Finite Group Databasebeta

← C2×#10595493 #11902428

Subgroups — C2×#10595493 #11902428

Order 1152.

4131 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64162C211yesmaximal, characteristic, complemented
4C22×C3×#217C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×Dic3×#67C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9#10595493C2116yesmaximal, direct product factor
10C2×#63969C211yesmaximal, characteristic, complemented
11C2×D3×#217C211yesmaximal, characteristic, complemented
12C2×#63964C211yesmaximal, characteristic, complemented
13C2×#63961C211yesmaximal, characteristic, complemented
14C2×#63959C211yesmaximal, characteristic, complemented
15C2×#63958C211yesmaximal, characteristic, complemented
16C2×#63952C211yesmaximal, characteristic, complemented
17C2×#5806—31nomaximal
18C2×#5490—31nomaximal
19C25×C32C2211yescharacteristic
20C24×C3×D3C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic, complemented
23C22×#638C2211yescharacteristic, complemented
24C22×C3×#67—28no—
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic
28C22×C3×#67C2211yescharacteristic
29C22×C3×#67C2218yescomplemented
30C23×C3×Dic3C2211yescharacteristic
31C23×C3×Dic3C2211yescharacteristic, complemented
32C23×C3×Dic3C2211yescharacteristic, complemented
33C22×#627C2211yescharacteristic, complemented
34C22×#626C2211yescharacteristic, complemented
35C22×#626C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic, complemented
37C2×#3804—28no—
38C2×#3804C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic, complemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41#64162C2218yescomplemented
42C2×#3757C2211yescharacteristic
43C2×#3757C2211yescharacteristic, complemented
44C2×#3757C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic
46C2×C3×#217C2211yescharacteristic
47C2×C3×#217C2218yescomplemented
48C2×C3×#217C2211yescharacteristic, complemented
49C2×C3×#217C2211yescharacteristic, complemented
50#63978C2218yescomplemented
51#63977C2218yescomplemented
52Dic3×#67C2218yescomplemented
53#63971C2218yescomplemented
54#63969C2218yescomplemented
55D3×#217C2218yescomplemented
56C2×#3724C2211yescharacteristic, complemented
57C2×#3724C2211yescharacteristic, complemented
58C2×Dic3⋊Dic3C2211yescharacteristic, complemented
59C2×Dic3⋊Dic3C2211yescharacteristic, complemented
60#63964C2218yescomplemented
61C2×#3722C2211yescharacteristic, complemented
62#63961C2218yescomplemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
65C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
66C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
67#63959C2218yescomplemented
68#63958C2218yescomplemented
69C2×Dic32C2211yescharacteristic, complemented
70#63952C2218yescomplemented
71C23×C3×D4—31no—
72C23×#67D311yescharacteristic, complemented
73C22×#237—31no—
74C22×#235—31no—
75C22×C3×C22⋊C4—31no—
76C2×#953—31no—
77C2×#953—31no—
78C2×#953—31no—
