Finite Group Databasebeta

← #11805035

Subgroups — #11805035

Order 1152.

1679 conjugacy classes of subgroups.

The subgroup lattice has 999 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
2C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×#63878C211yesmaximal, characteristic, complemented
4#10592689C211yesmaximal, characteristic, complemented
5C3×#4989C211yesmaximal, characteristic, complemented
6C3×#4987C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic
8#10591377C211yesmaximal, characteristic, complemented
9#10591368C211yesmaximal, characteristic, complemented
10#10591362C211yesmaximal, characteristic, complemented
11#10591266C211yesmaximal, characteristic, complemented
12#10591259C211yesmaximal, characteristic, complemented
13#10591258C211yesmaximal, characteristic, complemented
14#10591237C211yesmaximal, characteristic, complemented
15#10591237C211yesmaximal, characteristic, complemented
16#74595—31nomaximal
17#74009—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic, complemented
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
34C2×Dic3⋊Dic3C2211yescharacteristic, complemented
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic, complemented
43C2×Dic32C2211yescharacteristic, complemented
44C2×Dic32C2211yescharacteristic, complemented
45D3×(C2×D3)⋊C4—24no—
46D3×(C2×D3)⋊C4C418yescomplemented
47#63878—24no—
48#63658C2211yescharacteristic, complemented
49#63658C2211yescharacteristic, complemented
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C22×(C2×D3)⋊C4—31no—
57C22×(C2×D3)⋊C4—31no—
58C2×#892—31no—
59C2×D3×C22⋊C4—31no—
60C2×D3×C22⋊C4—31no—
61C2×#877—31no—
62C3×#385—31no—
63C3×#380—31no—
64C4×#217—31no—
65C4×#217—31no—
66#4990—31no—
67#4990—31no—
68#4990—31no—
69#4990—31no—
70#4990—61no—
71#4989—31no—
72#4989D311yescharacteristic, complemented
73#4987D311yescharacteristic, complemented
74#4955—31no—
75#4955—31no—
76#4950—31no—
77#4943—31no—
78Dic3×C22⋊C4—31no—
79#4670—31no—
80#4670—31no—
81#4669—31no—
82#4669—31no—
83#4666—31no—
84#4666—31no—
85#4666—31no—
86#4664—31no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×D32—22no—
91C22×D32—22no—
92C22×D32—22no—
93C22×D32—22no—
94C22×D32—41no—
95C22×D32—41no—
96C22×D32C2×C414yes—
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—41no—
112C2×C3×C4×D3—41no—
113C2×C3×C4×D3—41no—
114C2×C3×C4×D3C2×C414yescomplemented
115C2×D3×Dic3—22no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3C2×C414yescomplemented
121C32×C4⋊C4—41no—
122#3752—22no—
123#3752—41no—
124#3752C2×C414yescomplemented
125C4×C3⋊Dic3—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4C2×C414yes—
130C3×C4⋊Dic3—41no—
131C3×Dic3⋊C4—22no—
132Dic3⋊Dic3—22no—
133#3722—22no—
134#3722—41no—
135#3722C2×C414yescomplemented
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3C2×C414yes—
139(C2×D3)⋊Dic3D414yes—
140Dic32—22no—
141Dic32—41no—
142Dic32—41no—
143#2342—91noSylow
144C24×D3—31no—
145C24×D3—31no—
146C23×C3×C4—31no—
147C23×C3×C4—31no—
148C23×Dic3—31no—
149C23×Dic3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3C2×D311yescharacteristic
153C22×C4×D3C2×D311yescharacteristic
154C2×C3×C4⋊C4—21no—
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
158C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—38no—
