Finite Group Databasebeta

← #11803610

Subgroups — #11803610

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C2×#63971C211yesmaximal, characteristic
3C2×#63878C211yesmaximal, characteristic, complemented
4C3×#5213C211yesmaximal, characteristic, complemented
5C3×#5210C211yesmaximal, characteristic, complemented
6#10591707C211yesmaximal, characteristic, complemented
7#10591704C211yesmaximal, characteristic, complemented
8#10591701C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591384C211yesmaximal, characteristic, complemented
11#10591369C211yesmaximal, characteristic, complemented
12#10591290C211yesmaximal, characteristic, complemented
13#10591259C211yesmaximal, characteristic, complemented
14#10591257C211yesmaximal, characteristic, complemented
15#10591256C211yesmaximal, characteristic, complemented
16#74665—31nomaximal
17#74385—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C4×#638—24no—
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36#63971C418yescomplemented
37C2×#3724C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48C2×Dic32C2211yescharacteristic
49#63878—24no—
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#939—31no—
57C2×C4×#67—31no—
58C2×C4×#67—31no—
59C2×C4×#67—61no—
60C2×#892—31no—
61C2×#884—31no—
62C2×#877—31no—
63C3×#386—31no—
64C3×#385—31no—
65#5221—31no—
66#5213D311yescharacteristic, complemented
67#5210D311yescharacteristic, complemented
68#4989—31no—
69#4988—31no—
70#4976—31no—
71#4957—31no—
72#4957—31no—
73#4957—31no—
74#4957—31no—
75#4956—31no—
76#4951—31no—
77#4944—31no—
78#4942—31no—
79#4670—31no—
80#4669—31no—
81#4668—31no—
82#4667—31no—
83#4665—31no—
84#4649—31no—
85#4649—31no—
86#4647—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4—22no—
91C22×C32×C4—41no—
92C22×C32×C4—41no—
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—22no—
96C2×#638—22no—
97C2×#638C2×C414yes—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3—41no—
103C2×C4×C3⋊D3—41no—
104C2×C3×#67—41no—
105C2×C3×#67—41no—
106C2×C3×#67C2×C414yescomplemented
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×#626—41no—
115C2×#626—41no—
116C2×#626C2×C414yescomplemented
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3C2×C414yescomplemented
120#3757—22no—
121#3752—22no—
122#3750—22no—
123C4×C3⋊Dic3D414yescomplemented
124C3×#217—41no—
125C3×#217—41no—
126C3×#217C2×C414yescomplemented
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—41no—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—41no—
131#3724—22no—
132#3724C2×C414yescomplemented
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—41no—
135#3722—41no—
136#3722—41no—
137#3722C2×C414yescomplemented
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—41no—
140Dic32—22no—
141Dic32—41no—
142Dic32—41no—
143#2324—91noSylow
144C22×C3×D4—31no—
145C23×C3×C4—21no—
146C23×C3×C4C2×D311yescharacteristic
147C23×C3×C4C2×D311yescharacteristic
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—61no—
152C22×#67C2×D311yescharacteristic
153C23×Dic3—31no—
154C22×D12—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—61no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—61no—
171C2×#217C2×D311yescharacteristic
172C2×#217C2×D311yescharacteristic
173C2×#217C2×D311yescharacteristic
174#939—38no—
175C4×#67—64no—
176C4×#67—64no—
177C4×#67—68no—
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)⋊C4C2×D311yescharacteristic
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—61no—
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—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—61no—
213#892—64no—
214#884—38no—
215#877—64no—
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⋊#95C2×D311yescharacteristic