79C2×#953—61no—
80C22×#217—31no—
81C22×#217D311yescharacteristic, complemented
82#5806—316no—
83C2×#939—31no—
84C2×#939—31no—
85C2×#938—31no—
86C2×#936—31no—
87C2×#935—31no—
88C2×#935—31no—
89C2×D4×Dic3—31no—
90C2×#930—31no—
91C2×#929—31no—
92C2×C4×#67—31no—
93C2×C4×#67—31no—
94C2×#924—31no—
95C2×#885—31no—
96#5490—316no—
97C2×#884—31no—
98C2×#884—31no—
99C2×#883—31no—
100C2×#882—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⋊D3C2311yescharacteristic
112C23×C3×D3—24no—
113C23×C3×D3—24no—
114C23×C3×D3—42no—
115C23×C3×D3C2311yescharacteristic
116C23×C3×D3C2314yes—
117C23×C3×D3C2311yescharacteristic
118C2×#638—24no—
119C2×#638—24no—
120C2×#638—42no—
121C2×#638C2314yes—
122C2×#638C2314yescomplemented
123C2×#638C2314yescomplemented
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127C2×C3×#67—24no—
128C2×C3×#67—24no—
129C2×C3×#67—232no—
130C2×C3×#67—24no—
131C2×C3×#67D418yescomplemented
132C2×C3×#67C2314yes—
133C2×C3×#67C2314yes—
134C2×C3×#67C2314yes—
135C2×C3×#67C2314yes—
136C22×C3×Dic3—24no—
137C22×C3×Dic3—24no—
138C22×C3×Dic3—42no—
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2314yes—
145C22×C3×Dic3C2311yescharacteristic
146C22×C3×Dic3C2314yescomplemented
147C22×C3×Dic3C2314yescomplemented
148C2×#627—24no—
149C2×#627C2314yescomplemented
150C2×#626—24no—
151C2×#626—42no—
152C2×#626C2314yescomplemented
153C2×#626C2314yescomplemented
154C2×#624—24no—
155C2×#624C2314yescomplemented
156#3804—232no—
157C2×D3×Dic3—24no—
158C2×D3×Dic3—42no—
159C2×D3×Dic3C2314yescomplemented
160C2×D3×Dic3C2314yescomplemented
161#3757C2314yes—
162#3757C2314yescomplemented
163#3757C2314yescomplemented
164C3×#217C2314yes—
165C3×#217C2314yes—
166C3×#217C2314yescomplemented
167C3×#217C2314yescomplemented
168#3724C2314yescomplemented
169#3724C2314yescomplemented
170Dic3⋊Dic3C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yescomplemented
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—38no—
189C22×C3×D4—68no—
190C23×C3×C4—31no—
191C23×C3×C4—31no—
192C23×C3×C4—31no—
193C22×#67—28no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—61no—
203C22×#67—61no—
204C22×#67—61no—
205C22×#67C2×D311yescharacteristic
206C22×#67C2×D311yescharacteristic
207C22×#67C2×D311yescharacteristic
208C22×#67C2×D311yescharacteristic
209C22×#67C2×D318yescomplemented
210C23×Dic3—31no—
211C23×Dic3—31no—
212C23×Dic3C2×D311yescharacteristic
213C23×Dic3C2×D311yescharacteristic, complemented
214C23×Dic3C2×D311yescharacteristic, complemented
215C2×#237—38no—
216C2×#237—68no—
217C2×#235—38no—
218C2×#235—68no—
219C22×D12—31no—
220C22×D12—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3—31no—
225C22×Dic6—31no—
226C22×Dic6—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—38no—
232#953—38no—
233#953—38no—
234#953—38no—
235#953—68no—
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—31no—
245C2×#217—31no—
246C2×#217—38no—
247C2×#217—61no—
