Finite Group Databasebeta

← C2×#10595150 #11902441

Subgroups — C2×#10595150 #11902441

Order 1152.

3971 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C22×#3805C211yesmaximal, characteristic, complemented
3C2×#64144C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C2×#63976C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×Dic3×#67C211yesmaximal, characteristic, complemented
8C2×#63970C211yesmaximal, characteristic, complemented
9C2×D3×#217C211yesmaximal, characteristic, complemented
10C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
11C2×#63959C211yesmaximal, characteristic, complemented
12#10595150C2116yesmaximal, direct product factor
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63884C211yesmaximal, characteristic, complemented
15C2×#63879C211yesmaximal, characteristic, complemented
16C2×#63851C211yesmaximal, characteristic, complemented
17C2×#5806—31nomaximal
18C2×#5610—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C24×C3×D3C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic, complemented
26C22×C3×#67C2211yescharacteristic, complemented
27C23×C3×Dic3C2211yescharacteristic, complemented
28C2×C3×D3×D4—28no—
29C2×C3×D3×D4C2218yescomplemented
30C22×C3×D12C2211yescharacteristic
31C22×C3×C4×D3C2211yescharacteristic
32C22×#627C2211yescharacteristic, complemented
33C22×#625C2211yescharacteristic
34C22×#625C2211yescharacteristic, complemented
35C22×#625C2211yescharacteristic, complemented
36C2×#3805—28no—
37C2×#3805C2218yescomplemented
38C22×D3×Dic3C2211yescharacteristic, complemented
39C22×D3×Dic3C2211yescharacteristic, complemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3757C2211yescharacteristic, complemented
42C2×#3757C2211yescharacteristic, complemented
43C2×#3757C2211yescharacteristic, complemented
44#64144C2218yescomplemented
45C2×#3750C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47C2×C3×#217C2211yescharacteristic, complemented
48C3×#939C2218yescomplemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51#63976C2218yescomplemented
52#63976C2218yescomplemented
53Dic3×#67C2218yescomplemented
54#63970C2218yescomplemented
55D3×#217C2218yescomplemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2218yescomplemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
65#63959C2218yescomplemented
66C2×Dic32C2211yescharacteristic, complemented
67#63885C2218yescomplemented
68#63884C2218yescomplemented
69#63879C2218yescomplemented
70#63851C2218yescomplemented
71C23×C3×D4—31no—
72C22×#237—31no—
73C22×#237—31no—
74C22×D3×D4D311yescharacteristic, complemented
75C2×C3×#121—31no—
76C2×#953—31no—
77C2×#953—31no—
78C22×#217—31no—
79C22×#217—31no—
80#5806—316no—
81C2×#939—31no—
82C2×#939—31no—
83C2×#939D311yescharacteristic, complemented
84C2×#938—31no—
85C2×#937—31no—
86C2×#937—31no—
87C2×#936—31no—
88C2×#935—31no—
89C2×#935—31no—
90C2×#935—31no—
91C2×#935—61no—
92C2×D4×Dic3—31no—
93C2×C4×#67—31no—
94C2×C4×#67—31no—
95C22×(C2×D3)⋊C4—31no—
96C2×#924—31no—
97#5610—316no—
98C2×#896—31no—
99C2×#894—31no—
100C2×#885—31no—
101C2×#884—31no—
102C2×#67⋊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×D3C2311yescharacteristic
114C23×C3×D3C2314yes—
115C23×C3×D3C2314yes—
116C23×C3×D3C2311yescharacteristic
117C23×C3×D3C2311yescharacteristic
118C2×C32×D4—24no—
119C2×C32×D4C2314yes—
