Finite Group Databasebeta

← #11810333

Subgroups — #11810333

Order 1152.

1771 conjugacy classes of subgroups.

The subgroup lattice has 1099 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
4C2×D3×#217C211yesmaximal, characteristic, complemented
5C3×#5222C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591717C211yesmaximal, characteristic, complemented
8#10591713C211yesmaximal, characteristic, complemented
9#10591708C211yesmaximal, characteristic, complemented
10#10591706C211yesmaximal, characteristic, complemented
11#10591703C211yesmaximal, characteristic, complemented
12#10591372C211yesmaximal, characteristic, complemented
13#10591369C211yesmaximal, characteristic, complemented
14#10591303C211yesmaximal, characteristic, complemented
15#10591281C211yesmaximal, characteristic, complemented
16#82585—31nomaximal
17#77111—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic, complemented
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic, complemented
28#64144—24no—
29C2×#3750C2211yescharacteristic, complemented
30C2×#3750C2211yescharacteristic, complemented
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic, complemented
35C2×C3×#217C2211yescharacteristic, complemented
36C3×#937—24no—
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
40#67⋊Dic3—24no—
41D3×#217—24no—
42C2×#3724C2211yescharacteristic, complemented
43C2×Dic3⋊Dic3C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×Dic32C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×#120—31no—
58C22×#217—31no—
59C2×#937D311yescharacteristic
60C2×#935—31no—
61C2×#935—31no—
62C2×#935—61no—
63C2×D4×Dic3—31no—
64C2×#67⋊C4—31no—
65C2×D3×C22⋊C4—31no—
66C3×#394—31no—
67#5247—31no—
68#5222—31no—
69#5222D311yescharacteristic, complemented
70#5220—31no—
71#5220—31no—
72#4993—31no—
73#4989—31no—
74#4959—31no—
75#4958—31no—
76#4956—31no—
77#4955—31no—
78#4953—31no—
79#4952—31no—
80#4949—31no—
81#4946—31no—
82#4945—31no—
83#4944—31no—
84#4944—31no—
85#4942—31no—
86#4669—31no—
87#4667—31no—
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3—41no—
96C23×C3×D3—41no—
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C2×C32×D4—22no—
100C2×C32×D4—22no—
101C2×C32×D4—41no—
102C22×C32×C4C2311yescharacteristic
103C22×C3⋊Dic3—22no—
104C22×C3⋊Dic3—22no—
105C22×C3⋊Dic3—41no—
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C2×C3×#67—22no—
111C2×C3×#67—22no—
112C2×C3×#67—22no—
113C2×C3×#67—22no—
114C2×C3×#67—41no—
115C2×C3×#67D414yes—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—41no—
127C2×D3×Dic3—41no—
128#3757—22no—
129#3757—22no—
130#3757D414yescomplemented
131#3750—22no—
132#3750—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—22no—
136C3×#217—41no—
137C3×#217—41no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×Dic3⋊C4—41no—
141#3724—41no—
142Dic3⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—41no—
149Dic32—22no—
150#2418—91noSylow
151C25×C3—31no—
152C24×D3C2×D311yescharacteristic
153C22×C3×D4—21no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4C2×D311yescharacteristic
157C22×C3×D4C2×D311yescharacteristic
158C22×#67C2×D311yescharacteristic
159C22×#67C2×D311yescharacteristic
160C23×Dic3—31no—
161C23×Dic3—31no—
162C23×Dic3—31no—
163C23×Dic3—31no—