248C2×#217—61no—
249C2×#217—61no—
250C2×#217C2×D311yescharacteristic
251C2×#217C2×D311yescharacteristic
252C2×#217C2×D318yescomplemented
253C2×#217C2×D311yescharacteristic, complemented
254C2×#217C2×D311yescharacteristic, complemented
255#939—38no—
256#939—38no—
257#938—38no—
258#936—38no—
259#935—38no—
260#935—38no—
261D4×Dic3—38no—
262#930—38no—
263#929—38no—
264C4×#67—38no—
265C4×#67—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×C4⋊Dic3—31no—
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—31no—
281C2×C4×Dic3—31no—
282C2×C4×Dic3—31no—
283#885—38no—
284#884—38no—
285#884—38no—
286#883—38no—
287#882—38no—
288#67⋊C4—38no—
289D3×C22⋊C4—38no—
290#878—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—28no—
297C23×C32—22no—
298C23×C32—22no—
299C23×C32—28no—
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⋊D3C2412yes—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3—28no—
317C22×C3×D3—22no—
318C22×C3×D3—28no—
319C22×C3×D3—44no—
320C22×C3×D3—416no—
321C22×C3×D3C2×D414yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
324#638—28no—
325#638—28no—
326#638—44no—
327C2×C3⋊Dic3—22no—
328C2×C3⋊Dic3—22no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3C2412yes—
331C2×C3⋊Dic3C2412yes—
332C2×C3⋊Dic3C2412yes—
333C3×#67—28no—
334C3×#67—28no—
335C3×#67—28no—
336C3×#67C2×D4116yescomplemented
337C2×C3×Dic3—22no—
338C2×C3×Dic3—28no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—28no—
344C2×C3×Dic3—44no—
345C2×C3×Dic3C2×D414yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352#627—28no—
353#626—28no—
354#626—44no—
355#624—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—91no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—31no—
373C22×C22⋊C4—91no—
374C24×C3—24no—
375C24×C3—24no—
376C24×C3—24no—
377C24×C3—24no—
378C24×C3—21no—
379C24×C3—21no—
380C24×C3—21no—
381C24×C3—24no—
382C24×C3—31no—
383C24×C3—31no—
384C24×C3—34no—
385C24×C3—44no—
386C24×C3—44no—
387C24×C3—42no—
388C24×C3—42no—
389C24×C3—44no—
390C24×C3—64no—
391C24×C3—64no—
392C24×C3—122no—
393C24×C3C22×D311yescharacteristic
394C24×C3C22×D311yescharacteristic
395C24×C3C22×D314yes—
396C24×C3C22×D314yes—
397C24×C3C22×D311yescharacteristic
398C24×C3C22×D311yescharacteristic
399C24×C3C22×D311yescharacteristic
400C24×C3C22×D311yescharacteristic
401C23×D3—24no—
402C23×D3—24no—
403C23×D3—31no—
404C23×D3—31no—
405C23×D3—42no—
406C23×D3—61no—
407C23×D3C22×D311yescharacteristic
408C23×D3C22×D314yes—
409C23×D3C22×D311yescharacteristic
410C2×C3×D4—38no—
411C2×C3×D4—34no—
412C2×C3×D4—34no—
413C2×C3×D4—34no—
414C2×C3×D4—34no—
415C2×C3×D4—64no—
416C2×C3×D4—632no—
417C2×C3×D4—64no—
418C2×C3×D4—64no—
419C22×C3×C4—31no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—34no—
426C22×C3×C4—34no—
427C22×C3×C4—34no—
428C22×C3×C4—64no—
429C22×C3×C4—64no—
430C22×C3×C4—122no—
431C2×#67—24no—
432C2×#67—24no—
433C2×#67—232no—
