Finite Group Databasebeta

← #11805678

Subgroups — #11805678

Order 1152.

1529 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic, complemented
2C2×#67⋊Dic3C211yesmaximal, characteristic
3C2×#63877C211yesmaximal, characteristic, complemented
4C3×#5213C211yesmaximal, characteristic
5C3×C4×#217C211yesmaximal, characteristic, complemented
6#10591720C211yesmaximal, characteristic, complemented
7#10591713C211yesmaximal, characteristic
8#10591705C211yesmaximal, characteristic, complemented
9#10591369C211yesmaximal, characteristic, complemented
10#10591332C211yesmaximal, characteristic, complemented
11#10591281C211yesmaximal, characteristic, complemented
12#10591280C211yesmaximal, characteristic, complemented
13#10591251C211yesmaximal, characteristic, complemented
14#10591247C211yesmaximal, characteristic, complemented
15#10591243C211yesmaximal, characteristic, complemented
16#74673—31nomaximal
17#73461—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×#3750—24no—
24C2×#3750C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35#67⋊Dic3C418yescomplemented
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63877—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×D4×Dic3—31no—
57C22×Dic3⋊C4—31no—
58C22×Dic3⋊C4—31no—
59C22×Dic3⋊C4—61no—
60C2×#67⋊C4—31no—
61C2×#877—31no—
62C2×#872—31no—
63C3×#386—31no—
64C3×C4×C22⋊C4—31no—
65#5220—31no—
66#5213D311yescharacteristic
67C4×#217D311yescharacteristic, complemented
68#4958—31no—
69#4945—31no—
70#4944—31no—
71#4942—31no—
72#4942—31no—
73#4942—31no—
74Dic3×C22⋊C4—31no—
75Dic3×C22⋊C4—31no—
76#4940—31no—
77#4933—31no—
78C4×Dic3⋊C4—31no—
79#4669—31no—
80#4667—31no—
81#4654—31no—
82#4653—31no—
83#4652—31no—
84#4650—31no—
85#4650—31no—
86#4649—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4—22no—
90C22×C32×C4—22no—
91C22×C32×C4—41no—
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—22no—
95C22×C3⋊Dic3—22no—
96C22×C3⋊Dic3—22no—
97C22×C3⋊Dic3—22no—
98C22×C3⋊Dic3—41no—
99C22×C3⋊Dic3C2×C414yes—
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67C2×C414yes—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3C2×C414yescomplemented
117#3750—22no—
118#3750—22no—
119#3750—22no—
120#3750D414yescomplemented
121C3×#217—22no—
122C3×#217—22no—
123C3×#217C2×C414yes—
124C3×(C2×D3)⋊C4—22no—
125C3×(C2×D3)⋊C4—41no—
126C3×C4×Dic3—22no—
127C3×C4×Dic3—41no—
128#3724—22no—
129#3724—22no—
130Dic3⋊Dic3C2×C414yescomplemented
131(C2×D3)⋊Dic3—22no—
132(C2×D3)⋊Dic3—41no—
133(C2×D3)⋊Dic3C2×C414yescomplemented
134Dic32—22no—
135Dic32—41no—
136Dic32C2×C414yescomplemented
137#2352—91noSylow
138C22×C3×D4—31no—
139C23×C3×C4—21no—
140C23×C3×C4C2×D311yescharacteristic
141C23×C3×C4C2×D311yescharacteristic
142C22×#67C2×D311yescharacteristic
143C23×Dic3—31no—
144C23×Dic3—31no—
145C23×Dic3—31no—
146C23×Dic3—31no—
147C23×Dic3—31no—
148C23×Dic3—61no—
149C23×Dic3—61no—
150C22×C4×D3—31no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C42—31no—
157C2×C3×C42—31no—
158C2×#217—31no—
159C2×#217—31no—
160C2×#217—31no—
161C2×#217C2×D311yescharacteristic
162C2×#217C2×D311yescharacteristic
163C2×#217C2×D311yescharacteristic
164D4×Dic3—38no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4C2×D311yescharacteristic
169C2×(C2×D3)⋊C4C2×D311yescharacteristic
170C2×C4⋊Dic3—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
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×Dic3⋊C4—61no—
186C2×Dic3⋊C4—61no—
187C2×Dic3⋊C4—61no—
188C2×Dic3⋊C4—64no—
189C2×Dic3⋊C4—64no—
190C2×Dic3⋊C4—68no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3—31no—
196C2×C4×Dic3—31no—
197C2×C4×Dic3C2×D311yescharacteristic
