Finite Group Databasebeta

← #11812849

Subgroups — #11812849

Order 1152.

1519 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic, complemented
2C2×C3×#938C211yesmaximal, characteristic
3C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
4C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C3×#5222C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591721C211yesmaximal, characteristic, complemented
8#10591721C211yesmaximal, characteristic, complemented
9#10591719C211yesmaximal, characteristic, complemented
10#10591715C211yesmaximal, characteristic, complemented
11#10591701C211yesmaximal, characteristic, complemented
12#10591694C211yesmaximal, characteristic, complemented
13#10591342C211yesmaximal, characteristic, complemented
14#10591278C211yesmaximal, characteristic, complemented
15#10591263C211yesmaximal, characteristic, complemented
16#82655—31nomaximal
17#77117—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28#64144—24no—
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C3×#938—24no—
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40#67⋊Dic3—24no—
41C2×#3724C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48D3×Dic3⋊C4—24no—
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×#121—31no—
58C2×#938D311yescharacteristic
59C2×#935—31no—
60C2×#935—31no—
61C2×#935—61no—
62C2×D4×Dic3—31no—
63C22×Dic3⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C2×#67⋊C4—31no—
66C3×#394—31no—
67#5222D311yescharacteristic, complemented
68#5220—31no—
69#5220—31no—
70#5220—31no—
71#5210—31no—
72#4982—31no—
73#4981—31no—
74#4978—31no—
75#4956—31no—
76#4956—31no—
77#4956—31no—
78#4952—31no—
79#4952—31no—
80#4951—31no—
81#4950—31no—
82#4949—31no—
83#4949—31no—
84#4946—31no—
85#4944—31no—
86#4668—31no—
87#4655—31no—
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C2×C32×D4—22no—
92C2×C32×D4—22no—
93C2×C32×D4—41no—
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—22no—
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3—41no—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67D414yes—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—41no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—41no—
124#3757—22no—
125#3757—22no—
126#3757—22no—
127#3750—22no—
128#3750D414yescomplemented
129C3×#217—22no—
130C3×#217—22no—
131C3×#217—22no—
132C3×#217—22no—
133C3×#217—22no—
134C3×#217—41no—
135C3×C4⋊Dic3—22no—
136C3×Dic3⋊C4—22no—
137#3724—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—41no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143Dic32—22no—
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—
151C22×#67C2×D311yescharacteristic
152C22×#67C2×D311yescharacteristic
153C23×Dic3—31no—
154C23×Dic3—31no—
155C23×Dic3—31no—
156C23×Dic3—31no—
157C23×Dic3—61no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3C2×D311yescharacteristic
161C3×#121—64no—
162C2×C3×C4⋊C4—31no—
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×C3×C22⋊C4—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—61no—
179C2×#217—61no—
180C2×#217—61no—
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183C2×#217C2×D311yescharacteristic
184C2×#217C2×D311yescharacteristic
185C2×#217C2×D311yescharacteristic
186C2×#217C2×D311yescharacteristic
187#938—24no—
188#935—64no—
189#935—64no—
190#935—68no—
191D4×Dic3—64no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3C2×D311yescharacteristic
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—61no—
208C2×Dic3⋊C4—61no—
