Finite Group Databasebeta

← #11805021

Subgroups — #11805021

Order 1152.

1713 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63921C211yesmaximal, characteristic
2C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×#63878C211yesmaximal, characteristic, complemented
4C4×#3752C211yesmaximal, characteristic, complemented
5C3×#4940C211yesmaximal, characteristic, complemented
6C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic
8#10591375C211yesmaximal, characteristic, complemented
9#10591362C211yesmaximal, characteristic, complemented
10#10591305C211yesmaximal, characteristic, complemented
11#10591295C211yesmaximal, characteristic, complemented
12#10591290C211yesmaximal, characteristic, complemented
13#10591287C211yesmaximal, characteristic, complemented
14#10591284C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16#75833—31nomaximal
17#73575—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic, complemented
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
33C2×C3×C4×Dic3C2211yescharacteristic, complemented
34C2×Dic3⋊Dic3C2211yescharacteristic, complemented
35C2×Dic3⋊Dic3C2211yescharacteristic, complemented
36C2×Dic3⋊Dic3C2211yescharacteristic, complemented
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×Dic32C2211yescharacteristic, complemented
45#63921—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—
57C2×#892—31no—
58C2×D3×C22⋊C4—31no—
59C2×D3×C22⋊C4—31no—
60C2×D3×C22⋊C4—31no—
61C2×#877—31no—
62C3×#388—31no—
63C3×C4×C22⋊C4—31no—
64#5212—31no—
65#4989—31no—
66#4955—31no—
67#4955—31no—
68#4951—31no—
69#4945—31no—
70#4944—31no—
71#4943—31no—
72#4940—31no—
73#4940D311yescharacteristic, complemented
74C4×(C2×D3)⋊C4—31no—
75C4×(C2×D3)⋊C4—31no—
76C4×(C2×D3)⋊C4—31no—
77C4×(C2×D3)⋊C4—61no—
78C4×(C2×D3)⋊C4D311yescharacteristic, complemented
79#4670—31no—
80#4670—31no—
81#4668—31no—
82#4668—31no—
83#4668—31no—
84#4667—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
103C2×C4×C3⋊D3—22no—
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3—41no—
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×C4×D3—41no—
113C2×C3×C4×D3—41no—
114C2×C3×C4×D3C2×C414yescomplemented
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—41no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3C2×C414yescomplemented
121C32×C42—41no—
122#3752—22no—
123#3752C2×C414yes—
124C4×C3⋊Dic3—22no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—41no—
128C3×(C2×D3)⋊C4C2×C414yescomplemented
129C3×(C2×D3)⋊C4D414yes—
130C3×Dic3⋊C4—22no—
131C3×C4×Dic3—41no—
132Dic3⋊Dic3—22no—
133Dic3⋊Dic3—41no—
134Dic3⋊Dic3—41no—
135#3722—22no—
136#3722C2×C414yes—
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—41no—
141(C2×D3)⋊Dic3C2×C414yescomplemented
142Dic32—22no—
143#2342—91noSylow
144C24×D3—31no—
145C24×D3—31no—
146C23×C3×C4—31no—
147C23×Dic3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×C4×D3—61no—
154C22×C4×D3C2×D311yescharacteristic
155C2×C3×C4⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C42—21no—
162C2×C3×C42—31no—
163C2×C3×C42C2×D311yescharacteristic, complemented
164C2×C3×C42C2×D311yescharacteristic, complemented
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—38no—
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)⋊C4C2×D311yescharacteristic
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4C2×D311yescharacteristic, complemented
198C2×C4×Dic3—31no—
199C2×C4×Dic3—31no—
200C2×C4×Dic3—31no—
201C2×C4×Dic3—31no—
202C2×C4×Dic3—61no—
203C2×C4×Dic3C2×D311yescharacteristic, complemented
204#892—64no—
205D3×C22⋊C4—38no—
206D3×C22⋊C4—64no—
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⋊D3C22×C412yes—
233C22×C3⋊D3#4112yes—
234C22×C3⋊D3#4112yes—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3C22×C412yes—
246C22×C3×D3C22×C412yes—
247C22×C3×D3C2×D412yes—
