Finite Group Databasebeta

← #11802178

Subgroups — #11802178

Order 1152.

1547 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64092C211yesmaximal, characteristic
2C2×#63952C211yesmaximal, characteristic
3C2×C4×#624C211yesmaximal, characteristic, complemented
4C3×#4951C211yesmaximal, characteristic, complemented
5C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic
7#10591703C211yesmaximal, characteristic, complemented
8Dic3×#217C211yesmaximal, characteristic, complemented
9#10591378C211yesmaximal, characteristic, complemented
10#10591271C211yesmaximal, characteristic, complemented
11Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#10591243C211yesmaximal, characteristic, complemented
13#10591233C211yesmaximal, characteristic, complemented
14#10591219C211yesmaximal, characteristic, complemented
15#10591197C211yesmaximal, characteristic, complemented
16#75453—31nomaximal
17C4×#883—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28#64092C418yescomplemented
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63952—24no—
45C4×#624—24no—
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C4×#67—31no—
57C2×#883—31no—
58C2×#883—31no—
59C2×#883—61no—
60C2×#67⋊C4—31no—
61C2×C42×D3—31no—
62C2×C42×D3—31no—
63C3×#388—31no—
64C3×C4×C22⋊C4—31no—
65C4×#217—31no—
66#4989—31no—
67Dic3×C4⋊C4—31no—
68#4956—31no—
69#4956—31no—
70#4951D311yescharacteristic, complemented
71#4945—31no—
72#4944—31no—
73Dic3×C22⋊C4—31no—
74Dic3×C22⋊C4D311yescharacteristic, complemented
75C4×(C2×D3)⋊C4—31no—
76C4×C4⋊Dic3—31no—
77#4933—31no—
78C4×Dic3⋊C4—31no—
79#4668—31no—
80#4666—31no—
81#4664—31no—
82#4664—31no—
83#4654—31no—
84#4653—31no—
85#4652—31no—
86#4649—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C2×#638—22no—
92C2×#638—22no—
93C2×#638C2×C414yes—
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3C2×C414yescomplemented
100C22×C3×Dic3—22no—
101C22×C3×Dic3—22no—
102C22×C3×Dic3—22no—
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×#624—22no—
112C2×#624—22no—
113C2×#624—22no—
114C2×#624—22no—
115C2×#624—22no—
116C2×#624D414yes—
117C32×C22⋊C4C2×C414yescomplemented
118#3757C2×C414yescomplemented
119#3752C2×C414yescomplemented
120C4⋊(C3⋊Dic3)C2×C414yescomplemented
121#3750C2×C414yescomplemented
122C3×#217—22no—
123C3×#217—22no—
124C3×#217—22no—
125C3×C4⋊Dic3—22no—
126C3×C4×Dic3—22no—
127C3×C4×Dic3—22no—
128C3×C4×Dic3—22no—
129#3724—22no—
130#3724—22no—
131#3722—22no—
132#3722—22no—
133Dic32—22no—
134Dic32—22no—
135Dic32—22no—
136Dic32—22no—
137C4×#123—91noSylow
138C23×C3×C4—31no—
139C22×#67—31no—
140C22×#67—31no—
141C22×#67—61no—
142C23×Dic3C2×D311yescharacteristic
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—61no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4C2×D311yescharacteristic
156C2×C3×C22⋊C4C2×D311yescharacteristic
157C2×C3×C42—31no—
158C2×C3×C42—31no—
159C2×C3×C42—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—61no—
163C2×#217C2×D311yescharacteristic
164C2×#217C2×D311yescharacteristic
165C2×#217C2×D311yescharacteristic
166C4×#67—64no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—61no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—61no—
177C2×C4⋊Dic3C2×D311yescharacteristic
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—61no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3C2×D311yescharacteristic
194C2×C4×Dic3C2×D311yescharacteristic
195C2×C4×Dic3C2×D311yescharacteristic
196#883—38no—
197#883—38no—
198#883—68no—
199#67⋊C4—64no—
200C42×D3—64no—
201C42×D3—64no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95—31no—
205C3×#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