434C2×#67—24no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—34no—
442C2×#67—34no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—64no—
450C2×#67—64no—
451C2×#67—124no—
452C2×#67—124no—
453C2×#67—122no—
454C2×#67—122no—
455C2×#67—122no—
456C2×#67—124no—
457C2×#67#6718yescomplemented
458C2×#67C22×D314yes—
459C2×#67C22×D314yes—
460C2×#67C22×D314yes—
461C2×#67C22×D314yes—
462C22×Dic3—24no—
463C22×Dic3—24no—
464C22×Dic3—31no—
465C22×Dic3—31no—
466C22×Dic3—31no—
467C22×Dic3—31no—
468C22×Dic3—31no—
469C22×Dic3—31no—
470C22×Dic3—34no—
471C22×Dic3—34no—
472C22×Dic3—42no—
473C22×Dic3—61no—
474C22×Dic3—61no—
475C22×Dic3—61no—
476C22×Dic3—64no—
477C22×Dic3—122no—
478C22×Dic3C22×D314yes—
479C22×Dic3C22×D311yescharacteristic
480C22×Dic3C22×D311yescharacteristic
481C22×Dic3C22×D311yescharacteristic
482C22×Dic3C22×D311yescharacteristic
483C22×Dic3C22×D311yescharacteristic
484C22×Dic3C22×D311yescharacteristic
485C22×Dic3C22×D314yescomplemented
486C22×Dic3C22×D314yescomplemented
487#237—632no—
488#235—632no—
489C2×D12—34no—
490C2×D12—34no—
491C2×D12—64no—
492C2×D12—122no—
493C2×C4×D3—34no—
494C2×C4×D3—34no—
495C2×C4×D3—34no—
496C2×C4×D3—34no—
497C2×C4×D3—64no—
498C2×C4×D3—64no—
499C2×C4×D3—64no—
500C2×C4×D3—122no—
501C2×Dic6—34no—
502C2×Dic6—34no—
503C2×Dic6—64no—
504C2×Dic6—64no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4—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#217C22×D314yes—
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—
531(C2×D3)⋊C4—34no—
532C4⋊Dic3—34no—
533C4⋊Dic3—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—34no—
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4—34no—
540C4×Dic3—34no—
541C4×Dic3—34no—
542C22×C32—22no—
543C22×C32—28no—
544C22×C32—28no—
545C22×C32—22no—
546C22×C32—22no—
547C22×C32—22no—
548C22×C32—22no—
549C22×C32—22no—
550C22×C32—22no—
551C22×C32—416no—
552C22×C32—44no—
553C22×C32C22×D414yes—
554C22×C32C22×D412yes—
555C22×C32C2×#4112yes—
556C22×C32C2×#4114yescomplemented
557C22×C32H(5,𝔽2)12yes—
558C22×C32C2511yescharacteristic
559C2×C3⋊D3—22no—
560C2×C3⋊D3—22no—
561C2×C3⋊D3—22no—
562C2×C3⋊D3—44no—
563C2×C3×D3—28no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—22no—
568C2×C3×D3—22no—
569C2×C3×D3—416no—
570C2×C3×D3—44no—
571C2×C3×D3C22×D414yes—
572C3⋊Dic3—22no—
573C3⋊Dic3—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3—22no—
580C3×Dic3C22×D414yes—
581C25—31no—
582C25D3211yescharacteristic
583C2×#41—98no—
584C2×#41—188no—
585C22×Q8—91no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—31no—
589C22×D4—31no—
590C22×D4—38no—
591C22×D4—68no—
592C22×D4—91no—
593C22×D4—91no—
594C22×D4—91no—
595C22×D4—91no—
596C22×D4—91no—
597C23×C4—31no—
598C23×C4—31no—
599C23×C4—31no—
600C23×C4—91no—
601C23×C4—91no—
602C23×C4—91no—
603#124—98no—
604#123—98no—
605#123—98no—
606C22⋊Q8—98no—
607#121—98no—
608#121—98no—
609#121—98no—
610#120—98no—
611#120—98no—
612C4×D4—98no—