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×C4C22×C412yes—
264C2×C32×C4C2×D412yes—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3C22×C412yes—
274C4×C3⋊D3—44no—
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×Dic3C2×D412yes—
293C3×C4×D3—44no—
294#624—44no—
295D3×Dic3—28no—
296C2×#117—91no—
297C22×C22⋊C4—91no—
298C22×C22⋊C4—91no—
299#388—31no—
300#388—91no—
301#388—91no—
302#388—91no—
303#385—91no—
304#385—91no—
305#381—91no—
306#380—91no—
307#379—91no—
308C4×C22⋊C4—31no—
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—121no—
343C22×C3×C4—121no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—34no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—62no—
361C22×Dic3—62no—
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C2×C4×D3—34no—
369C2×C4×D3—41no—
370C2×C4×D3—41no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—64no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—122no—
383C2×C4×D3—121no—
384C2×C4×D3—121no—
385C2×C4×D3—121no—
386C2×C4×D3—121no—
387C2×C4×D3—122no—
388C2×C4×D3C4×D314yescomplemented
389C3×C4⋊C4—62no—
390C3×C22⋊C4—34no—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—62no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—121no—
395C3×C42—41no—
396C3×C42—41no—
397C3×C42—42no—
398C3×C42—121no—
399#217—34no—
400#217—62no—
401#217—62no—
402#217—62no—
403#217—121no—
404(C2×D3)⋊C4—22no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—41no—
412(C2×D3)⋊C4—64no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—64no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—121no—
422(C2×D3)⋊C4C4×D314yescomplemented
423(C2×D3)⋊C4D1214yes—
424C4⋊Dic3—62no—
425C4⋊Dic3—121no—
426C4⋊Dic3—121no—
427Dic3⋊C4—22no—
428Dic3⋊C4—62no—
429Dic3⋊C4—121no—
430Dic3⋊C4—121no—
431C4×Dic3—41no—
432C4×Dic3—62no—
433C4×Dic3—62no—
434C4×Dic3—62no—
435C4×Dic3—62no—
436C4×Dic3—122no—
437C22×C32C23×C411yescharacteristic
438C22×C32C22×D411yescharacteristic
439C22×C32C2×#4111yescharacteristic
440C22×C32C2×#4111yescharacteristic
441C22×C32C2×#4111yescharacteristic
442C22×C32H(5,𝔽2)11yescharacteristic
443C22×C32H(5,𝔽2)11yescharacteristic
444C2×C3⋊D3—22no—
445C2×C3⋊D3—22no—
446C2×C3⋊D3—22no—
447C2×C3⋊D3—22no—
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3#11714yescomplemented
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—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3C4×D414yes—
465D32—416no—
466C32×C4—22no—
467C32×C4—22no—
468C32×C4—41no—
469C3⋊Dic3—22no—
470C3⋊Dic3—41no—
471C3⋊Dic3—41no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C25—91no—
479C23×C4—31no—
480C23×C4—91no—
481C23×C4—91no—
482C23×C4—91no—
483#117—184no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C22⋊C4—31no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—98no—
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—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—184no—
504C2×C42—31no—
505C2×C42—91no—
506C2×C42—91no—
507C2×C42D3211yescharacteristic, complemented
508#95—31no—
509#95—31no—
510#95—31no—
511#95—31no—
512#95—91no—
513#95—91no—
514#95—91no—
515#95—91no—
516C23×C3—21no—
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×C3—61no—
530C23×C3—61no—
531C23×C3C23×D311yescharacteristic
532C23×C3C23×D311yescharacteristic
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—32no—
544C22×D3—32no—
545C22×D3—32no—
546C22×D3—32no—
547C22×D3—32no—
548C22×D3—32no—
549C22×D3—62no—
550C22×D3—62no—
551C22×D3—62no—
552C22×D3—68no—
553C22×D3—68no—
554C22×D3—68no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—61no—
561C22×D3—61no—
562C22×D3—61no—
563C22×D3—68no—
564C22×D3—121no—
565C22×D3—121no—
566C22×D3—121no—
567C22×D3—121no—
568C22×D3—124no—
569C22×D3—124no—
570C22×D3—124no—
571C22×D3—124no—
572C22×D3—124no—
573C22×D3—124no—
574C22×D3—124no—
575C22×D3—124no—
576C22×D3—124no—
577C22×D3—124no—
578C22×D3C2×C4×D312yes—