164C23×Dic3—61no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C3×#120—64no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—61no—
189C2×#217—61no—
190C2×#217—61no—
191C2×#217—64no—
192C2×#217C2×D311yescharacteristic
193C2×#217C2×D311yescharacteristic
194C2×#217C2×D311yescharacteristic
195C2×#217C2×D311yescharacteristic, complemented
196C2×#217C2×D311yescharacteristic, complemented
197#937—24no—
198#935—64no—
199#935—64no—
200#935—68no—
201D4×Dic3—64no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4C2×D311yescharacteristic
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×C4⋊Dic3—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—61no—
219C2×Dic3⋊C4—61no—
220C2×Dic3⋊C4C2×D311yescharacteristic, complemented
221C2×C4×Dic3—31no—
222C2×C4×Dic3—31no—
223#67⋊C4—64no—
224D3×C22⋊C4—64no—
225C3×#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95C2×D311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32C2×D412yes—
250C23×C32C2×D412yes—
251C23×C32C2411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—28no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3—44no—
269C22×C3×D3C2×D412yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C22×C3×D3#4112yes—
273C32×D4—44no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—44no—
288C2×C3⋊Dic3C2×D412yes—
289C2×C3⋊Dic3C2×D412yes—
290C3×#67—28no—
291C3×#67—44no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3C2×D412yes—
310D3×Dic3—44no—
311D3×Dic3—44no—
312C2×#123—91no—
313C2×#120—31no—
314C2×C4×D4—91no—
315C22×C22⋊C4—91no—
316#399—91no—
317#397—91no—
318#394—31no—
319#394—91no—
320#388—91no—
321#388—91no—
322#386—91no—
323#386—91no—
324#385—91no—
325#380—91no—
326#379—91no—
327C24×C3—21no—
328C24×C3—21no—
329C24×C3—31no—
330C24×C3—31no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—62no—
336C24×C3—121no—
337C24×C3—121no—
338C24×C3C22×D311yescharacteristic
339C24×C3C22×D311yescharacteristic
340C24×C3C22×D311yescharacteristic
341C24×C3C22×D311yescharacteristic
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—22no—
345C23×D3—22no—
346C23×D3—22no—
347C23×D3—41no—
348C23×D3—41no—
349C23×D3C22×D311yescharacteristic
350C23×D3C22×D311yescharacteristic
351C2×C3×D4—24no—
352C2×C3×D4—22no—
353C2×C3×D4—22no—
354C2×C3×D4—22no—
355C2×C3×D4—22no—
356C2×C3×D4—34no—
357C2×C3×D4—42no—
358C2×C3×D4—41no—
359C2×C3×D4—41no—
360C2×C3×D4—42no—
361C2×C3×D4—62no—
362C2×C3×D4—62no—
363C2×C3×D4—62no—
364C2×C3×D4—62no—
365C2×C3×D4—121no—
366C22×C3×C4—21no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C2×#67—22no—
376C2×#67—22no—
377C2×#67—22no—
378C2×#67—22no—
379C2×#67—41no—
380C2×#67#6714yes—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—61no—
390C22×Dic3—61no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—62no—
394C22×Dic3—62no—
395C22×Dic3—62no—
396C22×Dic3—62no—
397C22×Dic3—62no—
398C22×Dic3—62no—
399C22×Dic3—64no—
400C22×Dic3—62no—
401C22×Dic3—62no—
402C22×Dic3—122no—
403C22×Dic3—121no—
404C22×Dic3—121no—
405C22×Dic3—121no—
406C22×Dic3—121no—
407C22×Dic3—122no—
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C2×C4×D3—62no—
415C2×C4×D3—62no—
416C2×C4×D3—62no—
417C2×C4×D3—62no—
418C2×C4×D3—121no—
419C2×C4×D3—121no—
420C3×C4⋊C4—121no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—62no—
426C3×C22⋊C4—121no—
427C3×C22⋊C4—121no—
428#217—22no—
