Finite Group Databasebeta

← #11810319

Subgroups — #11810319

Order 1152.

1719 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
2C2×#63983C211yesmaximal, characteristic
3C2×#63966C211yesmaximal, characteristic, complemented
4C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5#10592658C211yesmaximal, characteristic, complemented
6C3×#4959C211yesmaximal, characteristic, complemented
7#10591721C211yesmaximal, characteristic, complemented
8#10591710C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591366C211yesmaximal, characteristic, complemented
11#10591305C211yesmaximal, characteristic, complemented
12#10591303C211yesmaximal, characteristic, complemented
13#10591289C211yesmaximal, characteristic, complemented
14#10591278C211yesmaximal, characteristic, complemented
15#10591204C211yesmaximal, characteristic, complemented
16#82404—31nomaximal
17#77112—31nomaximal
18C23×D32C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic, complemented
23C22×C3×C4×D3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic, complemented
26C2×#3757C2211yescharacteristic, complemented
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3750C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic, complemented
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37C3×#67⋊C4—24no—
38#63983—24no—
39#63966—24no—
40C2×Dic3⋊Dic3C2211yescharacteristic, complemented
41C2×Dic3⋊Dic3C2211yescharacteristic, complemented
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50D3×(C2×D3)⋊C4—24no—
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×C4×D4—31no—
58C2×#937—31no—
59C2×#937—31no—
60C2×#929—31no—
61C22×(C2×D3)⋊C4—31no—
62C2×#886—31no—
63C2×#67⋊C4D311yescharacteristic, complemented
64C2×D3×C22⋊C4—31no—
65C3×#394—31no—
66#5220—31no—
67#5220—31no—
68#5213—31no—
69#5210—31no—
70#4993—31no—
71#4992—31no—
72#4990—31no—
73#4987—31no—
74#4959—31no—
75#4959—31no—
76#4959—61no—
77#4959D311yescharacteristic, complemented
78#4956—31no—
79#4955—31no—
80#4955—31no—
81#4951—31no—
82#4949—31no—
83#4942—31no—
84#4940—31no—
85#4940—31no—
86#4675—31no—
87#4668—31no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×D32—22no—
93C22×D32—22no—
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—22no—
97C22×D32—41no—
98C22×D32—41no—
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—22no—
102C2×#638—22no—
103C2×#638—41no—
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67—22no—
111C2×C3×#67—41no—
112C2×C3×#67D414yes—
113C22×C3×Dic3—22no—
114C22×C3×Dic3—22no—
115C22×C3×Dic3—41no—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—22no—
124C2×C3×C4×D3—41no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—41no—
128C32×C22⋊C4—22no—
129#3757—41no—
130#3752—22no—
131#3752—41no—
132#3750—41no—
133C3×#217—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×Dic3⋊C4—22no—
138C3×Dic3⋊C4—41no—
139C3×C4×Dic3—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—22no—
142#3722—22no—
143#3722—22no—
144#3722D414yescomplemented
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149(C2×D3)⋊Dic3—41no—
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C23×C3×C4—31no—
156C23×C3×C4—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—61no—
160C22×#67C2×D311yescharacteristic
161C22×#67C2×D311yescharacteristic
162C23×Dic3—31no—
163C23×Dic3C2×D311yescharacteristic, complemented
164C22×C4×D3—31no—
165C22×C4×D3C2×D311yescharacteristic