209C2×Dic3⋊C4—64no—
210C2×Dic3⋊C4C2×D311yescharacteristic
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213D3×C4⋊C4—64no—
214#67⋊C4—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⋊#95—31no—
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×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32C2×D412yes—
245C23×C32C2411yescharacteristic
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3C2×D412yes—
251C22×C3×D3#4112yes—
252C22×C3×D3#4112yes—
253C32×D4—44no—
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—44no—
268C2×C3⋊Dic3C2×D412yes—
269C2×C3⋊Dic3C2×D412yes—
270C3×#67—28no—
271C3×#67—44no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
292C2×C3×Dic3#4112yes—
293C3×C4×D3—44no—
294D3×Dic3—28no—
295D3×Dic3—44no—
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—31no—
304#388—91no—
305#387—91no—
306#386—91no—
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—22no—
321C2×C3×D4—22no—
322C2×C3×D4—22no—
323C2×C3×D4—22no—
324C2×C3×D4—34no—
325C2×C3×D4—42no—
326C2×C3×D4—41no—
327C2×C3×D4—41no—
328C2×C3×D4—42no—
329C2×C3×D4—62no—
330C2×C3×D4—62no—
331C2×C3×D4—62no—
332C2×C3×D4—62no—
333C2×C3×D4—62no—
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—121no—
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C2×#67—22no—
348C2×#67—22no—
349C2×#67—22no—
350C2×#67—22no—
351C2×#67—22no—
352C2×#67#6714yes—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365C22×Dic3—62no—
366C22×Dic3—62no—
367C22×Dic3—62no—
368C22×Dic3—62no—
369C22×Dic3—62no—
370C22×Dic3—62no—
371C22×Dic3—62no—
372C22×Dic3—64no—
373C22×Dic3—62no—
374C22×Dic3—62no—
375C22×Dic3—122no—
376C22×Dic3—121no—
377C22×Dic3—121no—
378C22×Dic3—121no—
379C22×Dic3—122no—
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C2×C4×D3—22no—
388C2×C4×D3—22no—
389C2×C4×D3—41no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—62no—
395C2×C4×D3—121no—
396C3×C4⋊C4—62no—
397C3×C4⋊C4—62no—
398C3×C22⋊C4—62no—
399C3×C22⋊C4—62no—
400C3×C22⋊C4—62no—
401C3×C22⋊C4—62no—
402C3×C22⋊C4—62no—
403C3×C22⋊C4—121no—
404#217—22no—
405#217—22no—
406#217—22no—
407#217—22no—
408#217—22no—
409#217—41no—
410#217—62no—
411#217—62no—
412#217—62no—
413#217—62no—
414#217—62no—
415#217—62no—
416#217—62no—
417#217—62no—
418#217—64no—
419#217—64no—
420#217—64no—
421(C2×D3)⋊C4—62no—
422(C2×D3)⋊C4—62no—
423C4⋊Dic3—22no—
424C4⋊Dic3—62no—
425C4⋊Dic3—62no—
426C4⋊Dic3—121no—
427Dic3⋊C4—22no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—64no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434Dic3⋊C4—64no—
435Dic3⋊C4—62no—
436Dic3⋊C4—62no—
437Dic3⋊C4—62no—
438Dic3⋊C4—121no—
439C4×Dic3—62no—
440C4×Dic3—62no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32C22×D411yescharacteristic
456C22×C32C22×D411yescharacteristic
457C22×C32C2×#4111yescharacteristic
458C22×C32C2×#4111yescharacteristic
459C22×C32C2×#4111yescharacteristic
460C22×C32H(5,𝔽2)11yescharacteristic
461C22×C322−1+411yescharacteristic
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3#12314yescomplemented
469C32×C4—22no—
470C3⋊Dic3—22no—
471C3⋊Dic3—22no—
472C3⋊Dic3—41no—
473C3⋊Dic3—41no—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C22×D4—31no—
482C22×D4—31no—
483C22×D4D3211yescharacteristic
484C23×C4—31no—
485C23×C4—91no—
486C23×C4—91no—
487C23×C4—91no—
488#123—184no—
489#121—64no—
490C4×D4—184no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C4⋊C4—184no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C42—91no—
512#95—31no—
513#95—91no—
514#95—91no—
