—32no—
1071C2×C4—32no—
1072C2×C4—32no—
1073C2×C4—32no—
1074C2×C4—68no—
1075C2×C4—62no—
1076C2×C4—62no—
1077C2×C4—62no—
1078C2×C4—62no—
1079C2×C4—92no—
1080C2×C4—92no—
1081C2×C4—92no—
1082C2×C4—124no—
1083C2×C4—188no—
1084C2×C4—182no—
1085C2×C4—182no—
1086C2×C4—182no—
1087C2×C4—364no—
1088C2×C4C22×D3212yes—
1089C2×C3—24no—
1090C2×C3—24no—
1091C2×C3—21no—
1092C2×C3—21no—
1093C2×C3—21no—
1094C2×C3—24no—
1095C2×C3—44no—
1096C2×C3—42no—
1097C2×C3—42no—
1098C2×C3—64no—
1099C2×C3—64no—
1100C2×C3—82no—
1101C2×C3—122no—
1102C2×C3—122no—
1103C2×C3#560514yescomplemented
1104C2×C3#580414yescomplemented
1105C2×C3C22×D3×D411yescharacteristic
1106C2×C3C2×#100411yescharacteristic
1107C2×C3C2×#100411yescharacteristic
1108C2×C3C2×#100411yescharacteristic
1109C2×C3C2×#100911yescharacteristic
1110C2×C3C23×#6711yescharacteristic
1111D3—24no—
1112D3—24no—
1113D3—42no—
1114D3—42no—
1115D3—122no—
1116D3—122no—
1117D3—242no—
1118C22—22no—
1119C22—22no—
1120C22—28no—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—34no—
1125C22—34no—
1126C22—44no—
1127C22—62no—
1128C22—62no—
1129C22—62no—
1130C22—62no—
1131C22—68no—
1132C22—68no—
1133C22—62no—
1134C22—62no—
1135C22—62no—
1136C22—62no—
1137C22—62no—
1138C22—62no—
1139C22—1216no—
1140C22—1216no—
1141C22—124no—
1142C22—124no—
1143C22—182no—
1144C22—182no—
1145C22—182no—
1146C22—3616no—
1147C22—364no—
1148C22#6431312yes—
1149C22#6431412yes—
1150C22C2×D3×#6714yes—
1151C22C2×D3×#6712yes—
1152C22C23×D3211yescharacteristic
1153C4—22no—
1154C4—62no—
1155C4—62no—
1156C4—62no—
1157C4—62no—
1158C4—182no—
1159C4—182no—
1160C4—182no—
1161C3—21no—
1162C3C2×#560511yescharacteristic, complemented
1163C3C2×#580411yescharacteristic, complemented
1164C2—24no—
1165C2—42no—
1166C2—64no—
1167C2—64no—
1168C2—122no—
1169C2—122no—
1170C2—362no—
1171C2#1059530214yesdirect product factor
1172C2C2×#6431311yescharacteristic
1173C2C2×#6431411yescharacteristic
1174C2C22×D3×#6711yescharacteristic
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×C3×D3×D4C2semidirect
2. C22×D3×#67C2semidirect
3. C2×#64148C2semidirect
4. C2×C3×#939C2semidirect
5. C2×#63983C2semidirect
6. C2×#63980C2semidirect
7. C2×#63978C2semidirect
8. C2×#63977C2semidirect
9. C2×#63976C2semidirect
10. C2×#63969C2semidirect
11. C22×(C2×D3)⋊Dic3C2semidirect
12. #10595302C2direct (N × H)
13. C2×#63922C2semidirect
14. C2×#63905C2semidirect
15. C2×#63884C2semidirect
16. C2×#63850C2semidirect
20. C24×C3×D3C22semidirect
21. C23×D32C22semidirect
22. C22×C32×D4C22semidirect
23. C22×#638C22semidirect
24. C22×#638C22semidirect
25. C23×C3⋊Dic3C22semidirect
27. C22×C3×#67C22semidirect
28. C22×C3×#67C22semidirect
29. C22×C3×#67C22semidirect
30. C23×C3×Dic3C22semidirect
32. C2×C3×D3×D4C22semidirect
34. C22×C3×C4×D3C22semidirect
36. C2×D3×#67C22semidirect
