Finite Group Databasebeta

← #11807593

Subgroups — #11807593

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×#63983C211yesmaximal, characteristic
2#10592656C211yesmaximal, characteristic, complemented
3C3×#4958C211yesmaximal, characteristic, complemented
4C3×#4957C211yesmaximal, characteristic, complemented
5#10591711C211yesmaximal, characteristic, complemented
6#10591710C211yesmaximal, characteristic, complemented
7#10591707C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591287C211yesmaximal, characteristic, complemented
11#10591283C211yesmaximal, characteristic, complemented
12#10591281C211yesmaximal, characteristic, complemented
13#10591280C211yesmaximal, characteristic, complemented
14#10591258C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#76434—31nomaximal
17#74882—31nomaximal
18C23×D32C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic, complemented
23C2×C32×C22⋊C4C2211yescharacteristic, complemented
24C2×#3757C2211yescharacteristic, complemented
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic, complemented
28C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
29C2×C3×#217C2211yescharacteristic, complemented
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
35C2×C3×C4×Dic3C2211yescharacteristic, complemented
36#63983C418yescomplemented
37C2×Dic3⋊Dic3C2211yescharacteristic, complemented
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
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×#937—31no—
55C2×#937—31no—
56C3×#390—31no—
57C3×#386—31no—
58#5221—31no—
59#5220—31no—
60#5213—31no—
61#5213—31no—
62#4990—31no—
63#4990—31no—
64#4958—31no—
65#4958D311yescharacteristic, complemented
66#4957—31no—
67#4957—31no—
68#4957—31no—
69#4957—61no—
70#4957D311yescharacteristic, complemented
71#4955—31no—
72#4955—31no—
73#4955—31no—
74#4955—31no—
75#4945—31no—
76#4945—31no—
77#4944—31no—
78#4944—31no—
79#4940—31no—
80#4940—31no—
81#4670—31no—
82#4670—31no—
83#4669—31no—
84#4669—31no—
85C24×C32C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×D32—41no—
90C22×D32—41no—
91C22×D32—41no—
92C22×D32—41no—
93C22×D32—41no—
94C22×D32—41no—
95C22×D32C2×C414yescomplemented
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638—41no—
99C2×#638—41no—
100C2×#638C2×C414yes—
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C3×#67—41no—
105C2×C3×#67—41no—
106C2×C3×#67—41no—
107C2×C3×#67—41no—
108C2×C3×#67C2×C414yes—
109C2×C3×#67C2×C414yes—
110C22×C3×Dic3—41no—
111C22×C3×Dic3—41no—
112C22×C3×Dic3—41no—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C32×C22⋊C4—41no—
120#3757—41no—
121#3752—41no—
122#3752—41no—
123#3750—41no—
124C4×C3⋊Dic3—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×Dic3⋊C4—41no—
131C3×C4×Dic3—41no—
132Dic3⋊Dic3—41no—
133#3722—41no—
134#3722—41no—
135#3722C2×C414yescomplemented
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
144C24×D3—31no—
145C24×D3—31no—
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C23×C3×C4—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—61no—
152C22×#67C2×D311yescharacteristic
153C22×#67C2×D311yescharacteristic
154C23×Dic3C2×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⋊C4—31no—
162C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
163C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
164C2×C3×C42—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—61no—
174C2×#217C2×D311yescharacteristic, complemented
175#937—38no—
176#937—38no—
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—61no—
194C2×(C2×D3)⋊C4—61no—
195C2×(C2×D3)⋊C4C2×D311yescharacteristic
196C2×(C2×D3)⋊C4C2×D311yescharacteristic
197C2×(C2×D3)⋊C4C2×D311yescharacteristic
198C2×(C2×D3)⋊C4C2×D311yescharacteristic
199C2×C4⋊Dic3—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—61no—
204C2×Dic3⋊C4C2×D311yescharacteristic, complemented
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—61no—
210C2×C4×Dic3C2×D311yescharacteristic, complemented
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×D3C22×C412yes—
251C22×C3×D3C22×C412yes—
252C2×D32—44no—
253C2×D32—44no—
254C2×D32—44no—
255C2×D32—44no—
256C2×D32—44no—
257C2×D32—44no—
258C2×D32—44no—