120C22×C32×C4C2311yescharacteristic
121C22×C3⋊Dic3—24no—
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2314yescomplemented
127C2×C3×#67—24no—
128C2×C3×#67—24no—
129C2×C3×#67—42no—
130C2×C3×#67D418yescomplemented
131C2×C3×#67C2314yes—
132C2×C3×#67C2314yes—
133C2×C3×#67C2314yescomplemented
134C2×C3×#67C2314yescomplemented
135C22×C3×Dic3—42no—
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2314yescomplemented
141C3×D3×D4—232no—
142C2×C3×D12—24no—
143C2×C3×D12C2314yes—
144C2×C3×C4×D3—24no—
145C2×C3×C4×D3C2314yes—
146C2×#627—24no—
147C2×#627C2314yescomplemented
148C2×#625—24no—
149C2×#625—24no—
150C2×#625—42no—
151C2×#625C2314yes—
152C2×#625C2314yescomplemented
153C2×#625C2314yescomplemented
154#3805—232no—
155C2×D3×Dic3—24no—
156C2×D3×Dic3—24no—
157C2×D3×Dic3—42no—
158C2×D3×Dic3C2314yescomplemented
159C2×D3×Dic3C2314yescomplemented
160C2×D3×Dic3C2314yescomplemented
161#3757C2314yescomplemented
162#3757C2314yescomplemented
163#3757C2314yescomplemented
164#3750C2314yescomplemented
165#3750C2314yescomplemented
166C3×#217C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×Dic3⋊C4C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170(C2×D3)⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C25×C3—31no—
181C24×D3C2×D311yescharacteristic
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—21no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C22×C3×D4—38no—
189C22×C3×D4—31no—
190C22×C3×D4—68no—
191C22×C3×D4C2×D311yescharacteristic
192C22×C3×D4C2×D311yescharacteristic
193C23×C3×C4—31no—
194C23×C3×C4—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67C2×D311yescharacteristic
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic, complemented
204C22×#67C2×D311yescharacteristic, complemented
205C23×Dic3—31no—
206C23×Dic3—31no—
207C23×Dic3—31no—
208C23×Dic3—31no—
209C23×Dic3—31no—
210C23×Dic3—61no—
211C23×Dic3C2×D311yescharacteristic, complemented
212C2×#237—38no—
213C2×#237—38no—
214C2×#237—68no—
215C2×#237—68no—
216C2×D3×D4—28no—
217C2×D3×D4C2×D318yescomplemented
218C22×D12C2×D311yescharacteristic
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3C2×D311yescharacteristic
223C22×Dic6—31no—
224C22×Dic6—31no—
225C3×#121—38no—
226C2×C3×C4⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229#953—38no—
230#953—38no—
231C2×#217—31no—
232C2×#217—31no—
233C2×#217—31no—
234C2×#217—31no—
235C2×#217—31no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—31no—
244C2×#217—38no—
245C2×#217—38no—
246C2×#217—61no—
247C2×#217—61no—
248C2×#217—61no—
249C2×#217C2×D311yescharacteristic, complemented
250#939—38no—
251#939—38no—
252#939C2×D318yescomplemented
253#938—38no—
254#937—38no—
255#937—38no—
256#936—38no—
257#935—38no—
258#935—38no—
259#935—38no—
260#935—68no—
261D4×Dic3—38no—
262C4×#67—38no—
263C4×#67—38no—
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—31no—
271C2×(C2×D3)⋊C4—38no—
272C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
273C2×C4⋊Dic3—31no—
274#924—38no—
275C2×Dic3⋊C4—31no—
276C2×Dic3⋊C4—31no—
277C2×Dic3⋊C4—31no—
278C2×Dic3⋊C4—31no—
279C2×Dic3⋊C4—31no—
280C2×Dic3⋊C4—61no—
281C2×Dic3⋊C4—61no—
282C2×Dic3⋊C4C2×D311yescharacteristic, complemented
283C2×C4×Dic3—31no—
284C2×C4×Dic3—31no—
285#896—38no—
286#894—38no—
287#885—38no—
288#884—38no—
289#67⋊C4—38no—