166C3×C4×D4—64no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—21no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
175C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
176C2×C3×C42—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—61no—
185C2×#217C2×D311yescharacteristic, complemented
186#937—64no—
187#937—64no—
188#929—64no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
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)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4—64no—
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×(C2×D3)⋊C4C2×D311yescharacteristic
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—61no—
217C2×Dic3⋊C4C2×D311yescharacteristic, complemented
218C2×Dic3⋊C4C2×D311yescharacteristic, complemented
219C2×C4×Dic3C2×D311yescharacteristic, complemented
220#886—64no—
221#67⋊C4—24no—
222D3×C22⋊C4—64no—
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—31no—
233C3⋊#95—31no—
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—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3C2×D412yes—
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×D3C2×D412yes—
262C22×C3×D3#4112yes—
263C22×C3×D3#4112yes—
264C22×C3×D3#4112yes—
265C2×D32—28no—
266C2×D32—44no—
267C2×D32—44no—
268C2×D32—44no—
269C2×D32—44no—
270C2×D32—44no—
271C2×D32—44no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278#638—44no—
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—
288C3×#67—28no—
289C3×#67—44no—
290C2×C3×Dic3—21no—
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×Dic3—21no—
305C2×C3×Dic3—44no—
306C2×C3×Dic3C2×D412yes—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3C2×D412yes—
309C3×C4×D3—44no—
310D3×Dic3—44no—
311C2×#123—91no—
312C2×#120—91no—
313C2×C4×D4—31no—
314C22×C22⋊C4—91no—
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×C3C22×D311yescharacteristic
330C24×C3C22×D311yescharacteristic
331C23×D3—31no—
332C23×D3—31no—
333C23×D3—61no—
334C23×D3—62no—
335C23×D3—62no—
336C23×D3—62no—
337C23×D3—62no—
338C23×D3—62no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—62no—
343C23×D3—62no—
344C23×D3—121no—
345C23×D3—121no—
346C23×D3—121no—
347C23×D3—121no—
348C23×D3C22×D311yescharacteristic
349C23×D3C22×D311yescharacteristic
350C2×C3×D4—34no—
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4—62no—
354C2×C3×D4—62no—
355C2×C3×D4—121no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—62no—
365C22×C3×C4—62no—
366C22×C3×C4—62no—
367C22×C3×C4—62no—
368C22×C3×C4—121no—
369C22×C3×C4—121no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C2×#67—22no—
375C2×#67—22no—
376C2×#67—22no—
377C2×#67—22no—
378C2×#67—41no—
379C2×#67—62no—
380C2×#67—62no—
381C2×#67—62no—
382C2×#67—62no—
383C2×#67—122no—
384C2×#67—122no—
385C2×#67—121no—
386C2×#67—121no—
387C2×#67—122no—
388C2×#67#6714yes—
389C22×Dic3—22no—
390C22×Dic3—22no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—41no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3—62no—
402C22×Dic3—62no—
403C22×Dic3—121no—
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C2×C4×D3—22no—
411C2×C4×D3—22no—
412C2×C4×D3—41no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—121no—
416C3×C4⋊C4—62no—
417C3×C4⋊C4—121no—
418C3×C22⋊C4—22no—
419C3×C22⋊C4—22no—
420C3×C22⋊C4—42no—
421C3×C22⋊C4—62no—
422C3×C22⋊C4—62no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—62no—
425C3×C42—62no—
426#217—22no—
