Finite Group Databasebeta

← #11807598

Subgroups — #11807598

Order 1152.

1471 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63976C211yesmaximal, characteristic
2#10592643C211yesmaximal, characteristic, complemented
3C3×#4957C211yesmaximal, characteristic, complemented
4C3×#4955C211yesmaximal, characteristic, complemented
5#10591721C211yesmaximal, characteristic, complemented
6#10591706C211yesmaximal, characteristic, complemented
7#10591703C211yesmaximal, characteristic, complemented
8#10591386C211yesmaximal, characteristic, complemented
9#10591385C211yesmaximal, characteristic, complemented
10#10591363C211yesmaximal, characteristic, complemented
11#10591363C211yesmaximal, characteristic, complemented
12#10591285C211yesmaximal, characteristic, complemented
13#10591283C211yesmaximal, characteristic, complemented
14#10591280C211yesmaximal, characteristic, complemented
15#10591279C211yesmaximal, characteristic, complemented
16#76434—31nomaximal
17#73851—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×#625C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic, complemented
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3750C2211yescharacteristic, complemented
27C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38#63976C418yescomplemented
39C2×#3724C2211yescharacteristic, complemented
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47C2×Dic32C2211yescharacteristic, complemented
48#63658C2211yescharacteristic, complemented
49#63658C2211yescharacteristic, complemented
50#63579C2211yescharacteristic, complemented
51#63579C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54C2×#953—31no—
55C2×#937—31no—
56C3×#390—31no—
57C3×#379—31no—
58#5247—31no—
59#5220—31no—
60#4990—31no—
61#4990—31no—
62#4958—31no—
63#4958—31no—
64#4957—31no—
65#4957—31no—
66#4957—31no—
67#4957—31no—
68#4957D311yescharacteristic, complemented
69#4956—31no—
70#4956—31no—
71#4956—31no—
72#4955—31no—
73#4955D311yescharacteristic, complemented
74#4945—31no—
75#4945—31no—
76#4945—31no—
77#4944—31no—
78#4944—31no—
79#4944—31no—
80#4944—31no—
81#4944—31no—
82#4944—61no—
83#4940—31no—
84#4940—31no—
85C24×C32C2311yescharacteristic
86C23×C3×D3—41no—
87C23×C3×D3—41no—
88C23×C3×D3—41no—
89C23×C3×D3—41no—
90C23×C3×D3—41no—
91C23×C3×D3—41no—
92C23×C3×D3C2×C414yescomplemented
93C23×C3×D3C2311yescharacteristic
94C23×C3×D3C2311yescharacteristic
95C23×C3×D3C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C3×#67—41no—
103C2×C3×#67—41no—
104C2×C3×#67C2×C414yes—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×#625—41no—
111C2×#625—41no—
112C2×#625—41no—
113C2×#625—41no—
114C2×#625C2×C414yes—
115C2×#625C2×C414yes—
116C2×D3×Dic3—41no—
117C2×D3×Dic3—41no—
118C2×D3×Dic3—41no—
119C32×C22⋊C4—41no—
120#3757—41no—
121#3757C2×C414yescomplemented
122#3750—41no—
123C4×C3⋊Dic3—41no—
124C3×#217—41no—
125C3×#217—41no—
126C3×(C2×D3)⋊C4—41no—
127C3×(C2×D3)⋊C4—41no—
128C3×(C2×D3)⋊C4—41no—
129C3×(C2×D3)⋊C4—41no—
130C3×(C2×D3)⋊C4—41no—
131C3×(C2×D3)⋊C4—41no—
132C3×Dic3⋊C4—41no—
133C3×C4×Dic3—41no—
134#3724—41no—
135(C2×D3)⋊Dic3—41no—
136(C2×D3)⋊Dic3—41no—
137(C2×D3)⋊Dic3—41no—
138(C2×D3)⋊Dic3—41no—
139(C2×D3)⋊Dic3—41no—
140(C2×D3)⋊Dic3C2×C414yescomplemented
141(C2×D3)⋊Dic3C2×C414yescomplemented