198C2×C4×Dic3C2×D311yescharacteristic
199#67⋊C4—38no—
200#877—64no—
201#872—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×C32C22×C412yes—
227C23×C32#4112yes—
228C23×C32#4112yes—
229C23×C32C2411yescharacteristic
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3C22×C412yes—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—44no—
243C2×C32×C4C2×D412yes—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—28no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—44no—
253C2×C3⋊Dic3C22×C412yes—
254C2×C3⋊Dic3C22×C412yes—
255C2×C3⋊Dic3C2×D412yes—
256C2×C3⋊Dic3C2×D412yes—
257C2×C3⋊Dic3#4112yes—
258C3×#67—28no—
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—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C22×C412yes—
278C2×C3×Dic3C22×C412yes—
279C2×C3×Dic3C22×C412yes—
280D3×Dic3—28no—
281C2×C4×D4—91no—
282C2×#117—91no—
283C22×C4⋊C4—91no—
284#388—91no—
285#388—91no—
286#387—91no—
287#387—91no—
288#386—31no—
289#386—91no—
290#382—91no—
291#380—91no—
292#380—91no—
293C4×C4⋊C4—91no—
294C4×C22⋊C4—31no—
295C4×C22⋊C4—91no—
296C24×C3—21no—
297C24×C3—31no—
298C24×C3C22×D311yescharacteristic
299C24×C3C22×D311yescharacteristic
300C23×D3C22×D311yescharacteristic
301C2×C3×D4—34no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C22×C3×C4—24no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—42no—
319C22×C3×C4—41no—
320C22×C3×C4—41no—
321C22×C3×C4—42no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C2×#67—22no—
327C2×#67—22no—
328C2×#67C4×D314yes—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—34no—
332C22×Dic3—34no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—34no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—64no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—62no—
346C22×Dic3—62no—
347C22×Dic3—62no—
348C22×Dic3—62no—
349C22×Dic3—62no—
350C22×Dic3—62no—
351C22×Dic3—62no—
352C22×Dic3—62no—
353C22×Dic3—64no—
354C22×Dic3—64no—
355C22×Dic3—64no—
356C22×Dic3—62no—
357C22×Dic3—62no—
358C22×Dic3—122no—
359C22×Dic3—121no—
360C22×Dic3—121no—
361C22×Dic3—122no—
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C2×C4×D3—34no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C3×C22⋊C4—34no—
373C3×C22⋊C4—62no—
374C3×C22⋊C4—62no—
375C3×C22⋊C4—62no—
376C3×C22⋊C4—121no—
377C3×C42—62no—
378C3×C42—121no—
379#217—22no—
380#217—22no—
381#217—34no—
382#217—62no—
383#217—121no—
384#217C4×D314yes—
385(C2×D3)⋊C4—22no—
386(C2×D3)⋊C4—34no—
387(C2×D3)⋊C4—41no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—121no—
390C4⋊Dic3—34no—
391Dic3⋊C4—34no—
392Dic3⋊C4—34no—
393Dic3⋊C4—34no—
394Dic3⋊C4—64no—
395Dic3⋊C4—62no—
396Dic3⋊C4—62no—
397Dic3⋊C4—62no—
398Dic3⋊C4—62no—
399Dic3⋊C4—62no—
400Dic3⋊C4—62no—
401Dic3⋊C4—62no—
402Dic3⋊C4—62no—
403Dic3⋊C4—64no—
404Dic3⋊C4—64no—
405Dic3⋊C4—64no—
406Dic3⋊C4—62no—
407Dic3⋊C4—62no—
408C4×Dic3—22no—
409C4×Dic3—34no—
410C4×Dic3—34no—
411C4×Dic3—41no—
412C4×Dic3—62no—
413C4×Dic3—62no—
414C4×Dic3—121no—
415C4×Dic3—121no—
416C22×C32—22no—
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32#11714yescomplemented
423C22×C32C23×C411yescharacteristic
424C22×C32C22×D411yescharacteristic
425C22×C32C2×#4111yescharacteristic
426C22×C32C2×#4111yescharacteristic
427C22×C32C2×#4111yescharacteristic
428C22×C32H(5,𝔽2)11yescharacteristic
429C22×C322−1+411yescharacteristic
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C32×C4—22no—
438C32×C4—41no—
439C3⋊Dic3—22no—
440C3⋊Dic3—22no—
441C3⋊Dic3—41no—
442C3⋊Dic3C4×D414yes—
443C3×Dic3—22no—
444C3×Dic3—22no—
445C3×Dic3—22no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—31no—
451C23×C4—91no—
452C23×C4—91no—
453C23×C4—91no—
454C23×C4D3211yescharacteristic
