Finite Group Databasebeta

← #11806897

Subgroups — #11806897

Order 1152.

1877 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×#63979C211yesmaximal, characteristic
4C2×#63881C211yesmaximal, characteristic, complemented
5C2×#63879C211yesmaximal, characteristic, complemented
6C3×#5213C211yesmaximal, characteristic, complemented
7#10591721C211yesmaximal, characteristic, complemented
8#10591707C211yesmaximal, characteristic, complemented
9#10591704C211yesmaximal, characteristic, complemented
10#10591387C211yesmaximal, characteristic, complemented
11#10591385C211yesmaximal, characteristic, complemented
12#10591383C211yesmaximal, characteristic, complemented
13#10591382C211yesmaximal, characteristic, complemented
14#10591243C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#82343—31nomaximal
17#74679—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C4×#638—24no—
30C2×#3752C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C3×C4×#67—24no—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41#63979C418yescomplemented
42C2×#3724C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51C2×Dic32C2211yescharacteristic
52#63881—24no—
53#63879—24no—
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C2×C3×C4×D4—31no—
59C2×#940—31no—
60C2×#940—31no—
61C2×C4×#67—31no—
62C2×C4×#67—31no—
63C2×C4×#67—31no—
64C2×C4×#67—61no—
65C2×C4×#67D311yescharacteristic, complemented
66C2×#893—31no—
67C2×#67⋊C4—31no—
68C2×#67⋊C4—31no—
69C3×#386—31no—
70#5221—31no—
71#5220—31no—
72#5213—31no—
73#5213D311yescharacteristic, complemented
74Dic3×C4⋊C4—31no—
75#4957—31no—
76#4957—31no—
77#4957—31no—
78#4957—31no—
79#4957—31no—
80#4957—31no—
81#4956—31no—
82#4956—31no—
83#4939—31no—
84C4×Dic3⋊C4—31no—
85#4665—31no—
86#4665—31no—
87#4649—31no—
88#4649—31no—
89C24×C32C2311yescharacteristic
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×C32×C4—22no—
94C22×C32×C4—22no—
95C22×C32×C4—41no—
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638—22no—
99C2×#638—22no—
100C2×#638C2×C414yescomplemented
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—41no—
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—41no—
110C2×C3×#67—41no—
111C2×C3×#67C2×C414yescomplemented
112C2×C3×#67C2×C414yescomplemented
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—41no—
122C2×#626—22no—
123C2×#626—22no—
124C2×#626—41no—
125C2×#626—41no—
126C2×#626C2×C414yescomplemented
127C2×#626C2×C414yescomplemented
128C2×#625—22no—
129C2×#625—22no—
130C2×#625C2×C414yescomplemented
131C2×D3×Dic3—22no—
132C2×D3×Dic3—22no—
133C2×D3×Dic3—41no—
134#3757—22no—
135#3752—22no—
136#3750D414yescomplemented
137C4×C3⋊Dic3—22no—
138C3×#217—22no—
139C3×#217—41no—
140C3×(C2×D3)⋊C4—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×Dic3⋊C4D414yescomplemented
144C3×C4×Dic3—22no—
145#3724—22no—
146Dic3⋊Dic3—22no—
147#3722—22no—
148#3722—41no—
149(C2×D3)⋊Dic3—22no—
150(C2×D3)⋊Dic3—41no—
151(C2×D3)⋊Dic3—41no—
152Dic32—22no—
153Dic32—22no—
154Dic32C2×C414yescomplemented
155#2366—91noSylow
156C22×C3×D4—31no—
157C22×C3×D4—31no—
158C23×C3×C4—21no—
