Finite Group Databasebeta

← #11810336

Subgroups — #11810336

Order 1152.

1685 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#63976C211yesmaximal, characteristic
3C2×#63969C211yesmaximal, characteristic, complemented
4C2×#63879C211yesmaximal, characteristic, complemented
5#10592651C211yesmaximal, characteristic, complemented
6C3×#4959C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8#10591702C211yesmaximal, characteristic, complemented
9#10591390C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591363C211yesmaximal, characteristic, complemented
12#10591303C211yesmaximal, characteristic, complemented
13#10591295C211yesmaximal, characteristic, complemented
14#10591282C211yesmaximal, characteristic, complemented
15#10591277C211yesmaximal, characteristic, complemented
16#82128—31nomaximal
17#77111—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3750C2211yescharacteristic, complemented
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C3×D3×C22⋊C4—24no—
37#63976—24no—
38#63969—24no—
39C2×#3724C2211yescharacteristic, complemented
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×Dic3⋊Dic3C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
49C2×Dic32C2211yescharacteristic, complemented
50#63879—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C22×C3×C22⋊C4—31no—
58C2×#953—31no—
59C2×#937—31no—
60C2×#935—31no—
61C2×C4×#67—31no—
62C2×#883—31no—
63C2×#67⋊C4—31no—
64C2×D3×C22⋊C4D311yescharacteristic, complemented
65C3×#394—31no—
66#5247—31no—
67#5213—31no—
68#5212—31no—
69#5210—31no—
70#4993—31no—
71#4989—31no—
72#4961—31no—
73#4959—31no—
74#4959D311yescharacteristic, complemented
75#4958—31no—
76#4956—31no—
77#4956—31no—
78#4955—31no—
79#4952—31no—
80#4952—31no—
81#4952—61no—
82#4951—31no—
83#4949—31no—
84#4945—31no—
85#4945—31no—
86#4669—31no—
87#4667—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—41no—
95C23×C3×D3—41no—
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—41no—
118C2×C3×C4×D3—41no—
119C2×#625—22no—
120C2×#625—22no—
121C2×#625—22no—
122C2×#625—22no—
123C2×#625—41no—
124C2×#625D414yes—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—41no—
128C32×C22⋊C4—22no—
129#3757—22no—
130#3757—22no—
131#3750—22no—
132C3×#217—41no—
133C3×#217D414yescomplemented
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—41no—
138C3×Dic3⋊C4—41no—
139#3724—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—41no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—41no—
149Dic32—22no—
150#2418—91noSylow
151C25×C3—31no—
152C24×D3C2×D311yescharacteristic
153C22×C3×D4—31no—
154C23×C3×C4—31no—
155C23×C3×C4—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—31no—
160C22×#67C2×D311yescharacteristic
161C23×Dic3—31no—
162C22×C4×D3—31no—
163C22×C4×D3C2×D311yescharacteristic
164C22×C4×D3C2×D311yescharacteristic
165C2×C3×C4⋊C4—31no—
166C2×C3×C22⋊C4—21no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—64no—
174C2×C3×C22⋊C4C2×D311yescharacteristic
175C2×C3×C22⋊C4C2×D311yescharacteristic
176#953—64no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—61no—
189C2×#217—61no—
190C2×#217C2×D311yescharacteristic
191C2×#217C2×D311yescharacteristic
192#937—64no—
193#935—64no—
194C4×#67—64no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
205C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—61no—
215C2×Dic3⋊C4C2×D311yescharacteristic, complemented
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218#883—64no—
219#67⋊C4—64no—
220D3×C22⋊C4—24no—
221C3×#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—61no—
233C3⋊#95—61no—
234C3⋊#95—61no—
235C3⋊#95C2×D311yescharacteristic, complemented
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32C2×D412yes—
