Finite Group Databasebeta

← #11812865

Subgroups — #11812865

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic
3C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63962C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6#10591719C211yesmaximal, characteristic, complemented
7#10591718C211yesmaximal, characteristic, complemented
8#10591717C211yesmaximal, characteristic, complemented
9#10591713C211yesmaximal, characteristic, complemented
10#10591710C211yesmaximal, characteristic, complemented
11#10591709C211yesmaximal, characteristic, complemented
12#10591353C211yesmaximal, characteristic, complemented
13#10591334C211yesmaximal, characteristic, complemented
14#10591317C211yesmaximal, characteristic, complemented
15#10591287C211yesmaximal, characteristic, complemented
16#82655—31nomaximal
17#74703—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27D4×C3⋊Dic3—24no—
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C3×#939—24no—
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊Dic3—24no—
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44#63962—24no—
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×#121—31no—
58C2×#939D311yescharacteristic
59C2×#935—31no—
60C2×D4×Dic3—31no—
61C2×D4×Dic3—31no—
62C2×D4×Dic3—61no—
63C22×C4⋊Dic3—31no—
64C22×Dic3⋊C4—31no—
65C2×#886—31no—
66C3×#386—31no—
67#5222—31no—
68#5220—31no—
69#5220—31no—
70#5220D311yescharacteristic, complemented
71#5213—31no—
72#5210—31no—
73#4981—31no—
74#4978—31no—
75#4961—31no—
76#4958—31no—
77#4953—31no—
78#4952—31no—
79#4950—31no—
80#4950—31no—
81#4949—31no—
82#4946—31no—
83#4944—31no—
84#4677—31no—
85#4670—31no—
86#4661—31no—
87#4653—31no—
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C2×C32×D4—22no—
92C2×C32×D4—22no—
93C2×C32×D4D414yes—
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—22no—
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3—22no—
98C22×C3⋊Dic3—22no—
99C22×C3⋊Dic3—41no—
100C22×C3⋊Dic3—41no—
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67—41no—
111C22×C3×Dic3—22no—
112C22×C3×Dic3—22no—
113C22×C3×Dic3—22no—
114C22×C3×Dic3—22no—
115C22×C3×Dic3—22no—
116C22×C3×Dic3—41no—
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124#3757—22no—
125#3757—22no—
126C4⋊(C3⋊Dic3)—22no—
127C4×C3⋊Dic3—22no—
128C3×#217—22no—
129C3×#217—22no—
130C3×#217—22no—
131C3×#217—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×Dic3⋊C4—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3—41no—
139Dic3⋊Dic3D414yescomplemented
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—41no—
144#2443—91noSylow
145C22×C3×D4—21no—
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×C3×D4C2×D311yescharacteristic
149C22×C3×D4C2×D311yescharacteristic
150C23×C3×C4—31no—
151C23×C3×C4—31no—
152C22×#67C2×D311yescharacteristic
153C22×#67C2×D311yescharacteristic
154C23×Dic3—31no—
155C23×Dic3—31no—
156C23×Dic3—31no—
157C23×Dic3—31no—
158C23×Dic3—61no—
159C23×Dic3—61no—
160C23×Dic3C2×D311yescharacteristic
161C23×Dic3C2×D311yescharacteristic
162C3×#121—64no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—61no—
178C2×#217—61no—
179C2×#217C2×D311yescharacteristic
180C2×#217C2×D311yescharacteristic
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183#939—24no—
184#935—64no—
185D4×Dic3—68no—
186D4×Dic3—64no—
187D4×Dic3—64no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—31no—
199C2×C4⋊Dic3—31no—
200C2×C4⋊Dic3—31no—
201C2×C4⋊Dic3—61no—
202C2×C4⋊Dic3—64no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—64no—
210C2×Dic3⋊C4C2×D311yescharacteristic
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—61no—
214#886—64no—
215C3×#95—31no—