429#217—22no—
430#217—22no—
431#217—34no—
432#217—34no—
433#217—41no—
434#217—41no—
435#217—64no—
436#217—62no—
437#217—62no—
438#217—62no—
439#217—62no—
440#217—62no—
441#217—62no—
442#217—62no—
443#217—64no—
444#217—64no—
445#217—62no—
446#217—62no—
447#217—121no—
448(C2×D3)⋊C4—22no—
449(C2×D3)⋊C4—22no—
450(C2×D3)⋊C4—62no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—121no—
456C4⋊Dic3—62no—
457Dic3⋊C4—41no—
458Dic3⋊C4—62no—
459Dic3⋊C4—62no—
460Dic3⋊C4—62no—
461Dic3⋊C4—62no—
462Dic3⋊C4—64no—
463Dic3⋊C4—64no—
464Dic3⋊C4—62no—
465Dic3⋊C4—121no—
466Dic3⋊C4—121no—
467C4×Dic3—62no—
468C4×Dic3—62no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32C22×D411yescharacteristic
484C22×C32C22×D411yescharacteristic
485C22×C32C2×#4111yescharacteristic
486C22×C32C2×#4111yescharacteristic
487C22×C32C2×#4111yescharacteristic
488C22×C32H(5,𝔽2)11yescharacteristic
489C22×C32H(5,𝔽2)11yescharacteristic
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—416no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3#12314yescomplemented
505C32×C4—41no—
506C3⋊Dic3—22no—
507C3⋊Dic3—22no—
508C3⋊Dic3—41no—
509C3⋊Dic3—41no—
510C3×Dic3—22no—
511C3×Dic3—41no—
512C3×Dic3—41no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C25—31no—
517C22×D4—31no—
518C22×D4—31no—
519C22×D4D3211yescharacteristic
520C23×C4—91no—
521C23×C4—91no—
522C23×C4—91no—
523#123—184no—
524#120—64no—
525C4×D4—184no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C22⋊C4—91no—
547C2×C22⋊C4—184no—
548C2×C42—91no—
549#95—31no—
550#95—91no—
551#95—91no—
552#95—91no—
553#95—91no—
554#95—91no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—32no—
585C23×C3—32no—
586C23×C3—32no—
587C23×C3—32no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—41no—
595C23×C3—41no—
596C23×C3—41no—
597C23×C3—41no—
598C23×C3—68no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—61no—
609C23×C3—124no—
610C23×C3—124no—
611C23×C3—124no—
612C23×C3—124no—
613C23×C3—124no—
614C23×C3—124no—
615C23×C3D3×D412yes—
616C23×C3D3×D412yes—
617C23×C3D3×D412yes—
618C23×C3C2×#6712yes—
619C23×C3C23×D311yescharacteristic
620C23×C3C23×D311yescharacteristic
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—28no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—44no—
633C22×D3—44no—
634C22×D3—44no—
635C22×D3—44no—
636C22×D3—44no—
637C22×D3—44no—
638C22×D3#23712yes—
639C22×D3#23712yes—
640C22×D3#23712yes—
641C22×D3C2×#6712yes—
642C3×D4—44no—
643C3×D4—44no—
644C3×D4—48no—
645C3×D4—68no—
646C3×D4—124no—
647C2×C3×C4—22no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—32no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674#67—28no—
675#67—44no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—32no—
696C2×Dic3—32no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—62no—
708C2×Dic3—62no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—121no—
722C2×Dic3—121no—
723C2×Dic3—121no—
724C2×Dic3—121no—
725C2×Dic3—121no—
726C2×Dic3—121no—
727C2×Dic3—121no—
728C2×Dic3—121no—
729C2×Dic3—124no—
730C2×Dic3—124no—
731C2×Dic3—124no—
732C2×Dic3—124no—
733C2×Dic3—128no—
734C2×Dic3C2×#6712yes—
735C4×D3—124no—
736C4×D3—124no—
737C2×C32—42no—
738C2×C32—42no—
739C2×C32C2×#12311yescharacteristic
740C2×C32#52511yescharacteristic
741C2×C32#53811yescharacteristic