427#217—62no—
428#217—62no—
429#217—62no—
430#217—62no—
431#217—121no—
432#217—121no—
433#217—121no—
434#217—122no—
435(C2×D3)⋊C4—22no—
436(C2×D3)⋊C4—22no—
437(C2×D3)⋊C4—22no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
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—62no—
449(C2×D3)⋊C4—62no—
450(C2×D3)⋊C4—122no—
451(C2×D3)⋊C4—121no—
452(C2×D3)⋊C4—121no—
453(C2×D3)⋊C4—122no—
454(C2×D3)⋊C4—121no—
455C4⋊Dic3—62no—
456C4⋊Dic3—62no—
457Dic3⋊C4—22no—
458Dic3⋊C4—41no—
459Dic3⋊C4—62no—
460Dic3⋊C4—62no—
461Dic3⋊C4—121no—
462Dic3⋊C4—121no—
463Dic3⋊C4—122no—
464C4×Dic3—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32C22×D411yescharacteristic
473C22×C32C22×D411yescharacteristic
474C22×C32C2×#4111yescharacteristic
475C22×C32C2×#4111yescharacteristic
476C22×C32C2×#4111yescharacteristic
477C22×C32H(5,𝔽2)11yescharacteristic
478C22×C32H(5,𝔽2)11yescharacteristic
479C2×C3⋊D3—22no—
480C2×C3⋊D3—22no—
481C2×C3⋊D3—22no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3#12314yescomplemented
500D32—416no—
501C32×C4—41no—
502C32×C4—41no—
503C3⋊Dic3—41no—
504C3⋊Dic3—41no—
505C3⋊Dic3—41no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C3×Dic3—41no—
512C25—91no—
513C22×D4—31no—
514C22×D4—31no—
515C22×D4—91no—
516C23×C4—31no—
517C23×C4—31no—
518C23×C4—91no—
519#123—184no—
520#120—184no—
521C4×D4—64no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
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⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—184no—
543C2×C22⋊C4D3211yescharacteristic, complemented
544C2×C42—31no—
545#95—31no—
546#95—91no—
547#95—91no—
548#95—91no—
549#95—91no—
550#95—91no—
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—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—22no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—32no—
568C23×C3—32no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—41no—
574C23×C3—41no—
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×C3D3×D412yes—
586C23×C3C2×#6712yes—
587C23×C3C23×D311yescharacteristic
588C23×C3C23×D311yescharacteristic
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—32no—
600C22×D3—32no—
601C22×D3—62no—
602C22×D3—68no—
603C22×D3—68no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—61no—
615C22×D3—61no—
616C22×D3—121no—
617C22×D3—121no—
618C22×D3—121no—
619C22×D3—121no—
620C22×D3—121no—
621C22×D3—121no—
622C22×D3—124no—
623C22×D3—124no—
624C22×D3—124no—
625C22×D3—124no—
626C22×D3—124no—
627C22×D3—124no—
628C22×D3—124no—
629C22×D3—124no—
630C22×D3—124no—
631C22×D3—124no—
632C22×D3—124no—
633C22×D3—124no—
634C22×D3#23512yes—
635C22×D3#23512yes—
636C22×D3#23712yes—
637C22×D3C2×#6712yes—
638C3×D4—68no—
639C3×D4—124no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
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—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
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—124no—
677C2×C3×C4—124no—
678#67—28no—
679#67—44no—
680#67—124no—
681#67—124no—
682#67—128no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—21no—
696C2×Dic3—21no—
697C2×Dic3—21no—
698C2×Dic3—44no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—121no—
720C2×Dic3—121no—
721C2×Dic3—121no—
722C2×Dic3—121no—
723C2×Dic3—121no—
724C2×Dic3—121no—
725C2×Dic3—121no—
726C2×Dic3—124no—
727C2×Dic3D3×D412yes—
728C2×Dic3D3×D412yes—
729C2×Dic3C2×#6712yes—
730C4×D3—44no—