216C3×#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32C2×D412yes—
242C23×C32C2×D412yes—
243C23×C32#4112yes—
244C23×C32#4112yes—
245C23×C32C2411yescharacteristic
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C32×D4—28no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D412yes—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—44no—
269C2×C3⋊Dic3—44no—
270C2×C3⋊Dic3C2×D412yes—
271C3×#67—44no—
272C3×#67—44no—
273C2×C3×Dic3—28no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—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—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—44no—
293C2×C3×Dic3C2×D412yes—
294C2×C3×Dic3C2×D412yes—
295C2×C3×Dic3#4112yes—
296C2×#123—91no—
297C2×#121—31no—
298C2×C4×D4—91no—
299C22×C4⋊C4—91no—
300#399—91no—
301#398—91no—
302#397—91no—
303#394—91no—
304#388—91no—
305#387—91no—
306#386—31no—
307#386—91no—
308#386—91no—
309#385—91no—
310#385—91no—
311C24×C3—21no—
312C24×C3—21no—
313C24×C3—31no—
314C24×C3C22×D311yescharacteristic
315C24×C3C22×D311yescharacteristic
316C24×C3C22×D311yescharacteristic
317C24×C3C22×D311yescharacteristic
318C23×D3C22×D311yescharacteristic
319C2×C3×D4—24no—
320C2×C3×D4—24no—
321C2×C3×D4—22no—
322C2×C3×D4—22no—
323C2×C3×D4—22no—
324C2×C3×D4—22no—
325C2×C3×D4—24no—
326C2×C3×D4—62no—
327C2×C3×D4—62no—
328C2×C3×D4—62no—
329C2×C3×D4—62no—
330C2×C3×D4—62no—
331C2×C3×D4—121no—
332C2×C3×D4D1214yes—
333C2×C3×D4#6714yes—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—62no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4—121no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—22no—
351C2×#67—22no—
352C2×#67—22no—
353C2×#67—22no—
354C2×#67—22no—
355C2×#67—41no—
356C22×Dic3—22no—
357C22×Dic3—22no—
358C22×Dic3—22no—
359C22×Dic3—22no—
360C22×Dic3—22no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—41no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374C22×Dic3—62no—
375C22×Dic3—62no—
376C22×Dic3—62no—
377C22×Dic3—62no—
378C22×Dic3—64no—
379C22×Dic3—64no—
380C22×Dic3—62no—
381C22×Dic3—62no—
382C22×Dic3—62no—
383C22×Dic3—62no—
384C22×Dic3—122no—
385C22×Dic3—122no—
386C22×Dic3—121no—
387C22×Dic3—121no—
388C22×Dic3—121no—
389C22×Dic3—121no—
390C22×Dic3—122no—
391C22×Dic3—122no—
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C3×C4⋊C4—62no—
400C3×C22⋊C4—62no—
401C3×C22⋊C4—62no—
402C3×C22⋊C4—62no—
403C3×C22⋊C4—62no—
404C3×C22⋊C4—62no—
405#217—22no—
406#217—22no—
407#217—22no—
408#217—22no—
409#217—62no—
410#217—64no—
411#217—64no—
412#217—62no—
413#217—62no—
414#217—62no—
415#217—62no—
416#217—62no—
417#217—62no—
418#217—121no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—62no—
422(C2×D3)⋊C4—62no—
423(C2×D3)⋊C4—121no—
424C4⋊Dic3—34no—
425C4⋊Dic3—62no—
426C4⋊Dic3—62no—
427C4⋊Dic3—64no—
428C4⋊Dic3—62no—
429C4⋊Dic3—62no—
430C4⋊Dic3—62no—
431C4⋊Dic3—62no—
432C4⋊Dic3—121no—
433Dic3⋊C4—22no—
434Dic3⋊C4—34no—
435Dic3⋊C4—62no—
436Dic3⋊C4—62no—
437Dic3⋊C4—62no—
438Dic3⋊C4—62no—
439Dic3⋊C4—121no—
440C4×Dic3—64no—
441C4×Dic3—62no—
442C4×Dic3—62no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—22no—
451C22×C32—22no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32#12314yescomplemented
457C22×C32C22×D411yescharacteristic
458C22×C32C22×D411yescharacteristic
459C22×C32C2×#4111yescharacteristic
460C22×C32C2×#4111yescharacteristic
461C22×C32C2×#4111yescharacteristic
462C22×C32H(5,𝔽2)11yescharacteristic
463C22×C322−1+411yescharacteristic
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C32×C4—22no—
472C3⋊Dic3—22no—
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3⋊Dic3—41no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C3×Dic3—22no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C22×D4—31no—
