Finite Group Databasebeta

← #11803606

Subgroups — #11803606

Order 1152.

1465 conjugacy classes of subgroups.

The subgroup lattice has 991 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×#67C211yesmaximal, characteristic, complemented
2C2×#63958C211yesmaximal, characteristic
3C2×#63836C211yesmaximal, characteristic, complemented
4#10592656C211yesmaximal, characteristic, complemented
5C3×#4957C211yesmaximal, characteristic, complemented
6C3×#4946C211yesmaximal, characteristic, complemented
7#10591711C211yesmaximal, characteristic, complemented
8#10591701C211yesmaximal, characteristic, complemented
9#10591384C211yesmaximal, characteristic, complemented
10#10591372C211yesmaximal, characteristic, complemented
11#10591367C211yesmaximal, characteristic, complemented
12#10591364C211yesmaximal, characteristic, complemented
13#10591330C211yesmaximal, characteristic, complemented
14#10591287C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#76430—31nomaximal
17#74385—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38Dic3×#67—24no—
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46#63958C418yescomplemented
47C2×Dic32C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49#63836—24no—
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#938—31no—
57C2×D4×Dic3—31no—
58C2×C4×#67—31no—
59C2×#892—31no—
60C2×#884—31no—
61C2×#872—31no—
62C3×#390—31no—
63C3×#385—31no—
64#5213—31no—
65#4989—31no—
66#4988—31no—
67#4987—31no—
68#4976—31no—
69Dic3×C4⋊C4—31no—
70#4958—31no—
71#4958—31no—
72#4957—31no—
73#4957—31no—
74#4957—31no—
75#4957—61no—
76#4957D311yescharacteristic, complemented
77#4951—31no—
78#4946—31no—
79#4946D311yescharacteristic, complemented
80#4944—31no—
81#4944—31no—
82#4928—31no—
83#4670—31no—
84#4667—31no—
85#4665—31no—
86#4649—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638—41no—
93C2×#638—41no—
94C2×#638C2×C414yescomplemented
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67C2×C414yes—
101C22×C3×Dic3—22no—
102C22×C3×Dic3—41no—
103C22×C3×Dic3—41no—
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×#626—41no—
112C2×#626—41no—
113C2×#626C2×C414yescomplemented
114C2×#624—22no—
115C2×#624—22no—
116C2×#624C2×C414yescomplemented
117C2×D3×Dic3—22no—
118C2×D3×Dic3—41no—
119C2×D3×Dic3—41no—
120C32×C22⋊C4—41no—
121#3757—22no—
122#3752—22no—
123#3752—41no—
124#3750—41no—
125C4×C3⋊Dic3—41no—
126C3×#217—41no—
127C3×#217C2×C414yescomplemented
128C3×(C2×D3)⋊C4—41no—
129C3×(C2×D3)⋊C4—41no—
130C3×Dic3⋊C4—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—41no—
133C3×C4×Dic3—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3C2×C414yescomplemented
137#3722—22no—
138#3722—41no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3C2×C414yescomplemented
141Dic32—41no—
142Dic32D414yescomplemented
143#2324—91noSylow
144C22×C3×D4—31no—
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—61no—
150C22×#67C2×D311yescharacteristic
151C23×Dic3—31no—
152C23×Dic3C2×D311yescharacteristic
153C22×D12—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4C2×D311yescharacteristic
166C2×C3×C22⋊C4C2×D311yescharacteristic
167C2×C3×C42—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—61no—
173C2×#217C2×D311yescharacteristic
174C2×#217C2×D311yescharacteristic
175#938—38no—
176D4×Dic3—64no—
177C4×#67—64no—
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—61no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—61no—
201C2×Dic3⋊C4C2×D311yescharacteristic
202C2×Dic3⋊C4C2×D311yescharacteristic
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—61no—
211C2×C4×Dic3C2×D311yescharacteristic
212#892—64no—
213#884—38no—
214#872—64no—
215C3×#95—31no—
