Finite Group Databasebeta

← C2×#10595494 #11902430

Subgroups — C2×#10595494 #11902430

Order 1152.

4137 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic, complemented
2C22×#3805C211yesmaximal, characteristic, complemented
3C22×#3757C211yesmaximal, characteristic, complemented
4C2×C3×#953C211yesmaximal, characteristic, complemented
5C2×#63980C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C2×Dic3×#67C211yesmaximal, characteristic, complemented
9C2×#63970C211yesmaximal, characteristic, complemented
10C2×#63970C211yesmaximal, characteristic, complemented
11#10595494C2116yesmaximal, direct product factor
12C2×#63969C211yesmaximal, characteristic, complemented
13C2×D3×#217C211yesmaximal, characteristic, complemented
14C2×#63964C211yesmaximal, characteristic, complemented
15C2×#63962C211yesmaximal, characteristic, complemented
16C2×#63959C211yesmaximal, characteristic, complemented
17C2×#5806—31nomaximal
18C2×#5591—31nomaximal
19C25×C32C2211yescharacteristic
20C24×C3×D3C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic, complemented
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C3×#67—28no—
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic
28C22×C3×#67C2211yescharacteristic
29C22×C3×#67C2218yescomplemented
30C22×C3×#67C2211yescharacteristic, complemented
31C22×C3×#67C2211yescharacteristic, complemented
32C23×C3×Dic3C2211yescharacteristic
33C22×#627C2211yescharacteristic, complemented
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
42C2×#3757C2211yescharacteristic
43C2×#3757C2218yescomplemented
44C2×#3757C2211yescharacteristic, complemented
45C2×#3757C2211yescharacteristic, complemented
46C3×#953C2218yescomplemented
47C2×C3×#217C2211yescharacteristic
48C2×C3×#217C2211yescharacteristic, complemented
49C2×C3×#217C2211yescharacteristic, complemented
50#63980C2218yescomplemented
51#63976C2218yescomplemented
52#67⋊Dic3C2218yescomplemented
53Dic3×#67C2218yescomplemented
54#63970C2218yescomplemented
55#63970C2218yescomplemented
56#63969C2218yescomplemented
57D3×#217C2218yescomplemented
58C2×#3724C2211yescharacteristic, complemented
59C2×Dic3⋊Dic3C2211yescharacteristic, complemented
60C2×Dic3⋊Dic3C2211yescharacteristic, complemented
61C2×Dic3⋊Dic3C2211yescharacteristic, complemented
62#63964C2218yescomplemented
63#63962C2218yescomplemented
64C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
65C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
66C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
67C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
68C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
69#63959C2218yescomplemented
70C2×Dic32C2211yescharacteristic, complemented
71C23×C3×D4—31no—
72C23×#67D311yescharacteristic, complemented
73C22×#237—31no—
74C22×#237—31no—
75C2×C3×#120—31no—
76C2×#953—31no—
77C2×#953D311yescharacteristic, complemented
78C22×#217—31no—
79C22×#217—31no—
80C22×#217—31no—
81C22×#217—61no—
82#5806—316no—
83C2×#939—31no—
84C2×#939—31no—
85C2×#939—31no—
86C2×#939—31no—
87C2×#938—31no—
88C2×#938—31no—