290D3×C22⋊C4—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32C2×D414yes—
297C23×C32C2412yes—
298C23×C32C2412yes—
299C23×C32C2411yescharacteristic
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—28no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—28no—
312C22×C3×D3—28no—
313C22×C3×D3—28no—
314C22×C3×D3—44no—
315C22×C3×D3—44no—
316C22×C3×D3—416no—
317C22×C3×D3—416no—
318C22×C3×D3C2×D414yes—
319C22×C3×D3#4114yescomplemented
320C22×C3×D3C2412yes—
321C22×C3×D3C2412yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
324C32×D4—28no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327C2×C3⋊Dic3—22no—
328C2×C3⋊Dic3—28no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C3×#67—28no—
337C3×#67—28no—
338C3×#67—44no—
339C3×#67C2×D4116yescomplemented
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—44no—
344C2×C3×Dic3C2×D414yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C3×D12—28no—
350C3×C4×D3—28no—
351#627—28no—
352#625—28no—
353#625—28no—
354#625—44no—
355D3×Dic3—28no—
356D3×Dic3—28no—
357D3×Dic3—44no—
358C22×#41—91no—
359C23×D4—31no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—31no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—21no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—31no—
379C24×C3—31no—
380C24×C3—34no—
381C24×C3—34no—
382C24×C3—64no—
383C24×C3—64no—
384C24×C3—64no—
385C24×C3—64no—
386C24×C3—122no—
387C24×C3—122no—
388C24×C3C22×D311yescharacteristic
389C24×C3C22×D311yescharacteristic
390C24×C3C22×D311yescharacteristic
391C24×C3C22×D311yescharacteristic
392C23×D3—24no—
393C23×D3—24no—
394C23×D3—24no—
395C23×D3—24no—
396C23×D3—42no—
397C23×D3—42no—
398C23×D3C22×D311yescharacteristic
399C23×D3C22×D311yescharacteristic
400C23×D3C22×D314yes—
401C23×D3C22×D314yes—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C2×C3×D4—24no—
405C2×C3×D4—24no—
406C2×C3×D4—24no—
407C2×C3×D4—38no—
408C2×C3×D4—34no—
409C2×C3×D4—34no—
410C2×C3×D4—34no—
411C2×C3×D4—34no—
412C2×C3×D4—34no—
413C2×C3×D4—44no—
414C2×C3×D4—64no—
415C2×C3×D4—64no—
416C2×C3×D4—632no—
417C2×C3×D4—64no—
418C2×C3×D4—122no—
419C2×C3×D4C22×D314yes—
420C2×C3×D4C22×D314yes—
421C22×C3×C4—21no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—31no—
426C22×C3×C4—34no—
427C22×C3×C4—34no—
428C22×C3×C4—64no—
429C22×C3×C4—122no—
430C22×C3×C4C22×D311yescharacteristic
431C22×C3×C4C22×D311yescharacteristic
432C2×#67—24no—
433C2×#67—24no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—42no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—122no—
446C2×#67—122no—
447C2×#67#6718yescomplemented
448C2×#67C22×D314yes—
449C2×#67C22×D314yes—
450C2×#67C22×D314yescomplemented
451C2×#67C22×D314yescomplemented
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—31no—
460C22×Dic3—34no—
461C22×Dic3—34no—
462C22×Dic3—34no—
463C22×Dic3—34no—
464C22×Dic3—34no—
465C22×Dic3—42no—
466C22×Dic3—61no—
467C22×Dic3—61no—
468C22×Dic3—61no—
469C22×Dic3—61no—
470C22×Dic3—64no—
471C22×Dic3—64no—
472C22×Dic3—64no—
473C22×Dic3—64no—
474C22×Dic3—64no—
475C22×Dic3—124no—
476C22×Dic3—122no—
477C22×Dic3C22×D311yescharacteristic
478C22×Dic3C22×D311yescharacteristic
479C22×Dic3C22×D311yescharacteristic
480C22×Dic3C22×D311yescharacteristic
481C22×Dic3C22×D314yescomplemented
482#237—632no—
483#237—632no—
484D3×D4—232no—
485C2×D12—24no—
486C2×D12C22×D314yes—