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⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C3⋊#95C2×D311yescharacteristic
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32C22×C412yes—
229C23×C32C2411yescharacteristic
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3C22×C412yes—
235C22×C3⋊D3C2×D412yes—
236C22×C3⋊D3#4112yes—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C22×C412yes—
242C2×C32×C4C22×C412yes—
243#638—28no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C22×C412yes—
251C2×C3⋊Dic3C22×C412yes—
252C2×C3⋊Dic3C22×C412yes—
253C4×C3⋊D3—28no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
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×Dic3—21no—
264C2×C3×Dic3—21no—
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—44no—
273C2×C3×Dic3C2×D412yes—
274C2×C3×Dic3C2×D412yes—
275C2×C3×Dic3#4112yes—
276C2×C3×Dic3#4112yes—
277C2×C3×Dic3#4112yes—
278C2×C3×Dic3#4112yes—
279#624—28no—
280#624—28no—
281C2×#123—91no—
282C2×C4×D4—91no—
283C22×C42—91no—
284#388—31no—
285#388—91no—
286#387—91no—
287#387—91no—
288#386—91no—
289#385—91no—
290#381—91no—
291C4×C4⋊C4—91no—
292C4×C4⋊C4—91no—
293C4×C22⋊C4—31no—
294C4×C22⋊C4—91no—
295C4×C22⋊C4—91no—
296C24×C3—21no—
297C24×C3C22×D311yescharacteristic
298C24×C3C22×D311yescharacteristic
299C23×D3—31no—
300C23×D3—31no—
301C23×D3—61no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—62no—
313C22×C3×C4—62no—
314C22×C3×C4—62no—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67—34no—
320C2×#67—34no—
321C2×#67—64no—
322C2×#67—62no—
323C2×#67—62no—
324C2×#67—62no—
325C2×#67—62no—
326C2×#67—122no—
327C2×#67—122no—
328C22×Dic3—22no—
329C22×Dic3—22no—
330C22×Dic3—22no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C2×C4×D3—34no—
349C2×C4×D3—34no—
350C2×C4×D3—34no—
351C2×C4×D3—34no—
352C2×C4×D3—64no—
353C2×C4×D3—62no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—62no—
366C2×C4×D3—62no—
367C2×C4×D3—122no—
368C2×C4×D3—122no—
369C3×C4⋊C4—62no—
370C3×C22⋊C4—24no—
371C3×C22⋊C4—62no—
372C3×C22⋊C4—62no—
373C3×C22⋊C4—62no—
374C3×C22⋊C4C4×D314yescomplemented
375C3×C22⋊C4C4×D314yescomplemented
376C3×C42—62no—
377C3×C42—62no—
378C3×C42—62no—
379#217—22no—
380#217—22no—
381#217—22no—
382#217—34no—
383#217—34no—
384#217—64no—
385(C2×D3)⋊C4—34no—
386(C2×D3)⋊C4—34no—
387(C2×D3)⋊C4—64no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392C4⋊Dic3—22no—
393C4⋊Dic3—34no—
394C4⋊Dic3—34no—
395C4⋊Dic3—64no—
396Dic3⋊C4—34no—
397Dic3⋊C4—34no—
398Dic3⋊C4—64no—
399Dic3⋊C4—62no—
400Dic3⋊C4—62no—
401Dic3⋊C4—62no—
402Dic3⋊C4—62no—
403C4×Dic3—22no—
404C4×Dic3—22no—
405C4×Dic3—22no—
406C4×Dic3—62no—
407C4×Dic3—62no—
408C4×Dic3—62no—
409C4×Dic3—62no—
410C4×Dic3—62no—
411C4×Dic3—62no—
412C4×Dic3—62no—
413C4×Dic3—62no—
414C22×C32—22no—
415C22×C32—22no—
416C22×C32—22no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32C23×C411yescharacteristic
422C22×C32C22×D411yescharacteristic
423C22×C32C2×#4111yescharacteristic
424C22×C32C2×#4111yescharacteristic
425C22×C32C2×#4111yescharacteristic
426C22×C32C2×#4111yescharacteristic
427C22×C32C2×#4111yescharacteristic
428C2×C3⋊D3—22no—
429C2×C3⋊D3—22no—
430C2×C3⋊D3—22no—
431C2×C3⋊D3—22no—
432C2×C3⋊D3—22no—
433C2×C3⋊D3—22no—
434C2×C3⋊D3C4×D414yes—
435C32×C4—22no—
436C32×C4—22no—
437C3⋊Dic3—22no—
438C3⋊Dic3—22no—
439C3⋊Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—22no—
442C3×Dic3—22no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3#12314yescomplemented
448C22×D4—91no—
449C23×C4—31no—
450C23×C4—91no—
451C23×C4—91no—
452C23×C4—91no—
453#123—98no—