89C2×#937—31no—
90C2×#936—31no—
91C2×#935—31no—
92C2×#935—31no—
93C2×D4×Dic3—31no—
94C2×D4×Dic3—31no—
95C2×C4×#67—31no—
96C2×#924—31no—
97#5591—316no—
98C2×#886—31no—
99C2×#885—31no—
100C2×#883—31no—
101C2×#67⋊C4—31no—
102C2×D3×C22⋊C4—31no—
103C2×#878—31no—
104C24×C32—24no—
105C24×C32—24no—
106C24×C32—42no—
107C24×C32C2311yescharacteristic
108C24×C32C2314yes—
109C24×C32C2311yescharacteristic
110C24×C32C2311yescharacteristic
111C23×C3×D3—24no—
112C23×C3×D3—24no—
113C23×C3×D3—42no—
114C23×C3×D3C2311yescharacteristic
115C23×C3×D3C2311yescharacteristic
116C23×C3×D3C2314yes—
117C23×C3×D3C2311yescharacteristic
118C22×C3⋊Dic3—24no—
119C22×C3⋊Dic3—42no—
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2314yescomplemented
125C22×C3⋊Dic3C2314yescomplemented
126C2×C3×#67—24no—
127C2×C3×#67—24no—
128C2×C3×#67—24no—
129C2×C3×#67—24no—
130C2×C3×#67—232no—
131C2×C3×#67—24no—
132C2×C3×#67—42no—
133C2×C3×#67D418yescomplemented
134C2×C3×#67C2314yes—
135C2×C3×#67C2314yes—
136C2×C3×#67C2314yes—
137C2×C3×#67C2314yes—
138C2×C3×#67C2314yes—
139C2×C3×#67C2314yescomplemented
140C2×C3×#67C2314yescomplemented
141C22×C3×Dic3—24no—
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2311yescharacteristic
145C22×C3×Dic3C2311yescharacteristic
146C22×C3×Dic3C2314yes—
147C22×C3×Dic3C2311yescharacteristic
148C2×#627—24no—
149C2×#627C2314yescomplemented
150C2×#625—24no—
151C2×#625—42no—
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#3757C2314yes—
162#3757C2314yes—
163#3757C2314yescomplemented
164#3757C2314yescomplemented
165C3×#217C2314yes—
166C3×#217C2314yescomplemented
167C3×#217C2314yescomplemented
168#3724C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170Dic3⋊Dic3C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172(C2×D3)⋊Dic3C2314yescomplemented
173(C2×D3)⋊Dic3C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—21no—
180C25×C3—31no—
181C25×C3C2×D311yescharacteristic
182C25×C3C2×D311yescharacteristic
183C24×D3C2×D311yescharacteristic
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C22×C3×D4—31no—
189C22×C3×D4—38no—
190C22×C3×D4—31no—
191C22×C3×D4—31no—
192C22×C3×D4—68no—
193C23×C3×C4—31no—
194C22×#67—28no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67C2×D311yescharacteristic
200C22×#67C2×D311yescharacteristic
201C22×#67C2×D311yescharacteristic
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic
204C22×#67C2×D318yescomplemented
205C22×#67C2×D311yescharacteristic, complemented
206C22×#67C2×D311yescharacteristic, complemented
207C23×Dic3—31no—
208C23×Dic3—31no—
209C23×Dic3—31no—
210C23×Dic3—31no—
211C23×Dic3—31no—
212C23×Dic3—31no—
213C23×Dic3—31no—
214C23×Dic3—61no—
215C23×Dic3—61no—
216C23×Dic3C2×D311yescharacteristic
217C2×#237—38no—
218C2×#237—38no—
219C2×#237—68no—
220C2×#237—68no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×Dic6—31no—
225C22×Dic6—31no—
226C3×#120—38no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230#953—38no—
231#953C2×D318yescomplemented
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—38no—
241C2×#217—38no—
242C2×#217—31no—