487C2×C4×D3—24no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
490C2×C4×D3—34no—
491C2×C4×D3—64no—
492C2×C4×D3—64no—
493C2×C4×D3—122no—
494C2×C4×D3C22×D314yes—
495C2×Dic6—34no—
496C2×Dic6—34no—
497C2×Dic6—64no—
498C2×Dic6—64no—
499C3×C4⋊C4—34no—
500C3×C22⋊C4—34no—
501C3×C22⋊C4—34no—
502#217—34no—
503#217—34no—
504#217—34no—
505#217—34no—
506#217—34no—
507#217—34no—
508#217—34no—
509#217—34no—
510#217—34no—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—64no—
516#217—64no—
517#217—64no—
518#217C22×D314yescomplemented
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4C22×D314yescomplemented
527C4⋊Dic3—34no—
528Dic3⋊C4—34no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—64no—
534Dic3⋊C4—64no—
535Dic3⋊C4C22×D314yescomplemented
536C4×Dic3—34no—
537C4×Dic3—34no—
538C22×C32—28no—
539C22×C32—22no—
540C22×C32—22no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—44no—
545C22×C32C22×D414yes—
546C22×C32C22×D412yes—
547C22×C32C2×#4112yes—
548C22×C32H(5,𝔽2)12yes—
549C22×C32C2511yescharacteristic
550C2×C3×D3—28no—
551C2×C3×D3—28no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—416no—
563C2×C3×D3—416no—
564C2×C3×D3—44no—
565C2×C3×D3—44no—
566C2×C3×D3C22×D414yes—
567C2×C3×D3C2×#4114yescomplemented
568C32×C4—22no—
569C3⋊Dic3—22no—
570C3⋊Dic3—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3×Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3C22×D414yes—
577C25—31no—
578C25—31no—
579C2×#41—98no—
580C2×#41—188no—
581C22×Q8—91no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—38no—
587C22×D4—31no—
588C22×D4—68no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4D3211yescharacteristic
593C23×C4—31no—
594C23×C4—31no—
595C23×C4—91no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4—91no—
599#124—98no—
600#123—98no—
601#123—98no—
602C22⋊Q8—98no—
603#121—38no—
604#121—98no—
605#121—98no—
606#120—98no—
607#120—98no—
608C4×D4—98no—
609C4×D4—98no—
610C2×C4⋊C4—31no—
611C2×C4⋊C4—91no—
612C2×C4⋊C4—91no—
613C2×C4⋊C4—91no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—31no—
616C2×C22⋊C4—98no—
617C2×C22⋊C4—91no—
618C2×C22⋊C4—91no—
619C2×C22⋊C4—91no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—98no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C42—91no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
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—34no—
645C23×C3—32no—
646C23×C3—32no—
647C23×C3—32no—
648C23×C3—32no—
649C23×C3—42no—
650C23×C3—42no—
651C23×C3—42no—
652C23×C3—42no—
653C23×C3—42no—
654C23×C3—68no—
655C23×C3—68no—
656C23×C3—68no—
657C23×C3—62no—
658C23×C3—62no—
659C23×C3—62no—
660C23×C3—62no—
661C23×C3—68no—
662C23×C3—62no—
663C23×C3—62no—
664C23×C3—62no—
665C23×C3—62no—
666C23×C3—62no—
667C23×C3—62no—
668C23×C3—124no—
669C23×C3—124no—
670C23×C3—1216no—
671C23×C3—1216no—
672C23×C3D3×D414yes—
673C23×C3C2×#6714yes—
674C23×C3C23×D312yes—
675C23×C3C23×D312yes—
676C23×C3C23×D312yes—
677C23×C3C23×D312yes—
678C23×C3C23×D311yescharacteristic
679C23×C3C23×D311yescharacteristic
680C22×D3—22no—
681C22×D3—22no—
682C22×D3—22no—
683C22×D3—22no—
684C22×D3—22no—
685C22×D3—22no—
686C22×D3—22no—
687C22×D3—22no—
688C22×D3—22no—
689C22×D3—22no—
690C22×D3—28no—
691C22×D3—28no—
692C22×D3—28no—
693C22×D3—28no—
694C22×D3—44no—
695C22×D3—44no—
696C22×D3—416no—
697C22×D3—416no—
698C22×D3#23714yescomplemented