515#95—91no—
516#95—91no—
517#95—91no—
518#95—91no—
519#95—91no—
520C23×C3—22no—
521C23×C3—22no—
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—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—22no—
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—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—22no—
551C23×C3—32no—
552C23×C3—32no—
553C23×C3—32no—
554C23×C3—41no—
555C23×C3—41no—
556C23×C3—41no—
557C23×C3—41no—
558C23×C3—41no—
559C23×C3—41no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3D3×D412yes—
569C23×C3C2×#6712yes—
570C23×C3C23×D311yescharacteristic
571C23×C3C23×D311yescharacteristic
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3#23712yes—
577C22×D3#23712yes—
578C22×D3C2×#6712yes—
579C3×D4—44no—
580C3×D4—44no—
581C3×D4—48no—
582C3×D4—68no—
583C3×D4—124no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
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—124no—
613C2×C3×C4D3×D412yes—
614C2×C3×C4D3×D412yes—
615#67—28no—
616#67—44no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
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—32no—
637C2×Dic3—32no—
638C2×Dic3—32no—
639C2×Dic3—32no—
640C2×Dic3—62no—
641C2×Dic3—62no—
642C2×Dic3—68no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—62no—
652C2×Dic3—62no—
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—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3—121no—
673C2×Dic3—124no—
674C2×Dic3—124no—
675C2×Dic3—124no—
676C2×Dic3—128no—
677C2×Dic3#23712yes—
678C2×Dic3C2×#6712yes—
679C4×D3—44no—
680C4×D3—68no—
681C4×D3—124no—
682C2×C32—42no—
683C2×C32—81no—
684C2×C32C2×#12311yescharacteristic
685C2×C32#52511yescharacteristic
686C2×C32#53911yescharacteristic
687C2×C32D4211yescharacteristic
688C2×C32#54711yescharacteristic
689C2×C32#54811yescharacteristic
690C2×C32#55311yescharacteristic
691C3×D3—24no—
692C24—31no—
693C24C2×D3211yescharacteristic
694C24C2×D3211yescharacteristic
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—34no—
698C2×D4—41no—
699C2×D4—62no—
700C2×D4—62no—
701C2×D4—62no—
702C2×D4—62no—
703C2×D4—62no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—62no—
712C22×C4—62no—
713C22×C4—91no—
714C22×C4—91no—
715C22×C4—91no—
716C22×C4—91no—
717C22×C4—121no—
718C22×C4—182no—
719C22×C4—182no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—182no—
723C22×C4—182no—
724C22×C4—182no—
725C22×C4—361no—
726C22×C4—361no—
727C22×C4C2×D3211yescharacteristic
728C4⋊C4—62no—
729C4⋊C4—62no—
730C4⋊C4—94no—
731C4⋊C4—182no—
732C4⋊C4—182no—
733C4⋊C4—182no—
734C4⋊C4—182no—
735C4⋊C4—361no—
736C22⋊C4—62no—
737C22⋊C4—62no—
738C22⋊C4—62no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—121no—
742C22⋊C4—182no—
743C22⋊C4—182no—
744C22⋊C4—182no—
745C22⋊C4—182no—
746C22⋊C4—182no—
747C42—182no—
748C22×C3—24no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—34no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—81no—
801C22×C3—81no—
802C22×C3—81no—
803C22×C3—81no—
804C22×C3C2×D3×D411yescharacteristic
805C22×C3C2×D3×D411yescharacteristic
806C22×C3C2×D3×D411yescharacteristic
807C22×C3C2×#23711yescharacteristic
808C22×C3C2×#23711yescharacteristic
809C22×C3C2×#23711yescharacteristic
810C22×C3#100411yescharacteristic
811C22×C3#100411yescharacteristic
812C22×C3D3×#4111yescharacteristic
813C22×C3D3×#4111yescharacteristic
814C22×C3D3×#4111yescharacteristic
815C22×C3#101011yescharacteristic
816C22×C3#101011yescharacteristic
817C22×C3C22×#6711yescharacteristic
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—22no—