159C23×C3×C4—31no—
160C23×C3×C4C2×D311yescharacteristic
161C23×C3×C4C2×D311yescharacteristic
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—61no—
169C22×#67C2×D311yescharacteristic
170C22×#67C2×D311yescharacteristic
171C23×Dic3—31no—
172C22×D12—31no—
173C22×D12—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—61no—
178C22×C4×D3C2×D311yescharacteristic
179C3×C4×D4—64no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C42—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—61no—
193C2×#217C2×D311yescharacteristic
194C2×#217C2×D311yescharacteristic
195#940—38no—
196#940—38no—
197C4×#67—24no—
198C4×#67—64no—
199C4×#67—64no—
200C4×#67—64no—
201C4×#67—68no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—61no—
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×(C2×D3)⋊C4C2×D311yescharacteristic
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×C4⋊Dic3—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—61no—
222C2×Dic3⋊C4C2×D311yescharacteristic
223C2×C4×Dic3—31no—
224C2×C4×Dic3—31no—
225C2×C4×Dic3—31no—
226C2×C4×Dic3—31no—
227C2×C4×Dic3—31no—
228C2×C4×Dic3—31no—
229C2×C4×Dic3—31no—
230C2×C4×Dic3—31no—
231C2×C4×Dic3—61no—
232C2×C4×Dic3C2×D311yescharacteristic
233#893—64no—
234#67⋊C4—64no—
235#67⋊C4—64no—
236C3×#95—31no—
237C3×#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—31no—
241C3⋊#95—31no—
242C3⋊#95C2×D311yescharacteristic
243C3⋊#95C2×D311yescharacteristic
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32—21no—
248C23×C32—21no—
249C23×C32—21no—
250C23×C32C22×C412yes—
251C23×C32C2411yescharacteristic
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3C22×C412yes—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3C22×C412yes—
272C22×C3×D3C22×C412yes—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—44no—
278C2×C32×C4C2×D412yes—
279C2×C32×C4C2×D412yes—
280#638—28no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3C22×C412yes—
287C2×C3⋊Dic3C2×D412yes—
288C2×C3⋊Dic3C2×D412yes—
289C2×C3⋊Dic3#4112yes—
290C4×C3⋊D3—44no—
291C3×#67—28no—
292C3×#67—44no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C22×C412yes—
307C2×C3×Dic3C22×C412yes—
308C2×C3×Dic3C2×D412yes—
309C2×C3×Dic3C2×D412yes—
310C2×C3×Dic3#4112yes—
311C3×C4×D3—44no—
312#626—28no—
313#626—44no—
314#625—28no—
315D3×Dic3—44no—
316C2×#127—91no—
317C2×C4×D4—31no—
318C2×C4×D4—91no—
319C2×C4×D4—91no—
320C2×C4×D4—91no—
321#390—91no—
322#390—91no—
323#390—91no—
324#390—91no—
325#386—31no—
326#386—91no—
327#386—91no—
328#386—91no—
329C4×C4⋊C4—91no—
330C4×C4⋊C4—91no—
331C24×C3—21no—
332C24×C3—31no—
333C24×C3—31no—
334C24×C3C22×D311yescharacteristic
335C24×C3C22×D311yescharacteristic
336C23×D3—31no—
337C23×D3—31no—
338C23×D3—61no—
339C23×D3C22×D311yescharacteristic
340C23×D3C22×D311yescharacteristic
341C2×C3×D4—34no—
342C2×C3×D4—34no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—121no—
346C2×C3×D4—121no—
347C22×C3×C4—24no—
348C22×C3×C4—22no—
349C22×C3×C4—22no—
350C22×C3×C4—22no—
351C22×C3×C4—22no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—42no—
361C22×C3×C4—41no—
362C22×C3×C4—41no—