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—
275C3×#67—44no—
276C3×#67—44no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—44no—
294C2×C3×Dic3C22×C412yes—
295C2×C3×Dic3C22×C412yes—
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—31no—
307#386—91no—
308#386—91no—
309#379—91no—
310#379—91no—
311C24×C3—21no—
312C24×C3—31no—
313C24×C3—31no—
314C24×C3C22×D311yescharacteristic
315C24×C3C22×D311yescharacteristic
316C23×D3—31no—
317C23×D3—31no—
318C23×D3—34no—
319C23×D3—34no—
320C23×D3—61no—
321C23×D3—121no—
322C23×D3—121no—
323C23×D3—121no—
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×D3C22×D311yescharacteristic
334C23×D3C22×D311yescharacteristic
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4—121no—
338C2×C3×D4—121no—
339C2×C3×D4—121no—
340C2×C3×D4—121no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—121no—
350C22×C3×C4—121no—
351C22×C3×C4—121no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C2×#67—34no—
357C2×#67—34no—
358C2×#67—41no—
359C2×#67—41no—
360C2×#67—41no—
361C2×#67—41no—
362C2×#67—64no—
363C2×#67—121no—
364C2×#67—121no—
365C2×#67—121no—
366C2×#67—121no—
367C2×#67—122no—
368C2×#67—122no—
369C2×#67C4×D314yes—
370C2×#67C4×D314yes—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—41no—
378C22×Dic3—41no—
379C22×Dic3—41no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C3×C4⋊C4—121no—
390C3×C22⋊C4—41no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—42no—
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—41no—
402#217—121no—
403#217—121no—
404#217—121no—
405#217—121no—
406#217—121no—
407#217—121no—
408#217—122no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—41no—
414(C2×D3)⋊C4—41no—
415(C2×D3)⋊C4—41no—
416(C2×D3)⋊C4—41no—
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—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—41no—
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—
478D32—416no—
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—91no—
491C22×D4—31no—
492C22×D4—31no—
493C22×D4—91no—
494C23×C4—31no—
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—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⋊C4—91no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4D3211yescharacteristic, complemented
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×C3C2×C4×D312yes—
561C23×C3C2×C4×D312yes—
562C23×C3C23×D311yescharacteristic
563C23×C3C23×D311yescharacteristic
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—32no—
577C22×D3—32no—
578C22×D3—62no—
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—121no—
592C22×D3—121no—
593C22×D3—121no—
594C22×D3—121no—
595C22×D3—121no—
596C22×D3—121no—
597C22×D3—124no—
598C22×D3—124no—
599C22×D3—124no—
600C22×D3—124no—
601C22×D3—124no—
602C22×D3—124no—
603C22×D3—124no—
604C22×D3—124no—
605C22×D3—124no—
606C22×D3—124no—
607C22×D3—124no—
608C22×D3—124no—
609C22×D3—124no—
610C22×D3—124no—
611C22×D3C2×C4×D312yes—
612C22×D3C2×C4×D312yes—
613C3×D4—124no—
614C3×D4—124no—
615C2×C3×C4—22no—
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—21no—
627C2×C3×C4—21no—
628C2×C3×C4—32no—
629C2×C3×C4—32no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
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—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—124no—
652#67—44no—
653#67—44no—
654#67—124no—
655#67—124no—
656#67—128no—
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—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—44no—
676C2×Dic3—62no—
677C2×Dic3—62no—
678C2×Dic3—62no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—62no—
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—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—121no—
697C2×Dic3—121no—
698C2×Dic3—121no—
699C2×Dic3—121no—
700C2×Dic3—121no—
701C2×Dic3C2×C4×D312yes—
702C2×Dic3C2×C4×D312yes—
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—94no—
717C24—91no—
718C24—361no—
719C24—361no—
720C24—361no—
721C24—361no—
722C24—361no—
723C24—361no—
724C24C2×D3211yescharacteristic
725C2×D4—34no—
726C2×D4—34no—
727C2×D4—94no—
728C2×D4—121no—
729C2×D4—121no—
730C2×D4—121no—
731C2×D4—121no—
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—121no—
744C22×C4—121no—