699C22×D3C2×#6714yes—
700C22×D3C23×D312yes—
701C22×D3C23×D312yes—
702C22×D3C23×D312yes—
703C22×D3C23×D312yes—
704C3×D4—28no—
705C3×D4—28no—
706C3×D4—316no—
707C3×D4—48no—
708C3×D4—68no—
709C3×D4—68no—
710C3×D4—68no—
711C3×D4—124no—
712C2×C3×C4—22no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—34no—
716C2×C3×C4—32no—
717C2×C3×C4—32no—
718C2×C3×C4—32no—
719C2×C3×C4—32no—
720C2×C3×C4—42no—
721C2×C3×C4—68no—
722C2×C3×C4—62no—
723C2×C3×C4—62no—
724C2×C3×C4—62no—
725C2×C3×C4—124no—
726C2×C3×C4C23×D312yes—
727C2×C3×C4C23×D312yes—
728#67—28no—
729#67—28no—
730#67—44no—
731#67—68no—
732#67—68no—
733#67—68no—
734#67—68no—
735#67—124no—
736#67—124no—
737#67C2×#67116yescomplemented
738C2×Dic3—22no—
739C2×Dic3—22no—
740C2×Dic3—22no—
741C2×Dic3—32no—
742C2×Dic3—32no—
743C2×Dic3—32no—
744C2×Dic3—32no—
745C2×Dic3—32no—
746C2×Dic3—32no—
747C2×Dic3—32no—
748C2×Dic3—32no—
749C2×Dic3—44no—
750C2×Dic3—62no—
751C2×Dic3—62no—
752C2×Dic3—62no—
753C2×Dic3—62no—
754C2×Dic3—68no—
755C2×Dic3—62no—
756C2×Dic3—62no—
757C2×Dic3—68no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—62no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—68no—
765C2×Dic3—68no—
766C2×Dic3—122no—
767C2×Dic3—122no—
768C2×Dic3—122no—
769C2×Dic3—122no—
770C2×Dic3—128no—
771C2×Dic3—124no—
772C2×Dic3C2×#6714yes—
773C2×Dic3C23×D312yes—
774C2×Dic3C23×D312yes—
775C2×Dic3C23×D312yes—
776C2×Dic3C23×D312yes—
777D12—28no—
778C4×D3—28no—
779C4×D3—68no—
780C4×D3—68no—
781C4×D3—124no—
782Dic6—68no—
783Dic6—68no—
784C2×C32—24no—
785C2×C32—42no—
786C2×C32#54614yescomplemented
787C2×C32C23×D411yescharacteristic
788C2×C32C22×#4111yescharacteristic
789C2×C32C2×H(5,𝔽2)11yescharacteristic
790C3×D3—24no—
791C3×D3—24no—
792C3×D3—42no—
793C3×D3—42no—
794C24—31no—
795C24—31no—
796C24—31no—
797C24—31no—
798C24—34no—
799C24—34no—
800C24—64no—
801C24—64no—
802C24—64no—
803C24—64no—
804C24—122no—
805C24—122no—
806C24C2×D3211yescharacteristic
807C24C2×D3211yescharacteristic
808#41—1832no—
809C2×Q8—94no—
810C2×Q8—184no—
811C2×D4—24no—
812C2×D4—34no—
813C2×D4—38no—
814C2×D4—34no—
815C2×D4—34no—
816C2×D4—34no—
817C2×D4—34no—
818C2×D4—64no—
819C2×D4—64no—
820C2×D4—632no—
821C2×D4—64no—
822C2×D4—94no—
823C2×D4—94no—
824C2×D4—94no—
825C2×D4—122no—
826C2×D4—184no—
827C2×D4—184no—
828C2×D4—362no—
829C2×D4C2×D3214yes—
830C22×C4—31no—
831C22×C4—31no—
832C22×C4—31no—
833C22×C4—31no—
834C22×C4—34no—
835C22×C4—34no—
836C22×C4—64no—
837C22×C4—94no—
838C22×C4—94no—
839C22×C4—94no—
840C22×C4—94no—
841C22×C4—91no—
842C22×C4—91no—
843C22×C4—91no—
844C22×C4—91no—
845C22×C4—122no—
846C22×C4—184no—
847C22×C4—184no—
848C22×C4—184no—
849C22×C4—362no—
850C22×C4C2×D3211yescharacteristic
851C4⋊C4—34no—
852C4⋊C4—94no—
853C4⋊C4—94no—
854C4⋊C4—94no—
855C22⋊C4—34no—
856C22⋊C4—34no—
857C22⋊C4—94no—
858C22⋊C4—94no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C22⋊C4—94no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4—94no—
867C42—94no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—28no—
873C22×C3—28no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—24no—
884C22×C3—21no—
885C22×C3—34no—
886C22×C3—34no—
887C22×C3—42no—
888C22×C3—42no—
889C22×C3—48no—
890C22×C3—42no—
891C22×C3—42no—
892C22×C3—42no—
893C22×C3—44no—
894C22×C3—44no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—68no—
900C22×C3—68no—
