Finite Group Databasebeta

← #11807603

Subgroups — #11807603

Order 1152.

1629 conjugacy classes of subgroups.

The subgroup lattice has 1081 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63981C211yesmaximal, characteristic
2#10592654C211yesmaximal, characteristic, complemented
3C3×#4956C211yesmaximal, characteristic, complemented
4C3×#4945C211yesmaximal, characteristic, complemented
5#10591714C211yesmaximal, characteristic, complemented
6#10591707C211yesmaximal, characteristic, complemented
7#10591702C211yesmaximal, characteristic, complemented
8#10591384C211yesmaximal, characteristic, complemented
9#10591383C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11#10591382C211yesmaximal, characteristic, complemented
12#10591259C211yesmaximal, characteristic, complemented
13#10591259C211yesmaximal, characteristic, complemented
14#10591258C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#75840—31nomaximal
17#74882—31nomaximal
18C24×C3⋊D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic, complemented
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
33C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35#63981C418yescomplemented
36C2×Dic3⋊Dic3C2211yescharacteristic, complemented
37C2×Dic3⋊Dic3C2211yescharacteristic, complemented
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
45C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
46C2×Dic32C2211yescharacteristic, complemented
47C2×Dic32C2211yescharacteristic, complemented
48C3×C3⋊#95C2211yescharacteristic, complemented
49C3×C3⋊#95C2211yescharacteristic, complemented
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54C2×#937—31no—
55C2×#882—31no—
56C3×#388—31no—
57C3×#386—31no—
58#5221—31no—
59#5213—31no—
60#5213—31no—
61#4990—31no—
62#4988—31no—
63#4957—31no—
64#4957—31no—
65#4957—31no—
66#4956D311yescharacteristic, complemented
67#4955—31no—
68#4955—31no—
69#4955—31no—
70#4955—31no—
71#4955—61no—
72#4951—31no—
73#4945—31no—
74#4945D311yescharacteristic, complemented
75#4940—31no—
76#4939—31no—
77#4670—31no—
78#4670—31no—
79#4670—31no—
80#4669—31no—
81#4669—31no—
82#4669—31no—
83#4665—31no—
84#4665—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
100C2×C3×#67—41no—
101C2×C3×#67—41no—
102C2×C3×#67C2×C414yes—
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×C3×C4×D3—41no—
111C2×C3×C4×D3—41no—
112C2×C3×C4×D3—41no—
113C2×#626—41no—
114C2×#626—41no—
115C2×#626—41no—
116C2×#626—41no—
117C2×#626C2×C414yes—
118C2×#626C2×C414yes—
119C32×C22⋊C4—41no—
120#3757—41no—
121#3752—41no—
122#3752—41no—
123#3752—41no—
124#3752—41no—
125C3×#217—41no—
126C3×#217—41no—
127C3×#217C2×C414yescomplemented
128C3×(C2×D3)⋊C4—41no—
129C3×Dic3⋊C4—41no—
130C3×C4×Dic3—41no—
131Dic3⋊Dic3—41no—
132Dic3⋊Dic3—41no—
133#3722—41no—
134#3722—41no—
135#3722—41no—
136#3722—41no—
137#3722C2×C414yescomplemented
138#3722C2×C414yescomplemented
139(C2×D3)⋊Dic3—41no—
140(C2×D3)⋊Dic3—41no—
141Dic32—41no—
142Dic32—41no—
143#2375—91noSylow
144C24×D3—31no—
145C24×D3—31no—
146C24×D3—61no—
147C22×C3×D4—31no—
148C23×C3×C4—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67C2×D311yescharacteristic
152C22×D12—31no—
153C22×D12—31no—
154C22×C4×D3C2×D311yescharacteristic, complemented
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⋊C4C2×D311yescharacteristic
