Finite Group Databasebeta

← #11807596

Subgroups — #11807596

Order 1152.

1505 conjugacy classes of subgroups.

The subgroup lattice has 1059 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63977C211yesmaximal, characteristic
2#10592656C211yesmaximal, characteristic, complemented
3C3×#4955C211yesmaximal, characteristic, complemented
4C3×#4944C211yesmaximal, characteristic, complemented
5#10591722C211yesmaximal, characteristic, complemented
6#10591706C211yesmaximal, characteristic, complemented
7#10591702C211yesmaximal, characteristic, complemented
8#10591384C211yesmaximal, characteristic, complemented
9#10591383C211yesmaximal, characteristic, complemented
10#10591287C211yesmaximal, characteristic, complemented
11#10591283C211yesmaximal, characteristic, complemented
12#10591281C211yesmaximal, characteristic, complemented
13#10591280C211yesmaximal, characteristic, complemented
14#10591275C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#75840—31nomaximal
17#73851—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic, complemented
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3752C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic, complemented
27C2×#3750C2211yescharacteristic, complemented
28C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38#63977C418yescomplemented
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×#3722C2211yescharacteristic, complemented
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×Dic32C2211yescharacteristic, complemented
48C3×C3⋊#95C2211yescharacteristic, complemented
49C3×C3⋊#95C2211yescharacteristic, complemented
50#63579C2211yescharacteristic, complemented
51#63579C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54C2×#953—31no—
55C2×#882—31no—
56C3×#388—31no—
57C3×#379—31no—
58#5247—31no—
59#4990—31no—
60#4988—31no—
61#4957—31no—
62#4957—31no—
63#4957—31no—
64#4957—31no—
65#4957—61no—
66#4956—31no—
67#4956—31no—
68#4956—31no—
69#4956—31no—
70#4955—31no—
71#4955D311yescharacteristic, complemented
72#4951—31no—
73#4945—31no—
74#4945—31no—
75#4945—31no—
76#4944—31no—
77#4944—31no—
78#4944D311yescharacteristic, complemented
79#4940—31no—
80#4939—31no—
81#4670—31no—
82#4669—31no—
83#4665—31no—
84#4665—31no—
85C24×C32C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3—41no—
88C23×C3×D3—41no—
89C23×C3×D3—41no—
90C23×C3×D3—41no—
91C23×C3×D3—41no—
92C23×C3×D3—41no—
93C23×C3×D3C2×C414yescomplemented
94C23×C3×D3C2311yescharacteristic
95C23×C3×D3C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638—41no—
99C2×#638—41no—
100C2×#638C2×C414yes—
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×#626—41no—
111C2×#626—41no—
112C2×#626—41no—
113C2×#626—41no—
114C2×#626C2×C414yes—
115C2×#626C2×C414yes—
116C2×#624—41no—
117C2×#624—41no—
118C2×#624—41no—
119C32×C22⋊C4—41no—
120#3757—41no—
121#3752—41no—
122#3752—41no—
123#3750—41no—
124C4×C3⋊Dic3—41no—
125C3×#217—41no—
126C3×#217—41no—
127C3×#217C2×C414yescomplemented
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—
134Dic3⋊Dic3—41no—
135#3722—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×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—61no—
151C22×D12—31no—
152C22×D12—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C22⋊C4—21no—
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—61no—
177C2×#217C2×D311yescharacteristic
178C2×#217C2×D311yescharacteristic
179C2×#217C2×D311yescharacteristic
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
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)⋊C4—31no—
192C2×(C2×D3)⋊C4—61no—
193C2×(C2×D3)⋊C4—61no—
194C2×(C2×D3)⋊C4C2×D311yescharacteristic
195C2×(C2×D3)⋊C4C2×D311yescharacteristic
196C2×(C2×D3)⋊C4C2×D311yescharacteristic
197C2×(C2×D3)⋊C4C2×D311yescharacteristic
198C2×C4⋊Dic3—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—61no—
203C2×Dic3⋊C4C2×D311yescharacteristic, complemented
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—61no—
209C2×C4×Dic3C2×D311yescharacteristic, complemented
210#882—38no—