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—61no—
185C2×(C2×D3)⋊C4—61no—
186C2×(C2×D3)⋊C4—61no—
187C2×(C2×D3)⋊C4—64no—
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3C2×D311yescharacteristic, complemented
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4C2×D311yescharacteristic, complemented
196C2×C4×Dic3—31no—
197C2×C4×Dic3—31no—
198C2×C4×Dic3—31no—
199C2×C4×Dic3—31no—
200C2×C4×Dic3—31no—
201C2×C4×Dic3—31no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—61no—
205#892—64no—
206D3×C22⋊C4—38no—
207D3×C22⋊C4—64no—
208#877—64no—
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—
223C3⋊#95C2×D311yescharacteristic, complemented
224C3⋊#95C2×D311yescharacteristic, complemented
225C3⋊#95C2×D311yescharacteristic, complemented
226C3⋊#95C2×D311yescharacteristic, complemented
227C23×C32C2411yescharacteristic
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3C22×C412yes—
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×D3C22×C412yes—
244C22×C3×D3C22×C412yes—
245C22×C3×D3C2×D412yes—
246C22×C3×D3#4112yes—
247C22×C3×D3#4112yes—
248C22×C3×D3#4112yes—
249C2×D32—28no—
250C2×D32—28no—
251C2×D32—44no—
252C2×D32—44no—
253C2×D32—44no—
254C2×D32—44no—
255C2×D32—44no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C22×C412yes—
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⋊Dic3C22×C412yes—
273C2×C3⋊Dic3C2×D412yes—
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×Dic3C22×C412yes—
290C2×C3×Dic3C22×C412yes—
291C2×C3×Dic3C2×D412yes—
292C3×C4×D3—44no—
293C3×C4×D3—44no—
294D3×Dic3—28no—
295D3×Dic3—44no—
296C2×#117—91no—
297C22×C22⋊C4—91no—
298C22×C22⋊C4—91no—
299#388—91no—
300#388—91no—
301#388—91no—
302#388—91no—
303#385—31no—
304#385—91no—
305#381—91no—
306#380—31no—
307#379—91no—
308C4×C22⋊C4—91no—
309C4×C22⋊C4—91no—
310C4×C22⋊C4—91no—
311C24×C3—31no—
312C24×C3—31no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—34no—
316C23×D3—34no—
317C23×D3—61no—
318C23×D3—62no—
319C23×D3—62no—
320C23×D3—62no—
321C23×D3—62no—
322C23×D3—62no—
323C23×D3—62no—
324C23×D3—62no—
325C23×D3—62no—
326C23×D3—121no—
327C23×D3—121no—
328C23×D3—121no—
329C23×D3—121no—
330C23×D3C22×D311yescharacteristic
331C23×D3C22×D311yescharacteristic
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—34no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—62no—
343C22×C3×C4—62no—
344C22×C3×C4—121no—
345C22×C3×C4—121no—
346C22×C3×C4—121no—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—34no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—62no—
364C22×Dic3—62no—
365C22×Dic3—62no—
366C22×Dic3—62no—
367C22×Dic3—121no—
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—34no—
377C2×C4×D3—41no—
378C2×C4×D3—41no—
379C2×C4×D3—41no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—121no—
385C2×C4×D3C4×D314yescomplemented
386C3×C4⋊C4—41no—
387C3×C4⋊C4—41no—
388C3×C4⋊C4—42no—
389C3×C4⋊C4—62no—
390C3×C4⋊C4—121no—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—62no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—62no—
395#217—34no—
396#217—34no—
397#217—62no—
398#217—62no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—22no—
401(C2×D3)⋊C4—22no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—64no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—122no—