142Dic32—41no—
143#2375—91noSylow
144C25×C3—31no—
145C24×D3C2×D311yescharacteristic
146C22×C3×D4—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67C2×D311yescharacteristic
152C23×Dic3—31no—
153C22×C4×D3—31no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4C2×D311yescharacteristic
165C2×C3×C22⋊C4C2×D311yescharacteristic
166C2×C3×C42—31no—
167#953—38no—
168C2×#217—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—31no—
178C2×#217—31no—
179C2×#217—61no—
180C2×#217—61no—
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183#937—38no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×(C2×D3)⋊C4C2×D311yescharacteristic
195C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
196C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—61no—
202C2×Dic3⋊C4C2×D311yescharacteristic, complemented
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—61no—
208C2×C4×Dic3C2×D311yescharacteristic, complemented
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—61no—
222C3⋊#95—61no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32C22×C412yes—
230C23×C32C2411yescharacteristic
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—44no—
250C22×C3×D3—44no—
251C22×C3×D3—44no—
252C22×C3×D3—44no—
253C22×C3×D3—44no—
254C22×C3×D3—44no—
255C22×C3×D3—44no—
256C22×C3×D3C22×C412yes—
257C22×C3×D3C22×C412yes—
258C22×C3×D3C22×C412yes—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3C22×C412yes—
276C2×C3⋊Dic3C22×C412yes—
277C3×#67—44no—
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×Dic3C22×C412yes—
293#625—44no—
294#625—44no—
295D3×Dic3—44no—
296C2×#120—91no—
297#390—31no—
298#390—91no—
299#390—91no—
300#388—91no—
301#388—91no—
302#388—91no—
303#388—91no—
304#388—91no—
305#388—91no—
306#386—91no—
307#386—91no—
308#386—91no—
309#379—31no—
310#379—91no—
311C24×C3—21no—
312C24×C3—31no—
313C24×C3—31no—
314C24×C3—31no—
315C24×C3—34no—
316C24×C3—121no—
317C24×C3—121no—
318C24×C3—121no—
319C24×C3—121no—
320C24×C3—121no—
321C24×C3—121no—
322C24×C3C22×D311yescharacteristic
323C24×C3C22×D311yescharacteristic
324C23×D3—41no—
325C23×D3—41no—
326C23×D3—41no—
327C23×D3—41no—
328C23×D3—41no—
329C23×D3—41no—
330C23×D3C4×D314yescomplemented
331C23×D3C22×D311yescharacteristic
332C23×D3C22×D311yescharacteristic
333C23×D3C22×D311yescharacteristic
334C2×C3×D4—34no—
335C2×C3×D4—121no—
336C2×C3×D4—121no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C2×#67—34no—
349C2×#67—34no—
350C2×#67—34no—
351C2×#67—34no—
352C2×#67—41no—
353C2×#67—41no—
354C2×#67—121no—
355C2×#67—121no—
356C2×#67—121no—
357C2×#67—121no—
358C2×#67—121no—
359C2×#67—121no—
360C2×#67—121no—
361C2×#67—121no—
362C2×#67C4×D314yes—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374C22×Dic3—61no—
375C22×Dic3—121no—
376C22×Dic3—121no—
377C22×Dic3—121no—
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C2×C4×D3—121no—
384C2×C4×D3—121no—
385C2×C4×D3—121no—
386C3×C4⋊C4—121no—
387C3×C22⋊C4—41no—
388C3×C22⋊C4—41no—
389C3×C22⋊C4—42no—
390C3×C22⋊C4—121no—
391C3×C22⋊C4—121no—
392C3×C22⋊C4—121no—
393C3×C22⋊C4—121no—
394C3×C22⋊C4—121no—
395C3×C22⋊C4—121no—
396C3×C22⋊C4—121no—
397C3×C22⋊C4—121no—
398C3×C42—121no—
399#217—34no—
400#217—34no—
401#217—34no—
402#217—34no—
403#217—41no—