243C23×C32C2411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—28no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
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×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3C2×D412yes—
268C22×C3×D3C2×D412yes—
269C22×C3×D3#4112yes—
270C22×C3×D3#4112yes—
271C22×C3×D3#4112yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—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⋊Dic3C2×D412yes—
290C3×#67—44no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
305C2×C3×Dic3C2×D412yes—
306C3×C4×D3—44no—
307C3×C4×D3—44no—
308#625—28no—
309#625—44no—
310D3×Dic3—44no—
311C2×#123—91no—
312C2×#120—91no—
313C2×C4×D4—91no—
314C22×C22⋊C4—31no—
315#399—91no—
316#397—91no—
317#394—31no—
318#394—91no—
319#388—91no—
320#388—91no—
321#386—91no—
322#386—91no—
323#385—91no—
324#380—91no—
325#379—91no—
326C24×C3—21no—
327C24×C3—31no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—121no—
336C24×C3—121no—
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C23×D3—22no—
340C23×D3—22no—
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—41no—
345C23×D3—41no—
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D311yescharacteristic
348C23×D3C22×D311yescharacteristic
349C2×C3×D4—62no—
350C2×C3×D4—62no—
351C2×C3×D4—121no—
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—62no—
360C22×C3×C4—62no—
361C22×C3×C4—62no—
362C22×C3×C4—62no—
363C22×C3×C4—121no—
364C22×C3×C4—121no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—22no—
370C2×#67—22no—
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—41no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—62no—
377C2×#67—62no—
378C2×#67—62no—
379C2×#67—62no—
380C2×#67—62no—
381C2×#67—62no—
382C2×#67—121no—
383C2×#67—121no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—61no—
395C22×Dic3—61no—
396C22×Dic3—62no—
397C22×Dic3—62no—
398C22×Dic3—121no—
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C2×C4×D3—22no—
405C2×C4×D3—22no—
406C2×C4×D3—22no—
407C2×C4×D3—22no—
408C2×C4×D3—41no—
409C2×C4×D3—41no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—121no—
413C3×C4⋊C4—121no—
414C3×C22⋊C4—22no—
415C3×C22⋊C4—22no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—42no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C22⋊C4—121no—
422C3×C22⋊C4—121no—
423#217—41no—
424#217—62no—
425#217—62no—
426#217—62no—
427#217—62no—
428#217—62no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—62no—
434#217—122no—
435#217—122no—
436#217—121no—
437#217#6714yescomplemented
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—22no—
440(C2×D3)⋊C4—22no—
441(C2×D3)⋊C4—41no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—121no—
449C4⋊Dic3—62no—
450C4⋊Dic3—121no—
451Dic3⋊C4—41no—
452Dic3⋊C4—62no—
453Dic3⋊C4—62no—
454Dic3⋊C4—62no—
455Dic3⋊C4—62no—
456Dic3⋊C4—62no—
457Dic3⋊C4—122no—
458Dic3⋊C4—121no—
459C4×Dic3—62no—
460C4×Dic3—62no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C22×C32C22×D411yescharacteristic
470C22×C32C2×#4111yescharacteristic
471C22×C32C2×#4111yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32H(5,𝔽2)11yescharacteristic
474C22×C32H(5,𝔽2)11yescharacteristic
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—416no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3#12314yescomplemented
497C32×C4—41no—
498C32×C4—41no—
499C3⋊Dic3—22no—
500C3⋊Dic3—41no—
501C3⋊Dic3—41no—
502C3⋊Dic3—41no—
503C3×Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C25—31no—
509C22×D4—31no—
510C22×D4—91no—
511C22×D4—91no—
512C23×C4—31no—
513C23×C4—31no—
514C23×C4—91no—
515#123—184no—
516#120—184no—
517C4×D4—184no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—91no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—64no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4D3211yescharacteristic