416(C2×D3)⋊C4—121no—
417(C2×D3)⋊C4—121no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4—121no—
420(C2×D3)⋊C4—122no—
421(C2×D3)⋊C4C4×D314yes—
422C4⋊Dic3—41no—
423C4⋊Dic3—62no—
424Dic3⋊C4—22no—
425Dic3⋊C4—62no—
426C4×Dic3—62no—
427C4×Dic3—62no—
428C4×Dic3—62no—
429C4×Dic3—62no—
430C4×Dic3—122no—
431C4×Dic3—121no—
432C4×Dic3—121no—
433C4×Dic3—121no—
434C4×Dic3—121no—
435C22×C32C23×C411yescharacteristic
436C22×C32C22×D411yescharacteristic
437C22×C32C2×#4111yescharacteristic
438C22×C32C2×#4111yescharacteristic
439C22×C32C2×#4111yescharacteristic
440C22×C32H(5,𝔽2)11yescharacteristic
441C22×C32H(5,𝔽2)11yescharacteristic
442C2×C3⋊D3—22no—
443C2×C3⋊D3—22no—
444C2×C3⋊D3—22no—
445C2×C3⋊D3—41no—
446C2×C3⋊D3—41no—
447C2×C3⋊D3—41no—
448C2×C3⋊D3—41no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
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#11714yescomplemented
462C2×C3×D3C4×D414yes—
463D32—416no—
464C32×C4—22no—
465C32×C4—41no—
466C32×C4—41no—
467C3⋊Dic3—22no—
468C3⋊Dic3—22no—
469C3⋊Dic3—41no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C25—91no—
477C23×C4—31no—
478C23×C4—31no—
479C23×C4—91no—
480C23×C4—91no—
481#117—184no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4D3211yescharacteristic, complemented
486C2×C22⋊C4—31no—
487C2×C22⋊C4—31no—
488C2×C22⋊C4—31no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—98no—
491C2×C22⋊C4—91no—
492C2×C22⋊C4—91no—
493C2×C22⋊C4—91no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—184no—
502C2×C42—91no—
503C2×C42—91no—
504C2×C42—91no—
505C2×C42—91no—
506#95—31no—
507#95—31no—
508#95—31no—
509#95—31no—
510#95—91no—
511#95—91no—
512#95—91no—
513#95—91no—
514C23×C3—21no—
515C23×C3—32no—
516C23×C3—32no—
517C23×C3—32no—
518C23×C3—32no—
519C23×C3—32no—
520C23×C3—32no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3C23×D311yescharacteristic
530C23×C3C23×D311yescharacteristic
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—32no—
540C22×D3—32no—
541C22×D3—62no—
542C22×D3—68no—
543C22×D3—68no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—68no—
557C22×D3—68no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3—121no—
562C22×D3—121no—
563C22×D3—121no—
564C22×D3—124no—
565C22×D3—124no—
566C22×D3—124no—
567C22×D3—124no—
568C22×D3—124no—
569C22×D3—124no—
570C22×D3—124no—
571C22×D3—124no—
572C22×D3—124no—
573C22×D3—124no—
574C22×D3C2×C4×D312yes—
575C22×D3C2×C4×D312yes—
576C22×D3D3×D412yes—
577C22×D3#23712yes—
578C22×D3#23912yes—
579C22×D3#23912yes—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—22no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—22no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—32no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—124no—
624C2×C3×C4—124no—
625C2×C3×C4C2×C4×D312yes—
626C2×C3×C4C2×C4×D312yes—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—62no—
647C2×Dic3—62no—
648C2×Dic3—68no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—121no—
664C2×Dic3—121no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3—124no—
671C2×Dic3C2×C4×D312yes—
672C2×Dic3C2×C4×D312yes—
673C2×Dic3D3×D412yes—
674C4×D3—44no—
675C4×D3—44no—
676C4×D3—68no—
677C4×D3—124no—
678C2×C32C2×#11711yescharacteristic
679C2×C32C2×C4×D411yescharacteristic
680C2×C32#51811yescharacteristic