613C4×D4—98no—
614C2×C4⋊C4—91no—
615C2×C4⋊C4—91no—
616C2×C4⋊C4—91no—
617C2×C4⋊C4—91no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—38no—
623C2×C22⋊C4—98no—
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—91no—
631C2×C22⋊C4—91no—
632C2×C42—91no—
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—24no—
642C23×C3—22no—
643C23×C3—28no—
644C23×C3—28no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—28no—
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—28no—
651C23×C3—22no—
652C23×C3—22no—
653C23×C3—22no—
654C23×C3—22no—
655C23×C3—21no—
656C23×C3—24no—
657C23×C3—24no—
658C23×C3—34no—
659C23×C3—32no—
660C23×C3—32no—
661C23×C3—42no—
662C23×C3—42no—
663C23×C3—42no—
664C23×C3—42no—
665C23×C3—42no—
666C23×C3—48no—
667C23×C3—42no—
668C23×C3—48no—
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—68no—
680C23×C3—62no—
681C23×C3—62no—
682C23×C3—124no—
683C23×C3—1216no—
684C23×C3#23514yescomplemented
685C23×C3D3×D414yes—
686C23×C3#23714yescomplemented
687C23×C3C2×#6714yes—
688C23×C3C23×D312yes—
689C23×C3C23×D312yes—
690C23×C3C23×D312yes—
691C23×C3C23×D312yes—
692C23×C3C23×D312yes—
693C23×C3C23×D312yes—
694C23×C3C23×D311yescharacteristic
695C23×C3C23×D311yescharacteristic
696C22×D3—22no—
697C22×D3—22no—
698C22×D3—22no—
699C22×D3—28no—
700C22×D3—22no—
701C22×D3—22no—
702C22×D3—28no—
703C22×D3—32no—
704C22×D3—32no—
705C22×D3—44no—
706C22×D3—416no—
707C22×D3—62no—
708C22×D3—62no—
709C22×D3—62no—
710C22×D3—62no—
711C22×D3—62no—
712C22×D3—62no—
713C22×D3—62no—
714C22×D3—122no—
715C22×D3—122no—
716C22×D3—122no—
717C22×D3C2×#6714yes—
718C22×D3C23×D312yes—
719C22×D3C23×D312yes—
720C3×D4—316no—
721C3×D4—68no—
722C3×D4—68no—
723C3×D4—68no—
724C2×C3×C4—34no—
725C2×C3×C4—32no—
726C2×C3×C4—32no—
727C2×C3×C4—32no—
728C2×C3×C4—32no—
729C2×C3×C4—32no—
730C2×C3×C4—32no—
731C2×C3×C4—68no—
732C2×C3×C4—62no—
733C2×C3×C4—62no—
734C2×C3×C4—62no—
735C2×C3×C4—62no—
736C2×C3×C4—62no—
737C2×C3×C4—68no—
738C2×C3×C4—124no—
739#67—28no—
740#67—28no—
741#67—28no—
742#67—68no—
743#67—68no—
744#67—68no—
745#67—68no—
746#67—68no—
747#67—128no—
748#67—128no—
749#67—124no—
750#67—124no—
751#67—124no—
752#67—128no—
753#67C2×#67116yescomplemented
754C2×Dic3—22no—
755C2×Dic3—22no—
756C2×Dic3—28no—
757C2×Dic3—22no—
758C2×Dic3—22no—
759C2×Dic3—22no—
760C2×Dic3—28no—
761C2×Dic3—32no—
762C2×Dic3—32no—
763C2×Dic3—32no—
764C2×Dic3—32no—
765C2×Dic3—32no—
766C2×Dic3—32no—
767C2×Dic3—44no—
768C2×Dic3—62no—
769C2×Dic3—62no—
770C2×Dic3—62no—
771C2×Dic3—68no—
772C2×Dic3—62no—
773C2×Dic3—62no—
774C2×Dic3—62no—
775C2×Dic3—62no—
776C2×Dic3—62no—
777C2×Dic3—62no—
778C2×Dic3—122no—
779C2×Dic3—122no—
780C2×Dic3—122no—
781C2×Dic3—124no—
782C2×Dic3C2×#6714yes—
783C2×Dic3C23×D312yes—
784C2×Dic3C23×D312yes—
785C2×Dic3C23×D312yes—
786C2×Dic3C23×D312yes—
787C2×Dic3C23×D312yes—
788C2×Dic3C23×D312yes—
789D12—68no—
790D12—124no—
791C4×D3—68no—
792C4×D3—68no—
793C4×D3—68no—