579C22×D3C2×C4×D312yes—
580C22×D3C2×D1212yes—
581C22×D3#23512yes—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—21no—
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—22no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—32no—
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×C4C2×C4×D312yes—
625C2×C3×C4C2×C4×D312yes—
626C2×C3×C4C2×D1212yes—
627C2×C3×C4D3×D412yes—
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—21no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—62no—
646C2×Dic3—68no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—62no—
652C2×Dic3—62no—
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—61no—
664C2×Dic3—61no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3—121no—
671C2×Dic3C2×C4×D312yes—
672C2×Dic3C2×C4×D312yes—
673C2×Dic3C2×D1212yes—
674C4×D3—44no—
675C4×D3—68no—
676C4×D3—124no—
677C4×D3—124no—
678C4×D3—124no—
679C4×D3—124no—
680C4×D3—128no—
681C2×C32C2×#11711yescharacteristic
682C2×C32C2×C4×D411yescharacteristic
683C2×C32#51811yescharacteristic
684C2×C32#54611yescharacteristic
685C2×C32#54611yescharacteristic
686C2×C32#55111yescharacteristic
687C2×C32#55111yescharacteristic
688C3⋊D3—24no—
689C3×D3—24no—
690C3×D3—42no—
691C24—31no—
692C24—31no—
693C24—94no—
694C24—91no—
695C24—182no—
696C24—182no—
697C24—182no—
698C24—182no—
699C24—361no—
700C24—361no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—34no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—94no—
709C22×C4—91no—
710C22×C4—91no—
711C22×C4—91no—
712C22×C4—121no—
713C22×C4—121no—
714C22×C4—182no—
715C22×C4—182no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—182no—
719C22×C4—182no—
720C22×C4—361no—
721C22×C4—361no—
722C22×C4C2×D3211yescharacteristic
723C22×C4C2×D3211yescharacteristic
724C22×C4C2×D3211yescharacteristic
725C4⋊C4—62no—
726C4⋊C4—182no—
727C4⋊C4—361no—
728C4⋊C4—361no—
729C22⋊C4—34no—
730C22⋊C4—34no—
731C22⋊C4—62no—
732C22⋊C4—62no—
733C22⋊C4—94no—
734C22⋊C4—94no—
735C22⋊C4—94no—
736C22⋊C4—121no—
737C22⋊C4—182no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C22⋊C4—182no—
742C22⋊C4—361no—
743C42—41no—
744C42—121no—
745C42—182no—
746C42—182no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—34no—
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—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3C22×C4×D311yescharacteristic
769C22×C3C22×C4×D311yescharacteristic
770C22×C3C22×D1211yescharacteristic
771C22×C3C2×#23511yescharacteristic
772C22×C3C2×D3×D411yescharacteristic
773C22×C3#100411yescharacteristic
774C22×C3#100411yescharacteristic
775C22×C3#100411yescharacteristic
776C22×C3D3×#4111yescharacteristic
777C22×C3D3×#4111yescharacteristic
778C22×C3D3×#4111yescharacteristic
779C22×C3D3×#4111yescharacteristic
780C22×C3D3×#4111yescharacteristic
781C22×C3#100911yescharacteristic
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—34no—
792C2×D3—34no—
793C2×D3—41no—
794C2×D3—41no—
795C2×D3—41no—
796C2×D3—41no—
797C2×D3—64no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—62no—
803C2×D3—62no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—122no—
811C2×D3—122no—
812C2×D3—122no—
813C2×D3—122no—
814C2×D3—122no—
815C2×D3—122no—
816C2×D3—1216no—
817C2×D3—1216no—
818C2×D3C4×D1214yes—
819C3×C4—24no—
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—42no—
825C3×C4—42no—
826C3×C4—41no—
827C3×C4—41no—
828C3×C4—62no—
829C3×C4—62no—
830C3×C4—62no—
831C3×C4—121no—
832C3×C4—121no—
833C3×C4—121no—
834Dic3—22no—
835Dic3—22no—
836Dic3—22no—
837Dic3—41no—
838Dic3—41no—
839Dic3—41no—
840Dic3—62no—
841Dic3—62no—
842Dic3—122no—
843Dic3—122no—
844Dic3—122no—
845Dic3—121no—
846Dic3—121no—
847Dic3—121no—
848Dic3—121no—
849C32#234211yescharacteristic, complemented, Sylow
850C23—32no—
851C23—32no—
852C23—32no—
853C23—32no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—92no—