243C2×#217—31no—
244C2×#217—31no—
245C2×#217—31no—
246C2×#217—31no—
247C2×#217—38no—
248C2×#217—61no—
249C2×#217—61no—
250C2×#217—61no—
251C2×#217—61no—
252C2×#217—68no—
253C2×#217C2×D311yescharacteristic
254C2×#217C2×D311yescharacteristic, complemented
255C2×#217C2×D311yescharacteristic, complemented
256#939—38no—
257#939—38no—
258#939—38no—
259#939—38no—
260#938—38no—
261#938—38no—
262#937—38no—
263#936—38no—
264#935—38no—
265#935—38no—
266D4×Dic3—38no—
267D4×Dic3—38no—
268C4×#67—38no—
269C2×(C2×D3)⋊C4—31no—
270C2×(C2×D3)⋊C4—31no—
271C2×(C2×D3)⋊C4—31no—
272C2×(C2×D3)⋊C4—31no—
273C2×(C2×D3)⋊C4—31no—
274C2×C4⋊Dic3—31no—
275C2×C4⋊Dic3—31no—
276C2×C4⋊Dic3—31no—
277#924—38no—
278C2×Dic3⋊C4—31no—
279C2×Dic3⋊C4—31no—
280C2×Dic3⋊C4—31no—
281C2×Dic3⋊C4—31no—
282C2×Dic3⋊C4—31no—
283C2×C4×Dic3—31no—
284C2×C4×Dic3—31no—
285#886—38no—
286#885—38no—
287#883—38no—
288#67⋊C4—38no—
289D3×C22⋊C4—38no—
290#878—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—28no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32—28no—
298C23×C32—22no—
299C23×C32—22no—
300C23×C32—44no—
301C23×C32—416no—
302C23×C32C2×D414yes—
303C23×C32#4114yescomplemented
304C23×C32C2412yes—
305C23×C32C2412yes—
306C23×C32C2412yes—
307C23×C32C2411yescharacteristic
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—28no—
315C22×C3×D3—22no—
316C22×C3×D3—22no—
317C22×C3×D3—28no—
318C22×C3×D3—44no—
319C22×C3×D3—416no—
320C22×C3×D3C2×D414yes—
321C22×C3×D3C2412yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
324C2×C3⋊Dic3—22no—
325C2×C3⋊Dic3—28no—
326C2×C3⋊Dic3—22no—
327C2×C3⋊Dic3—22no—
328C2×C3⋊Dic3—22no—
329C2×C3⋊Dic3—44no—
330C2×C3⋊Dic3C2412yes—
331C2×C3⋊Dic3C2412yes—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C3×#67—28no—
335C3×#67—28no—
336C3×#67—28no—
337C3×#67—28no—
338C3×#67—28no—
339C3×#67—44no—
340C3×#67C2×D4116yescomplemented
341C2×C3×Dic3—22no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—22no—
344C2×C3×Dic3—22no—
345C2×C3×Dic3—28no—
346C2×C3×Dic3C2×D414yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352#627—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—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—31no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—28no—
375C24×C3—24no—
376C24×C3—24no—
377C24×C3—24no—
378C24×C3—24no—
379C24×C3—21no—
380C24×C3—21no—
381C24×C3—24no—
382C24×C3—21no—
383C24×C3—31no—
384C24×C3—31no—
385C24×C3—31no—
386C24×C3—34no—
387C24×C3—44no—
388C24×C3—42no—
389C24×C3—42no—
390C24×C3—44no—
391C24×C3—64no—
392C24×C3—64no—
393C24×C3—122no—
394C24×C3C22×D311yescharacteristic
395C24×C3C22×D311yescharacteristic
396C24×C3C22×D314yes—
397C24×C3C22×D314yes—
398C24×C3C22×D311yescharacteristic
399C24×C3C22×D311yescharacteristic
400C24×C3C22×D311yescharacteristic
401C24×C3C22×D311yescharacteristic
402C23×D3—24no—
403C23×D3—24no—
404C23×D3—42no—
405C23×D3C22×D311yescharacteristic
406C23×D3C22×D311yescharacteristic
407C23×D3C22×D314yes—
408C23×D3C22×D311yescharacteristic
409C2×C3×D4—38no—
410C2×C3×D4—34no—
411C2×C3×D4—34no—
412C2×C3×D4—34no—
413C2×C3×D4—34no—