540C2×C42—91no—
541#95—31no—
542#95—91no—
543#95—91no—
544#95—91no—
545#95—91no—
546#95—91no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—22no—
561C23×C3—32no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—68no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—124no—
590C23×C3—124no—
591C23×C3—124no—
592C23×C3—124no—
593C23×C3—124no—
594C23×C3—124no—
595C23×C3D3×D412yes—
596C23×C3C2×#6712yes—
597C23×C3C23×D311yescharacteristic
598C23×C3C23×D311yescharacteristic
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—28no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
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—44no—
617C22×D3—44no—
618C22×D3—44no—
619C22×D3—44no—
620C22×D3—44no—
621C22×D3—44no—
622C22×D3#23512yes—
623C22×D3#23512yes—
624C22×D3D3×D412yes—
625C22×D3D3×D412yes—
626C22×D3#23712yes—
627C3×D4—124no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—124no—
662C2×C3×C4—124no—
663#67—44no—
664#67—68no—
665#67—68no—
666#67—124no—
667#67—124no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—62no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—121no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—124no—
718C2×Dic3C2×#6712yes—
719C2×Dic3C2×#6712yes—
720C4×D3—44no—
721C4×D3—44no—
722C4×D3—124no—
723C2×C32—42no—
724C2×C32C2×#12311yescharacteristic
725C2×C32#52511yescharacteristic
726C2×C32#53811yescharacteristic
727C2×C32D4211yescharacteristic
728C2×C32#54611yescharacteristic
729C2×C32#54611yescharacteristic
730C2×C32#55111yescharacteristic
731C3×D3—24no—
732C3×D3—42no—
733C3×D3—42no—
734C24—31no—
735C24—31no—
736C24—31no—
737C24—62no—
738C24—62no—
739C24—62no—
740C24—62no—
741C24—62no—
742C24—121no—
743C24—121no—
744C24C2×D3211yescharacteristic
745C2×D4—62no—
746C2×D4—62no—
747C2×D4—94no—
748C2×D4—121no—
749C2×D4—182no—
750C2×D4—182no—
751C2×D4—182no—
752C2×D4—182no—
753C2×D4—361no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—62no—
760C22×C4—62no—
761C22×C4—62no—
762C22×C4—62no—
763C22×C4—91no—
764C22×C4—91no—
765C22×C4—91no—
766C22×C4—91no—
767C22×C4—121no—
768C22×C4—121no—
769C22×C4—182no—
770C22×C4—182no—
771C22×C4—361no—
772C22×C4C2×D3211yescharacteristic
773C22×C4C2×D3211yescharacteristic
774C4⋊C4—121no—
775C4⋊C4—182no—
776C4⋊C4—182no—
777C4⋊C4—182no—
778C4⋊C4—361no—
779C22⋊C4—22no—
780C22⋊C4—34no—
781C22⋊C4—62no—
782C22⋊C4—62no—
783C22⋊C4—62no—
784C22⋊C4—121no—
785C22⋊C4—121no—
786C22⋊C4—182no—
787C22⋊C4—182no—
788C22⋊C4—182no—
789C22⋊C4—182no—
790C22⋊C4—182no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—361no—
795C42—182no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—34no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—81no—
834C22×C3—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—1216no—
838C22×C3—121no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3C2×#23511yescharacteristic
847C22×C3C2×#23511yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C22×C3C2×D3×D411yescharacteristic
850C22×C3C2×D3×D411yescharacteristic
851C22×C3C2×#23711yescharacteristic
852C22×C3#100411yescharacteristic
853C22×C3#100411yescharacteristic
854C22×C3#100411yescharacteristic
855C22×C3#100411yescharacteristic
856C22×C3D3×#4111yescharacteristic
857C22×C3D3×#4111yescharacteristic
858C22×C3D3×#4111yescharacteristic
859C22×C3C22×#6711yescharacteristic
860C2×D3—22no—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—416no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3#88314yescomplemented
882C3×C4—41no—
883C3×C4—41no—
884C3×C4—41no—
885C3×C4—41no—
886C3×C4—62no—
887C3×C4—62no—
888C3×C4—81no—
889C3×C4—81no—
890C3×C4—121no—
891C3×C4—121no—
892C3×C4—121no—
893Dic3—22no—
894Dic3—22no—
895Dic3—41no—
896Dic3—41no—