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⋊#95C2×D311yescharacteristic, complemented
222C3⋊#95C2×D311yescharacteristic, complemented
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⋊D3C22×C412yes—
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—21no—
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×D3—44no—
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—
265#638—44no—
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⋊Dic3C22×C412yes—
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×Dic3C22×C412yes—
292C2×C3×Dic3C22×C412yes—
293#626—44no—
294#626—44no—
295#624—44no—
296C2×#120—91no—
297#390—91no—
298#390—91no—
299#390—91no—
300#388—31no—
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—34no—
315C24×C3—121no—
316C24×C3—121no—
317C24×C3—121no—
318C24×C3—121no—
319C24×C3—121no—
320C24×C3—121no—
321C24×C3C22×D311yescharacteristic
322C24×C3C22×D311yescharacteristic
323C23×D3—31no—
324C23×D3—31no—
325C23×D3—41no—
326C23×D3—41no—
327C23×D3—41no—
328C23×D3—41no—
329C23×D3—41no—
330C23×D3—41no—
331C23×D3—61no—
332C23×D3C4×D314yescomplemented
333C23×D3C22×D311yescharacteristic
334C23×D3C22×D311yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C2×#67—34no—
348C2×#67—34no—
349C2×#67—34no—
350C2×#67—34no—
351C2×#67—64no—
352C2×#67—121no—
353C2×#67—121no—
354C2×#67—121no—
355C2×#67—121no—
356C2×#67—121no—
357C2×#67—121no—
358C2×#67—121no—
359C2×#67—121no—
360C2×#67—122no—
361C2×#67—122no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C2×D12—34no—
378C2×D12—34no—
379C2×D12—121no—
380C2×D12—121no—
381C2×D12—121no—
382C2×D12—121no—
383C2×C4×D3—121no—
384C2×C4×D3—121no—
385C2×C4×D3—121no—
386C2×C4×D3—121no—
387C2×C4×D3—121no—
388C2×C4×D3—121no—
389C3×C4⋊C4—121no—
390C3×C22⋊C4—34no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—41no—
393C3×C22⋊C4—42no—
394C3×C22⋊C4—121no—
395C3×C22⋊C4—121no—
396C3×C22⋊C4—121no—
397C3×C22⋊C4—121no—
398C3×C22⋊C4—121no—
399C3×C22⋊C4—121no—
400C3×C42—121no—
401#217—34no—
402#217—34no—
403#217—41no—
404#217—41no—
405#217—121no—
406#217—121no—
407#217—121no—
408#217—121no—
409#217—121no—
410#217—121no—
411#217—122no—
412#217C4×D314yescomplemented
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—41no—
416(C2×D3)⋊C4—41no—
417(C2×D3)⋊C4—41no—
418(C2×D3)⋊C4—41no—
419(C2×D3)⋊C4—121no—
420(C2×D3)⋊C4—121no—
421(C2×D3)⋊C4—121no—
422(C2×D3)⋊C4—121no—
423(C2×D3)⋊C4—121no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4—122no—
426(C2×D3)⋊C4—121no—
427(C2×D3)⋊C4—121no—
428(C2×D3)⋊C4—121no—
429(C2×D3)⋊C4—121no—
430(C2×D3)⋊C4—122no—
431C4⋊Dic3—121no—
432Dic3⋊C4—41no—
433Dic3⋊C4—121no—
434Dic3⋊C4—121no—
435Dic3⋊C4—121no—
436Dic3⋊C4—122no—
437C4×Dic3—41no—
438C4×Dic3—121no—
439C4×Dic3—121no—
440C4×Dic3—121no—
441C4×Dic3—121no—
442C4×Dic3—122no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32C23×C411yescharacteristic
451C22×C32H(5,𝔽2)11yescharacteristic
452C22×C32H(5,𝔽2)11yescharacteristic
453C22×C32H(5,𝔽2)11yescharacteristic
454C22×C32H(5,𝔽2)11yescharacteristic
455C22×C32H(5,𝔽2)11yescharacteristic
456C22×C32H(5,𝔽2)11yescharacteristic
457C2×C3⋊D3—22no—
458C2×C3⋊D3—22no—
459C2×C3⋊D3—22no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—416no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C32×C4—41no—
480C32×C4—41no—
481C3⋊Dic3—22no—
482C3⋊Dic3—41no—
483C3⋊Dic3—41no—
484C3×Dic3—22no—
485C3×Dic3—22no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C25—31no—
491C22×D4—91no—
492C22×D4—91no—
493C22×D4—91no—
494C23×C4—91no—
495#120—98no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C22⋊C4—31no—
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×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4D3211yescharacteristic
517C2×C42—31no—
518C2×C42—91no—
519C2×C42—91no—
520#95—31no—
521#95—31no—
522#95—91no—
523#95—91no—
524#95—91no—
525#95—91no—
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—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—22no—
540C23×C3—32no—
541C23×C3—32no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—41no—