38. C22×#626C22semidirect
40. C22×#625C22semidirect
41. C22×D3×Dic3C22semidirect
42. C2×#3757C22semidirect
43. #64148C22semidirect
44. C2×#3752C22semidirect
45. C2×#3750C22semidirect
46. C2×C3×#217C22semidirect
47. C3×#939C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. #63983C22semidirect
51. #63980C22semidirect
52. #63978C22semidirect
53. #63977C22semidirect
54. #63976C22semidirect
55. #63969C22semidirect
56. C2×#3724C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. C2×(C2×D3)⋊Dic3C22semidirect
65. C2×(C2×D3)⋊Dic3C22semidirect
66. C2×(C2×D3)⋊Dic3C22semidirect
67. #63922C22semidirect
68. #63905C22semidirect
69. #63884C22semidirect
70. #63850C22semidirect
74. C22×D3×D4D3semidirect
86. C2×#939D3semidirect
112. C23×C3×D3D4semidirect
118. C23×C3×D3C23semidirect
122. C22×D32C23semidirect
124. C2×C32×D4C23semidirect
128. C2×#638C23semidirect
129. C2×#638C23semidirect
134. C22×C3⋊Dic3C23semidirect
140. C2×C3×#67C23semidirect
141. C2×C3×#67C23semidirect
142. C2×C3×#67C23semidirect
148. C22×C3×Dic3C23semidirect
153. C2×C3×C4×D3C23semidirect
158. C2×#626C23semidirect
162. C2×#625C23semidirect
164. C2×D3×Dic3C23semidirect
165. #3757C23semidirect
166. #3752C23semidirect
167. #3750C23semidirect
168. C3×#217C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×Dic3⋊C4C23semidirect
171. #3724C23semidirect
172. Dic3⋊Dic3C23semidirect
173. #3722C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
178. (C2×D3)⋊Dic3C23semidirect
179. (C2×D3)⋊Dic3C23semidirect
180. (C2×D3)⋊Dic3C23semidirect
187. C24×D3C2×D3semidirect
196. C22×C3×D4C2×D3semidirect
197. C22×C3×D4C2×D3semidirect
215. C22×#67C2×D3semidirect
216. C22×#67C2×D3semidirect
217. C22×#67C2×D3semidirect
222. C23×Dic3C2×D3semidirect
226. C2×D3×D4C2×D3semidirect
231. C22×C4×D3C2×D3semidirect
249. C2×#217C2×D3semidirect
256. #939C2×D3semidirect
279. C2×(C2×D3)⋊C4C2×D3semidirect
287. C2×Dic3⋊C4C2×D3semidirect
326. C22×C3×D3C2×D4semidirect
417. C23×D3#67semidirect
423. C23×D3C22×D3semidirect
439. C2×C3×D4C22×D3semidirect
440. C2×C3×D4C22×D3semidirect
482. C2×#67C22×D3semidirect
483. C2×#67C22×D3semidirect
484. C2×#67C22×D3semidirect
507. C22×Dic3C22×D3semidirect
519. C2×C4×D3C22×D3semidirect
533. #217C22×D3semidirect
546. (C2×D3)⋊C4C22×D3semidirect
554. Dic3⋊C4C22×D3semidirect
616. C22×D4D32semidirect
740. C22×D3C2×#67semidirect
823. C2×C32#534semidirect
876. C2×D4C2×D32semidirect
1015. C32C2×#534semidirect
1103. C2×C3#5605semidirect
1104. C2×C3#5804semidirect
1162. C3C2×#5605semidirect
1163. C3C2×#5804semidirect
1171. C2#10595302direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C22×D3×#672
C2×#641482
C2×C3×#9392
C2×#639832
C2×#639802
C2×#639782
C2×#639772
C2×#639762
C2×#639692
C22×(C2×D3)⋊Dic32
#105953022
C2×#639222
C2×#639052
C2×#638842
C2×#638502
C2×#58043
C2×#56053