484C22×D4—31no—
485C22×D4D3211yescharacteristic
486C23×C4—31no—
487C23×C4—31no—
488C23×C4—91no—
489C23×C4—91no—
490#123—184no—
491#121—64no—
492C4×D4—184no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—184no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C42—91no—
514#95—31no—
515#95—31no—
516#95—91no—
517#95—91no—
518#95—91no—
519#95—91no—
520#95—91no—
521#95—91no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3C2×D1212yes—
565C23×C3C2×D1212yes—
566C23×C3#23712yes—
567C23×C3#23712yes—
568C23×C3#23712yes—
569C23×C3#23712yes—
570C23×C3C2×#6712yes—
571C23×C3C2×#6712yes—
572C23×C3C23×D311yescharacteristic
573C23×C3C23×D311yescharacteristic
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C3×D4—216no—
582C3×D4—28no—
583C3×D4—28no—
584C3×D4—124no—
585C3×D4—124no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—22no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—68no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—124no—
616C2×C3×C4C2×D1212yes—
617C2×C3×C4C2×#6712yes—
618#67—44no—
619#67—44no—
620C2×Dic3—28no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—44no—
642C2×Dic3—62no—
643C2×Dic3—62no—
644C2×Dic3—62no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—62no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3—121no—
673C2×Dic3—121no—
674C2×Dic3—121no—
675C2×Dic3—121no—
676C2×Dic3—124no—
677C2×Dic3—124no—
678C2×Dic3—124no—
679C2×Dic3—124no—
680C2×Dic3—128no—
681C2×Dic3—128no—
682C2×Dic3D3×D412yes—
683C2×Dic3D3×D412yes—
684C2×Dic3#23712yes—
685C2×C32—24no—
686C2×C32—42no—
687C2×C32C2×#12311yescharacteristic
688C2×C32#52511yescharacteristic
689C2×C32#53911yescharacteristic
690C2×C32D4211yescharacteristic
691C2×C32#54711yescharacteristic
692C2×C32#54811yescharacteristic
693C2×C32#55311yescharacteristic
694C3×D3—81no—
695C24—31no—
696C24C2×D3211yescharacteristic
697C24C2×D3211yescharacteristic
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—62no—
701C2×D4—62no—
702C2×D4—62no—
703C2×D4—62no—
704C2×D4—62no—
705C2×D4—121no—
706C2×D4#62614yes—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—62no—
715C22×C4—62no—
716C22×C4—62no—
717C22×C4—62no—
718C22×C4—62no—
719C22×C4—91no—
720C22×C4—91no—
721C22×C4—91no—
722C22×C4—91no—
723C22×C4—121no—
724C22×C4—182no—
725C22×C4—182no—
726C22×C4—182no—
727C22×C4—182no—
728C22×C4—361no—
729C22×C4—361no—
730C22×C4C2×D3211yescharacteristic
731C4⋊C4—62no—
732C4⋊C4—94no—
733C4⋊C4—182no—
734C4⋊C4—182no—
735C4⋊C4—182no—
736C4⋊C4—182no—
737C4⋊C4—182no—
738C4⋊C4—361no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—62no—
742C22⋊C4—62no—
743C22⋊C4—62no—
744C22⋊C4—182no—
745C22⋊C4—182no—
746C22⋊C4—182no—
747C22⋊C4—182no—
748C22⋊C4—182no—
749C22⋊C4—361no—
750C42—182no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—24no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—24no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3—42no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—121no—
799C22×C3—121no—
800C22×C3—121no—
801C22×C3—121no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3—121no—
805C22×C3#88614yescomplemented
806C22×C3#93514yescomplemented
807C22×C3C22×D1211yescharacteristic
808C22×C3C2×D3×D411yescharacteristic
809C22×C3C2×D3×D411yescharacteristic
810C22×C3C2×#23711yescharacteristic
811C22×C3C2×#23711yescharacteristic
812C22×C3C2×#23711yescharacteristic
813C22×C3C2×#23711yescharacteristic
814C22×C3C2×#23711yescharacteristic
815C22×C3#100411yescharacteristic
816C22×C3D3×#4111yescharacteristic
817C22×C3#100911yescharacteristic
818C22×C3#101011yescharacteristic
819C22×C3#101011yescharacteristic
820C22×C3C22×#6711yescharacteristic