901C22×C3—62no—
902C22×C3—62no—
903C22×C3—62no—
904C22×C3—62no—
905C22×C3—62no—
906C22×C3—62no—
907C22×C3—84no—
908C22×C3—1216no—
909C22×C3—1216no—
910C22×C3—124no—
911C22×C3—124no—
912C22×C3C2×D3×D414yes—
913C22×C3C2×D3×D412yes—
914C22×C3C2×#23712yes—
915C22×C3#100412yes—
916C22×C3#100412yes—
917C22×C3D3×#4112yes—
918C22×C3C22×#6714yes—
919C22×C3C22×#6712yes—
920C22×C3C24×D311yescharacteristic
921C22×C3C24×D311yescharacteristic
922C2×D3—22no—
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—28no—
927C2×D3—28no—
928C2×D3—22no—
929C2×D3—22no—
930C2×D3—22no—
931C2×D3—22no—
932C2×D3—22no—
933C2×D3—22no—
934C2×D3—416no—
935C2×D3—416no—
936C2×D3—44no—
937C2×D3—44no—
938C2×D3C2×#23714yescomplemented
939C2×D3C22×#6714yes—
940C3×C4—22no—
941C3×C4—22no—
942C3×C4—34no—
943C3×C4—42no—
944C3×C4—62no—
945C3×C4—62no—
946C3×C4—62no—
947Dic3—22no—
948Dic3—22no—
949Dic3—22no—
950Dic3—62no—
951Dic3—62no—
952Dic3—62no—
953Dic3—62no—
954Dic3—62no—
955Dic3—62no—
956Dic3—62no—
957Dic3—62no—
958Dic3—122no—
959Dic3—122no—
960Dic3—122no—
961Dic3—122no—
962Dic3C22×#6714yes—
963C32C2×#54611yescharacteristic, complemented, Sylow
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—34no—
970C23—34no—
971C23—32no—
972C23—32no—
973C23—32no—
974C23—32no—
975C23—68no—
976C23—68no—
977C23—68no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—68no—
988C23—62no—
989C23—124no—
990C23—124no—
991C23—1216no—
992C23—1216no—
993C23D3×#6714yes—
994C23C22×D3212yes—
995C23C22×D3212yes—
996C23C22×D3211yescharacteristic
997Q8—188no—
998D4—28no—
999D4—316no—
1000D4—68no—
1001D4—68no—
1002D4—68no—
1003D4—124no—
1004D4—188no—
1005D4—188no—
1006D4—364no—
1007C2×C4—22no—
1008C2×C4—34no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—68no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—92no—
1018C2×C4—92no—
1019C2×C4—92no—
1020C2×C4—92no—
1021C2×C4—124no—
1022C2×C4—188no—
1023C2×C4—188no—
1024C2×C4—182no—
1025C2×C4—182no—
1026C2×C4—182no—
1027C2×C4—182no—
1028C2×C4—188no—
1029C2×C4—364no—
1030C2×C4C22×D3212yes—
1031C2×C3—24no—
1032C2×C3—24no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—24no—
1036C2×C3—21no—
1037C2×C3—44no—
1038C2×C3—42no—
1039C2×C3—42no—
1040C2×C3—64no—
1041C2×C3—64no—
1042C2×C3—82no—
1043C2×C3—122no—
1044C2×C3—122no—
1045C2×C3#561014yescomplemented
1046C2×C3#580614yescomplemented
1047C2×C3C22×D3×D411yescharacteristic
1048C2×C3C22×#23711yescharacteristic
1049C2×C3C2×#100411yescharacteristic
1050C2×C3C2×#100411yescharacteristic
1051C2×C3C2×D3×#4111yescharacteristic
1052C2×C3C23×#6711yescharacteristic
1053D3—24no—
1054D3—24no—
1055D3—42no—
1056D3—42no—
1057C22—22no—
1058C22—22no—
1059C22—28no—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—34no—
1064C22—34no—
1065C22—44no—
1066C22—62no—
1067C22—62no—
1068C22—62no—
1069C22—68no—
1070C22—68no—
1071C22—62no—
1072C22—62no—
1073C22—62no—
1074C22—62no—
1075C22—62no—
1076C22—62no—
1077C22—62no—
1078C22—1216no—
1079C22—1216no—
1080C22—124no—
1081C22—124no—
1082C22D3×#23712yes—
1083C22#6431312yes—
1084C22C2×D3×#6714yes—
1085C22C2×D3×#6712yes—
1086C22C23×D3211yescharacteristic
1087C4—22no—
1088C4—34no—
1089C4—62no—
1090C4—62no—
1091C4—62no—
1092C4—182no—
1093C4—182no—
1094C4—182no—
1095C4—182no—
1096C3—21no—
1097C3C2×#561011yescharacteristic, complemented
1098C3C2×#580611yescharacteristic, complemented