414C2×C3×D4—34no—
415C2×C3×D4—34no—
416C2×C3×D4—34no—
417C2×C3×D4—64no—
418C2×C3×D4—632no—
419C2×C3×D4—64no—
420C2×C3×D4—64no—
421C2×C3×D4—64no—
422C2×C3×D4—64no—
423C2×C3×D4—122no—
424C22×C3×C4—31no—
425C22×C3×C4—31no—
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—31no—
429C22×C3×C4—34no—
430C22×C3×C4—64no—
431C2×#67—24no—
432C2×#67—24no—
433C2×#67—24no—
434C2×#67—24no—
435C2×#67—232no—
436C2×#67—24no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—42no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—122no—
445C2×#67—122no—
446C2×#67#6718yescomplemented
447C2×#67C22×D314yes—
448C2×#67C22×D314yes—
449C2×#67C22×D314yes—
450C2×#67C22×D314yes—
451C2×#67C22×D314yes—
452C2×#67C22×D314yescomplemented
453C2×#67C22×D314yescomplemented
454C22×Dic3—24no—
455C22×Dic3—34no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—31no—
460C22×Dic3—31no—
461C22×Dic3—31no—
462C22×Dic3—31no—
463C22×Dic3—31no—
464C22×Dic3—34no—
465C22×Dic3—34no—
466C22×Dic3—34no—
467C22×Dic3—34no—
468C22×Dic3—34no—
469C22×Dic3—34no—
470C22×Dic3—61no—
471C22×Dic3—61no—
472C22×Dic3—61no—
473C22×Dic3—61no—
474C22×Dic3—64no—
475C22×Dic3—64no—
476C22×Dic3—64no—
477C22×Dic3—64no—
478C22×Dic3—64no—
479C22×Dic3—64no—
480C22×Dic3—124no—
481C22×Dic3—122no—
482C22×Dic3—122no—
483C22×Dic3—122no—
484C22×Dic3—124no—
485C22×Dic3C22×D314yes—
486C22×Dic3C22×D311yescharacteristic
487C22×Dic3C22×D311yescharacteristic
488C22×Dic3C22×D311yescharacteristic
489C22×Dic3C22×D311yescharacteristic
490C22×Dic3C22×D311yescharacteristic
491#237—632no—
492#237—632no—
493C2×C4×D3—34no—
494C2×C4×D3—34no—
495C2×C4×D3—34no—
496C2×C4×D3—64no—
497C2×C4×D3—64no—
498C2×C4×D3—122no—
499C2×Dic6—34no—
500C2×Dic6—34no—
501C2×Dic6—64no—
502C2×Dic6—64no—
503C3×C22⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4—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—34no—
516#217—34no—
517#217—34no—
518#217—34no—
519#217—64no—
520#217—64no—
521#217—64no—
522#217—64no—
523#217C22×D314yes—
524#217C22×D314yescomplemented
525#217C22×D314yescomplemented
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—34no—
531C4⋊Dic3—34no—
532C4⋊Dic3—34no—
533C4⋊Dic3—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—34no—
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539C4×Dic3—34no—
540C4×Dic3—34no—
541C22×C32—28no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—28no—
546C22×C32—22no—
547C22×C32—22no—
548C22×C32—22no—
549C22×C32—22no—
550C22×C32—416no—
551C22×C32—44no—
552C22×C32C22×D414yes—
553C22×C32C22×D412yes—
554C22×C32C2×#4112yes—
555C22×C32C2×#4114yescomplemented
556C22×C32H(5,𝔽2)12yes—
557C22×C32C2511yescharacteristic
558C2×C3×D3—28no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—416no—
568C2×C3×D3—44no—
569C2×C3×D3—44no—
570C2×C3×D3C22×D414yes—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3⋊Dic3—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3C22×D414yes—
580C25—31no—
581C25D3211yescharacteristic
582C2×#41—98no—
583C2×#41—188no—
584C22×Q8—91no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—31no—