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—41no—
824C2×D3—41no—
825C2×D3—41no—
826C2×D3—41no—
827C2×D3—41no—
828C3×C4—24no—
829C3×C4—22no—
830C3×C4—22no—
831C3×C4—62no—
832C3×C4—62no—
833C3×C4—62no—
834C3×C4—121no—
835C3×C4—121no—
836C3×C4—121no—
837C3×C4—121no—
838Dic3—22no—
839Dic3—22no—
840Dic3—22no—
841Dic3—41no—
842Dic3—41no—
843Dic3—41no—
844Dic3—41no—
845Dic3—64no—
846Dic3—62no—
847Dic3—62no—
848Dic3—122no—
849Dic3—122no—
850Dic3—122no—
851Dic3—121no—
852Dic3—121no—
853Dic3—121no—
854Dic3—121no—
855Dic3—121no—
856Dic3—121no—
857C32#244311yescharacteristic, complemented, Sylow
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—61no—
869C23—61no—
870C23—61no—
871C23—61no—
872C23—61no—
873C23—61no—
874C23—61no—
875C23#380512yes—
876C23#380512yes—
877C23C2×#62612yes—
878C23C2×#62612yes—
879C23C22×D3211yescharacteristic
880D4—28no—
881D4—124no—
882D4—124no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—32no—
886C2×C4—32no—
887C2×C4—32no—
888C2×C4—68no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—92no—
908C2×C4—124no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—181no—
913C2×C4—181no—
914C2×C4—181no—
915C2×C4—181no—
916C2×C4—181no—
917C2×C4—181no—
918C2×C4—181no—
919C2×C4—181no—
920C2×C4—364no—
921C2×C4—364no—
922C2×C4C2×#62612yes—
923C2×C3—24no—
924C2×C3—24no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—44no—
933C2×C3—44no—
934C2×C3—42no—
935C2×C3—42no—
936C2×C3—241no—
937C2×C3C2×#88611yescharacteristic
938C2×C3D4×D1211yescharacteristic
939C2×C3#555511yescharacteristic
940C2×C3#558611yescharacteristic
941C2×C3#559811yescharacteristic
942C2×C3#559811yescharacteristic
943C2×C3#560111yescharacteristic
944C2×C3#560211yescharacteristic
945C2×C3#560611yescharacteristic
946C2×C3#561811yescharacteristic
947C2×C3#566511yescharacteristic
948C2×C3C2×#93511yescharacteristic
949C2×C3D4×#6711yescharacteristic
950C2×C3#582411yescharacteristic
951D3—81no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—121no—
972C22#6396214yescomplemented
973C22#6430911yescharacteristic
974C22D32×D411yescharacteristic
975C22D3×#23711yescharacteristic
976C22#6431411yescharacteristic
977C22C2×#380511yescharacteristic
978C22C2×#380511yescharacteristic
979C22C22×#62611yescharacteristic
980C4—22no—
981C4—62no—
982C4—62no—
983C4—62no—
984C4—121no—
985C4—121no—
986C4—121no—
987C4—121no—
988C4—182no—
989C4—361no—
990C4—361no—
991C4—361no—
992C3—21no—
993C3#7470311yescharacteristic, complemented
994C3#8265511yescharacteristic, complemented
995C2—24no—
996C2—42no—
997C2—241no—
998C2#1059513011yescharacteristic
999C2#1059514211yescharacteristic
1000C2#1059518911yescharacteristic
1001C2#1059522011yescharacteristic
1002C2D4×#62611yescharacteristic
1003C2#1059524811yescharacteristic
1004C2C2×#6396211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×C3×#939C2
hypercenterC22×D4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
3. C22×Dic3⋊Dic3C2semidirect
4. C2×#63962C2semidirect
5. C3×#5220C2semidirect
6. #10591719C2semidirect
7. #10591718C2semidirect
8. #10591717C2semidirect
9. #10591713C2semidirect
10. #10591710C2semidirect
11. #10591709C2semidirect
12. #10591353C2semidirect
13. #10591334C2semidirect
14. #10591317C2semidirect
15. #10591287C2semidirect
70. #5220D3semidirect
139. Dic3⋊Dic3D4semidirect
456. C22×C32#123semidirect
805. C22×C3#886semidirect
806. C22×C3#935semidirect
857. C32#2443semidirect
972. C22#63962semidirect
993. C3#74703semidirect
994. C3#82655semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9392
C22×Dic3⋊Dic32
C2×#639622
C3×#52202
#105917192
#105917182
#105917172
#105917132
#105917102
#105917092
#105913532
#105913342
#105913172
#105912872
#826553
#747033