363C22×C3×C4—42no—
364C22×C3×C4—62no—
365C22×C3×C4—62no—
366C22×C3×C4—121no—
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C2×#67—22no—
372C2×#67—22no—
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—41no—
380C2×#67—41no—
381C2×#67—64no—
382C2×#67—62no—
383C2×#67—62no—
384C2×#67—62no—
385C2×#67—62no—
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67—64no—
391C2×#67—64no—
392C2×#67—62no—
393C2×#67—62no—
394C2×#67—121no—
395C2×#67—121no—
396C2×#67C4×D314yescomplemented
397C2×#67C4×D314yescomplemented
398C22×Dic3—31no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—31no—
404C22×Dic3—61no—
405C22×Dic3—61no—
406C22×Dic3—61no—
407C22×Dic3—62no—
408C22×Dic3—62no—
409C22×Dic3—121no—
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C2×D12—34no—
417C2×D12—34no—
418C2×D12—62no—
419C2×D12—62no—
420C2×D12—121no—
421C2×D12—121no—
422C2×C4×D3—22no—
423C2×C4×D3—22no—
424C2×C4×D3—41no—
425C2×C4×D3—62no—
426C2×C4×D3—62no—
427C2×C4×D3—62no—
428C2×C4×D3—64no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—62no—
432C2×C4×D3—122no—
433C2×C4×D3—121no—
434C2×C4×D3—121no—
435C2×C4×D3—121no—
436C2×C4×D3—122no—
437C3×C4⋊C4—34no—
438C3×C22⋊C4—62no—
439C3×C22⋊C4—62no—
440C3×C22⋊C4—62no—
441C3×C22⋊C4—62no—
442C3×C22⋊C4—121no—
443C3×C42—62no—
444#217—22no—
445#217—41no—
446#217—62no—
447#217—62no—
448#217—62no—
449#217—64no—
450#217—121no—
451#217—121no—
452(C2×D3)⋊C4—22no—
453(C2×D3)⋊C4—22no—
454(C2×D3)⋊C4—22no—
455(C2×D3)⋊C4—62no—
456(C2×D3)⋊C4—62no—
457(C2×D3)⋊C4—64no—
458(C2×D3)⋊C4—62no—
459(C2×D3)⋊C4—62no—
460(C2×D3)⋊C4—62no—
461(C2×D3)⋊C4—121no—
462(C2×D3)⋊C4—121no—
463(C2×D3)⋊C4—121no—
464(C2×D3)⋊C4—121no—
465C4⋊Dic3—62no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—64no—
469Dic3⋊C4—62no—
470Dic3⋊C4—62no—
471Dic3⋊C4—62no—
472Dic3⋊C4#6714yescomplemented
473C4×Dic3—22no—
474C4×Dic3—34no—
475C4×Dic3—34no—
476C4×Dic3—62no—
477C4×Dic3—62no—
478C4×Dic3—62no—
479C4×Dic3—62no—
480C4×Dic3—62no—
481C4×Dic3—64no—
482C4×Dic3—62no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32—41no—
489C22×C32—41no—
490C22×C32C23×C411yescharacteristic
491C22×C32C22×D411yescharacteristic
492C22×C32C22×D411yescharacteristic
493C22×C32C2×#4111yescharacteristic
494C22×C32C2×#4111yescharacteristic
495C22×C32H(5,𝔽2)11yescharacteristic
496C22×C32H(5,𝔽2)11yescharacteristic
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—41no—
501C2×C3⋊D3—41no—
502C2×C3⋊D3—41no—
503C2×C3⋊D3—41no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—41no—
511C2×C3×D3—41no—
512C2×C3×D3—41no—
513C2×C3×D3—41no—
514C2×C3×D3—41no—
515C2×C3×D3—41no—
516C2×C3×D3—41no—
517C2×C3×D3—41no—
518C32×C4—22no—
519C32×C4—22no—
520C3⋊Dic3—22no—
521C3⋊Dic3—41no—
522C3⋊Dic3C4×D414yescomplemented
523C3×Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—41no—
526C3×Dic3—41no—
527C3×Dic3—41no—
528C3×Dic3C4×D414yescomplemented
529C22×D4—31no—
530C22×D4—31no—
531C22×D4—91no—
532C22×D4—91no—
533C22×D4—91no—
534C22×D4—91no—
535C23×C4—31no—
536C23×C4—91no—
537C23×C4—91no—
538C23×C4D3211yescharacteristic
539#127—98no—
540C4×D4—64no—
541C4×D4—184no—