162C2×C3×C22⋊C4C2×D311yescharacteristic
163C2×C3×C42—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—61no—
169C2×#217C2×D311yescharacteristic
170C2×#217C2×D311yescharacteristic
171C2×#217C2×D311yescharacteristic
172#937—38no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
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—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—61no—
196C2×(C2×D3)⋊C4—61no—
197C2×(C2×D3)⋊C4—61no—
198C2×(C2×D3)⋊C4—61no—
199C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
200C2×C4⋊Dic3—31no—
201C2×C4⋊Dic3—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4C2×D311yescharacteristic, complemented
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
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⋊#95C2×D311yescharacteristic, complemented
220C3⋊#95C2×D311yescharacteristic, complemented
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⋊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—44no—
244C22×C3⋊D3—44no—
245C22×C3⋊D3—44no—
246C22×C3⋊D3—44no—
247C22×C3⋊D3—44no—
248C22×C3⋊D3—44no—
249C22×C3⋊D3—44no—
250C22×C3⋊D3C22×C412yes—
251C22×C3⋊D3C22×C412yes—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
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—
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×Dic3C22×C412yes—
291C2×C3×Dic3C22×C412yes—
292C2×C3×Dic3C22×C412yes—
293C3×C4×D3—44no—
294#626—44no—
295#626—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—31no—
307#386—91no—
308#386—91no—
309#379—91no—
310#379—91no—
311C24×C3—21no—
312C24×C3—31no—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C23×D3—31no—
316C23×D3—31no—
317C23×D3—31no—
318C23×D3—31no—
319C23×D3—34no—
320C23×D3—34no—
321C23×D3—61no—
322C23×D3—61no—
323C23×D3—64no—
324C23×D3—121no—
325C23×D3—121no—
326C23×D3—121no—
327C23×D3—121no—
328C23×D3—121no—
329C23×D3—121no—
330C23×D3—121no—
331C23×D3—121no—
332C23×D3—121no—
333C23×D3—121no—
334C23×D3—121no—
335C23×D3—121no—
336C23×D3—122no—
337C23×D3—122no—
338C23×D3—122no—
339C23×D3—122no—
340C23×D3—122no—
341C23×D3—122no—
342C23×D3C22×D311yescharacteristic
343C2×C3×D4—34no—
344C2×C3×D4—121no—
345C2×C3×D4—121no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—121no—
356C22×C3×C4—121no—
357C22×C3×C4—121no—
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C2×#67—34no—
363C2×#67—34no—
364C2×#67—41no—
365C2×#67—41no—
366C2×#67—121no—
367C2×#67—121no—
368C2×#67—121no—
369C2×#67—121no—
370C2×#67C4×D314yes—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C2×D12—34no—
385C2×D12—34no—
386C2×D12—121no—
387C2×D12—121no—
388C2×D12—121no—
389C2×D12—121no—
390C2×C4×D3—41no—
391C2×C4×D3—41no—
392C2×C4×D3—41no—
393C3×C4⋊C4—121no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—41no—
396C3×C22⋊C4—41no—
397C3×C22⋊C4—42no—
398C3×C22⋊C4—121no—
399C3×C22⋊C4—121no—
400C3×C22⋊C4—121no—
401C3×C42—121no—
402#217—41no—
403#217—41no—
404#217—121no—
405#217—121no—
406#217—121no—
407#217—121no—
408#217—122no—
409#217C4×D314yescomplemented
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—41no—
415(C2×D3)⋊C4—121no—
416(C2×D3)⋊C4—121no—
417(C2×D3)⋊C4—121no—
418(C2×D3)⋊C4—121no—
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—121no—
426(C2×D3)⋊C4—121no—
427(C2×D3)⋊C4—121no—
428(C2×D3)⋊C4—121no—
429(C2×D3)⋊C4—121no—