824C2×D3#93514yescomplemented
825C3×C4—22no—
826C3×C4—22no—
827C3×C4—42no—
828C3×C4—62no—
829C3×C4—62no—
830C3×C4—121no—
831C3×C4—121no—
832C3×C4—121no—
833C3×C4—121no—
834C3×C4—121no—
835Dic3—22no—
836Dic3—22no—
837Dic3—41no—
838Dic3—41no—
839Dic3—41no—
840Dic3—41no—
841Dic3—41no—
842Dic3—62no—
843Dic3—62no—
844Dic3—62no—
845Dic3—62no—
846Dic3—122no—
847Dic3—122no—
848Dic3—122no—
849Dic3—122no—
850Dic3—121no—
851Dic3—121no—
852Dic3—121no—
853Dic3—121no—
854C32#244311yescharacteristic, complemented, Sylow
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—21no—
868C23—32no—
869C23—32no—
870C23—32no—
871C23—61no—
872C23—61no—
873C23—61no—
874C23—61no—
875C23D3×#6712yes—
876C23C22×D3211yescharacteristic
877D4—44no—
878D4—68no—
879D4—124no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
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—92no—
904C2×C4—92no—
905C2×C4—124no—
906C2×C4—188no—
907C2×C4—181no—
908C2×C4—181no—
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—364no—
918C2×C4—364no—
919C2×C4#381112yes—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—44no—
928C2×C3—42no—
929C2×C3—42no—
930C2×C3—64no—
931C2×C3—82no—
932C2×C3—81no—
933C2×C3—81no—
934C2×C3#559011yescharacteristic
935C2×C3#559811yescharacteristic
936C2×C3#560111yescharacteristic
937C2×C3#560211yescharacteristic
938C2×C3#560611yescharacteristic
939C2×C3#560611yescharacteristic
940C2×C3#561111yescharacteristic
941C2×C3#561411yescharacteristic
942C2×C3D3×#12311yescharacteristic
943C2×C3#566011yescharacteristic
944C2×C3#567711yescharacteristic
945C2×C3C2×#93511yescharacteristic
946C2×C3D4×#6711yescharacteristic
947C2×C3#582411yescharacteristic
948D3—24no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—34no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—62no—
970C22#6430911yescharacteristic
971C22D3×#23711yescharacteristic
972C22D3×#23711yescharacteristic
973C22D3×#23711yescharacteristic
974C22C2×D3×#6711yescharacteristic
975C22C2×#381111yescharacteristic
976C22#6433011yescharacteristic
977C4—22no—
978C4—62no—
979C4—62no—
980C4—121no—
981C4—121no—
982C4—121no—
983C4—121no—
984C4—121no—
985C4—182no—
986C4—182no—
987C4—361no—
988C4—361no—
989C3—21no—
990C3#7711711yescharacteristic, complemented
991C3#8265511yescharacteristic, complemented
992C2—42no—
993C2—64no—
994C2—81no—
995C2D3×#93511yescharacteristic
996C2#1059515111yescharacteristic
997C2#1059516111yescharacteristic
998C2#1059517411yescharacteristic
999C2#1059517911yescharacteristic
1000C2#1059530611yescharacteristic
1001C2#1059552611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×C3×#938C2
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×#64144C2semidirect
3. C2×#67⋊Dic3C2semidirect
4. C2×D3×Dic3⋊C4C2semidirect
5. C3×#5222C2semidirect
6. #10591721C2semidirect
7. #10591721C2semidirect
8. #10591721C2semidirect
9. #10591719C2semidirect
10. #10591715C2semidirect
11. #10591701C2semidirect
12. #10591694C2semidirect
13. #10591342C2semidirect
14. #10591278C2semidirect
15. #10591263C2semidirect
67. #5222D3semidirect
128. #3750D4semidirect
468. C2×C3×D3#123semidirect
824. C2×D3#935semidirect
854. C32#2443semidirect
990. C3#77117semidirect
991. C3#82655semidirect

Maximal subgroups

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

subgroupindex
C2×#641442
C2×C3×#9382
C2×#67⋊Dic32
C2×D3×Dic3⋊C42
C3×#52222
#105917212
#105917192
#105917152
#105917012
#105916942
#105913422
#105912782
#105912632
#826553
#771173