865C23—92no—
866C23—92no—
867C23—188no—
868C23—188no—
869C23—181no—
870C23—181no—
871C23—181no—
872C23—181no—
873C23—364no—
874C23—364no—
875C23—364no—
876C23—364no—
877C23—364no—
878C23C22×D3211yescharacteristic
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—32no—
887C2×C4—32no—
888C2×C4—32no—
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—61no—
903C2×C4—61no—
904C2×C4—92no—
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—181no—
915C2×C4—364no—
916C2×C4—364no—
917C2×C4C4×D3212yes—
918C2×C4D3×D1212yes—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—64no—
927C2×C3—122no—
928C2×C3C2×C4×D1211yescharacteristic
929C2×C3#548611yescharacteristic
930C2×C3D3×#11711yescharacteristic
931C2×C3D3×#11711yescharacteristic
932C2×C3C4×D3×D411yescharacteristic
933C2×C3#554511yescharacteristic
934C2×C3#555411yescharacteristic
935C2×C3#555411yescharacteristic
936C2×C3#555611yescharacteristic
937C2×C3#555611yescharacteristic
938C2×C3#561011yescharacteristic
939C2×C3#565911yescharacteristic
940C2×C3#567611yescharacteristic
941C2×C3#570511yescharacteristic
942D3—24no—
943D3—42no—
944D3—64no—
945D3—64no—
946D3—124no—
947C22—34no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—62no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—62no—
956C22—62no—
957C22—94no—
958C22—121no—
959C22—121no—
960C22—121no—
961C22—121no—
962C22—182no—
963C22—182no—
964C22—182no—
965C22—182no—
966C22—182no—
967C22—182no—
968C22—3616no—
969C22C2×C4×D3211yescharacteristic
970C22C2×D3×D1211yescharacteristic
971C22D3×#23511yescharacteristic
972C22#6430611yescharacteristic
973C22#6430611yescharacteristic
974C22#6430711yescharacteristic
975C22#6433011yescharacteristic
976C4—22no—
977C4—22no—
978C4—41no—
979C4—62no—
980C4—62no—
981C4—62no—
982C4—121no—
983C4—121no—
984C4—121no—
985C4—182no—
986C4—361no—
987C4—361no—
988C3—21no—
989C3#7357511yescharacteristic, complemented
990C3#7583311yescharacteristic, complemented
991C2—64no—
992C2—122no—
993C2—184no—
994C2#1059399211yescharacteristic
995C2C4×D3×D1211yescharacteristic
996C2#1059400511yescharacteristic
997C2#1059401811yescharacteristic
998C2#1059505611yescharacteristic
999C2#1059507511yescharacteristic
1000C2#1059508811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×D32C22
hypercenterC2×C42D32
hypocenterC32#2342
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#63878C2semidirect
4. C4×#3752C2semidirect
5. C3×#4940C2semidirect
6. C3×C4×(C2×D3)⋊C4C2semidirect
8. #10591375C2semidirect
9. #10591362C2semidirect
10. #10591305C2semidirect
11. #10591295C2semidirect
12. #10591290C2semidirect
13. #10591287C2semidirect
14. #10591284C2semidirect
15. #10591233C2semidirect
23. C2×C32×C42C22semidirect
26. C2×C4×C3⋊Dic3C22semidirect
32. C2×C3×Dic3⋊C4C22semidirect
33. C2×C3×C4×Dic3C22semidirect
34. C2×Dic3⋊Dic3C22semidirect
35. C2×Dic3⋊Dic3C22semidirect
36. C2×Dic3⋊Dic3C22semidirect
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
73. #4940D3semidirect
78. C4×(C2×D3)⋊C4D3semidirect
114. C2×C3×C4×D3C2×C4semidirect
120. C2×D3×Dic3C2×C4semidirect
128. C3×(C2×D3)⋊C4C2×C4semidirect
141. (C2×D3)⋊Dic3C2×C4semidirect
163. C2×C3×C42C2×D3semidirect
164. C2×C3×C42C2×D3semidirect
197. C2×Dic3⋊C4C2×D3semidirect
203. C2×C4×Dic3C2×D3semidirect
223. C3⋊#95C2×D3semidirect
224. C3⋊#95C2×D3semidirect
225. C3⋊#95C2×D3semidirect
226. C3⋊#95C2×D3semidirect
388. C2×C4×D3C4×D3semidirect
422. (C2×D3)⋊C4C4×D3semidirect
450. C2×C3⋊D3#117semidirect
507. C2×C42D32semidirect
849. C32#2342semidirect
989. C3#73575semidirect
990. C3#75833semidirect

Maximal subgroups

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

subgroupindex
C2×#639212
C2×D3×(C2×D3)⋊C42
C2×#638782
C4×#37522
C3×#49402
C3×C4×(C2×D3)⋊C42
#105913992
#105913752
#105913622
#105913052
#105912952
#105912902
#105912872
#105912842
#105912332
#758333
#735753