455C4×D4—98no—
456#117—184no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—91no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—184no—
465C2×C22⋊C4—31no—
466C2×C22⋊C4—31no—
467C2×C22⋊C4—31no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—91no—
471C2×C22⋊C4—91no—
472C2×C22⋊C4—91no—
473C2×C42—31no—
474C2×C42—31no—
475C2×C42—91no—
476C2×C42—91no—
477C2×C42—91no—
478#95—31no—
479#95—31no—
480#95—31no—
481#95—31no—
482#95—91no—
483#95—91no—
484#95—91no—
485#95—91no—
486#95—91no—
487#95—91no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—32no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3—61no—
509C23×C3—61no—
510C23×C3—61no—
511C23×C3C2×C4×D312yes—
512C23×C3C2×C4×D312yes—
513C23×C3#23512yes—
514C23×C3#23512yes—
515C23×C3#23712yes—
516C23×C3#23712yes—
517C23×C3C23×D311yescharacteristic
518C23×C3C23×D311yescharacteristic
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3C2×C4×D312yes—
526C3×D4—68no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—22no—
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—22no—
539C2×C3×C4—32no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—44no—
547C2×C3×C4—44no—
548C2×C3×C4—48no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
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×C4D3×D412yes—
568C2×C3×C4D3×D412yes—
569#67—28no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
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—32no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—68no—
604C2×Dic3—68no—
605C2×Dic3—68no—
606C2×Dic3—62no—
607C2×Dic3—616no—
608C2×Dic3—62no—
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—62no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—121no—
627C2×Dic3—121no—
628C2×Dic3—124no—
629C2×Dic3—124no—
630C2×Dic3—128no—
631C2×Dic3C2×C4×D312yes—
632C2×Dic3C2×C4×D312yes—
633C2×Dic3C2×C4×D312yes—
634C4×D3—68no—
635C2×C32—24no—
636C2×C32C2×#11711yescharacteristic
637C2×C32C2×C4×D411yescharacteristic
638C2×C32#52011yescharacteristic
639C2×C32#54611yescharacteristic
640C2×C32#54811yescharacteristic
641C2×C32#55211yescharacteristic
642C2×C32#55311yescharacteristic
643C3×D3—42no—
644C24—31no—
645C24C2×D3211yescharacteristic
646C2×D4—34no—
647C2×D4—62no—
648C2×D4—62no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—31no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—41no—
659C22×C4—94no—
660C22×C4—91no—
661C22×C4—91no—
662C22×C4—91no—
663C22×C4—94no—
664C22×C4—91no—
665C22×C4—182no—
666C22×C4—182no—
667C22×C4—182no—
668C22×C4—182no—
669C22×C4—182no—
670C22×C4—182no—
671C22×C4—361no—
672C22×C4C2×D3211yescharacteristic
673C22×C4C2×D3211yescharacteristic
674C4⋊C4—94no—
675C4⋊C4—94no—
676C4⋊C4—182no—
677C4⋊C4—182no—
678C4⋊C4—182no—
679C4⋊C4—182no—
680C4⋊C4—182no—
681C22⋊C4—34no—
682C22⋊C4—62no—
683C22⋊C4—62no—
684C22⋊C4—62no—
685C22⋊C4—94no—
686C22⋊C4—121no—
687C22⋊C4—182no—
688C22⋊C4—361no—
689C42—62no—
690C42—94no—
691C42—121no—
692C42—182no—
693C42—361no—
694C22×C3—24no—
695C22×C3—24no—
696C22×C3—24no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—24no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3#87214yescomplemented
728C22×C3#87714yescomplemented
729C22×C3C22×C4×D311yescharacteristic
730C22×C3C22×C4×D311yescharacteristic
731C22×C3C2×#23511yescharacteristic
732C22×C3C2×#23511yescharacteristic
733C22×C3C2×D3×D411yescharacteristic
734C22×C3C2×D3×D411yescharacteristic
735C22×C3C2×#23711yescharacteristic
736C22×C3C2×#23711yescharacteristic
737C22×C3#100411yescharacteristic
738C22×C3#100411yescharacteristic
739C22×C3D3×#4111yescharacteristic
740C22×C3D3×#4111yescharacteristic
741C22×C3#101011yescharacteristic