430(C2×D3)⋊C4—121no—
431(C2×D3)⋊C4—121no—
432(C2×D3)⋊C4—121no—
433(C2×D3)⋊C4—122no—
434(C2×D3)⋊C4—122no—
435(C2×D3)⋊C4—122no—
436(C2×D3)⋊C4—122no—
437C4⋊Dic3—121no—
438C4⋊Dic3—121no—
439Dic3⋊C4—41no—
440Dic3⋊C4—121no—
441Dic3⋊C4—121no—
442C4×Dic3—41no—
443C4×Dic3—121no—
444C4×Dic3—121no—
445C4×Dic3—121no—
446C4×Dic3—121no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C23×C411yescharacteristic
455C22×C32H(5,𝔽2)11yescharacteristic
456C22×C32H(5,𝔽2)11yescharacteristic
457C22×C32H(5,𝔽2)11yescharacteristic
458C22×C32H(5,𝔽2)11yescharacteristic
459C22×C32H(5,𝔽2)11yescharacteristic
460C22×C32H(5,𝔽2)11yescharacteristic
461C2×C3⋊D3—22no—
462C2×C3⋊D3—22no—
463C2×C3⋊D3—22no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—22no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3—416no—
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—
475C2×C3⋊D3—41no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C32×C4—41no—
484C32×C4—41no—
485C3⋊Dic3—41no—
486C3⋊Dic3—41no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—41no—
491C3×Dic3—41no—
492C3×Dic3—41no—
493C3×Dic3—41no—
494C25—91no—
495C22×D4—31no—
496C22×D4—91no—
497C22×D4—91no—
498C23×C4—31no—
499#120—98no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—91no—
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×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C22⋊C4D3211yescharacteristic
521C2×C42—31no—
522C2×C42—91no—
523C2×C42—91no—
524#95—31no—
525#95—31no—
526#95—31no—
527#95—31no—
528#95—91no—
529#95—91no—
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—32no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3C2×C4×D312yes—
558C23×C3C2×C4×D312yes—
559C23×C3C23×D311yescharacteristic
560C23×C3C23×D311yescharacteristic
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—32no—
568C22×D3—32no—
569C22×D3—32no—
570C22×D3—32no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—62no—
574C22×D3—62no—
575C22×D3—62no—
576C22×D3—62no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—61no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
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—121no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—124no—
610C22×D3—124no—
611C22×D3—124no—
612C22×D3—124no—
613C22×D3—124no—
614C22×D3—124no—
615C22×D3—128no—
616C22×D3—128no—
617C22×D3—128no—
618C22×D3—128no—
619C22×D3—128no—
620C22×D3—128no—
621C22×D3—128no—
622C22×D3—124no—
623C22×D3—124no—
624C22×D3—124no—
625C22×D3—124no—
626C22×D3—124no—
627C22×D3—124no—
628C22×D3—124no—
629C22×D3—124no—
630C22×D3C2×C4×D312yes—
631C3×D4—124no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
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—124no—
672#67—44no—
673#67—124no—
674#67—124no—
675C2×Dic3—21no—
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—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—121no—
706C2×Dic3—121no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—121no—
711C2×Dic3C2×C4×D312yes—
712C2×Dic3C2×C4×D312yes—
713C2×Dic3C2×C4×D312yes—
714D12—124no—
715D12—124no—
716C4×D3—44no—
717C2×C32—42no—
718C2×C32#51811yescharacteristic
719C2×C32#51811yescharacteristic
720C2×C32#51811yescharacteristic
721C2×C32#56011yescharacteristic
722C2×C32#56011yescharacteristic
723C2×C32#56011yescharacteristic
724C2×C32H(3,𝔽4)11yescharacteristic