216C3×#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C23×C32—21no—
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32C22×C412yes—
234C23×C32C2411yescharacteristic
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⋊D3C22×C412yes—
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×D3C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255#638—44no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3C22×C412yes—
264C2×C3⋊Dic3C2×D412yes—
265C3×#67—28no—
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×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—44no—
282C2×C3×Dic3C22×C412yes—
283C2×C3×Dic3C22×C412yes—
284C2×C3×Dic3C22×C412yes—
285C2×C3×Dic3C2×D412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3#4112yes—
288#626—44no—
289#624—28no—
290D3×Dic3—44no—
291C2×#121—91no—
292C2×C4×D4—91no—
293C2×#117—91no—
294#390—31no—
295#390—91no—
296#390—91no—
297#389—91no—
298#388—91no—
299#388—91no—
300#386—91no—
301#386—91no—
302#385—31no—
303#385—91no—
304#380—91no—
305C4×C4⋊C4—91no—
306C24×C3—21no—
307C24×C3—31no—
308C24×C3C22×D311yescharacteristic
309C24×C3C22×D311yescharacteristic
310C23×D3—31no—
311C23×D3—31no—
312C23×D3—61no—
313C23×D3C22×D311yescharacteristic
314C2×C3×D4—34no—
315C2×C3×D4—62no—
316C2×C3×D4—62no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—62no—
327C22×C3×C4—121no—
328C22×C3×C4—121no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—22no—
334C2×#67—22no—
335C2×#67—34no—
336C2×#67—34no—
337C2×#67—34no—
338C2×#67—64no—
339C2×#67—121no—
340C2×#67—121no—
341C2×#67—121no—
342C2×#67—121no—
343C2×#67—121no—
344C2×#67—121no—
345C2×#67—122no—
346C2×#67—122no—
347C2×#67C4×D314yes—
348C22×Dic3—22no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—41no—
356C22×Dic3—41no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—62no—
361C22×Dic3—121no—
362C22×Dic3—121no—
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C2×D12—34no—
371C2×D12—121no—
372C2×D12—121no—
373C2×C4×D3—34no—
374C2×C4×D3—34no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—121no—
381C2×C4×D3—121no—
382C3×C4⋊C4—62no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4—121no—
385C3×C22⋊C4—34no—
386C3×C22⋊C4—41no—
387C3×C22⋊C4—41no—
388C3×C22⋊C4—42no—
389C3×C22⋊C4—121no—
390C3×C22⋊C4—121no—
391C3×C22⋊C4—121no—
392C3×C42—62no—
393#217—34no—
394#217—41no—
395#217—62no—
396#217—62no—
397#217—62no—
398#217—122no—
399#217C4×D314yescomplemented
400(C2×D3)⋊C4—34no—
401(C2×D3)⋊C4—41no—
402(C2×D3)⋊C4—41no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—122no—
409(C2×D3)⋊C4—121no—
410(C2×D3)⋊C4—121no—
411(C2×D3)⋊C4—121no—
412(C2×D3)⋊C4—121no—
413(C2×D3)⋊C4—122no—
414C4⋊Dic3—34no—
415C4⋊Dic3—62no—
416C4⋊Dic3—62no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—34no—
420Dic3⋊C4—41no—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—121no—
424Dic3⋊C4—121no—
425Dic3⋊C4—122no—
426C4×Dic3—22no—
427C4×Dic3—34no—
428C4×Dic3—34no—
429C4×Dic3—121no—
430C4×Dic3—121no—
431C4×Dic3—121no—
432C4×Dic3—121no—
433C4×Dic3—122no—
434C22×C32—22no—
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32C23×C411yescharacteristic
442C22×C32C22×D411yescharacteristic
443C22×C32C2×#4111yescharacteristic
444C22×C32H(5,𝔽2)11yescharacteristic
445C22×C32H(5,𝔽2)11yescharacteristic
446C22×C32H(5,𝔽2)11yescharacteristic
447C22×C322−1+411yescharacteristic
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C32×C4—41no—
463C32×C4—41no—
464C3⋊Dic3—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—41no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3C4×D414yes—
474C22×D4—31no—
475C22×D4—91no—
476C22×D4—91no—
477C23×C4—31no—
478C23×C4—91no—
479C23×C4—91no—