742C2×C32D4211yescharacteristic
743C2×C32#54611yescharacteristic
744C2×C32#54611yescharacteristic
745C2×C32#55111yescharacteristic
746C3×D3—24no—
747C3×D3—42no—
748C24—31no—
749C24—31no—
750C24—62no—
751C24—62no—
752C24—62no—
753C24—62no—
754C24—62no—
755C24—121no—
756C24—121no—
757C24C2×D3211yescharacteristic
758C24C2×D3211yescharacteristic
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—34no—
762C2×D4—41no—
763C2×D4—62no—
764C2×D4—62no—
765C2×D4—62no—
766C2×D4—62no—
767C2×D4—121no—
768C22×C4—31no—
769C22×C4—31no—
770C22×C4—31no—
771C22×C4—31no—
772C22×C4—31no—
773C22×C4—31no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—91no—
778C22×C4—182no—
779C22×C4—182no—
780C22×C4—182no—
781C22×C4—182no—
782C22×C4—182no—
783C22×C4—182no—
784C22×C4—361no—
785C22×C4—361no—
786C22×C4—361no—
787C22×C4C2×D3211yescharacteristic
788C4⋊C4—121no—
789C4⋊C4—182no—
790C4⋊C4—182no—
791C4⋊C4—182no—
792C4⋊C4—361no—
793C22⋊C4—62no—
794C22⋊C4—62no—
795C22⋊C4—62no—
796C22⋊C4—62no—
797C22⋊C4—62no—
798C22⋊C4—94no—
799C22⋊C4—121no—
800C22⋊C4—121no—
801C22⋊C4—182no—
802C22⋊C4—182no—
803C22⋊C4—182no—
804C22⋊C4—182no—
805C22⋊C4—182no—
806C22⋊C4—182no—
807C22⋊C4—182no—
808C22⋊C4—361no—
809C42—182no—
810C22×C3—24no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—34no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—81no—
866C22×C3—81no—
867C22×C3—81no—
868C22×C3—81no—
869C22×C3—1216no—
870C22×C3—121no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3—121no—
874C22×C3C2×D3×D411yescharacteristic
875C22×C3C2×D3×D411yescharacteristic
876C22×C3C2×D3×D411yescharacteristic
877C22×C3C2×#23711yescharacteristic
878C22×C3C2×#23711yescharacteristic
879C22×C3C2×#23711yescharacteristic
880C22×C3#100411yescharacteristic
881C22×C3#100411yescharacteristic
882C22×C3#100411yescharacteristic
883C22×C3#100411yescharacteristic
884C22×C3D3×#4111yescharacteristic
885C22×C3D3×#4111yescharacteristic
886C22×C3D3×#4111yescharacteristic
887C22×C3C22×#6711yescharacteristic
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—22no—
892C2×D3—22no—
893C2×D3—22no—
894C2×D3—22no—
895C2×D3—22no—
896C2×D3—22no—
897C2×D3—416no—
898C2×D3—41no—
899C2×D3—41no—
900C2×D3—41no—
901C2×D3—41no—
902C2×D3#93514yescomplemented
903C3×C4—42no—
904C3×C4—41no—
905C3×C4—41no—
906C3×C4—62no—
907C3×C4—121no—
908C3×C4—121no—
909C3×C4—121no—
910C3×C4—121no—
911C3×C4—121no—
912Dic3—22no—
913Dic3—41no—
914Dic3—41no—
915Dic3—41no—
916Dic3—41no—
917Dic3—41no—
918Dic3—62no—
919Dic3—62no—
920Dic3—62no—
921Dic3—62no—
922Dic3—122no—
923Dic3—122no—
924Dic3—122no—
925Dic3—122no—
926Dic3—121no—
927Dic3—121no—
928Dic3—121no—
929Dic3—121no—
930C32#241811yescharacteristic, complemented, Sylow
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—32no—
944C23—32no—
945C23—32no—
946C23—32no—
947C23—68no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—61no—
956C23—61no—
957C23—61no—
958C23—124no—
959C23—124no—
960C23—124no—
961C23—124no—
962C23—124no—
963C23—124no—
964C23D3×#6712yes—
965C23#381112yes—
966C23C22×D3211yescharacteristic
967D4—44no—
968D4—68no—
969D4—124no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—32no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—92no—
992C2×C4—92no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—181no—
997C2×C4—181no—
998C2×C4—181no—