542C4×D4—184no—
543C4×D4—184no—
544C2×C4⋊C4—31no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C4⋊C4—91no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C42—31no—
561C2×C42—91no—
562C2×C42—91no—
563C2×C42—91no—
564C2×C42—91no—
565#95—31no—
566#95—31no—
567#95—91no—
568#95—91no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—22no—
585C23×C3—32no—
586C23×C3—32no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3C2×C4×D312yes—
604C23×C3C2×C4×D312yes—
605C23×C3C23×D311yescharacteristic
606C23×C3C23×D311yescharacteristic
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—32no—
620C22×D3—32no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—61no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—61no—
635C22×D3—61no—
636C22×D3—121no—
637C22×D3—121no—
638C22×D3—121no—
639C22×D3—121no—
640C22×D3C2×C4×D312yes—
641C22×D3C2×C4×D312yes—
642C3×D4—68no—
643C3×D4—124no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—44no—
664C2×C3×C4—44no—
665C2×C3×C4—48no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—124no—
680C2×C3×C4D3×D412yes—
681C2×C3×C4D3×D412yes—
682C2×C3×C4D3×D412yes—
683C2×C3×C4C2×#6712yes—
684#67—28no—
685#67—44no—
686#67—68no—
687#67—68no—
688#67—68no—
689#67—68no—
690#67—616no—
691#67—68no—
692#67—124no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—21no—
699C2×Dic3—21no—
700C2×Dic3—21no—
701C2×Dic3—21no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—21no—
705C2×Dic3—21no—
706C2×Dic3—32no—
707C2×Dic3—32no—
708C2×Dic3—32no—
709C2×Dic3—32no—
710C2×Dic3—32no—
711C2×Dic3—32no—
712C2×Dic3—32no—
713C2×Dic3—32no—
714C2×Dic3—62no—
715C2×Dic3—62no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—62no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—61no—
728C2×Dic3—61no—
729C2×Dic3—121no—
730C2×Dic3—121no—
731C2×Dic3—121no—
732C2×Dic3—121no—
733C2×Dic3—124no—
734C2×Dic3C2×C4×D312yes—
735C2×Dic3C2×C4×D312yes—
736C2×Dic3#23512yes—
737C2×Dic3C2×#6712yes—
738C2×Dic3C2×#6712yes—
739D12—68no—
740D12—124no—
741C4×D3—44no—
742C4×D3—124no—
743C4×D3—124no—
744C4×D3—124no—
745C4×D3—128no—
746C2×C32—42no—
747C2×C32C2×C4×D411yescharacteristic
748C2×C32C2×C4×D411yescharacteristic
749C2×C32#51811yescharacteristic
750C2×C32D4211yescharacteristic
751C2×C32#55011yescharacteristic
752C2×C32#55011yescharacteristic
753C2×C32#55911yescharacteristic
754C3⋊D3—42no—
755C3×D3—42no—
756C3×D3—42no—
757C24—31no—
758C24—31no—
759C24—91no—
760C24C2×D3211yescharacteristic
761C2×D4—34no—
762C2×D4—34no—
763C2×D4—62no—
764C2×D4—62no—
765C2×D4—94no—
766C2×D4—94no—
767C2×D4—94no—
768C2×D4—94no—
769C2×D4—121no—
770C2×D4—121no—
771C2×D4—182no—
772C2×D4—182no—
773C2×D4—182no—
774C2×D4—182no—
775C2×D4—182no—
776C2×D4—182no—
777C2×D4—361no—
778C2×D4—361no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—31no—
784C22×C4—31no—
785C22×C4—31no—
786C22×C4—31no—
787C22×C4—41no—
788C22×C4—62no—
789C22×C4—62no—
790C22×C4—91no—
791C22×C4—91no—
792C22×C4—91no—
793C22×C4—121no—
794C22×C4—182no—
795C22×C4—182no—
796C22×C4—182no—
797C22×C4—182no—
798C22×C4—361no—
799C22×C4—361no—