794C4×D3—124no—
795Dic6—68no—
796Dic6—68no—
797C2×C32—24no—
798C2×C32—24no—
799C2×C32—42no—
800C2×C32#54614yescomplemented
801C2×C32C23×D411yescharacteristic
802C2×C32C22×#4111yescharacteristic
803C2×C32C2×H(5,𝔽2)11yescharacteristic
804C3⋊D3—42no—
805C3×D3—24no—
806C3×D3—42no—
807C24—24no—
808C24—24no—
809C24—31no—
810C24—31no—
811C24—34no—
812C24—42no—
813C24—64no—
814C24—64no—
815C24—91no—
816C24—122no—
817C24C2×D3211yescharacteristic
818C24C2×D3214yes—
819C24C2×D3211yescharacteristic
820C24C2×D3211yescharacteristic
821#41—1832no—
822C2×Q8—94no—
823C2×Q8—184no—
824C2×D4—34no—
825C2×D4—38no—
826C2×D4—34no—
827C2×D4—34no—
828C2×D4—34no—
829C2×D4—64no—
830C2×D4—632no—
831C2×D4—64no—
832C2×D4—64no—
833C2×D4—94no—
834C2×D4—94no—
835C2×D4—94no—
836C2×D4—94no—
837C2×D4—94no—
838C2×D4—184no—
839C2×D4—184no—
840C2×D4—184no—
841C2×D4—362no—
842C2×D4—362no—
843C22×C4—31no—
844C22×C4—34no—
845C22×C4—34no—
846C22×C4—31no—
847C22×C4—31no—
848C22×C4—31no—
849C22×C4—31no—
850C22×C4—31no—
851C22×C4—34no—
852C22×C4—64no—
853C22×C4—64no—
854C22×C4—94no—
855C22×C4—94no—
856C22×C4—94no—
857C22×C4—91no—
858C22×C4—91no—
859C22×C4—91no—
860C22×C4—122no—
861C22×C4—184no—
862C22×C4—184no—
863C22×C4—362no—
864C4⋊C4—94no—
865C4⋊C4—94no—
866C4⋊C4—94no—
867C4⋊C4—94no—
868C22⋊C4—34no—
869C22⋊C4—34no—
870C22⋊C4—34no—
871C22⋊C4—34no—
872C22⋊C4—94no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C22⋊C4—94no—
877C22⋊C4—94no—
878C22⋊C4—94no—
879C22⋊C4—94no—
880C42—94no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—28no—
890C22×C3—28no—
891C22×C3—28no—
892C22×C3—28no—
893C22×C3—24no—
894C22×C3—22no—
895C22×C3—22no—
896C22×C3—22no—
897C22×C3—22no—
898C22×C3—22no—
899C22×C3—22no—
900C22×C3—22no—
901C22×C3—24no—
902C22×C3—22no—
903C22×C3—24no—
904C22×C3—22no—
905C22×C3—21no—
906C22×C3—34no—
907C22×C3—42no—
908C22×C3—42no—
909C22×C3—42no—
910C22×C3—42no—
911C22×C3—48no—
912C22×C3—48no—
913C22×C3—42no—
914C22×C3—42no—
915C22×C3—416no—
916C22×C3—416no—
917C22×C3—48no—
918C22×C3—432no—
919C22×C3—44no—
920C22×C3—44no—
921C22×C3—62no—
922C22×C3—62no—
923C22×C3—68no—
924C22×C3—62no—
925C22×C3—62no—
926C22×C3—62no—
927C22×C3—1216no—
928C22×C3—124no—
929C22×C3C2×#23512yes—
930C22×C3C2×#23514yescomplemented
931C22×C3C2×D3×D414yes—
932C22×C3C2×D3×D412yes—
933C22×C3C2×#23712yes—
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—416no—
948C2×D3—44no—
949C2×D3—62no—
950C2×D3—62no—
951C2×D3—62no—
952C2×D3—62no—
953C2×D3—62no—
954C2×D3—62no—
955C2×D3—122no—
956C2×D3—122no—
957C2×D3—122no—
958C2×D3—124no—
959C2×D3—124no—
960C2×D3—244no—
961C2×D3C22×#6714yes—
962C3×C4—34no—
963C3×C4—62no—
964C3×C4—62no—
965C3×C4—62no—
966C3×C4—62no—
967C3×C4—62no—
968Dic3—22no—
969Dic3—22no—
970Dic3—22no—
971Dic3—22no—
972Dic3—22no—
973Dic3—62no—
974Dic3—62no—
975Dic3—62no—
976Dic3—62no—
977Dic3—62no—
978Dic3—62no—
979Dic3—122no—
980Dic3—122no—
981Dic3—122no—