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—124no—
561C23×C3—124no—
562C23×C3—124no—
563C23×C3—124no—
564C23×C3—124no—
565C23×C3—124no—
566C23×C3—124no—
567C23×C3C2×C4×D312yes—
568C23×C3C2×C4×D312yes—
569C23×C3C23×D311yescharacteristic
570C23×C3C23×D311yescharacteristic
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
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—32no—
584C22×D3—32no—
585C22×D3—44no—
586C22×D3—44no—
587C22×D3—44no—
588C22×D3—44no—
589C22×D3—44no—
590C22×D3—44no—
591C22×D3—44no—
592C22×D3—62no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3C2×C4×D312yes—
612C22×D3C2×C4×D312yes—
613C2×C3×C4—22no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—32no—
627C2×C3×C4—32no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649#67—124no—
650#67—124no—
651#67—124no—
652#67—124no—
653#67—128no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—62no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—121no—
693C2×Dic3—121no—
694C2×Dic3—121no—
695C2×Dic3—121no—
696C2×Dic3—121no—
697C2×Dic3C2×C4×D312yes—
698C2×Dic3C2×C4×D312yes—
699D12—124no—
700D12—124no—
701C4×D3—124no—
702C4×D3—124no—
703C2×C32—42no—
704C2×C32#51811yescharacteristic
705C2×C32#51811yescharacteristic
706C2×C32#51811yescharacteristic
707C2×C32#56011yescharacteristic
708C2×C32#56011yescharacteristic
709C2×C32#56011yescharacteristic
710C2×C32H(3,𝔽4)11yescharacteristic
711C3⋊D3—42no—
712C3×D3—42no—
713C3×D3—42no—
714C24—31no—
715C24—31no—
716C24—34no—
717C24—91no—
718C24—121no—
719C24—121no—
720C24—121no—
721C24—121no—
722C24—121no—
723C24—121no—
724C24C2×D3211yescharacteristic
725C2×D4—94no—
726C2×D4—94no—
727C2×D4—94no—
728C2×D4—361no—
729C2×D4—361no—
730C2×D4—361no—
731C2×D4—361no—
732C2×D4—361no—
733C2×D4—361no—
734C22×C4—31no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—91no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—361no—
744C22×C4—361no—
745C22×C4—361no—
746C22×C4C2×D3211yescharacteristic
747C22×C4C2×D3211yescharacteristic
748C4⋊C4—121no—
749C4⋊C4—361no—
750C4⋊C4—361no—
751C22⋊C4—34no—
752C22⋊C4—41no—
753C22⋊C4—94no—
754C22⋊C4—94no—
755C22⋊C4—121no—
756C22⋊C4—121no—
757C22⋊C4—121no—
758C22⋊C4—121no—
759C22⋊C4—121no—
760C22⋊C4—121no—
761C22⋊C4—361no—
762C22⋊C4—361no—
763C22⋊C4—361no—
764C22⋊C4—361no—
765C22⋊C4—361no—
766C22⋊C4—361no—
767C22⋊C4—361no—
768C22⋊C4—361no—
769C42—121no—
770C42—361no—
771C42—361no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—22no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—81no—
803C22×C3—81no—
804C22×C3—81no—
805C22×C3—81no—
806C22×C3—1216no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3—121no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3C22×C4×D311yescharacteristic
816C22×C3C22×C4×D311yescharacteristic
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
827C22×C3#100911yescharacteristic
828C22×C3#100911yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—416no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—122no—
851C2×D3—122no—
852C2×D3—122no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—121no—
859C2×D3—121no—
860C2×D3—121no—
861C2×D3—241no—
862C2×D3—241no—
863C2×D3—241no—
864C2×D3—241no—
865C3×C4—42no—
866C3×C4—41no—
867C3×C4—41no—
868C3×C4—41no—
869C3×C4—41no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—81no—
873C3×C4—121no—
874C3×C4—121no—
875C3×C4—121no—
876C3×C4—121no—
877Dic3—22no—
878Dic3—22no—
879Dic3—41no—
880Dic3—41no—
881Dic3—41no—
882Dic3—41no—
883Dic3—64no—
884Dic3—62no—
885Dic3—62no—
886Dic3—122no—
887Dic3—121no—
888Dic3—121no—
889Dic3—121no—
890Dic3—121no—
891Dic3—241no—
892C32#237511yescharacteristic, complemented, Sylow
893C23—21no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—32no—
900C23—32no—
901C23—61no—
902C23—61no—
903C23—61no—
904C23—61no—
905C23—61no—
906C23—61no—
907C23—61no—
908C23—61no—
909C23—61no—
910C23—61no—
911C23—61no—
912C23—61no—
913C23—92no—
914C23—124no—
915C23—124no—
916C23—124no—
917C23—124no—
918C23—124no—
919C23—124no—
920C23—124no—
921C23—181no—
922C23—181no—
923C23—181no—
