Finite Group Databasebeta

← #11812880

Subgroups — #11812880

Order 1152.

1491 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
2C2×#63978C211yesmaximal, characteristic
3C2×#63952C211yesmaximal, characteristic, complemented
4C2×#63854C211yesmaximal, characteristic, complemented
5#10592912C211yesmaximal, characteristic, complemented
6C3×#5213C211yesmaximal, characteristic, complemented
7#10591710C211yesmaximal, characteristic, complemented
8#10591693C211yesmaximal, characteristic, complemented
9#10591392C211yesmaximal, characteristic, complemented
10#10591378C211yesmaximal, characteristic, complemented
11#10591345C211yesmaximal, characteristic, complemented
12#10591326C211yesmaximal, characteristic, complemented
13#10591324C211yesmaximal, characteristic, complemented
14#10591307C211yesmaximal, characteristic, complemented
15#10591270C211yesmaximal, characteristic, complemented
16#82195—31nomaximal
17#74704—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3—24no—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36#63978—24no—
37C2×#3724C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×#3724C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63952—24no—
48#63854—24no—
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C22×C3×C4⋊C4—31no—
58C2×#939—31no—
59C2×#930—31no—
60C2×C4×#67—31no—
61C22×C4⋊Dic3D311yescharacteristic, complemented
62C2×#894—31no—
63C2×#883—31no—
64C2×#67⋊C4—31no—
65C3×#386—31no—
66#5220—31no—
67#5213—31no—
68#5213—31no—
69#5213—31no—
70#5213—61no—
71#5213D311yescharacteristic, complemented
72#5210—31no—
73#4993—31no—
74#4992—31no—
75#4991—31no—
76#4990—31no—
77#4989—31no—
78#4982—31no—
79#4980—31no—
80#4961—31no—
81#4951—31no—
82#4949—31no—
83#4946—31no—
84#4674—31no—
85#4668—31no—
86#4657—31no—
87#4654—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4—22no—
92C22×C32×C4—22no—
93C22×C32×C4—22no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—22no—
97C2×#638—22no—
98C2×#638D414yes—
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3—22no—
107C22×C3×Dic3—22no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3—41no—
110C22×C3×Dic3—41no—
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—41no—
121C2×#624—22no—
122C2×#624—22no—
123C2×#624—41no—
124#3757—22no—
125#3752—22no—
126#3752—22no—
127C3×#217—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×C4⋊Dic3—22no—
131C3×C4⋊Dic3—22no—
132C3×C4⋊Dic3—22no—
133C3×C4⋊Dic3D414yescomplemented
134#3724—22no—
135#3724—22no—
136#3724—41no—
137Dic3⋊Dic3—22no—
138#3722—22no—
139#3722—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—41no—
143Dic32—22no—
144#2443—91noSylow
145C22×C3×D4—31no—
146C23×C3×C4—21no—
147C23×C3×C4—31no—
148C23×C3×C4—31no—
149C23×C3×C4C2×D311yescharacteristic
150C23×C3×C4C2×D311yescharacteristic
151C22×#67—31no—
152C22×#67—31no—
153C22×#67—31no—
154C22×#67—61no—
155C22×#67C2×D311yescharacteristic
156C23×Dic3C2×D311yescharacteristic
157C23×Dic3C2×D311yescharacteristic
158C22×D12—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—64no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—61no—
175C2×#217C2×D311yescharacteristic
176#939—64no—
177#930—64no—
178C4×#67—64no—
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—61no—
191C2×(C2×D3)⋊C4—61no—
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×C4⋊Dic3—24no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3C2×D311yescharacteristic
197C2×C4⋊Dic3C2×D311yescharacteristic
198C2×C4⋊Dic3C2×D311yescharacteristic
199C2×C4⋊Dic3C2×D311yescharacteristic
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209#894—64no—
210#883—64no—
211#67⋊C4—64no—
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—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—61no—