404#217—41no—
405#217—64no—
406#217—121no—
407#217—121no—
408#217—121no—
409#217—121no—
410#217—121no—
411#217—121no—
412#217—121no—
413#217—122no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—41no—
417(C2×D3)⋊C4—41no—
418(C2×D3)⋊C4—41no—
419(C2×D3)⋊C4—41no—
420(C2×D3)⋊C4—41no—
421(C2×D3)⋊C4—41no—
422(C2×D3)⋊C4—121no—
423(C2×D3)⋊C4—121no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4—121no—
426(C2×D3)⋊C4—121no—
427Dic3⋊C4—41no—
428Dic3⋊C4—121no—
429Dic3⋊C4—121no—
430Dic3⋊C4—121no—
431Dic3⋊C4—121no—
432Dic3⋊C4—122no—
433C4×Dic3—41no—
434C4×Dic3—121no—
435C4×Dic3—121no—
436C4×Dic3—121no—
437C4×Dic3—121no—
438C4×Dic3—122no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32C23×C411yescharacteristic
447C22×C32H(5,𝔽2)11yescharacteristic
448C22×C32H(5,𝔽2)11yescharacteristic
449C22×C32H(5,𝔽2)11yescharacteristic
450C22×C32H(5,𝔽2)11yescharacteristic
451C22×C32H(5,𝔽2)11yescharacteristic
452C22×C32H(5,𝔽2)11yescharacteristic
453C2×C3×D3—22no—
454C2×C3×D3—22no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—416no—
463C2×C3×D3—41no—
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—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C32×C4—41no—
476C32×C4—41no—
477C3⋊Dic3—22no—
478C3⋊Dic3—22no—
479C3⋊Dic3—41no—
480C3⋊Dic3—41no—
481C3×Dic3—22no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C3×Dic3—41no—
486C25—31no—
487C22×D4—31no—
488C22×D4—91no—
489C22×D4—91no—
490C23×C4—91no—
491#120—98no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4D3211yescharacteristic
513C2×C42—31no—
514C2×C42—91no—
515C2×C42—91no—
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—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—22no—
536C23×C3—32no—
537C23×C3—32no—
538C23×C3—32no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—124no—
564C23×C3—124no—
565C23×C3—124no—
566C23×C3—124no—
567C23×C3—124no—
568C23×C3—124no—
569C23×C3—124no—
570C23×C3C2×C4×D312yes—
571C23×C3C2×C4×D312yes—
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—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—44no—
593C22×D3—44no—
594C22×D3—44no—
595C22×D3—44no—
596C22×D3—44no—
597C22×D3—44no—
598C22×D3—44no—
599C22×D3C2×C4×D312yes—
600C22×D3C2×C4×D312yes—
601C22×D3C2×C4×D312yes—
602C3×D4—124no—
603C2×C3×C4—22no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—32no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636#67—44no—
637#67—124no—
638#67—124no—
639#67—124no—
640#67—124no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—62no—
660C2×Dic3—62no—
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—62no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—121no—
683C2×Dic3—121no—
684C2×Dic3—121no—
685C2×Dic3—121no—
686C2×Dic3—121no—
687C2×Dic3—121no—
688C2×Dic3—121no—
689C2×Dic3—121no—
690C2×Dic3—121no—
691C2×Dic3—124no—
692C2×Dic3C2×C4×D312yes—
693C4×D3—124no—
694C2×C32—42no—
695C2×C32#51811yescharacteristic
696C2×C32#51811yescharacteristic
697C2×C32#51811yescharacteristic
698C2×C32#56011yescharacteristic
699C2×C32#56011yescharacteristic
700C2×C32#56011yescharacteristic
701C2×C32H(3,𝔽4)11yescharacteristic
702C3×D3—42no—
703C3×D3—42no—
704C3×D3—42no—
705C24—31no—
706C24—31no—
707C24—31no—
708C24—34no—
709C24—121no—
710C24—121no—
711C24—121no—