800C22×C4C2×D3211yescharacteristic
801C22×C4C2×D3211yescharacteristic
802C4⋊C4—34no—
803C4⋊C4—94no—
804C4⋊C4—182no—
805C4⋊C4—182no—
806C22⋊C4—62no—
807C22⋊C4—62no—
808C22⋊C4—62no—
809C22⋊C4—62no—
810C22⋊C4—121no—
811C22⋊C4—182no—
812C22⋊C4—182no—
813C22⋊C4—182no—
814C22⋊C4—182no—
815C22⋊C4—361no—
816C22⋊C4—361no—
817C22⋊C4—361no—
818C42—62no—
819C42—94no—
820C42—182no—
821C42—182no—
822C42—182no—
823C22×C3—24no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—121no—
858C22×C3—121no—
859C22×C3—121no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3C22×C4×D311yescharacteristic
866C22×C3C22×C4×D311yescharacteristic
867C22×C3C2×#23511yescharacteristic
868C22×C3C2×D3×D411yescharacteristic
869C22×C3C2×D3×D411yescharacteristic
870C22×C3C2×D3×D411yescharacteristic
871C22×C3#100411yescharacteristic
872C22×C3#100411yescharacteristic
873C22×C3#100411yescharacteristic
874C22×C3D3×#4111yescharacteristic
875C22×C3D3×#4111yescharacteristic
876C22×C3D3×#4111yescharacteristic
877C22×C3#100911yescharacteristic
878C22×C3C22×#6711yescharacteristic
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—41no—
886C2×D3—41no—
887C2×D3—41no—
888C2×D3—41no—
889C2×D3—41no—
890C2×D3—41no—
891C2×D3—41no—
892C2×D3—41no—
893C2×D3—64no—
894C2×D3—62no—
895C2×D3—62no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—122no—
901C2×D3—122no—
902C2×D3—122no—
903C2×D3—122no—
904C2×D3—122no—
905C2×D3—122no—
906C2×D3—121no—
907C2×D3—121no—
908C2×D3—121no—
909C2×D3—121no—
910C2×D3—121no—
911C2×D3—121no—
912C2×D3—121no—
913C2×D3—121no—
914C3×C4—24no—
915C3×C4—22no—
916C3×C4—22no—
917C3×C4—22no—
918C3×C4—22no—
919C3×C4—34no—
920C3×C4—42no—
921C3×C4—62no—
922C3×C4—62no—
923C3×C4—121no—
924C3×C4—121no—
925C3×C4—121no—
926Dic3—22no—
927Dic3—22no—
928Dic3—34no—
929Dic3—34no—
930Dic3—41no—
931Dic3—41no—
932Dic3—41no—
933Dic3—64no—
934Dic3—62no—
935Dic3—62no—
936Dic3—122no—
937Dic3—122no—
938Dic3—121no—
939Dic3—121no—
940Dic3C4×#6714yescomplemented
941C32#236611yescharacteristic, complemented, Sylow
942C23—21no—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—32no—
949C23—32no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—61no—
956C23—61no—
957C23—61no—
958C23—61no—
959C23—61no—
960C23—61no—
961C23—61no—
962C23—92no—
963C23—181no—
964C23—181no—
965C23—181no—
966C23—181no—
967C23—181no—
968C23—181no—
969C23C4×D3212yes—
970C23C22×D3211yescharacteristic
971D4—68no—
972D4—124no—
973D4—188no—
974D4—188no—
975D4—188no—
976D4—364no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—32no—
982C2×C4—32no—
983C2×C4—32no—
984C2×C4—32no—
985C2×C4—32no—
986C2×C4—44no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—61no—
995C2×C4—61no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—61no—
999C2×C4—61no—
1000C2×C4—92no—
1001C2×C4—92no—
1002C2×C4—92no—
1003C2×C4—92no—
1004C2×C4—124no—
1005C2×C4—181no—
1006C2×C4—181no—
1007C2×C4—181no—
1008C2×C4—181no—
1009C2×C4—181no—
1010C2×C4—364no—
1011C2×C4—364no—
1012C2×C4D3×#6712yes—
1013C2×C4#381112yes—
1014C2×C3—21no—
1015C2×C3—21no—
1016C2×C3—21no—
1017C2×C3—21no—