227C3⋊#95—61no—
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32C2×D412yes—
235C23×C32#4112yes—
236C23×C32#4112yes—
237C23×C32C2411yescharacteristic
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⋊D3C2×D412yes—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C2×C32×C4—28no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D412yes—
258C2×C32×C4#4112yes—
259#638—28no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3C2×D412yes—
269C3×#67—44no—
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×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—44no—
290C2×C3×Dic3—44no—
291C2×C3×Dic3C2×D412yes—
292C2×C3×Dic3C2×D412yes—
293#626—44no—
294#624—44no—
295C2×#123—91no—
296C2×#121—91no—
297C2×C4×D4—91no—
298C22×C4⋊C4—31no—
299#399—91no—
300#398—91no—
301#397—91no—
302#394—91no—
303#388—91no—
304#387—91no—
305#386—31no—
306#386—91no—
307#386—91no—
308#385—91no—
309#385—91no—
310C24×C3—21no—
311C24×C3—31no—
312C24×C3C22×D311yescharacteristic
313C24×C3C22×D311yescharacteristic
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—61no—
317C23×D3C22×D311yescharacteristic
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C22×C3×C4—22no—
322C22×C3×C4—22no—
323C22×C3×C4—22no—
324C22×C3×C4—22no—
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—42no—
337C22×C3×C4—42no—
338C22×C3×C4—42no—
339C22×C3×C4—62no—
340C22×C3×C4—62no—
341C22×C3×C4—62no—
342C22×C3×C4—62no—
343C22×C3×C4—121no—
344C22×C3×C4—121no—
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C2×#67—22no—
350C2×#67—22no—
351C2×#67—22no—
352C2×#67—34no—
353C2×#67—34no—
354C2×#67—64no—
355C2×#67—62no—
356C2×#67—62no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—62no—
361C2×#67—122no—
362C2×#67—122no—
363C2×#67—121no—
364C22×Dic3—22no—
365C22×Dic3—22no—
366C22×Dic3—22no—
367C22×Dic3—22no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—41no—
375C22×Dic3—41no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C2×D12—62no—
387C2×D12—62no—
388C2×D12—121no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3—121no—
394C2×C4×D3—121no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—62no—
397C3×C4⋊C4—62no—
398C3×C4⋊C4—62no—
399C3×C22⋊C4—62no—
400C3×C22⋊C4—62no—
401C3×C22⋊C4—62no—
402#217—22no—
403#217—62no—
404#217—62no—
405#217—62no—
406#217—62no—
407#217—122no—
408#217—121no—
409(C2×D3)⋊C4—22no—
410(C2×D3)⋊C4—22no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—62no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—122no—
422(C2×D3)⋊C4—122no—
423(C2×D3)⋊C4—121no—
424C4⋊Dic3—22no—
425C4⋊Dic3—22no—
426C4⋊Dic3—22no—
427C4⋊Dic3—62no—
428C4⋊Dic3#6714yescomplemented
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434Dic3⋊C4—121no—
435Dic3⋊C4—121no—
436C4×Dic3—62no—
437C4×Dic3—62no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32#12314yescomplemented
445C22×C32C22×D411yescharacteristic
446C22×C32C22×D411yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C22×C32C2×#4111yescharacteristic
449C22×C32C2×#4111yescharacteristic
450C22×C32H(5,𝔽2)11yescharacteristic
451C22×C322−1+411yescharacteristic
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3—22no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C32×C4—22no—
467C32×C4—22no—
468C3⋊Dic3—22no—
469C3⋊Dic3—41no—
470C3⋊Dic3—41no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C22×D4—31no—
479C22×D4—91no—
480C22×D4—91no—
481C23×C4—31no—
482C23×C4—31no—
483C23×C4—91no—
484C23×C4D3211yescharacteristic
485#123—184no—
486#121—184no—
487C4×D4—184no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—64no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
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×C22⋊C4—91no—
508C2×C42—91no—
509#95—31no—
510#95—31no—