454C4×D4—184no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4—91no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—91no—
460C2×C22⋊C4—31no—
461C2×C22⋊C4—31no—
462C2×C22⋊C4—31no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—91no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—91no—
467C2×C22⋊C4D3211yescharacteristic
468C2×C42—31no—
469C2×C42—31no—
470C2×C42—31no—
471C2×C42—91no—
472C2×C42—91no—
473C2×C42—91no—
474C2×C42—91no—
475C2×C42—184no—
476#95—31no—
477#95—31no—
478#95—31no—
479#95—31no—
480#95—91no—
481#95—91no—
482#95—91no—
483#95—91no—
484#95—91no—
485#95—91no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—22no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3C2×C4×D312yes—
507C23×C3C2×C4×D312yes—
508C23×C3C23×D311yescharacteristic
509C23×C3C23×D311yescharacteristic
510C22×D3—32no—
511C22×D3—32no—
512C22×D3—32no—
513C22×D3—32no—
514C22×D3—32no—
515C22×D3—32no—
516C22×D3—62no—
517C22×D3—62no—
518C22×D3—62no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—121no—
528C22×D3—121no—
529C22×D3—121no—
530C22×D3—121no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—32no—
546C2×C3×C4—32no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—124no—
570C2×C3×C4C2×C4×D312yes—
571C2×C3×C4C2×C4×D312yes—
572C2×C3×C4C2×C4×D312yes—
573C2×C3×C4C2×C4×D312yes—
574#67—68no—
575#67—68no—
576#67—128no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—44no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—121no—
618C2×Dic3—121no—
619C2×Dic3—121no—
620C2×Dic3—121no—
621C2×Dic3—121no—
622C2×Dic3—121no—
623C2×Dic3#23512yes—
624C2×Dic3#23512yes—
625C2×Dic3D3×D412yes—
626C2×Dic3D3×D412yes—
627C2×Dic3#23712yes—
628C2×Dic3#23712yes—
629C4×D3—68no—
630C4×D3—68no—
631C4×D3—68no—
632C4×D3—68no—
633C4×D3—68no—
634C4×D3—68no—
635C4×D3—128no—
636C2×C32—42no—
637C2×C32C2×C4×D411yescharacteristic
638C2×C32C4×#4111yescharacteristic
639C2×C32C4×#4111yescharacteristic
640C2×C32C2×#12311yescharacteristic
641C2×C32#52511yescharacteristic
642C2×C32#52911yescharacteristic
643C2×C32#52911yescharacteristic
644C3⋊D3—24no—
645C24—91no—
646C24C2×D3211yescharacteristic
647C2×D4—94no—
648C2×D4—182no—
649C2×D4—182no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—31no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—94no—
662C22×C4—91no—
663C22×C4—91no—
664C22×C4—91no—
665C22×C4—94no—
666C22×C4—182no—
667C22×C4—182no—
668C22×C4—182no—
669C22×C4—182no—
670C22×C4—182no—
671C22×C4—182no—
672C22×C4—182no—
673C22×C4C2×D3211yescharacteristic
674C22×C4C2×D3211yescharacteristic
675C4⋊C4—62no—
676C4⋊C4—94no—
677C4⋊C4—94no—
678C4⋊C4—182no—
679C4⋊C4—182no—
680C22⋊C4—62no—
681C22⋊C4—62no—
682C22⋊C4—62no—
683C22⋊C4—94no—
684C22⋊C4—94no—
685C22⋊C4—182no—
686C22⋊C4—182no—
687C22⋊C4#62414yescomplemented
688C42—62no—
689C42—62no—
690C42—62no—
691C42—182no—
692C42—182no—
693C42—182no—
694C42—182no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—81no—
723C22×C3C22×C4×D311yescharacteristic
724C22×C3C22×C4×D311yescharacteristic
725C22×C3C2×#23511yescharacteristic
726C22×C3C2×#23511yescharacteristic
727C22×C3C2×D3×D411yescharacteristic
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C2×#23711yescharacteristic
730C22×C3C2×#23711yescharacteristic
731C22×C3D3×#4111yescharacteristic
732C22×C3D3×#4111yescharacteristic
733C22×C3D3×#4111yescharacteristic
734C22×C3D3×#4111yescharacteristic
735C22×C3D3×#4111yescharacteristic
736C22×C3D3×#4111yescharacteristic
737C2×D3—34no—
738C2×D3—34no—
739C2×D3—64no—
740C2×D3—62no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—62no—
752C2×D3—122no—
753C2×D3—122no—
754C2×D3—122no—
755C2×D3—122no—
756C2×D3—122no—