924C23—181no—
925C23—181no—
926C23—181no—
927C23C4×D3212yes—
928C23C22×D3211yescharacteristic
929D4—364no—
930D4—364no—
931D4—364no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—32no—
939C2×C4—32no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—61no—
944C2×C4—61no—
945C2×C4—61no—
946C2×C4—61no—
947C2×C4—61no—
948C2×C4—61no—
949C2×C4—61no—
950C2×C4—61no—
951C2×C4—61no—
952C2×C4—61no—
953C2×C4—61no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—92no—
957C2×C4—181no—
958C2×C4—181no—
959C2×C4—181no—
960C2×C4—181no—
961C2×C4—181no—
962C2×C4—181no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—364no—
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—42no—
974C2×C3—42no—
975C2×C3—82no—
976C2×C3—122no—
977C2×C3—122no—
978C2×C3#548611yescharacteristic
979C2×C3#548611yescharacteristic
980C2×C3#548611yescharacteristic
981C2×C3#552111yescharacteristic
982C2×C3#554511yescharacteristic
983C2×C3#554511yescharacteristic
984C2×C3#559411yescharacteristic
985C2×C3#559511yescharacteristic
986C2×C3#559511yescharacteristic
987C2×C3#559511yescharacteristic
988C2×C3#562011yescharacteristic
989C2×C3#566611yescharacteristic
990C2×C3#568311yescharacteristic
991C2×C3#571111yescharacteristic
992D3—42no—
993D3—42no—
994D3—122no—
995D3—122no—
996D3—242no—
997C22—22no—
998C22—22no—
999C22—22no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—62no—
1008C22—62no—
1009C22—62no—
1010C22—1216no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—121no—
1015C22—121no—
1016C22—121no—
1017C22—121no—
1018C22—121no—
1019C22—182no—
1020C22—182no—
1021C22—182no—
1022C22—361no—
1023C22—361no—
1024C22—361no—
1025C22—361no—
1026C22C2×C4×D3211yescharacteristic
1027C22#6430711yescharacteristic
1028C22#6431311yescharacteristic
1029C22#6431411yescharacteristic
1030C22#6431411yescharacteristic
1031C22#6431411yescharacteristic
1032C22#6433011yescharacteristic
1033C4—41no—
1034C4—41no—
1035C4—62no—
1036C4—62no—
1037C4—121no—
1038C4—121no—
1039C4—121no—
1040C4—121no—
1041C4—182no—
1042C4—361no—
1043C4—361no—
1044C3—21no—
1045C3#7385111yescharacteristic, complemented
1046C3#7584011yescharacteristic, complemented
1047C2—42no—
1048C2—122no—
1049C2—122no—
1050C2—362no—
1051C2#1059418211yescharacteristic
1052C2#1059423611yescharacteristic
1053C2#1059425411yescharacteristic
1054C2#1059430911yescharacteristic
1055C2#1059505611yescharacteristic
1056C2#1059525711yescharacteristic
1057C2#1059526111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63977C2
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. #10592656C2semidirect
3. C3×#4955C2semidirect
4. C3×#4944C2semidirect
5. #10591722C2semidirect
6. #10591706C2semidirect
7. #10591702C2semidirect
8. #10591384C2semidirect
9. #10591383C2semidirect
10. #10591287C2semidirect
11. #10591283C2semidirect
12. #10591281C2semidirect
13. #10591280C2semidirect
14. #10591275C2semidirect
15. #10591275C2semidirect
22. C22×#624C22semidirect
25. C2×#3752C22semidirect
26. C2×#3752C22semidirect
27. C2×#3750C22semidirect
28. C2×C4×C3⋊Dic3C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×C4×Dic3C22semidirect
38. #63977C4semidirect
39. C2×Dic3⋊Dic3C22semidirect
40. C2×#3722C22semidirect
47. C2×Dic32C22semidirect
48. C3×C3⋊#95C22semidirect
49. C3×C3⋊#95C22semidirect
50. #63579C22semidirect
51. #63579C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
71. #4955D3semidirect
78. #4944D3semidirect
93. C23×C3×D3C2×C4semidirect
127. C3×#217C2×C4semidirect
140. (C2×D3)⋊Dic3C2×C4semidirect
141. (C2×D3)⋊Dic3C2×C4semidirect
203. C2×Dic3⋊C4C2×D3semidirect
209. C2×C4×Dic3C2×D3semidirect
221. C3⋊#95C2×D3semidirect
222. C3⋊#95C2×D3semidirect
332. C23×D3C4×D3semidirect
412. #217C4×D3semidirect
892. C32#2375semidirect
1045. C3#73851semidirect
1046. C3#75840semidirect

Maximal subgroups

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

subgroupindex
C2×#639772
#105926562
C3×#49552
C3×#49442
#105917222
#105917062
#105917022
#105913842
#105913832
#105912872
#105912832
#105912812
#105912802
#105912752
#758403
#738513