511#95—91no—
512#95—91no—
513#95—91no—
514#95—91no—
515#95—91no—
516#95—91no—
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—21no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
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×C3—61no—
540C23×C3#23512yes—
541C23×C3#23512yes—
542C23×C3D3×D412yes—
543C23×C3D3×D412yes—
544C23×C3#23712yes—
545C23×C3#23912yes—
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—21no—
555C22×D3—32no—
556C22×D3—32no—
557C22×D3—62no—
558C22×D3—61no—
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—121no—
571C22×D3—121no—
572C22×D3—121no—
573C22×D3—121no—
574C22×D3—121no—
575C22×D3—121no—
576C3×D4—124no—
577C2×C3×C4—28no—
578C2×C3×C4—28no—
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—21no—
586C2×C3×C4—21no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
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—48no—
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—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—124no—
616C2×C3×C4—124no—
617C2×C3×C4#23512yes—
618C2×C3×C4D3×D412yes—
619C2×C3×C4#23712yes—
620C2×C3×C4C2×#6712yes—
621#67—44no—
622#67—68no—
623#67—68no—
624#67—128no—
625#67—124no—
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—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—44no—
648C2×Dic3—44no—
649C2×Dic3—62no—
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—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3—121no—
673C2×Dic3—121no—
674C2×Dic3C2×#6712yes—
675C2×Dic3C2×#6712yes—
676D12—124no—
677C4×D3—124no—
678C4×D3—124no—
679C2×C32—24no—
680C2×C32C2×#12311yescharacteristic
681C2×C32#52511yescharacteristic
682C2×C32#53911yescharacteristic
683C2×C32D4211yescharacteristic
684C2×C32#54711yescharacteristic
685C2×C32#54811yescharacteristic
686C2×C32#55311yescharacteristic
687C3⋊D3—42no—
688C3×D3—81no—
689C24—31no—
690C24—91no—
691C24C2×D3211yescharacteristic
692C2×D4—62no—
693C2×D4—62no—
694C2×D4—62no—
695C2×D4—94no—
696C2×D4—182no—
697C2×D4—182no—
698C2×D4—182no—
699C2×D4—182no—
700C2×D4—361no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—62no—
712C22×C4—62no—
713C22×C4—62no—
714C22×C4—62no—
715C22×C4—91no—
716C22×C4—91no—
717C22×C4—91no—
718C22×C4—121no—
719C22×C4—121no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—361no—
723C22×C4C2×D3211yescharacteristic
724C22×C4C2×D3211yescharacteristic
725C4⋊C4—34no—
726C4⋊C4—62no—
727C4⋊C4—62no—
728C4⋊C4—62no—
729C4⋊C4—182no—
730C4⋊C4—182no—
731C4⋊C4—182no—
732C4⋊C4—361no—
733C22⋊C4—62no—
734C22⋊C4—62no—
735C22⋊C4—62no—
736C22⋊C4—182no—
737C22⋊C4—182no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C22⋊C4—182no—
742C22⋊C4—182no—
743C22⋊C4—361no—
744C42—182no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—24no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3#88314yescomplemented
779C22×C3#89414yescomplemented
780C22×C3C2×#23511yescharacteristic
781C22×C3C2×#23511yescharacteristic
782C22×C3C2×#23511yescharacteristic
783C22×C3C2×D3×D411yescharacteristic
784C22×C3C2×D3×D411yescharacteristic
785C22×C3C2×D3×D411yescharacteristic
786C22×C3C2×#23711yescharacteristic
787C22×C3C2×#23711yescharacteristic
788C22×C3#100411yescharacteristic
789C22×C3C2×#23911yescharacteristic
790C22×C3#100711yescharacteristic
791C22×C3#100911yescharacteristic
792C22×C3#101011yescharacteristic
793C22×C3C22×#6711yescharacteristic
794C2×D3—41no—
795C2×D3—41no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
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—121no—
811C2×D3—121no—
812C2×D3—121no—
813C2×D3—121no—
814C2×D3—121no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—121no—
818C2×D3—241no—
819C2×D3—241no—
820C2×D3—241no—
821C2×D3—241no—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—22no—