589C22×D4—31no—
590C22×D4—31no—
591C22×D4—38no—
592C22×D4—31no—
593C22×D4—68no—
594C22×D4—91no—
595C22×D4—91no—
596C23×C4—31no—
597C23×C4—91no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601C23×C4—91no—
602#124—98no—
603#123—98no—
604#123—98no—
605C22⋊Q8—98no—
606#121—98no—
607#121—98no—
608#121—98no—
609#120—38no—
610#120—98no—
611C4×D4—98no—
612C4×D4—98no—
613C2×C4⋊C4—91no—
614C2×C4⋊C4—91no—
615C2×C4⋊C4—91no—
616C2×C4⋊C4—91no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—98no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C22⋊C4—98no—
631C2×C42—91no—
632C23×C3—24no—
633C23×C3—24no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—22no—
641C23×C3—22no—
642C23×C3—24no—
643C23×C3—216no—
644C23×C3—28no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—22no—
648C23×C3—28no—
649C23×C3—28no—
650C23×C3—22no—
651C23×C3—22no—
652C23×C3—28no—
653C23×C3—22no—
654C23×C3—22no—
655C23×C3—22no—
656C23×C3—22no—
657C23×C3—21no—
658C23×C3—24no—
659C23×C3—24no—
660C23×C3—34no—
661C23×C3—32no—
662C23×C3—32no—
663C23×C3—32no—
664C23×C3—42no—
665C23×C3—42no—
666C23×C3—48no—
667C23×C3—42no—
668C23×C3—42no—
669C23×C3—44no—
670C23×C3—44no—
671C23×C3—416no—
672C23×C3—416no—
673C23×C3—48no—
674C23×C3—432no—
675C23×C3—68no—
676C23×C3—62no—
677C23×C3—62no—
678C23×C3—62no—
679C23×C3—62no—
680C23×C3—62no—
681C23×C3—68no—
682C23×C3—62no—
683C23×C3—62no—
684C23×C3—62no—
685C23×C3—124no—
686C23×C3—1216no—
687C23×C3D3×D414yes—
688C23×C3#23714yescomplemented
689C23×C3#23714yescomplemented
690C23×C3C2×#6714yes—
691C23×C3C23×D312yes—
692C23×C3C23×D312yes—
693C23×C3C23×D312yes—
694C23×C3C23×D312yes—
695C23×C3C23×D312yes—
696C23×C3C23×D312yes—
697C23×C3C23×D311yescharacteristic
698C23×C3C23×D311yescharacteristic
699C22×D3—22no—
700C22×D3—22no—
701C22×D3—22no—
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—28no—
705C22×D3—22no—
706C22×D3—22no—
707C22×D3—22no—
708C22×D3—28no—
709C22×D3—44no—
710C22×D3—416no—
711C22×D3C2×#6714yes—
712C22×D3C23×D312yes—
713C22×D3C23×D312yes—
714C22×D3C23×D312yes—
715C3×D4—316no—
716C3×D4—68no—
717C3×D4—68no—
718C3×D4—68no—
719C3×D4—68no—
720C3×D4—68no—
721C3×D4—124no—
722C2×C3×C4—34no—
723C2×C3×C4—32no—
724C2×C3×C4—32no—
725C2×C3×C4—32no—
726C2×C3×C4—32no—
727C2×C3×C4—32no—
728C2×C3×C4—68no—
729C2×C3×C4—62no—
730C2×C3×C4—62no—
731C2×C3×C4—62no—
732C2×C3×C4—62no—
733#67—28no—
734#67—28no—
735#67—28no—
736#67—28no—
737#67—28no—
738#67—44no—
739#67—68no—
740#67—68no—
741#67—124no—
742#67—124no—
743#67C2×#67116yescomplemented
744C2×Dic3—22no—
745C2×Dic3—22no—
746C2×Dic3—22no—
747C2×Dic3—22no—
748C2×Dic3—28no—
749C2×Dic3—32no—
750C2×Dic3—32no—
751C2×Dic3—32no—
752C2×Dic3—32no—
753C2×Dic3—32no—
754C2×Dic3—32no—
755C2×Dic3—32no—
756C2×Dic3—32no—
757C2×Dic3—62no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—68no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—68no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—62no—
768C2×Dic3—62no—
769C2×Dic3—62no—
770C2×Dic3—62no—
771C2×Dic3—68no—
772C2×Dic3—68no—
773C2×Dic3—122no—
774C2×Dic3—122no—
775C2×Dic3—128no—