742C22×C3#101011yescharacteristic
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C3×C4—22no—
751C3×C4—22no—
752C3×C4—42no—
753C3×C4—42no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—62no—
757C3×C4—62no—
758C3×C4—62no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4—121no—
762C3×C4—121no—
763Dic3—22no—
764Dic3—22no—
765Dic3—22no—
766Dic3—34no—
767Dic3—34no—
768Dic3—41no—
769Dic3—41no—
770Dic3—41no—
771Dic3—41no—
772Dic3—64no—
773Dic3—64no—
774Dic3—62no—
775Dic3—62no—
776Dic3—62no—
777Dic3—62no—
778Dic3—122no—
779Dic3—122no—
780Dic3—121no—
781Dic3—121no—
782C32#235211yescharacteristic, complemented, Sylow
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—32no—
788C23—61no—
789C23—61no—
790C23—61no—
791C23—61no—
792C23—61no—
793C23—61no—
794C23#379512yes—
795C23C4×D3212yes—
796C23#380412yes—
797C23C22×D3211yescharacteristic
798D4—68no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—44no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
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—92no—
827C2×C4—92no—
828C2×C4—92no—
829C2×C4—92no—
830C2×C4—92no—
831C2×C4—188no—
832C2×C4—188no—
833C2×C4—181no—
834C2×C4—181no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—364no—
841C2×C4#381112yes—
842C2×C3—28no—
843C2×C3—24no—
844C2×C3—24no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—122no—
853C2×C3C2×#87211yescharacteristic
854C2×C3C2×#87711yescharacteristic
855C2×C3#549011yescharacteristic
856C2×C3#553111yescharacteristic
857C2×C3#554011yescharacteristic
858C2×C3C4×D3×D411yescharacteristic
859C2×C3C4×D3×D411yescharacteristic
860C2×C3#554611yescharacteristic
861C2×C3#554611yescharacteristic
862C2×C3#555211yescharacteristic
863C2×C3#559111yescharacteristic
864C2×C3#559811yescharacteristic
865C2×C3#560111yescharacteristic
866C2×C3#565011yescharacteristic
867D3—42no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22#6387714yescomplemented
882C22C2×#379511yescharacteristic
883C22#6429811yescharacteristic
884C22C2×C4×D3211yescharacteristic
885C22#6430611yescharacteristic
886C22C2×#380411yescharacteristic
887C22C2×#381111yescharacteristic
888C22#6433011yescharacteristic
889C4—22no—
890C4—41no—
891C4—62no—
892C4—62no—
893C4—62no—
894C4—94no—
895C4—121no—
896C4—121no—
897C4—121no—
898C4—121no—
899C4—182no—
900C4—182no—
901C4—361no—
902C3—21no—
903C3#7346111yescharacteristic, complemented
904C3#7467311yescharacteristic, complemented
905C2—24no—
906C2—122no—
907C2C2×#6387711yescharacteristic
908C2#1059487611yescharacteristic
909C2#1059491811yescharacteristic
910C2#1059496011yescharacteristic
911C2#1059496211yescharacteristic
912C2C4×#381111yescharacteristic
913C2#1059550011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3750C2semidirect
3. C2×#63877C2semidirect
5. C3×C4×#217C2semidirect
6. #10591720C2semidirect
8. #10591705C2semidirect
9. #10591369C2semidirect
10. #10591332C2semidirect
11. #10591281C2semidirect
12. #10591280C2semidirect
13. #10591251C2semidirect
14. #10591247C2semidirect
15. #10591243C2semidirect
35. #67⋊Dic3C4semidirect
67. C4×#217D3semidirect
116. C2×D3×Dic3C2×C4semidirect
120. #3750D4semidirect
130. Dic3⋊Dic3C2×C4semidirect
133. (C2×D3)⋊Dic3C2×C4semidirect
136. Dic32C2×C4semidirect
422. C22×C32#117semidirect
727. C22×C3#872semidirect
728. C22×C3#877semidirect
782. C32#2352semidirect
881. C22#63877semidirect
903. C3#73461semidirect
904. C3#74673semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C2×#67⋊Dic32
C2×#638772
C3×#52132
C3×C4×#2172
#105917202
#105917132
#105917052
#105913692
#105913322
#105912812
#105912802
#105912512
#105912472
#105912432
#746733
#734613