681C2×C32#54611yescharacteristic
682C2×C32#54611yescharacteristic
683C2×C32#55111yescharacteristic
684C2×C32#55111yescharacteristic
685C3⋊D3—42no—
686C3×D3—24no—
687C3×D3—24no—
688C24—31no—
689C24—31no—
690C24—94no—
691C24—91no—
692C24—182no—
693C24—182no—
694C24—182no—
695C24—182no—
696C24—361no—
697C24—361no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—34no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—62no—
706C22×C4—62no—
707C22×C4—94no—
708C22×C4—91no—
709C22×C4—91no—
710C22×C4—91no—
711C22×C4—121no—
712C22×C4—121no—
713C22×C4—121no—
714C22×C4—182no—
715C22×C4—182no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—361no—
719C22×C4C2×D3211yescharacteristic
720C22×C4C2×D3211yescharacteristic
721C22×C4C2×D3211yescharacteristic
722C4⋊C4—41no—
723C4⋊C4—62no—
724C4⋊C4—121no—
725C4⋊C4—182no—
726C22⋊C4—34no—
727C22⋊C4—62no—
728C22⋊C4—62no—
729C22⋊C4—62no—
730C22⋊C4—94no—
731C22⋊C4—94no—
732C22⋊C4—94no—
733C22⋊C4—94no—
734C22⋊C4—182no—
735C22⋊C4—182no—
736C22⋊C4—182no—
737C22⋊C4—182no—
738C22⋊C4—361no—
739C22⋊C4—361no—
740C42—182no—
741C42—182no—
742C42—361no—
743C42—361no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—34no—
752C22×C3—34no—
753C22×C3—62no—
754C22×C3—62no—
755C22×C3—62no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3C22×C4×D311yescharacteristic
766C22×C3C22×C4×D311yescharacteristic
767C22×C3C2×D3×D411yescharacteristic
768C22×C3C2×D3×D411yescharacteristic
769C22×C3C2×#23711yescharacteristic
770C22×C3#100411yescharacteristic
771C22×C3#100411yescharacteristic
772C22×C3#100411yescharacteristic
773C22×C3C2×#23911yescharacteristic
774C22×C3C2×#23911yescharacteristic
775C22×C3D3×#4111yescharacteristic
776C22×C3D3×#4111yescharacteristic
777C22×C3D3×#4111yescharacteristic
778C22×C3#100911yescharacteristic
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—122no—
798C2×D3—122no—
799C2×D3—122no—
800C2×D3—1216no—
801C2×D3—1216no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—241no—
811C2×D3—241no—
812C2×D3—241no—
813C2×D3—241no—
814C2×D3#89214yescomplemented
815C2×D3#89314yes—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—42no—
819C3×C4—42no—
820C3×C4—41no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—62no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—81no—
828C3×C4—121no—
829C3×C4—121no—
830C3×C4—121no—
831Dic3—22no—
832Dic3—22no—
833Dic3—22no—
834Dic3—41no—
835Dic3—41no—
836Dic3—41no—
837Dic3—62no—
838Dic3—62no—
839Dic3—62no—
840Dic3—62no—
841Dic3—122no—
842Dic3—122no—
843Dic3—121no—
844Dic3—121no—
845Dic3—241no—
846C32#234211yescharacteristic, complemented, Sylow
847C23—32no—
848C23—32no—
849C23—32no—
850C23—32no—
851C23—32no—
852C23—32no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—92no—
862C23—188no—
863C23—188no—
864C23—181no—
865C23—181no—
866C23—181no—
867C23—181no—
868C23—181no—
869C23—181no—
870C23—364no—
871C23—364no—
872C23—364no—
873C23—364no—
874C23—364no—
875C23C22×D3211yescharacteristic
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—32no—
885C2×C4—32no—
886C2×C4—32no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—92no—
903C2×C4—92no—
904C2×C4—124no—
905C2×C4—124no—
906C2×C4—188no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—181no—
913C2×C4—181no—
914C2×C4—364no—