1018C2×C3—21no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—44no—
1022C2×C3—42no—
1023C2×C3—42no—
1024C2×C3—122no—
1025C2×C3—122no—
1026C2×C3#548611yescharacteristic
1027C2×C3C4×D3×D411yescharacteristic
1028C2×C3C4×D3×D411yescharacteristic
1029C2×C3C4×D3×D411yescharacteristic
1030C2×C3#554511yescharacteristic
1031C2×C3#555311yescharacteristic
1032C2×C3#555911yescharacteristic
1033C2×C3#559011yescharacteristic
1034C2×C3#559911yescharacteristic
1035C2×C3#559911yescharacteristic
1036C2×C3#566411yescharacteristic
1037C2×C3C2×C4×#6711yescharacteristic
1038C2×C3D4×#6711yescharacteristic
1039C2×C3#583411yescharacteristic
1040D3—42no—
1041D3—42no—
1042D3—124no—
1043D3—122no—
1044D3—122no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—62no—
1053C22—62no—
1054C22—62no—
1055C22—62no—
1056C22—62no—
1057C22—62no—
1058C22—121no—
1059C22—121no—
1060C22—121no—
1061C22—121no—
1062C22—121no—
1063C22—121no—
1064C22—121no—
1065C22—121no—
1066C22—182no—
1067C22—182no—
1068C22—182no—
1069C22—361no—
1070C22—361no—
1071C22—361no—
1072C22—361no—
1073C22C2×C4×D3211yescharacteristic
1074C22D3×#23511yescharacteristic
1075C22#6430611yescharacteristic
1076C22#6430711yescharacteristic
1077C22C2×D3×#6711yescharacteristic
1078C22C2×#381111yescharacteristic
1079C22#6433011yescharacteristic
1080C4—22no—
1081C4—22no—
1082C4—34no—
1083C4—62no—
1084C4—62no—
1085C4—94no—
1086C4—121no—
1087C4—121no—
1088C4—121no—
1089C4—182no—
1090C4—361no—
1091C3—21no—
1092C3#7467911yescharacteristic, complemented
1093C3#8234311yescharacteristic, complemented
1094C2—42no—
1095C2—122no—
1096C2—122no—
1097C2—362no—
1098C2#1059491911yescharacteristic
1099C2#1059495711yescharacteristic
1100C2#1059500611yescharacteristic
1101C2C4×D3×#6711yescharacteristic
1102C2#1059505611yescharacteristic
1103C2C4×#381111yescharacteristic
1104C2#1059552611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63979C2
hypercenterC23×C4D32
hypocenterC32#2366
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
2. C2×C3×C4×#67C2semidirect
4. C2×#63881C2semidirect
5. C2×#63879C2semidirect
6. C3×#5213C2semidirect
7. #10591721C2semidirect
8. #10591707C2semidirect
9. #10591704C2semidirect
10. #10591387C2semidirect
11. #10591385C2semidirect
12. #10591383C2semidirect
13. #10591382C2semidirect
14. #10591243C2semidirect
15. #10591241C2semidirect
41. #63979C4semidirect
65. C2×C4×#67D3semidirect
73. #5213D3semidirect
100. C2×#638C2×C4semidirect
111. C2×C3×#67C2×C4semidirect
112. C2×C3×#67C2×C4semidirect
126. C2×#626C2×C4semidirect
127. C2×#626C2×C4semidirect
130. C2×#625C2×C4semidirect
136. #3750D4semidirect
143. C3×Dic3⋊C4D4semidirect
154. Dic32C2×C4semidirect
396. C2×#67C4×D3semidirect
397. C2×#67C4×D3semidirect
472. Dic3⋊C4#67semidirect
522. C3⋊Dic3C4×D4semidirect
528. C3×Dic3C4×D4semidirect
940. Dic3C4×#67semidirect
941. C32#2366semidirect
1092. C3#74679semidirect
1093. C3#82343semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×C4×#672
C2×#639792
C2×#638812
C2×#638792
C3×#52132
#105917212
#105917072
#105917042
#105913872
#105913852
#105913832
#105913822
#105912432
#105912412
#823433
#746793