897Dic3—41no—
898Dic3—62no—
899Dic3—62no—
900Dic3—122no—
901Dic3—121no—
902Dic3—121no—
903Dic3—121no—
904Dic3—121no—
905Dic3—121no—
906Dic3—121no—
907Dic3—241no—
908Dic3—241no—
909Dic3—241no—
910C32#241811yescharacteristic, complemented, Sylow
911C23—21no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—32no—
918C23—32no—
919C23—32no—
920C23—32no—
921C23—32no—
922C23—68no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—124no—
940C23—124no—
941C23—124no—
942C23—124no—
943C23—124no—
944C23—124no—
945C23D3×#6712yes—
946C23C22×D3211yescharacteristic
947D4—124no—
948D4—188no—
949D4—364no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—92no—
972C2×C4—124no—
973C2×C4—124no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—181no—
982C2×C4—181no—
983C2×C4—181no—
984C2×C4—181no—
985C2×C4—364no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—42no—
994C2×C3—42no—
995C2×C3—64no—
996C2×C3—82no—
997C2×C3—122no—
998C2×C3—122no—
999C2×C3C2×#88311yescharacteristic
1000C2×C3#549011yescharacteristic
1001C2×C3#549411yescharacteristic
1002C2×C3#549511yescharacteristic
1003C2×C3#559011yescharacteristic
1004C2×C3#561011yescharacteristic
1005C2×C3#561011yescharacteristic
1006C2×C3#561311yescharacteristic
1007C2×C3D3×#12311yescharacteristic
1008C2×C3#565611yescharacteristic
1009C2×C3#567911yescharacteristic
1010C2×C3#579111yescharacteristic
1011C2×C3D4×#6711yescharacteristic
1012C2×C3#580611yescharacteristic
1013D3—24no—
1014D3—42no—
1015D3—42no—
1016C22—22no—
1017C22—22no—
1018C22—22no—
1019C22—34no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—62no—
1036C22—1216no—
1037C22—121no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22—121no—
1045C22D3×#23511yescharacteristic
1046C22D3×#23511yescharacteristic
1047C22D32×D411yescharacteristic
1048C22D3×#23711yescharacteristic
1049C22#6431311yescharacteristic
1050C22#6431311yescharacteristic
1051C22C2×D3×#6711yescharacteristic
1052C4—41no—
1053C4—41no—
1054C4—62no—
1055C4—62no—
1056C4—121no—
1057C4—121no—
1058C4—121no—
1059C4—182no—
1060C4—361no—
1061C4—361no—
1062C4—361no—
1063C3—21no—
1064C3#7711111yescharacteristic, complemented
1065C3#8212811yescharacteristic, complemented
1066C2—42no—
1067C2—64no—
1068C2—122no—
1069C2—122no—
1070C2#1059409211yescharacteristic
1071C2#1059419511yescharacteristic
1072C2D3×#88311yescharacteristic
1073C2#1059427311yescharacteristic
1074C2#1059489611yescharacteristic
1075C2#1059515011yescharacteristic
1076C2#1059528711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63976C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C22⋊C4C2semidirect
3. C2×#63969C2semidirect
4. C2×#63879C2semidirect
5. #10592651C2semidirect
6. C3×#4959C2semidirect
7. #10591706C2semidirect
8. #10591702C2semidirect
9. #10591390C2semidirect
10. #10591381C2semidirect
11. #10591363C2semidirect
12. #10591303C2semidirect
13. #10591295C2semidirect
14. #10591282C2semidirect
15. #10591277C2semidirect
24. C22×D3×Dic3C22semidirect
28. C2×#3750C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
39. C2×#3724C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. C2×Dic32C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
64. C2×D3×C22⋊C4D3semidirect
74. #4959D3semidirect
133. C3×#217D4semidirect
204. C2×(C2×D3)⋊C4C2×D3semidirect
205. C2×(C2×D3)⋊C4C2×D3semidirect
215. C2×Dic3⋊C4C2×D3semidirect
235. C3⋊#95C2×D3semidirect
437. #217#67semidirect
496. C2×C3×D3#123semidirect
881. C2×D3#883semidirect
910. C32#2418semidirect
1064. C3#77111semidirect
1065. C3#82128semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C22⋊C42
C2×#639762
C2×#639692
C2×#638792
#105926512
C3×#49592
#105917062
#105917022
#105913902
#105913812
#105913632
#105913032
#105912952
#105912822
#105912772
#821283
#771113