825C3×C4—22no—
826C3×C4—42no—
827C3×C4—42no—
828C3×C4—62no—
829C3×C4—62no—
830C3×C4—121no—
831C3×C4—121no—
832C3×C4—121no—
833C3×C4—121no—
834C3×C4—121no—
835Dic3—22no—
836Dic3—22no—
837Dic3—41no—
838Dic3—41no—
839Dic3—41no—
840Dic3—41no—
841Dic3—41no—
842Dic3—62no—
843Dic3—62no—
844Dic3—122no—
845Dic3—121no—
846Dic3—121no—
847Dic3—121no—
848Dic3—121no—
849Dic3—241no—
850Dic3—241no—
851C32#244311yescharacteristic, complemented, Sylow
852C23—21no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—92no—
864C23—181no—
865C23—181no—
866C23—181no—
867C23—181no—
868C23—181no—
869C23—181no—
870C23#379912yes—
871C23#380212yes—
872C23#380412yes—
873C23C22×D3211yescharacteristic
874D4—124no—
875D4—188no—
876D4—364no—
877C2×C4—28no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—32no—
883C2×C4—32no—
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—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—92no—
904C2×C4—124no—
905C2×C4—124no—
906C2×C4—181no—
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×C4#380412yes—
916C2×C4D3×#6712yes—
917C2×C3—24no—
918C2×C3—24no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—44no—
927C2×C3—241no—
928C2×C3C2×#88311yescharacteristic
929C2×C3C2×#89411yescharacteristic
930C2×C3#550711yescharacteristic
931C2×C3#551411yescharacteristic
932C2×C3#551511yescharacteristic
933C2×C3#555211yescharacteristic
934C2×C3#556511yescharacteristic
935C2×C3#558611yescharacteristic
936C2×C3#560911yescharacteristic
937C2×C3#561111yescharacteristic
938C2×C3#566511yescharacteristic
939C2×C3#579111yescharacteristic
940C2×C3D4×#6711yescharacteristic
941C2×C3#581711yescharacteristic
942D3—81no—
943D3—122no—
944D3—122no—
945D3—242no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—121no—
953C22—121no—
954C22—121no—
955C22—121no—
956C22—121no—
957C22—121no—
958C22—121no—
959C22—182no—
960C22—182no—
961C22—182no—
962C22—361no—
963C22—361no—
964C22—361no—
965C22—361no—
966C22#6385414yescomplemented
967C22#6429711yescharacteristic
968C22C2×#379911yescharacteristic
969C22C2×#380211yescharacteristic
970C22#6430711yescharacteristic
971C22C2×#380411yescharacteristic
972C22C2×#380411yescharacteristic
973C22C2×D3×#6711yescharacteristic
974C4—22no—
975C4—22no—
976C4—62no—
977C4—62no—
978C4—121no—
979C4—121no—
980C4—121no—
981C4—121no—
982C4—121no—
983C4—182no—
984C4—361no—
985C4—361no—
986C3—21no—
987C3#7470411yescharacteristic, complemented
988C3#8219511yescharacteristic, complemented
989C2—24no—
990C2—241no—
991C2—362no—
992C2C2×#6385411yescharacteristic
993C2#1059484311yescharacteristic
994C2#1059490211yescharacteristic
995C2#1059492811yescharacteristic
996C2#1059498711yescharacteristic
997C2#1059506911yescharacteristic
998C2#1059549811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC2×#63978C2
hypercenterC23×C4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4⋊Dic3C2semidirect
3. C2×#63952C2semidirect
4. C2×#63854C2semidirect
5. #10592912C2semidirect
6. C3×#5213C2semidirect
7. #10591710C2semidirect
8. #10591693C2semidirect
9. #10591392C2semidirect
10. #10591378C2semidirect
11. #10591345C2semidirect
12. #10591326C2semidirect
13. #10591324C2semidirect
14. #10591307C2semidirect
15. #10591270C2semidirect
61. C22×C4⋊Dic3D3semidirect
71. #5213D3semidirect
133. C3×C4⋊Dic3D4semidirect
428. C4⋊Dic3#67semidirect
444. C22×C32#123semidirect
778. C22×C3#883semidirect
779. C22×C3#894semidirect
851. C32#2443semidirect
966. C22#63854semidirect
987. C3#74704semidirect
988. C3#82195semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C2×#639782
C2×#639522
C2×#638542
#105929122
C3×#52132
#105917102
#105916932
#105913922
#105913782
#105913452
#105913262
#105913242
#105913072
#105912702
#821953
#747043