999C2×C4—181no—
1000C2×C4—181no—
1001C2×C4—181no—
1002C2×C4—181no—
1003C2×C4—364no—
1004C2×C4—364no—
1005C2×C4—364no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—44no—
1014C2×C3—42no—
1015C2×C3—42no—
1016C2×C3—42no—
1017C2×C3—42no—
1018C2×C3—64no—
1019C2×C3—82no—
1020C2×C3—122no—
1021C2×C3#558611yescharacteristic
1022C2×C3#558711yescharacteristic
1023C2×C3#559011yescharacteristic
1024C2×C3#559111yescharacteristic
1025C2×C3#559311yescharacteristic
1026C2×C3#561011yescharacteristic
1027C2×C3#561011yescharacteristic
1028C2×C3#561311yescharacteristic
1029C2×C3D3×#12311yescharacteristic
1030C2×C3#565611yescharacteristic
1031C2×C3#567911yescharacteristic
1032C2×C3C2×#93511yescharacteristic
1033C2×C3D4×#6711yescharacteristic
1034C2×C3#580611yescharacteristic
1035D3—24no—
1036D3—42no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—34no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—62no—
1053C22—62no—
1054C22—62no—
1055C22—62no—
1056C22—62no—
1057C22—62no—
1058C22—62no—
1059C22—62no—
1060C22—62no—
1061C22—1216no—
1062C22—121no—
1063C22—121no—
1064C22—121no—
1065C22—121no—
1066C22D3×#23711yescharacteristic
1067C22D3×#23711yescharacteristic
1068C22D3×#23711yescharacteristic
1069C22#6431311yescharacteristic
1070C22C2×D3×#6711yescharacteristic
1071C22C2×#381111yescharacteristic
1072C22#6433011yescharacteristic
1073C4—41no—
1074C4—62no—
1075C4—121no—
1076C4—121no—
1077C4—121no—
1078C4—121no—
1079C4—121no—
1080C4—182no—
1081C4—182no—
1082C4—361no—
1083C4—361no—
1084C3—21no—
1085C3#7711111yescharacteristic, complemented
1086C3#8258511yescharacteristic, complemented
1087C2—42no—
1088C2—42no—
1089C2—64no—
1090C2—122no—
1091C2D3×#93511yescharacteristic
1092C2#1059515011yescharacteristic
1093C2#1059516011yescharacteristic
1094C2#1059517611yescharacteristic
1095C2#1059518011yescharacteristic
1096C2#1059530711yescharacteristic
1097C2#1059552611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×C3×#937C2
hypercenterC22×D4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64144C2semidirect
3. C2×#67⋊Dic3C2semidirect
4. C2×D3×#217C2semidirect
5. C3×#5222C2semidirect
6. #10591721C2semidirect
7. #10591717C2semidirect
8. #10591713C2semidirect
9. #10591708C2semidirect
10. #10591706C2semidirect
11. #10591703C2semidirect
12. #10591372C2semidirect
13. #10591369C2semidirect
14. #10591303C2semidirect
15. #10591281C2semidirect
20. C23×C3⋊Dic3C22semidirect
27. C2×#3757C22semidirect
29. C2×#3750C22semidirect
30. C2×#3750C22semidirect
34. C2×C3×#217C22semidirect
35. C2×C3×#217C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
42. C2×#3724C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic32C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
69. #5222D3semidirect
130. #3757D4semidirect
195. C2×#217C2×D3semidirect
196. C2×#217C2×D3semidirect
220. C2×Dic3⋊C4C2×D3semidirect
236. C3⋊#95C2×D3semidirect
504. C2×C3×D3#123semidirect
902. C2×D3#935semidirect
930. C32#2418semidirect
1085. C3#77111semidirect
1086. C3#82585semidirect

Maximal subgroups

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

subgroupindex
C2×#641442
C2×C3×#9372
C2×#67⋊Dic32
C2×D3×#2172
C3×#52222
#105917212
#105917172
#105917132
#105917082
#105917062
#105917032
#105913722
#105913692
#105913032
#105912812
#825853
#771113