480#121—98no—
481C4×D4—184no—
482#117—184no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
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⋊C4D3211yescharacteristic
502C2×C42—31no—
503C2×C42—91no—
504C2×C42—91no—
505C2×C42—91no—
506#95—31no—
507#95—31no—
508#95—91no—
509#95—91no—
510#95—91no—
511#95—91no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—22no—
526C23×C3—32no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3C2×C4×D312yes—
540C23×C3C2×C4×D312yes—
541C23×C3C23×D311yescharacteristic
542C23×C3C23×D311yescharacteristic
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—32no—
550C22×D3—32no—
551C22×D3—62no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
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—61no—
564C22×D3—121no—
565C22×D3—121no—
566C22×D3—121no—
567C22×D3—121no—
568C22×D3—121no—
569C22×D3—121no—
570C22×D3C2×C4×D312yes—
571C3×D4—68no—
572C2×C3×C4—22no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—124no—
612#67—28no—
613#67—124no—
614#67—124no—
615#67—124no—
616#67—128no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—32no—
633C2×Dic3—32no—
634C2×Dic3—32no—
635C2×Dic3—32no—
636C2×Dic3—44no—
637C2×Dic3—62no—
638C2×Dic3—62no—
639C2×Dic3—62no—
640C2×Dic3—62no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—121no—
656C2×Dic3—121no—
657C2×Dic3—121no—
658C2×Dic3—121no—
659C2×Dic3—121no—
660C2×Dic3—124no—
661C2×Dic3C2×C4×D312yes—
662C2×Dic3C2×C4×D312yes—
663C2×Dic3C2×C4×D312yes—
664C2×Dic3D3×D412yes—
665C2×Dic3D3×D412yes—
666C2×Dic3#23712yes—
667D12—124no—
668C4×D3—68no—
669C4×D3—68no—
670C4×D3—124no—
671C2×C32—42no—
672C2×C32C2×C4×D411yescharacteristic
673C2×C32#51811yescharacteristic
674C2×C32#52011yescharacteristic
675C2×C32#53511yescharacteristic
676C2×C32#53711yescharacteristic
677C2×C32#54011yescharacteristic
678C2×C32#54211yescharacteristic
679C3⋊D3—42no—
680C3×D3—42no—
681C24—31no—
682C24—91no—
683C24C2×D3211yescharacteristic
684C2×D4—34no—
685C2×D4—62no—
686C2×D4—62no—
687C2×D4—94no—
688C2×D4—94no—
689C2×D4—361no—
690C2×D4—361no—
691C2×D4—361no—
692C2×D4—361no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—62no—
701C22×C4—94no—
702C22×C4—91no—
703C22×C4—91no—
704C22×C4—91no—
705C22×C4—121no—
706C22×C4—121no—
707C22×C4—182no—
708C22×C4—182no—
709C22×C4—182no—
710C22×C4—361no—
711C22×C4—361no—
712C22×C4C2×D3211yescharacteristic
713C22×C4C2×D3211yescharacteristic
714C4⋊C4—62no—
715C4⋊C4—62no—
716C4⋊C4—94no—
717C4⋊C4—121no—
718C4⋊C4—182no—
719C4⋊C4—182no—
720C4⋊C4—361no—
721C22⋊C4—34no—
722C22⋊C4—41no—
723C22⋊C4—94no—
724C22⋊C4—121no—
725C22⋊C4—121no—
726C22⋊C4—121no—
727C22⋊C4—182no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—182no—
731C22⋊C4—361no—
732C22⋊C4—361no—
733C42—62no—
734C42—94no—
735C42—361no—
736C42—361no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—81no—
765C22×C3—81no—
766C22×C3—81no—
767C22×C3—81no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3C22×C4×D311yescharacteristic
773C22×C3C22×C4×D311yescharacteristic
774C22×C3C2×D3×D411yescharacteristic
775C22×C3C2×D3×D411yescharacteristic
776C22×C3C2×#23711yescharacteristic
777C22×C3#100411yescharacteristic
778C22×C3#100411yescharacteristic
779C22×C3#100411yescharacteristic
780C22×C3#100411yescharacteristic
781C22×C3#100711yescharacteristic
782C22×C3D3×#4111yescharacteristic
783C22×C3#100911yescharacteristic
784C22×C3#100911yescharacteristic
785C22×C3#101011yescharacteristic
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—122no—
800C2×D3—122no—
801C2×D3—122no—
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—
814C3×C4—34no—
815C3×C4—42no—
816C3×C4—41no—
817C3×C4—41no—
818C3×C4—41no—
819C3×C4—41no—