776C2×Dic3—122no—
777C2×Dic3—122no—
778C2×Dic3—124no—
779C2×Dic3—124no—
780C2×Dic3—124no—
781C2×Dic3—128no—
782C2×Dic3C2×#6714yes—
783C2×Dic3C23×D312yes—
784C2×Dic3C23×D312yes—
785C2×Dic3C23×D312yes—
786C2×Dic3C23×D312yes—
787C2×Dic3C23×D312yes—
788C4×D3—68no—
789C4×D3—68no—
790C4×D3—124no—
791Dic6—68no—
792Dic6—68no—
793C2×C32—24no—
794C2×C32—24no—
795C2×C32—42no—
796C2×C32#54614yescomplemented
797C2×C32C23×D411yescharacteristic
798C2×C32C22×#4111yescharacteristic
799C2×C32C2×H(5,𝔽2)11yescharacteristic
800C3×D3—24no—
801C3×D3—42no—
802C3×D3—42no—
803C24—24no—
804C24—24no—
805C24—31no—
806C24—31no—
807C24—31no—
808C24—34no—
809C24—42no—
810C24—64no—
811C24—64no—
812C24—122no—
813C24C2×D3211yescharacteristic
814C24C2×D3214yes—
815C24C2×D3211yescharacteristic
816C24C2×D3211yescharacteristic
817#41—1832no—
818C2×Q8—94no—
819C2×Q8—184no—
820C2×D4—34no—
821C2×D4—38no—
822C2×D4—34no—
823C2×D4—34no—
824C2×D4—34no—
825C2×D4—34no—
826C2×D4—34no—
827C2×D4—34no—
828C2×D4—64no—
829C2×D4—632no—
830C2×D4—64no—
831C2×D4—64no—
832C2×D4—64no—
833C2×D4—64no—
834C2×D4—94no—
835C2×D4—94no—
836C2×D4—122no—
837C2×D4—184no—
838C2×D4—362no—
839C22×C4—31no—
840C22×C4—34no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—31no—
844C22×C4—31no—
845C22×C4—64no—
846C22×C4—94no—
847C22×C4—94no—
848C22×C4—94no—
849C22×C4—94no—
850C22×C4—91no—
851C22×C4—91no—
852C22×C4—91no—
853C22×C4—91no—
854C22×C4—94no—
855C22×C4—184no—
856C22×C4—184no—
857C22×C4—184no—
858C22×C4—362no—
859C22×C4—362no—
860C4⋊C4—94no—
861C4⋊C4—94no—
862C4⋊C4—94no—
863C4⋊C4—94no—
864C22⋊C4—34no—
865C22⋊C4—34no—
866C22⋊C4—34no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C42—94no—
877C22×C3—24no—
878C22×C3—24no—
879C22×C3—216no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—22no—
888C22×C3—28no—
889C22×C3—28no—
890C22×C3—28no—
891C22×C3—28no—
892C22×C3—24no—
893C22×C3—22no—
894C22×C3—22no—
895C22×C3—22no—
896C22×C3—22no—
897C22×C3—22no—
898C22×C3—22no—
899C22×C3—22no—
900C22×C3—24no—
901C22×C3—24no—
902C22×C3—22no—
903C22×C3—22no—
904C22×C3—21no—
905C22×C3—34no—
906C22×C3—42no—
907C22×C3—42no—
908C22×C3—48no—
909C22×C3—42no—
910C22×C3—42no—
911C22×C3—416no—
912C22×C3—416no—
913C22×C3—432no—
914C22×C3—48no—
915C22×C3—44no—
916C22×C3—44no—
917C22×C3—62no—
918C22×C3—62no—
919C22×C3—68no—
920C22×C3—62no—
921C22×C3—62no—
922C22×C3—62no—
923C22×C3—62no—
924C22×C3—62no—
925C22×C3—62no—
926C22×C3—1216no—
927C22×C3—124no—
928C22×C3—124no—
929C22×C3C2×D3×D414yes—
930C22×C3C2×D3×D412yes—
931C22×C3C2×#23712yes—
932C22×C3C2×#23712yes—
933C22×C3C2×#23714yescomplemented
934C22×C3C2×#23714yescomplemented
935C22×C3#100412yes—
936C22×C3#100412yes—
937C22×C3C22×#6714yes—
938C22×C3C22×#6712yes—
939C22×C3C24×D311yescharacteristic
940C22×C3C24×D311yescharacteristic
941C2×D3—22no—
942C2×D3—22no—
943C2×D3—28no—
944C2×D3—22no—
945C2×D3—22no—
946C2×D3—22no—
947C2×D3—22no—
948C2×D3—22no—
949C2×D3—22no—
950C2×D3—416no—
951C2×D3—44no—
952C2×D3—44no—
953C2×D3C22×#6714yes—
954C3×C4—34no—
955C3×C4—62no—
956C3×C4—62no—
957C3×C4—62no—
958C3×C4—62no—