731C4×D3—124no—
732C2×C32—42no—
733C2×C32C2×#12311yescharacteristic
734C2×C32#52511yescharacteristic
735C2×C32#53811yescharacteristic
736C2×C32D4211yescharacteristic
737C2×C32#54611yescharacteristic
738C2×C32#54611yescharacteristic
739C2×C32#55111yescharacteristic
740C3⋊D3—42no—
741C3×D3—24no—
742C3×D3—42no—
743C24—31no—
744C24—31no—
745C24—91no—
746C24—182no—
747C24—182no—
748C24—182no—
749C24—182no—
750C24—182no—
751C24—361no—
752C24—361no—
753C24C2×D3211yescharacteristic
754C2×D4—34no—
755C2×D4—62no—
756C2×D4—62no—
757C2×D4—62no—
758C2×D4—62no—
759C2×D4—121no—
760C2×D4—182no—
761C2×D4—182no—
762C2×D4—361no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—62no—
770C22×C4—62no—
771C22×C4—62no—
772C22×C4—62no—
773C22×C4—91no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—121no—
777C22×C4—121no—
778C22×C4—182no—
779C22×C4—182no—
780C22×C4—361no—
781C22×C4C2×D3211yescharacteristic
782C22×C4C2×D3211yescharacteristic
783C4⋊C4—62no—
784C4⋊C4—121no—
785C4⋊C4—182no—
786C4⋊C4—182no—
787C4⋊C4—361no—
788C22⋊C4—22no—
789C22⋊C4—62no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—62no—
793C22⋊C4—94no—
794C22⋊C4—182no—
795C22⋊C4—182no—
796C22⋊C4—182no—
797C22⋊C4—182no—
798C22⋊C4—182no—
799C22⋊C4—182no—
800C22⋊C4—182no—
801C22⋊C4—361no—
802C22⋊C4—361no—
803C22⋊C4—361no—
804C42—62no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—34no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—62no—
838C22×C3—62no—
839C22×C3—81no—
840C22×C3—81no—
841C22×C3—81no—
842C22×C3—81no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3C2×#23511yescharacteristic
848C22×C3C2×#23511yescharacteristic
849C22×C3C2×D3×D411yescharacteristic
850C22×C3C2×D3×D411yescharacteristic
851C22×C3C2×D3×D411yescharacteristic
852C22×C3C2×#23711yescharacteristic
853C22×C3#100411yescharacteristic
854C22×C3#100411yescharacteristic
855C22×C3D3×#4111yescharacteristic
856C22×C3D3×#4111yescharacteristic
857C22×C3D3×#4111yescharacteristic
858C22×C3#100911yescharacteristic
859C22×C3#100911yescharacteristic
860C22×C3C22×#6711yescharacteristic
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—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—122no—
881C2×D3—122no—
882C2×D3—122no—
883C2×D3—1216no—
884C2×D3—1216no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—241no—
894C2×D3—241no—
895C2×D3—241no—
896C2×D3—241no—
897C2×D3#92914yescomplemented
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—62no—
905C3×C4—81no—
906C3×C4—81no—
907C3×C4—121no—
908C3×C4—121no—
909C3×C4—121no—
910Dic3—22no—
911Dic3—22no—
912Dic3—22no—
913Dic3—41no—
914Dic3—41no—
915Dic3—41no—
916Dic3—122no—
917Dic3—122no—
918Dic3—121no—
919Dic3—121no—
920Dic3—121no—
921Dic3—121no—
922Dic3—121no—
923Dic3—121no—
924Dic3—241no—
925C32#241811yescharacteristic, complemented, Sylow
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—21no—
932C23—32no—
933C23—32no—
934C23—32no—
935C23—32no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23—61no—
944C23—61no—
945C23—61no—
946C23—92no—
947C23—188no—
948C23—181no—
949C23—181no—
950C23—181no—
951C23—181no—
952C23—181no—
953C23—181no—
954C23—364no—
955C23—364no—
956C23—364no—
957C23—364no—
958C23—364no—
959C23—364no—
960C23D3×#6712yes—
961C23C22×D3211yescharacteristic
962D4—68no—
963D4—124no—
964D4—364no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—32no—
972C2×C4—32no—
973C2×C4—32no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—61no—