982Dic3C22×#6714yes—
983C32C2×#54611yescharacteristic, complemented, Sylow
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—28no—
990C23—28no—
991C23—22no—
992C23—22no—
993C23—34no—
994C23—32no—
995C23—32no—
996C23—44no—
997C23—416no—
998C23—68no—
999C23—62no—
1000C23—62no—
1001C23—62no—
1002C23—68no—
1003C23—62no—
1004C23—62no—
1005C23—92no—
1006C23—124no—
1007C23—1216no—
1008C23—182no—
1009C23—182no—
1010C23—182no—
1011C23#380414yescomplemented
1012C23D3×#6714yes—
1013C23C22×D3212yes—
1014C23C22×D3212yes—
1015C23C22×D3212yes—
1016C23C22×D3211yescharacteristic
1017Q8—188no—
1018D4—316no—
1019D4—68no—
1020D4—68no—
1021D4—68no—
1022D4—188no—
1023D4—188no—
1024D4—188no—
1025D4—364no—
1026D4—364no—
1027C2×C4—34no—
1028C2×C4—32no—
1029C2×C4—32no—
1030C2×C4—32no—
1031C2×C4—32no—
1032C2×C4—32no—
1033C2×C4—32no—
1034C2×C4—68no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—68no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—92no—
1042C2×C4—92no—
1043C2×C4—92no—
1044C2×C4—124no—
1045C2×C4—188no—
1046C2×C4—188no—
1047C2×C4—182no—
1048C2×C4—182no—
1049C2×C4—182no—
1050C2×C4—364no—
1051C2×C3—24no—
1052C2×C3—24no—
1053C2×C3—24no—
1054C2×C3—24no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—24no—
1059C2×C3—44no—
1060C2×C3—44no—
1061C2×C3—44no—
1062C2×C3—42no—
1063C2×C3—42no—
1064C2×C3—64no—
1065C2×C3—122no—
1066C2×C3#549014yescomplemented
1067C2×C3#580614yescomplemented
1068C2×C3C22×#23511yescharacteristic
1069C2×C3C22×D3×D411yescharacteristic
1070C2×C3C22×#23711yescharacteristic
1071C2×C3C2×#100411yescharacteristic
1072C2×C3C2×#100411yescharacteristic
1073C2×C3C23×#6711yescharacteristic
1074D3—24no—
1075D3—42no—
1076D3—122no—
1077D3—122no—
1078D3—242no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—28no—
1084C22—28no—
1085C22—22no—
1086C22—22no—
1087C22—22no—
1088C22—34no—
1089C22—416no—
1090C22—44no—
1091C22—62no—
1092C22—62no—
1093C22—68no—
1094C22—62no—
1095C22—62no—
1096C22—62no—
1097C22—1216no—
1098C22—124no—
1099C22—182no—
1100C22—182no—
1101C22—182no—
1102C22—364no—
1103C22C2×#380412yes—
1104C22C2×#380414yescomplemented
1105C22C2×D3×#6714yes—
1106C22C2×D3×#6712yes—
1107C22#6433012yes—
1108C22C23×D3211yescharacteristic
1109C4—34no—
1110C4—62no—
1111C4—62no—
1112C4—62no—
1113C4—62no—
1114C4—62no—
1115C4—182no—
1116C4—182no—
1117C4—182no—
1118C3—21no—
1119C3C2×#549011yescharacteristic, complemented
1120C3C2×#580611yescharacteristic, complemented
1121C2—24no—
1122C2—24no—
1123C2—42no—
1124C2—64no—
1125C2—122no—
1126C2—362no—
1127C2#1059549314yesdirect product factor
1128C2C22×#380411yescharacteristic
1129C2C22×D3×#6711yescharacteristic
1130C2C2×#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×#3804C2semidirect
3. C2×#64162C2semidirect
4. C22×C3×#217C2semidirect
5. C2×#63978C2semidirect
6. C2×#63977C2semidirect
7. C2×Dic3×#67C2semidirect
8. C2×#63971C2semidirect
9. #10595493C2direct (N × H)