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32C22×C412yes—
235C23×C32C2411yescharacteristic
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⋊D3C22×C412yes—
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×D3C22×C412yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—44no—
256C2×C32×C4C2×D412yes—
257#638—28no—
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—
265C2×C3⋊Dic3C2×D412yes—
266C2×C3⋊Dic3#4112yes—
267C4×C3⋊D3—44no—
268C3×#67—44no—
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—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3C22×C412yes—
288C2×C3×Dic3C22×C412yes—
289C2×C3×Dic3C22×C412yes—
290#626—44no—
291D3×Dic3—28no—
292C2×#121—91no—
293C2×C4×D4—91no—
294C2×#117—91no—
295#390—91no—
296#390—91no—
297#390—91no—
298#389—91no—
299#388—91no—
300#388—91no—
301#386—31no—
302#386—91no—
303#385—31no—
304#385—91no—
305#380—91no—
306C4×C4⋊C4—91no—
307C24×C3—21no—
308C24×C3—31no—
309C24×C3C22×D311yescharacteristic
310C24×C3C22×D311yescharacteristic
311C23×D3—31no—
312C23×D3—31no—
313C23×D3—61no—
314C23×D3C22×D311yescharacteristic
315C2×C3×D4—34no—
316C2×C3×D4—121no—
317C2×C3×D4—121no—
318C22×C3×C4—24no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—41no—
331C22×C3×C4—41no—
332C22×C3×C4—41no—
333C22×C3×C4—41no—
334C22×C3×C4—42no—
335C22×C3×C4—42no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C2×#67—34no—
341C2×#67—34no—
342C2×#67—34no—
343C2×#67—41no—
344C2×#67—41no—
345C2×#67—64no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—64no—
351C2×#67—64no—
352C2×#67—121no—
353C2×#67—121no—
354C2×#67C4×D314yescomplemented
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—34no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365C22×Dic3—62no—
366C22×Dic3—62no—
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C2×D12—34no—
375C2×D12—121no—
376C2×D12—121no—
377C2×C4×D3—34no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—64no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—121no—
384C2×C4×D3—121no—
385C2×C4×D3—121no—
386C2×C4×D3—121no—
387C2×C4×D3—122no—
388C2×C4×D3—122no—
389C3×C4⋊C4—62no—
390C3×C4⋊C4—121no—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—62no—
393C3×C22⋊C4—121no—
394C3×C22⋊C4—121no—
395C3×C22⋊C4—121no—
396#217—41no—
397#217—41no—
398#217—62no—
399#217—62no—
400#217—62no—
401#217—64no—
402#217—121no—
403#217C4×D314yescomplemented
404(C2×D3)⋊C4—22no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—41no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—64no—
412(C2×D3)⋊C4—121no—
413(C2×D3)⋊C4—121no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4—121no—
416(C2×D3)⋊C4—121no—
417C4⋊Dic3—62no—
418C4⋊Dic3—121no—
419Dic3⋊C4—22no—
420Dic3⋊C4—34no—
421Dic3⋊C4—34no—
422Dic3⋊C4—41no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—64no—
429Dic3⋊C4—121no—
430C4×Dic3—34no—
431C4×Dic3—34no—
432C4×Dic3—64no—
433C4×Dic3—62no—
434C4×Dic3—62no—
435C4×Dic3—121no—
436C4×Dic3—121no—
437C4×Dic3—121no—
438C4×Dic3—121no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32C23×C411yescharacteristic
447C22×C32C22×D411yescharacteristic
448C22×C32C2×#4111yescharacteristic
449C22×C32H(5,𝔽2)11yescharacteristic
450C22×C32H(5,𝔽2)11yescharacteristic
451C22×C32H(5,𝔽2)11yescharacteristic
452C22×C322−1+411yescharacteristic
453C2×C3⋊D3—22no—
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C32×C4—22no—
468C32×C4—41no—
469C3⋊Dic3—22no—
470C3⋊Dic3—41no—
471C3⋊Dic3C4×D414yes—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C22×D4—31no—
480C22×D4—91no—
481C22×D4—91no—
482C23×C4—91no—
483C23×C4—91no—
484C23×C4D3211yescharacteristic
485#121—98no—
486C4×D4—184no—
487#117—184no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C42—91no—
508C2×C42—91no—
509C2×C42—91no—
510C2×C42—91no—