989C2×C4—124no—
990C2×C4—124no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—181no—
997C2×C4—181no—
998C2×C4—181no—
999C2×C4—181no—
1000C2×C4—364no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—64no—
1011C2×C3—82no—
1012C2×C3—122no—
1013C2×C3#554711yescharacteristic
1014C2×C3#555011yescharacteristic
1015C2×C3#555611yescharacteristic
1016C2×C3#556011yescharacteristic
1017C2×C3#559111yescharacteristic
1018C2×C3#560611yescharacteristic
1019C2×C3#560911yescharacteristic
1020C2×C3#561011yescharacteristic
1021C2×C3D3×#12311yescharacteristic
1022C2×C3#565811yescharacteristic
1023C2×C3#567811yescharacteristic
1024C2×C3C2×#92911yescharacteristic
1025C2×C3D4×#6711yescharacteristic
1026C2×C3#582911yescharacteristic
1027D3—24no—
1028D3—42no—
1029D3—122no—
1030D3—122no—
1031D3—242no—
1032C22—22no—
1033C22—22no—
1034C22—22no—
1035C22—34no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—62no—
1048C22—62no—
1049C22—121no—
1050C22—121no—
1051C22—121no—
1052C22—121no—
1053C22—182no—
1054C22—182no—
1055C22—182no—
1056C22—3616no—
1057C22—361no—
1058C22—361no—
1059C22—361no—
1060C22—361no—
1061C22D3×#23511yescharacteristic
1062C22D3×#23511yescharacteristic
1063C22D32×D411yescharacteristic
1064C22D3×#23711yescharacteristic
1065C22#6431411yescharacteristic
1066C22#6431411yescharacteristic
1067C22C2×D3×#6711yescharacteristic
1068C4—41no—
1069C4—41no—
1070C4—62no—
1071C4—62no—
1072C4—62no—
1073C4—121no—
1074C4—121no—
1075C4—121no—
1076C4—361no—
1077C4—361no—
1078C4—361no—
1079C3—21no—
1080C3#7711211yescharacteristic, complemented
1081C3#8240411yescharacteristic, complemented
1082C2—42no—
1083C2—64no—
1084C2—122no—
1085C2—362no—
1086C2#1059428311yescharacteristic
1087C2#1059428611yescharacteristic
1088C2#1059429811yescharacteristic
1089C2#1059429911yescharacteristic
1090C2D3×#92911yescharacteristic
1091C2#1059529111yescharacteristic
1092C2#1059530411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63983C2
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×#67⋊C4C2semidirect
3. C2×#63966C2semidirect
4. C2×D3×(C2×D3)⋊C4C2semidirect
5. #10592658C2semidirect
6. C3×#4959C2semidirect
7. #10591721C2semidirect
8. #10591710C2semidirect
9. #10591399C2semidirect
10. #10591366C2semidirect
11. #10591305C2semidirect
12. #10591303C2semidirect
13. #10591289C2semidirect
14. #10591278C2semidirect
15. #10591204C2semidirect
22. C23×C3×Dic3C22semidirect
25. C2×C32×C22⋊C4C22semidirect
26. C2×#3757C22semidirect
29. C2×#3750C22semidirect
30. C2×C3×#217C22semidirect
34. C2×C3×Dic3⋊C4C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×C4×Dic3C22semidirect
40. C2×Dic3⋊Dic3C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
63. C2×#67⋊C4D3semidirect
77. #4959D3semidirect
144. #3722D4semidirect
163. C23×Dic3C2×D3semidirect
174. C2×C3×C22⋊C4C2×D3semidirect
175. C2×C3×C22⋊C4C2×D3semidirect
185. C2×#217C2×D3semidirect
217. C2×Dic3⋊C4C2×D3semidirect
218. C2×Dic3⋊C4C2×D3semidirect
219. C2×C4×Dic3C2×D3semidirect
235. C3⋊#95C2×D3semidirect
499. C2×C3×D3#123semidirect
543. C2×C22⋊C4D32semidirect
897. C2×D3#929semidirect
925. C32#2418semidirect
1080. C3#77112semidirect
1081. C3#82404semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C2×#639832
C2×#639662
C2×D3×(C2×D3)⋊C42
#105926582
C3×#49592
#105917212
#105917102
#105913992
#105913662
#105913052
#105913032
#105912892
#105912782
#105912042
#824043
#771123