959Dic3—22no—
960Dic3—22no—
961Dic3—22no—
962Dic3—22no—
963Dic3—62no—
964Dic3—62no—
965Dic3—62no—
966Dic3—62no—
967Dic3—62no—
968Dic3—62no—
969Dic3—62no—
970Dic3—62no—
971Dic3—122no—
972Dic3—122no—
973Dic3—122no—
974Dic3—122no—
975Dic3C22×#6714yes—
976C32C2×#54611yescharacteristic, complemented, Sylow
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—28no—
983C23—28no—
984C23—22no—
985C23—22no—
986C23—34no—
987C23—32no—
988C23—32no—
989C23—32no—
990C23—44no—
991C23—416no—
992C23—68no—
993C23—62no—
994C23—62no—
995C23—62no—
996C23—62no—
997C23—68no—
998C23—62no—
999C23—62no—
1000C23—62no—
1001C23—62no—
1002C23—124no—
1003C23—1216no—
1004C23#380514yescomplemented
1005C23D3×#6714yes—
1006C23C22×D3212yes—
1007C23C22×D3212yes—
1008C23C22×D3212yes—
1009C23C22×D3211yescharacteristic
1010Q8—188no—
1011D4—316no—
1012D4—68no—
1013D4—68no—
1014D4—68no—
1015D4—68no—
1016D4—68no—
1017D4—124no—
1018D4—188no—
1019D4—364no—
1020C2×C4—34no—
1021C2×C4—32no—
1022C2×C4—32no—
1023C2×C4—32no—
1024C2×C4—32no—
1025C2×C4—32no—
1026C2×C4—68no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—92no—
1032C2×C4—92no—
1033C2×C4—92no—
1034C2×C4—92no—
1035C2×C4—188no—
1036C2×C4—188no—
1037C2×C4—182no—
1038C2×C4—182no—
1039C2×C4—188no—
1040C2×C4—182no—
1041C2×C4—182no—
1042C2×C4—364no—
1043C2×C4—364no—
1044C2×C3—28no—
1045C2×C3—24no—
1046C2×C3—24no—
1047C2×C3—24no—
1048C2×C3—24no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—24no—
1053C2×C3—44no—
1054C2×C3—44no—
1055C2×C3—42no—
1056C2×C3—42no—
1057C2×C3—64no—
1058C2×C3—122no—
1059C2×C3—122no—
1060C2×C3#559114yescomplemented
1061C2×C3#580614yescomplemented
1062C2×C3C22×D3×D411yescharacteristic
1063C2×C3C22×#23711yescharacteristic
1064C2×C3C22×#23711yescharacteristic
1065C2×C3C2×#100411yescharacteristic
1066C2×C3C2×#100411yescharacteristic
1067C2×C3C23×#6711yescharacteristic
1068D3—24no—
1069D3—42no—
1070D3—42no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—28no—
1076C22—28no—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—34no—
1081C22—416no—
1082C22—44no—
1083C22—62no—
1084C22—62no—
1085C22—68no—
1086C22—62no—
1087C22—62no—
1088C22—62no—
1089C22—62no—
1090C22—62no—
1091C22—62no—
1092C22—1216no—
1093C22—124no—
1094C22—124no—
1095C22C2×#380512yes—
1096C22C2×#380514yescomplemented
1097C22C2×D3×#6714yes—
1098C22C2×D3×#6712yes—
1099C22#6433012yes—
1100C22C23×D3211yescharacteristic
1101C4—34no—
1102C4—62no—
1103C4—62no—
1104C4—62no—
1105C4—62no—
1106C4—182no—
1107C4—182no—
1108C4—182no—
1109C4—182no—
1110C3—21no—
1111C3C2×#559111yescharacteristic, complemented
1112C3C2×#580611yescharacteristic, complemented
1113C2—24no—
1114C2—24no—
1115C2—42no—
1116C2—64no—
1117C2—122no—
1118C2—122no—
1119C2#1059549414yesdirect product factor
1120C2C22×#380511yescharacteristic
1121C2C22×D3×#6711yescharacteristic
1122C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC25×C32C22
socleC23×C32C24
hypercenterC25D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C23×C3×#67C2semidirect
2. C22×#3805C2semidirect
3. C22×#3757C2semidirect
4. C2×C3×#953C2semidirect