712C24—121no—
713C24—121no—
714C24—121no—
715C24C2×D3211yescharacteristic
716C2×D4—34no—
717C2×D4—94no—
718C2×D4—94no—
719C2×D4—121no—
720C2×D4—121no—
721C2×D4—361no—
722C2×D4—361no—
723C2×D4—361no—
724C2×D4—361no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—91no—
731C22×C4—91no—
732C22×C4—91no—
733C22×C4—91no—
734C22×C4—361no—
735C22×C4—361no—
736C22×C4—361no—
737C22×C4C2×D3211yescharacteristic
738C22×C4C2×D3211yescharacteristic
739C4⋊C4—121no—
740C4⋊C4—361no—
741C4⋊C4—361no—
742C22⋊C4—41no—
743C22⋊C4—94no—
744C22⋊C4—94no—
745C22⋊C4—94no—
746C22⋊C4—121no—
747C22⋊C4—121no—
748C22⋊C4—121no—
749C22⋊C4—121no—
750C22⋊C4—121no—
751C22⋊C4—121no—
752C22⋊C4—121no—
753C22⋊C4—121no—
754C22⋊C4—361no—
755C22⋊C4—361no—
756C22⋊C4—361no—
757C22⋊C4—361no—
758C22⋊C4—361no—
759C22⋊C4—361no—
760C42—121no—
761C42—361no—
762C42—361no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—42no—
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—62no—
788C22×C3—62no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—81no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3—1216no—
801C22×C3—121no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3—121no—
805C22×C3—121no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3—121no—
812C22×C3—121no—
813C22×C3C22×C4×D311yescharacteristic
814C22×C3C22×C4×D311yescharacteristic
815C22×C3#100411yescharacteristic
816C22×C3#100411yescharacteristic
817C22×C3#100411yescharacteristic
818C22×C3#100411yescharacteristic
819C22×C3#100411yescharacteristic
820C22×C3#100411yescharacteristic
821C22×C3#100411yescharacteristic
822C22×C3#100411yescharacteristic
823C22×C3#100411yescharacteristic
824C22×C3#100411yescharacteristic
825C22×C3#100911yescharacteristic
826C22×C3#100911yescharacteristic
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—416no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—41no—
847C2×D3—41no—
848C2×D3—41no—
849C3×C4—42no—
850C3×C4—41no—
851C3×C4—41no—
852C3×C4—41no—
853C3×C4—41no—
854C3×C4—62no—
855C3×C4—81no—
856C3×C4—121no—
857C3×C4—121no—
858C3×C4—121no—
859C3×C4—121no—
860Dic3—22no—
861Dic3—41no—
862Dic3—41no—
863Dic3—41no—
864Dic3—41no—
865Dic3—62no—
866Dic3—62no—
867Dic3—62no—
868Dic3—62no—
869Dic3—122no—
870Dic3—122no—
871Dic3—122no—
872Dic3—121no—
873Dic3—121no—
874Dic3—121no—
875Dic3—121no—
876Dic3—241no—
877C32#237511yescharacteristic, complemented, Sylow
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—32no—
885C23—32no—
886C23—32no—
887C23—61no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—61no—
903C23—61no—
904C23—61no—
905C23—124no—
906C23—124no—
907C23—124no—
908C23—124no—
909C23—124no—
910C23—124no—
911C23—124no—
912C23C4×D3212yes—
913C23C22×D3211yescharacteristic
914D4—124no—
915D4—364no—
916D4—364no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—32no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—92no—
939C2×C4—92no—
940C2×C4—181no—
941C2×C4—181no—
942C2×C4—181no—
943C2×C4—181no—
944C2×C4—181no—
945C2×C4—181no—
946C2×C4—181no—
947C2×C4—181no—
948C2×C4—181no—
949C2×C4—181no—
950C2×C4—364no—
951C2×C3—21no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—42no—
959C2×C3—42no—
960C2×C3—82no—
961C2×C3—122no—
962C2×C3—122no—
963C2×C3—122no—