757C2×D3—122no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—34no—
763C3×C4—42no—
764C3×C4—42no—
765C3×C4—62no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4—121no—
771C3×C4—121no—
772Dic3—22no—
773Dic3—22no—
774Dic3—22no—
775Dic3—41no—
776Dic3—41no—
777Dic3—41no—
778Dic3—41no—
779Dic3—62no—
780Dic3—62no—
781Dic3—62no—
782Dic3—62no—
783Dic3—62no—
784Dic3—62no—
785Dic3—122no—
786Dic3—122no—
787Dic3—122no—
788Dic3#88314yescomplemented
789C32C4×#12311yescharacteristic, complemented, Sylow
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—92no—
797C23—92no—
798C23—92no—
799C23—181no—
800C23—181no—
801C23—181no—
802C23—181no—
803C23C2×#62412yes—
804C23C22×D3211yescharacteristic
805D4—188no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—92no—
835C2×C4—92no—
836C2×C4—92no—
837C2×C4—124no—
838C2×C4—188no—
839C2×C4—188no—
840C2×C4—188no—
841C2×C4—181no—
842C2×C4—181no—
843C2×C4—181no—
844C2×C4—181no—
845C2×C4—181no—
846C2×C4—181no—
847C2×C4C2×#62412yes—
848C2×C4C2×#62412yes—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—42no—
857C2×C3—42no—
858C2×C3—82no—
859C2×C3C4×#23511yescharacteristic
860C2×C3C2×#88311yescharacteristic
861C2×C3#552211yescharacteristic
862C2×C3#552811yescharacteristic
863C2×C3C4×#23711yescharacteristic
864C2×C3C4×#23711yescharacteristic
865C2×C3C4×D3×D411yescharacteristic
866C2×C3C4×D3×D411yescharacteristic
867C2×C3#554711yescharacteristic
868C2×C3#555711yescharacteristic
869C2×C3#560611yescharacteristic
870C2×C3D3×#12311yescharacteristic
871C2×C3#568011yescharacteristic
872C2×C3#570611yescharacteristic
873D3—64no—
874D3—64no—
875D3—124no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—94no—
884C22—182no—
885C22—182no—
886C22—182no—
887C22—182no—
888C22—182no—
889C22—182no—
890C22D3×#23511yescharacteristic
891C22D3×#23511yescharacteristic
892C22D32×D411yescharacteristic
893C22D3×#23711yescharacteristic
894C22D3×#23711yescharacteristic
895C22#6431211yescharacteristic
896C22C22×#62411yescharacteristic
897C4—22no—
898C4—22no—
899C4—34no—
900C4—62no—
901C4—62no—
902C4—62no—
903C4—121no—
904C4—121no—
905C4—121no—
906C4—121no—
907C4—182no—
908C4—182no—
909C4—182no—
910C3—21no—
911C3C4×#88311yescharacteristic, complemented
912C3#7545311yescharacteristic, complemented
913C2—42no—
914C2—184no—
915C2#1059409911yescharacteristic
916C2#1059410711yescharacteristic
917C2D3×#88311yescharacteristic
918C2#1059428611yescharacteristic
919C2#1059495411yescharacteristic
920C2D4×#62411yescharacteristic
921C2#1059519011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#624C2semidirect
4. C3×#4951C2semidirect
5. C3×Dic3×C22⋊C4C2semidirect
7. #10591703C2semidirect
8. Dic3×#217C2semidirect
9. #10591378C2semidirect
10. #10591271C2semidirect
11. Dic3×C4⋊Dic3C2semidirect
12. #10591243C2semidirect
13. #10591233C2semidirect
14. #10591219C2semidirect
15. #10591197C2semidirect
28. #64092C4semidirect
70. #4951D3semidirect
74. Dic3×C22⋊C4D3semidirect
99. C2×C4×C3⋊D3C2×C4semidirect
117. C32×C22⋊C4C2×C4semidirect
118. #3757C2×C4semidirect
119. #3752C2×C4semidirect
120. C4⋊(C3⋊Dic3)C2×C4semidirect
121. #3750C2×C4semidirect
374. C3×C22⋊C4C4×D3semidirect
375. C3×C22⋊C4C4×D3semidirect
447. C3×Dic3#123semidirect
687. C22⋊C4#624semidirect
788. Dic3#883semidirect
789. C32C4×#123semidirect
911. C3C4×#883semidirect
912. C3#75453semidirect

Maximal subgroups

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

subgroupindex
C2×#640922
C2×#639522
C2×C4×#6242
C3×#49512
C3×Dic3×C22⋊C42
#105917222
#105917032
Dic3×#2172
#105913782
#105912712
Dic3×C4⋊Dic32
#105912432
#105912332
#105912192
#105911972
#754533
C4×#8833