5. C2×#63980C2semidirect
6. C2×#63976C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. C2×Dic3×#67C2semidirect
9. C2×#63970C2semidirect
10. C2×#63970C2semidirect
11. #10595494C2direct (N × H)
12. C2×#63969C2semidirect
13. C2×D3×#217C2semidirect
14. C2×#63964C2semidirect
15. C2×#63962C2semidirect
16. C2×#63959C2semidirect
21. C23×C3⋊Dic3C22semidirect
22. C23×C3⋊Dic3C22semidirect
29. C22×C3×#67C22semidirect
30. C22×C3×#67C22semidirect
31. C22×C3×#67C22semidirect
33. C22×#627C22semidirect
34. C22×#625C22semidirect
35. C22×#625C22semidirect
37. C2×#3805C22semidirect
38. C22×D3×Dic3C22semidirect
39. C22×D3×Dic3C22semidirect
40. C22×D3×Dic3C22semidirect
43. C2×#3757C22semidirect
44. C2×#3757C22semidirect
45. C2×#3757C22semidirect
46. C3×#953C22semidirect
48. C2×C3×#217C22semidirect
49. C2×C3×#217C22semidirect
50. #63980C22semidirect
51. #63976C22semidirect
52. #67⋊Dic3C22semidirect
53. Dic3×#67C22semidirect
54. #63970C22semidirect
55. #63970C22semidirect
56. #63969C22semidirect
57. D3×#217C22semidirect
58. C2×#3724C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
60. C2×Dic3⋊Dic3C22semidirect
61. C2×Dic3⋊Dic3C22semidirect
62. #63964C22semidirect
63. #63962C22semidirect
64. C2×(C2×D3)⋊Dic3C22semidirect
65. C2×(C2×D3)⋊Dic3C22semidirect
66. C2×(C2×D3)⋊Dic3C22semidirect
67. C2×(C2×D3)⋊Dic3C22semidirect
68. C2×(C2×D3)⋊Dic3C22semidirect
69. #63959C22semidirect
70. C2×Dic32C22semidirect
72. C23×#67D3semidirect
77. C2×#953D3semidirect
124. C22×C3⋊Dic3C23semidirect
125. C22×C3⋊Dic3C23semidirect
133. C2×C3×#67D4semidirect
139. C2×C3×#67C23semidirect
140. C2×C3×#67C23semidirect
149. C2×#627C23semidirect
152. C2×#625C23semidirect
153. C2×#625C23semidirect
158. C2×D3×Dic3C23semidirect
159. C2×D3×Dic3C23semidirect
160. C2×D3×Dic3C23semidirect
163. #3757C23semidirect
164. #3757C23semidirect
166. C3×#217C23semidirect
167. C3×#217C23semidirect
168. #3724C23semidirect
169. Dic3⋊Dic3C23semidirect
170. Dic3⋊Dic3C23semidirect
171. Dic3⋊Dic3C23semidirect
172. (C2×D3)⋊Dic3C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
204. C22×#67C2×D3semidirect
205. C22×#67C2×D3semidirect
206. C22×#67C2×D3semidirect
231. #953C2×D3semidirect
254. C2×#217C2×D3semidirect
255. C2×#217C2×D3semidirect
303. C23×C32#41semidirect
340. C3×#67C2×D4semidirect
446. C2×#67#67semidirect
452. C2×#67C22×D3semidirect
453. C2×#67C22×D3semidirect
524. #217C22×D3semidirect
525. #217C22×D3semidirect
555. C22×C32C2×#41semidirect
688. C23×C3#237semidirect
689. C23×C3#237semidirect
743. #67C2×#67semidirect
796. C2×C32#546semidirect
933. C22×C3C2×#237semidirect
934. C22×C3C2×#237semidirect
976. C32C2×#546semidirect
1004. C23#3805semidirect
1060. C2×C3#5591semidirect
1061. C2×C3#5806semidirect
1096. C22C2×#3805semidirect
1111. C3C2×#5591semidirect
1112. C3C2×#5806semidirect
1119. C2#10595494direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×#38052
C22×#37572
C2×C3×#9532
C2×#639802
C2×#639762
C2×#67⋊Dic32
C2×Dic3×#672
C2×#639702
#105954942
C2×#639692
C2×D3×#2172
C2×#639642
C2×#639622
C2×#639592
C2×#58063
C2×#55913