964C2×C3#548611yescharacteristic
965C2×C3#548611yescharacteristic
966C2×C3#548611yescharacteristic
967C2×C3#548611yescharacteristic
968C2×C3#554511yescharacteristic
969C2×C3#554511yescharacteristic
970C2×C3#559411yescharacteristic
971C2×C3#559511yescharacteristic
972C2×C3#559511yescharacteristic
973C2×C3#559511yescharacteristic
974C2×C3#562011yescharacteristic
975C2×C3#562011yescharacteristic
976C2×C3#568311yescharacteristic
977C2×C3#572011yescharacteristic
978D3—42no—
979D3—42no—
980D3—42no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—41no—
985C22—41no—
986C22—41no—
987C22—41no—
988C22—62no—
989C22—62no—
990C22—62no—
991C22—62no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—1216no—
998C22—121no—
999C22—121no—
1000C22—121no—
1001C22—121no—
1002C22—121no—
1003C22—121no—
1004C22—121no—
1005C22—121no—
1006C22—121no—
1007C22—121no—
1008C22—121no—
1009C22—121no—
1010C22C2×C4×D3211yescharacteristic
1011C22#6430711yescharacteristic
1012C22#6431311yescharacteristic
1013C22#6431311yescharacteristic
1014C22#6431311yescharacteristic
1015C22#6431411yescharacteristic
1016C22#6433011yescharacteristic
1017C4—41no—
1018C4—41no—
1019C4—62no—
1020C4—121no—
1021C4—121no—
1022C4—121no—
1023C4—121no—
1024C4—182no—
1025C4—182no—
1026C4—361no—
1027C4—361no—
1028C3—21no—
1029C3#7385111yescharacteristic, complemented
1030C3#7643411yescharacteristic, complemented
1031C2—42no—
1032C2—122no—
1033C2—122no—
1034C2—122no—
1035C2#1059418111yescharacteristic
1036C2#1059423411yescharacteristic
1037C2#1059425411yescharacteristic
1038C2#1059430911yescharacteristic
1039C2#1059505611yescharacteristic
1040C2#1059525811yescharacteristic
1041C2#1059525911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63976C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2375
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592643C2semidirect
3. C3×#4957C2semidirect
4. C3×#4955C2semidirect
5. #10591721C2semidirect
6. #10591706C2semidirect
7. #10591703C2semidirect
8. #10591386C2semidirect
9. #10591385C2semidirect
10. #10591363C2semidirect
11. #10591363C2semidirect
12. #10591285C2semidirect
13. #10591283C2semidirect
14. #10591280C2semidirect
15. #10591279C2semidirect
22. C22×D3×Dic3C22semidirect
26. C2×#3750C22semidirect
27. C2×C4×C3⋊Dic3C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×C4×Dic3C22semidirect
38. #63976C4semidirect
39. C2×#3724C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×Dic32C22semidirect
48. #63658C22semidirect
49. #63658C22semidirect
50. #63579C22semidirect
51. #63579C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
68. #4957D3semidirect
73. #4955D3semidirect
92. C23×C3×D3C2×C4semidirect
121. #3757C2×C4semidirect
140. (C2×D3)⋊Dic3C2×C4semidirect
141. (C2×D3)⋊Dic3C2×C4semidirect
195. C2×(C2×D3)⋊C4C2×D3semidirect
196. C2×(C2×D3)⋊C4C2×D3semidirect
202. C2×Dic3⋊C4C2×D3semidirect
208. C2×C4×Dic3C2×D3semidirect
330. C23×D3C4×D3semidirect
877. C32#2375semidirect
1029. C3#73851semidirect
1030. C3#76434semidirect

Maximal subgroups

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

subgroupindex
C2×#639762
#105926432
C3×#49572
C3×#49552
#105917212
#105917062
#105917032
#105913862
#105913852
#105913632
#105912852
#105912832
#105912802
#105912792
#764343
#738513