511#95—31no—
512#95—31no—
513#95—31no—
514#95—31no—
515#95—91no—
516#95—91no—
517C23×C3—22no—
518C23×C3—22no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—22no—
533C23×C3—32no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3C2×C4×D312yes—
545C23×C3C2×C4×D312yes—
546C23×C3C23×D311yescharacteristic
547C23×C3C23×D311yescharacteristic
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—32no—
555C22×D3—32no—
556C22×D3—62no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3—61no—
560C22×D3—61no—
561C22×D3—61no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—121no—
572C22×D3—121no—
573C22×D3—121no—
574C22×D3—121no—
575C22×D3C2×C4×D312yes—
576C3×D4—124no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
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—22no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—48no—
597C2×C3×C4—44no—
598C2×C3×C4—44no—
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—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4D3×D412yes—
618C2×C3×C4D3×D412yes—
619#67—44no—
620#67—68no—
621#67—68no—
622#67—616no—
623#67—124no—
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—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—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—68no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—62no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3C2×C4×D312yes—
671C2×Dic3C2×C4×D312yes—
672C2×Dic3C2×C4×D312yes—
673D12—124no—
674C4×D3—68no—
675C4×D3—128no—
676C4×D3—124no—
677C4×D3—124no—
678C2×C32—42no—
679C2×C32C2×C4×D411yescharacteristic
680C2×C32#51811yescharacteristic
681C2×C32#52011yescharacteristic
682C2×C32#53511yescharacteristic
683C2×C32#53711yescharacteristic
684C2×C32#54011yescharacteristic
685C2×C32#54211yescharacteristic
686C3⋊D3—42no—
687C3×D3—42no—
688C24—31no—
689C24—91no—
690C24C2×D3211yescharacteristic
691C2×D4—34no—
692C2×D4—94no—
693C2×D4—94no—
694C2×D4—121no—
695C2×D4—121no—
696C2×D4—182no—
697C2×D4—182no—
698C2×D4—361no—
699C2×D4—361no—
700C22×C4—22no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—94no—
711C22×C4—91no—
712C22×C4—91no—
713C22×C4—91no—
714C22×C4—182no—
715C22×C4—182no—
716C22×C4—182no—
717C22×C4—361no—
718C22×C4—361no—
719C22×C4C2×D3211yescharacteristic
720C22×C4C2×D3211yescharacteristic
721C4⋊C4—62no—
722C4⋊C4—94no—
723C4⋊C4—121no—
724C4⋊C4—182no—
725C4⋊C4—182no—
726C4⋊C4—182no—
727C4⋊C4—361no—
728C22⋊C4—34no—
729C22⋊C4—62no—
730C22⋊C4—94no—
731C22⋊C4—121no—
732C22⋊C4—121no—
733C22⋊C4—121no—
734C22⋊C4—182no—
735C22⋊C4—182no—
736C22⋊C4—182no—
737C22⋊C4—361no—
738C22⋊C4—361no—
739C22⋊C4—361no—
740C42—94no—
741C42—182no—
742C42—361no—
743C42—361no—
744C22×C3—24no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3C22×C4×D311yescharacteristic
780C22×C3C22×C4×D311yescharacteristic
781C22×C3C2×D3×D411yescharacteristic
782C22×C3C2×D3×D411yescharacteristic
783C22×C3#100411yescharacteristic
784C22×C3#100411yescharacteristic
785C22×C3#100411yescharacteristic
786C22×C3#100411yescharacteristic
787C22×C3#100411yescharacteristic
788C22×C3#100711yescharacteristic
789C22×C3D3×#4111yescharacteristic
790C22×C3D3×#4111yescharacteristic
791C22×C3#100911yescharacteristic
792C22×C3#101011yescharacteristic
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—64no—
801C2×D3—62no—
802C2×D3—62no—
803C2×D3—62no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—122no—
808C2×D3—122no—
809C2×D3—122no—
810C2×D3—122no—
811C2×D3—122no—
812C2×D3—122no—
813C2×D3—121no—
814C2×D3—121no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—121no—
818C2×D3—121no—
819C2×D3—121no—
820C2×D3—121no—
821C3×C4—24no—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—42no—
825C3×C4—41no—
826C3×C4—41no—
827C3×C4—62no—