725C3⋊D3—42no—
726C3⋊D3—42no—
727C3×D3—42no—
728C24—31no—
729C24—91no—
730C24—91no—
731C24—94no—
732C24—361no—
733C24—361no—
734C24—361no—
735C24—361no—
736C24—361no—
737C24—361no—
738C24C2×D3211yescharacteristic
739C2×D4—34no—
740C2×D4—94no—
741C2×D4—94no—
742C2×D4—121no—
743C2×D4—121no—
744C2×D4—361no—
745C2×D4—361no—
746C2×D4—361no—
747C2×D4—361no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—121no—
758C22×C4—121no—
759C22×C4—121no—
760C22×C4C2×D3211yescharacteristic
761C22×C4C2×D3211yescharacteristic
762C4⋊C4—121no—
763C4⋊C4—361no—
764C4⋊C4—361no—
765C22⋊C4—34no—
766C22⋊C4—41no—
767C22⋊C4—94no—
768C22⋊C4—94no—
769C22⋊C4—121no—
770C22⋊C4—121no—
771C22⋊C4—121no—
772C22⋊C4—361no—
773C22⋊C4—361no—
774C22⋊C4—361no—
775C22⋊C4—361no—
776C22⋊C4—361no—
777C22⋊C4—361no—
778C22⋊C4—361no—
779C22⋊C4—361no—
780C22⋊C4—361no—
781C22⋊C4—361no—
782C22⋊C4—361no—
783C42—121no—
784C42—361no—
785C42—361no—
786C22×C3—24no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—42no—
805C22×C3—42no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3C22×C4×D311yescharacteristic
822C22×C3C22×C4×D311yescharacteristic
823C22×C3#100411yescharacteristic
824C22×C3#100411yescharacteristic
825C22×C3#100411yescharacteristic
826C22×C3#100411yescharacteristic
827C22×C3#100411yescharacteristic
828C22×C3#100411yescharacteristic
829C22×C3#100911yescharacteristic
830C22×C3#100911yescharacteristic
831C22×C3#100911yescharacteristic
832C22×C3#100911yescharacteristic
833C22×C3#100911yescharacteristic
834C22×C3#100911yescharacteristic
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—64no—
843C2×D3—64no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—122no—
857C2×D3—122no—
858C2×D3—122no—
859C2×D3—122no—
860C2×D3—122no—
861C2×D3—122no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—122no—
865C2×D3—122no—
866C2×D3—122no—
867C2×D3—122no—
868C2×D3—1232no—
869C2×D3—1216no—
870C2×D3—1216no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C3×C4—41no—
888C3×C4—41no—
889C3×C4—41no—
890C3×C4—41no—
891C3×C4—62no—
892C3×C4—62no—
893C3×C4—62no—
894C3×C4—81no—
895C3×C4—81no—
896C3×C4—121no—
897C3×C4—121no—
898C3×C4—121no—
899C3×C4—121no—
900Dic3—22no—
901Dic3—22no—
902Dic3—22no—
903Dic3—41no—
904Dic3—41no—
905Dic3—41no—
906Dic3—41no—
907Dic3—121no—
908Dic3—121no—
909Dic3—121no—
910Dic3—121no—
911Dic3—241no—
912Dic3—241no—
913C32#237511yescharacteristic, complemented, Sylow
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—32no—
921C23—61no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—92no—
928C23—92no—
929C23—181no—
930C23—181no—
931C23—181no—
932C23—181no—
933C23—181no—
934C23—181no—
935C23—181no—
936C23—181no—
937C23—181no—
938C23—181no—
939C23—181no—
940C23—181no—
941C23—364no—
942C23—364no—
943C23—364no—
944C23—364no—
945C23—364no—
946C23—364no—
947C23—364no—
948C23C4×D3212yes—
949C23C22×D3211yescharacteristic
950D4—124no—
951D4—364no—
952D4—364no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—32no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—124no—
981C2×C4—181no—
982C2×C4—181no—
983C2×C4—181no—
984C2×C4—181no—
985C2×C4—181no—
986C2×C4—181no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—44no—
995C2×C3—42no—
996C2×C3—42no—
997C2×C3—122no—
998C2×C3#548611yescharacteristic