745C22×C4—121no—
746C22×C4C2×D3211yescharacteristic
747C22×C4C2×D3211yescharacteristic
748C4⋊C4—121no—
749C4⋊C4—361no—
750C4⋊C4—361no—
751C22⋊C4—41no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C22⋊C4—94no—
755C22⋊C4—121no—
756C22⋊C4—121no—
757C22⋊C4—121no—
758C22⋊C4—121no—
759C22⋊C4—121no—
760C22⋊C4—361no—
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—121no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3—121no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3C22×C4×D311yescharacteristic
815C22×C3C22×C4×D311yescharacteristic
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#100911yescharacteristic
825C22×C3#100911yescharacteristic
826C22×C3#100911yescharacteristic
827C22×C3#100911yescharacteristic
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—122no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—1216no—
852C2×D3—1216no—
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—181no—
915C23—181no—
916C23—181no—
917C23—181no—
918C23—181no—
919C23—181no—
920C23—364no—
921C23—364no—
922C23—364no—
923C23—364no—
924C23—364no—
925C23—364no—
926C23—364no—
927C23C4×D3212yes—
928C23C22×D3211yescharacteristic
929D4—124no—
930D4—124no—
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—124no—
958C2×C4—181no—
959C2×C4—181no—
960C2×C4—181no—
961C2×C4—181no—
962C2×C4—181no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—181no—
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#554511yescharacteristic
981C2×C3#554511yescharacteristic
982C2×C3#554511yescharacteristic
983C2×C3#554511yescharacteristic
984C2×C3#559411yescharacteristic
985C2×C3#562011yescharacteristic
986C2×C3#562011yescharacteristic
987C2×C3#562011yescharacteristic
988C2×C3#562011yescharacteristic
989C2×C3#566611yescharacteristic
990C2×C3#568311yescharacteristic
991C2×C3#572011yescharacteristic
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—121no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—121no—
1015C22—121no—
1016C22—121no—
1017C22—121no—
1018C22—182no—
1019C22—182no—
1020C22—182no—
1021C22—3616no—
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#7488211yescharacteristic, complemented
1046C3#7643411yescharacteristic, complemented
1047C2—42no—
1048C2—122no—
1049C2—122no—
1050C2—362no—
1051C2#1059425411yescharacteristic
1052C2#1059425611yescharacteristic
1053C2#1059430811yescharacteristic
1054C2#1059430911yescharacteristic
1055C2#1059505611yescharacteristic
1056C2#1059531211yescharacteristic
1057C2#1059531311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63983C2
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×#4958C2semidirect
4. C3×#4957C2semidirect
5. #10591711C2semidirect
6. #10591710C2semidirect
7. #10591707C2semidirect
8. #10591399C2semidirect
9. #10591399C2semidirect
10. #10591287C2semidirect
11. #10591283C2semidirect
12. #10591281C2semidirect
13. #10591280C2semidirect
14. #10591258C2semidirect
15. #10591194C2semidirect
22. C23×C3×Dic3C22semidirect
23. C2×C32×C22⋊C4C22semidirect
24. C2×#3757C22semidirect
27. C2×#3750C22semidirect
28. C2×C4×C3⋊Dic3C22semidirect
29. C2×C3×#217C22semidirect
34. C2×C3×Dic3⋊C4C22semidirect
35. C2×C3×C4×Dic3C22semidirect
36. #63983C4semidirect
37. C2×Dic3⋊Dic3C22semidirect
47. C2×Dic32C22semidirect
48. C3×C3⋊#95C22semidirect
49. C3×C3⋊#95C22semidirect
50. #63579C22semidirect
51. #63579C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
65. #4958D3semidirect
70. #4957D3semidirect
95. C22×D32C2×C4semidirect
135. #3722C2×C4semidirect
140. (C2×D3)⋊Dic3C2×C4semidirect
141. (C2×D3)⋊Dic3C2×C4semidirect
154. C23×Dic3C2×D3semidirect
162. C2×C3×C22⋊C4C2×D3semidirect
163. C2×C3×C22⋊C4C2×D3semidirect
174. C2×#217C2×D3semidirect
204. C2×Dic3⋊C4C2×D3semidirect
210. C2×C4×Dic3C2×D3semidirect
221. C3⋊#95C2×D3semidirect
222. C3⋊#95C2×D3semidirect
516. C2×C22⋊C4D32semidirect
892. C32#2375semidirect
1045. C3#74882semidirect
1046. C3#76434semidirect

Maximal subgroups

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

subgroupindex
C2×#639832
#105926562
C3×#49582
C3×#49572
#105917112
#105917102
#105917072
#105913992
#105912872
#105912832
#105912812
#105912802
#105912582
#105911942
#764343
#748823