820C3×C4—62no—
821C3×C4—62no—
822C3×C4—62no—
823C3×C4—81no—
824C3×C4—121no—
825C3×C4—121no—
826C3×C4—121no—
827Dic3—22no—
828Dic3—22no—
829Dic3—22no—
830Dic3—41no—
831Dic3—41no—
832Dic3—41no—
833Dic3—64no—
834Dic3—62no—
835Dic3—62no—
836Dic3—62no—
837Dic3—62no—
838Dic3—122no—
839Dic3—121no—
840Dic3—121no—
841Dic3—241no—
842Dic3#67⋊C414yes—
843C32#232411yescharacteristic, complemented, Sylow
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—32no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—92no—
858C23—181no—
859C23—181no—
860C23—181no—
861C23—181no—
862C23—181no—
863C23—181no—
864C23C4×D3212yes—
865C23C22×D3211yescharacteristic
866D4—68no—
867D4—364no—
868D4—364no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—32no—
880C2×C4—32no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
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—92no—
897C2×C4—92no—
898C2×C4—124no—
899C2×C4—188no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—364no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—42no—
916C2×C3—42no—
917C2×C3—82no—
918C2×C3—122no—
919C2×C3C2×#67⋊C411yescharacteristic
920C2×C3#550411yescharacteristic
921C2×C3C4×D3×D411yescharacteristic
922C2×C3#554511yescharacteristic
923C2×C3#554511yescharacteristic
924C2×C3#554611yescharacteristic
925C2×C3#559211yescharacteristic
926C2×C3#560711yescharacteristic
927C2×C3#560811yescharacteristic
928C2×C3#562911yescharacteristic
929C2×C3#564011yescharacteristic
930C2×C3#566311yescharacteristic
931C2×C3#568211yescharacteristic
932C2×C3#571911yescharacteristic
933D3—42no—
934D3—122no—
935D3—122no—
936D3—242no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—62no—
945C22—62no—
946C22—62no—
947C22—121no—
948C22—121no—
949C22—121no—
950C22—121no—
951C22—182no—
952C22—182no—
953C22—182no—
954C22—361no—
955C22—361no—
956C22—361no—
957C22—361no—
958C22#6429711yescharacteristic
959C22C2×C4×D3211yescharacteristic
960C22D32×D411yescharacteristic
961C22D3×#23711yescharacteristic
962C22#6431411yescharacteristic
963C22#6431411yescharacteristic
964C22#6433011yescharacteristic
965C4—34no—
966C4—41no—
967C4—41no—
968C4—62no—
969C4—62no—
970C4—62no—
971C4—121no—
972C4—121no—
973C4—121no—
974C4—182no—
975C4—182no—
976C4—361no—
977C3—21no—
978C3#7438511yescharacteristic, complemented
979C3#7643011yescharacteristic, complemented
980C2—42no—
981C2—122no—
982C2—362no—
983C2#1059406911yescharacteristic
984C2#1059413911yescharacteristic
985C2D3×#67⋊C411yescharacteristic
986C2#1059425611yescharacteristic
987C2#1059487411yescharacteristic
988C2#1059519211yescharacteristic
989C2#1059528511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63958C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×Dic3×#67C2semidirect
3. C2×#63836C2semidirect
4. #10592656C2semidirect
5. C3×#4957C2semidirect
6. C3×#4946C2semidirect
7. #10591711C2semidirect
8. #10591701C2semidirect
9. #10591384C2semidirect
10. #10591372C2semidirect
11. #10591367C2semidirect
12. #10591364C2semidirect
13. #10591330C2semidirect
14. #10591287C2semidirect
15. #10591241C2semidirect
46. #63958C4semidirect
76. #4957D3semidirect
79. #4946D3semidirect
94. C2×#638C2×C4semidirect
113. C2×#626C2×C4semidirect
116. C2×#624C2×C4semidirect
127. C3×#217C2×C4semidirect
136. Dic3⋊Dic3C2×C4semidirect
140. (C2×D3)⋊Dic3C2×C4semidirect
142. Dic32D4semidirect
399. #217C4×D3semidirect
843. C32#2324semidirect
978. C3#74385semidirect
979. C3#76430semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×#672
C2×#639582
C2×#638362
#105926562
C3×#49572
C3×#49462
#105917112
#105917012
#105913842
#105913722
#105913672
#105913642
#105913302
#105912872
#105912412
#764303
#743853