1099C2—24no—
1100C2—42no—
1101C2—64no—
1102C2—64no—
1103C2—122no—
1104C2—122no—
1105C2#1059515014yesdirect product factor
1106C2C2×D3×#23711yescharacteristic
1107C2C2×#6431311yescharacteristic
1108C2C22×D3×#6711yescharacteristic
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×C3×D3×D4C2semidirect
2. C22×#3805C2semidirect
3. C2×#64144C2semidirect
4. C2×C3×#939C2semidirect
5. C2×#63976C2semidirect
6. C2×#63976C2semidirect
7. C2×Dic3×#67C2semidirect
8. C2×#63970C2semidirect
9. C2×D3×#217C2semidirect
10. C22×(C2×D3)⋊Dic3C2semidirect
11. C2×#63959C2semidirect
12. #10595150C2direct (N × H)
13. C2×#63885C2semidirect
14. C2×#63884C2semidirect
15. C2×#63879C2semidirect
16. C2×#63851C2semidirect
22. C23×C3⋊Dic3C22semidirect
25. C22×C3×#67C22semidirect
26. C22×C3×#67C22semidirect
27. C23×C3×Dic3C22semidirect
29. C2×C3×D3×D4C22semidirect
32. C22×#627C22semidirect
34. C22×#625C22semidirect
35. C22×#625C22semidirect
37. C2×#3805C22semidirect
38. C22×D3×Dic3C22semidirect
39. C22×D3×Dic3C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×#3757C22semidirect
42. C2×#3757C22semidirect
43. C2×#3757C22semidirect
44. #64144C22semidirect
45. C2×#3750C22semidirect
46. C2×#3750C22semidirect
47. C2×C3×#217C22semidirect
48. C3×#939C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. #63976C22semidirect
52. #63976C22semidirect
53. Dic3×#67C22semidirect
54. #63970C22semidirect
55. D3×#217C22semidirect
56. C2×Dic3⋊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. #63959C22semidirect
66. C2×Dic32C22semidirect
67. #63885C22semidirect
68. #63884C22semidirect
69. #63879C22semidirect
70. #63851C22semidirect
74. C22×D3×D4D3semidirect
83. C2×#939D3semidirect
126. C22×C3⋊Dic3C23semidirect
130. C2×C3×#67D4semidirect
133. C2×C3×#67C23semidirect
134. C2×C3×#67C23semidirect
140. C22×C3×Dic3C23semidirect
147. C2×#627C23semidirect
152. C2×#625C23semidirect
153. C2×#625C23semidirect
158. C2×D3×Dic3C23semidirect
159. C2×D3×Dic3C23semidirect
160. C2×D3×Dic3C23semidirect
161. #3757C23semidirect
162. #3757C23semidirect
163. #3757C23semidirect
164. #3750C23semidirect
165. #3750C23semidirect
166. C3×#217C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×Dic3⋊C4C23semidirect
169. Dic3⋊Dic3C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
203. C22×#67C2×D3semidirect
204. C22×#67C2×D3semidirect
211. C23×Dic3C2×D3semidirect
217. C2×D3×D4C2×D3semidirect
249. C2×#217C2×D3semidirect
252. #939C2×D3semidirect
272. C2×(C2×D3)⋊C4C2×D3semidirect
282. C2×Dic3⋊C4C2×D3semidirect
319. C22×C3×D3#41semidirect
339. C3×#67C2×D4semidirect
447. C2×#67#67semidirect
450. C2×#67C22×D3semidirect
451. C2×#67C22×D3semidirect
481. C22×Dic3C22×D3semidirect
518. #217C22×D3semidirect
526. (C2×D3)⋊C4C22×D3semidirect
535. Dic3⋊C4C22×D3semidirect
567. C2×C3×D3C2×#41semidirect
698. C22×D3#237semidirect
737. #67C2×#67semidirect
786. C2×C32#546semidirect
938. C2×D3C2×#237semidirect
963. C32C2×#546semidirect
1045. C2×C3#5610semidirect
1046. C2×C3#5806semidirect
1097. C3C2×#5610semidirect
1098. C3C2×#5806semidirect
1105. C2#10595150direct (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×#38052
C2×#641442
C2×C3×#9392
C2×#639762
C2×Dic3×#672
C2×#639702
C2×D3×#2172
C22×(C2×D3)⋊Dic32
C2×#639592
#105951502
C2×#638852
C2×#638842
C2×#638792
C2×#638512
C2×#58063
C2×#56103