999C2×C3#552111yescharacteristic
1000C2×C3#554511yescharacteristic
1001C2×C3#554511yescharacteristic
1002C2×C3#554511yescharacteristic
1003C2×C3#554511yescharacteristic
1004C2×C3#559411yescharacteristic
1005C2×C3#562011yescharacteristic
1006C2×C3#562011yescharacteristic
1007C2×C3#562011yescharacteristic
1008C2×C3#566611yescharacteristic
1009C2×C3#566611yescharacteristic
1010C2×C3#568311yescharacteristic
1011C2×C3#571111yescharacteristic
1012D3—42no—
1013D3—124no—
1014D3—124no—
1015D3—122no—
1016D3—122no—
1017D3—122no—
1018D3—122no—
1019C22—22no—
1020C22—22no—
1021C22—22no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—121no—
1030C22—121no—
1031C22—121no—
1032C22—121no—
1033C22—182no—
1034C22—182no—
1035C22—182no—
1036C22—182no—
1037C22—182no—
1038C22—182no—
1039C22—3616no—
1040C22—361no—
1041C22—361no—
1042C22—361no—
1043C22—361no—
1044C22—361no—
1045C22—361no—
1046C22—361no—
1047C22—361no—
1048C22C2×C4×D3211yescharacteristic
1049C22#6430811yescharacteristic
1050C22#6431411yescharacteristic
1051C22#6431411yescharacteristic
1052C22#6431411yescharacteristic
1053C22#6431411yescharacteristic
1054C22#6433011yescharacteristic
1055C4—41no—
1056C4—41no—
1057C4—62no—
1058C4—62no—
1059C4—62no—
1060C4—121no—
1061C4—121no—
1062C4—121no—
1063C4—121no—
1064C4—361no—
1065C4—361no—
1066C3—21no—
1067C3#7488211yescharacteristic, complemented
1068C3#7584011yescharacteristic, complemented
1069C2—42no—
1070C2—122no—
1071C2—362no—
1072C2—362no—
1073C2#1059418211yescharacteristic
1074C2#1059424211yescharacteristic
1075C2#1059424411yescharacteristic
1076C2#1059425611yescharacteristic
1077C2#1059505811yescharacteristic
1078C2#1059526211yescharacteristic
1079C2#1059526411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63981C2
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. #10592654C2semidirect
3. C3×#4956C2semidirect
4. C3×#4945C2semidirect
5. #10591714C2semidirect
6. #10591707C2semidirect
7. #10591702C2semidirect
8. #10591384C2semidirect
9. #10591383C2semidirect
10. #10591382C2semidirect
11. #10591382C2semidirect
12. #10591259C2semidirect
13. #10591259C2semidirect
14. #10591258C2semidirect
15. #10591194C2semidirect
20. C22×C3×C4×D3C22semidirect
32. C2×C3×(C2×D3)⋊C4C22semidirect
33. C2×C3×Dic3⋊C4C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. #63981C4semidirect
36. C2×Dic3⋊Dic3C22semidirect
37. C2×Dic3⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×Dic32C22semidirect
47. C2×Dic32C22semidirect
48. C3×C3⋊#95C22semidirect
49. C3×C3⋊#95C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
66. #4956D3semidirect
74. #4945D3semidirect
92. C23×C3⋊D3C2×C4semidirect
127. C3×#217C2×C4semidirect
137. #3722C2×C4semidirect
138. #3722C2×C4semidirect
154. C22×C4×D3C2×D3semidirect
199. C2×(C2×D3)⋊C4C2×D3semidirect
204. C2×Dic3⋊C4C2×D3semidirect
209. C2×C4×Dic3C2×D3semidirect
219. C3⋊#95C2×D3semidirect
220. C3⋊#95C2×D3semidirect
221. C3⋊#95C2×D3semidirect
222. C3⋊#95C2×D3semidirect
409. #217C4×D3semidirect
913. C32#2375semidirect
1067. C3#74882semidirect
1068. C3#75840semidirect

Maximal subgroups

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

subgroupindex
C2×#639812
#105926542
C3×#49562
C3×#49452
#105917142
#105917072
#105917022
#105913842
#105913832
#105913822
#105912592
#105912582
#105911942
#758403
#748823