828C3×C4—62no—
829C3×C4—62no—
830C3×C4—121no—
831C3×C4—121no—
832C3×C4—121no—
833C3×C4—121no—
834Dic3—22no—
835Dic3—22no—
836Dic3—22no—
837Dic3—34no—
838Dic3—34no—
839Dic3—41no—
840Dic3—41no—
841Dic3—41no—
842Dic3—41no—
843Dic3—64no—
844Dic3—62no—
845Dic3—62no—
846Dic3—122no—
847Dic3—122no—
848Dic3—121no—
849Dic3—121no—
850C32#232411yescharacteristic, complemented, Sylow
851C23—21no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—32no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—92no—
865C23—181no—
866C23—181no—
867C23—181no—
868C23—181no—
869C23—181no—
870C23—181no—
871C23C4×D3212yes—
872C23C22×D3211yescharacteristic
873D4—124no—
874D4—188no—
875D4—364no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—44no—
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—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—92no—
904C2×C4—92no—
905C2×C4—92no—
906C2×C4—92no—
907C2×C4—188no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—181no—
913C2×C4—364no—
914C2×C4#381112yes—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—44no—
923C2×C3—42no—
924C2×C3—42no—
925C2×C3—122no—
926C2×C3#548611yescharacteristic
927C2×C3#550411yescharacteristic
928C2×C3C4×D3×D411yescharacteristic
929C2×C3C4×D3×D411yescharacteristic
930C2×C3#554511yescharacteristic
931C2×C3#554611yescharacteristic
932C2×C3#559211yescharacteristic
933C2×C3#559211yescharacteristic
934C2×C3#560811yescharacteristic
935C2×C3#561511yescharacteristic
936C2×C3#562911yescharacteristic
937C2×C3#564011yescharacteristic
938C2×C3#566211yescharacteristic
939C2×C3#566311yescharacteristic
940D3—42no—
941D3—124no—
942D3—122no—
943D3—122no—
944C22—22no—
945C22—22no—
946C22—22no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—62no—
952C22—62no—
953C22—62no—
954C22—121no—
955C22—121no—
956C22—121no—
957C22—121no—
958C22—182no—
959C22—182no—
960C22—182no—
961C22—361no—
962C22—361no—
963C22—361no—
964C22—361no—
965C22#6429711yescharacteristic
966C22C2×C4×D3211yescharacteristic
967C22#6430611yescharacteristic
968C22#6430711yescharacteristic
969C22C2×#381111yescharacteristic
970C22#6433011yescharacteristic
971C22#6433011yescharacteristic
972C4—22no—
973C4—41no—
974C4—62no—
975C4—62no—
976C4—62no—
977C4—94no—
978C4—121no—
979C4—121no—
980C4—121no—
981C4—121no—
982C4—182no—
983C4—361no—
984C3—21no—
985C3#7438511yescharacteristic, complemented
986C3#7466511yescharacteristic, complemented
987C2—42no—
988C2—122no—
989C2—362no—
990C2#1059487411yescharacteristic
991C2#1059492311yescharacteristic
992C2#1059496411yescharacteristic
993C2#1059503111yescharacteristic
994C2#1059505611yescharacteristic
995C2C4×#381111yescharacteristic
996C2#1059550211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63971C2
hypercenterC23×C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
3. C2×#63878C2semidirect
4. C3×#5213C2semidirect
5. C3×#5210C2semidirect
6. #10591707C2semidirect
7. #10591704C2semidirect
8. #10591701C2semidirect
9. #10591387C2semidirect
10. #10591384C2semidirect
11. #10591369C2semidirect
12. #10591290C2semidirect
13. #10591259C2semidirect
14. #10591257C2semidirect
15. #10591256C2semidirect
36. #63971C4semidirect
66. #5213D3semidirect
67. #5210D3semidirect
106. C2×C3×#67C2×C4semidirect
116. C2×#626C2×C4semidirect
119. C2×D3×Dic3C2×C4semidirect
123. C4×C3⋊Dic3D4semidirect
126. C3×#217C2×C4semidirect
132. #3724C2×C4semidirect
137. #3722C2×C4semidirect
354. C2×#67C4×D3semidirect
403. #217C4×D3semidirect
850. C32#2324semidirect
985. C3#74385semidirect
986. C3#74665semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×#639712
C2×#638782
C3×#52132
C3×#52102
#105917072
#105917042
#105917012
#105913872
#105913842
#105913692
#105912902
#105912592
#105912572
#105912562
#746653
#743853