10. C2×#63969C2semidirect
11. C2×D3×#217C2semidirect
12. C2×#63964C2semidirect
13. C2×#63961C2semidirect
14. C2×#63959C2semidirect
15. C2×#63958C2semidirect
16. C2×#63952C2semidirect
22. C22×#638C22semidirect
23. C22×#638C22semidirect
29. C22×C3×#67C22semidirect
31. C23×C3×Dic3C22semidirect
32. C23×C3×Dic3C22semidirect
33. C22×#627C22semidirect
34. C22×#626C22semidirect
35. C22×#626C22semidirect
36. C22×#624C22semidirect
38. C2×#3804C22semidirect
39. C22×D3×Dic3C22semidirect
40. C22×D3×Dic3C22semidirect
41. #64162C22semidirect
43. C2×#3757C22semidirect
44. C2×#3757C22semidirect
47. C2×C3×#217C22semidirect
48. C2×C3×#217C22semidirect
49. C2×C3×#217C22semidirect
50. #63978C22semidirect
51. #63977C22semidirect
52. Dic3×#67C22semidirect
53. #63971C22semidirect
54. #63969C22semidirect
55. D3×#217C22semidirect
56. C2×#3724C22semidirect
57. C2×#3724C22semidirect
58. C2×Dic3⋊Dic3C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
60. #63964C22semidirect
61. C2×#3722C22semidirect
62. #63961C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. C2×(C2×D3)⋊Dic3C22semidirect
65. C2×(C2×D3)⋊Dic3C22semidirect
66. C2×(C2×D3)⋊Dic3C22semidirect
67. #63959C22semidirect
68. #63958C22semidirect
69. C2×Dic32C22semidirect
70. #63952C22semidirect
72. C23×#67D3semidirect
81. C22×#217D3semidirect
122. C2×#638C23semidirect
123. C2×#638C23semidirect
131. C2×C3×#67D4semidirect
146. C22×C3×Dic3C23semidirect
147. C22×C3×Dic3C23semidirect
149. C2×#627C23semidirect
152. C2×#626C23semidirect
153. C2×#626C23semidirect
155. C2×#624C23semidirect
159. C2×D3×Dic3C23semidirect
160. C2×D3×Dic3C23semidirect
162. #3757C23semidirect
163. #3757C23semidirect
166. C3×#217C23semidirect
167. C3×#217C23semidirect
168. #3724C23semidirect
169. #3724C23semidirect
170. Dic3⋊Dic3C23semidirect
171. Dic3⋊Dic3C23semidirect
172. #3722C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
209. C22×#67C2×D3semidirect
213. C23×Dic3C2×D3semidirect
214. C23×Dic3C2×D3semidirect
252. C2×#217C2×D3semidirect
253. C2×#217C2×D3semidirect
254. C2×#217C2×D3semidirect
303. C23×C32#41semidirect
336. C3×#67C2×D4semidirect
457. C2×#67#67semidirect
485. C22×Dic3C22×D3semidirect
486. C22×Dic3C22×D3semidirect
524. #217C22×D3semidirect
525. #217C22×D3semidirect
556. C22×C32C2×#41semidirect
684. C23×C3#235semidirect
686. C23×C3#237semidirect
753. #67C2×#67semidirect
800. C2×C32#546semidirect
930. C22×C3C2×#235semidirect
934. C22×C3C2×#237semidirect
983. C32C2×#546semidirect
1011. C23#3804semidirect
1066. C2×C3#5490semidirect
1067. C2×C3#5806semidirect
1104. C22C2×#3804semidirect
1119. C3C2×#5490semidirect
1120. C3C2×#5806semidirect
1127. C2#10595493direct (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×#38042
C2×#641622
C22×C3×#2172
C2×#639782
C2×#639772
C2×Dic3×#672
C2×#639712
#105954932
C2×#639692
C2×D3×#2172
C2×#639642
C2×#639612
C2×#639592
C2×#639582
C2×#639522
C2×#58063
C2×#54903