915C2×C4C4×D3212yes—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—64no—
924C2×C3—64no—
925C2×C3#548611yescharacteristic
926C2×C3C2×#89211yescharacteristic
927C2×C3C2×#89311yescharacteristic
928C2×C3D3×#11711yescharacteristic
929C2×C3C4×D3×D411yescharacteristic
930C2×C3#554511yescharacteristic
931C2×C3#559111yescharacteristic
932C2×C3#561011yescharacteristic
933C2×C3#561011yescharacteristic
934C2×C3#563011yescharacteristic
935C2×C3#563711yescharacteristic
936C2×C3#563711yescharacteristic
937C2×C3#563711yescharacteristic
938C2×C3#565811yescharacteristic
939D3—24no—
940D3—24no—
941D3—122no—
942D3—122no—
943D3—242no—
944C22—34no—
945C22—34no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—62no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—182no—
959C22—182no—
960C22—182no—
961C22—3616no—
962C22—361no—
963C22—361no—
964C22—361no—
965C22—361no—
966C22C2×C4×D3211yescharacteristic
967C22#6430711yescharacteristic
968C22D32×D411yescharacteristic
969C22D3×#23711yescharacteristic
970C22D3×#23911yescharacteristic
971C22D3×#23911yescharacteristic
972C22#6433011yescharacteristic
973C4—22no—
974C4—41no—
975C4—41no—
976C4—62no—
977C4—62no—
978C4—62no—
979C4—121no—
980C4—121no—
981C4—121no—
982C4—182no—
983C4—182no—
984C4—361no—
985C3—21no—
986C3#7400911yescharacteristic, complemented
987C3#7459511yescharacteristic, complemented
988C2—64no—
989C2—64no—
990C2—362no—
991C2D3×#89211yescharacteristic
992C2D3×#89311yescharacteristic
993C2#1059462211yescharacteristic
994C2#1059464711yescharacteristic
995C2#1059505611yescharacteristic
996C2#1059529011yescharacteristic
997C2#1059543611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×D32C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2342
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63878C2semidirect
4. #10592689C2semidirect
5. C3×#4989C2semidirect
6. C3×#4987C2semidirect
8. #10591377C2semidirect
9. #10591368C2semidirect
10. #10591362C2semidirect
11. #10591266C2semidirect
12. #10591259C2semidirect
13. #10591258C2semidirect
14. #10591237C2semidirect
15. #10591237C2semidirect
23. C2×C32×C4⋊C4C22semidirect
27. C2×C4×C3⋊Dic3C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C2×C3×Dic3⋊C4C22semidirect
34. C2×Dic3⋊Dic3C22semidirect
42. C2×Dic32C22semidirect
43. C2×Dic32C22semidirect
44. C2×Dic32C22semidirect
46. D3×(C2×D3)⋊C4C4semidirect
48. #63658C22semidirect
49. #63658C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
72. #4989D3semidirect
73. #4987D3semidirect
114. C2×C3×C4×D3C2×C4semidirect
120. C2×D3×Dic3C2×C4semidirect
124. #3752C2×C4semidirect
135. #3722C2×C4semidirect
157. C2×C3×C4⋊C4C2×D3semidirect
158. C2×C3×C4⋊C4C2×D3semidirect
193. C2×C4⋊Dic3C2×D3semidirect
195. C2×Dic3⋊C4C2×D3semidirect
223. C3⋊#95C2×D3semidirect
224. C3⋊#95C2×D3semidirect
225. C3⋊#95C2×D3semidirect
226. C3⋊#95C2×D3semidirect
385. C2×C4×D3C4×D3semidirect
461. C2×C3×D3#117semidirect
485. C2×C4⋊C4D32semidirect
814. C2×D3#892semidirect
846. C32#2342semidirect
986. C3#74009semidirect
987. C3#74595semidirect

Maximal subgroups

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

subgroupindex
C2×D3×(C2×D3)⋊C42
C2×#638782
#105926892
C3×#49892
C3×#49872
#105913992
#105913772
#105913682
#105913622
#105912662
#105912592
#105912582
#105912372
#745953
#740093