Finite Group Databasebeta

← #11810327

Subgroups — #11810327

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2C2×#63922C211yesmaximal, characteristic
3C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#63905C211yesmaximal, characteristic, complemented
5#10592692C211yesmaximal, characteristic, complemented
6C3×#4992C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591388C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591369C211yesmaximal, characteristic, complemented
12#10591292C211yesmaximal, characteristic, complemented
13#10591279C211yesmaximal, characteristic, complemented
14#10591278C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#82404—31nomaximal
17#77669—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic, complemented
22C22×#626C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3750C2211yescharacteristic, complemented
30C2×#3750C2211yescharacteristic, complemented
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C3×C4×Dic3C2211yescharacteristic, complemented
37C3×#893—24no—
38C2×#3724C2211yescharacteristic, complemented
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48#63922—24no—
49D3×(C2×D3)⋊C4—24no—
50#63905—24no—
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×C4×D4—31no—
58C2×#937—31no—
59C2×#929—31no—
60C22×(C2×D3)⋊C4—31no—
61C2×#893D311yescharacteristic, complemented
62C2×#883—31no—
63C2×#882—31no—
64C2×D3×C22⋊C4—31no—
65C3×#397—31no—
66#5220—31no—
67#5213—31no—
68#5210—31no—
69#4993—31no—
70#4993—31no—
71#4993—61no—
72#4992D311yescharacteristic, complemented
73#4959—31no—
74#4959—31no—
75#4959—31no—
76#4955—31no—
77#4955—31no—
78#4944—31no—
79#4942—31no—
80#4940—31no—
81#4940—31no—
82#4672—31no—
83#4670—31no—
84#4668—31no—
85#4667—31no—
86#4665—31no—
87#4665—31no—
88C23×C3⋊D3C2311yescharacteristic
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
101C22×C32×C4C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×C3×D12—22no—
111C2×C3×D12—22no—
112C2×C3×D12D414yes—
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×#626—22no—
120C2×#626—22no—
121C2×#626—41no—
122C2×#625—22no—
123C2×#625—22no—
124C2×#625—41no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—41no—
128C32×C4⋊C4—22no—
129#3752—22no—
130#3752—22no—
131#3752—41no—
132#3750—22no—
133#3750—41no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×C4×Dic3—22no—
140#3724—41no—
141Dic3⋊Dic3—22no—
142#3722—22no—
143#3722—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—41no—
148(C2×D3)⋊Dic3—41no—
149(C2×D3)⋊Dic3D414yescomplemented
150#2418—91noSylow
151C24×D3—31no—
152C24×D3—31no—
153C22×C3×D4—31no—
154C23×C3×C4—31no—
155C23×C3×C4—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—31no—
159C23×Dic3—31no—
160C22×D12—31no—
161C22×D12C2×D311yescharacteristic
162C22×C4×D3—31no—
163C22×C4×D3C2×D311yescharacteristic
164C22×C4×D3C2×D311yescharacteristic, complemented
165C3×C4×D4—64no—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
168C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C42—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181#937—64no—
182#929—64no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
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—61no—
200C2×(C2×D3)⋊C4—61no—
201C2×(C2×D3)⋊C4—61no—
202C2×(C2×D3)⋊C4—64no—
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
208C2×C4⋊Dic3—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—61no—
217C2×Dic3⋊C4—61no—
218C2×C4×Dic3C2×D311yescharacteristic, complemented
219#893—24no—
220#883—64no—
221#882—64no—
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—61no—
233C3⋊#95C2×D311yescharacteristic, complemented
234C3⋊#95C2×D311yescharacteristic, complemented
235C3⋊#95C2×D311yescharacteristic, complemented
236C23×C32C2411yescharacteristic
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3#4112yes—
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×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×D3C2×D412yes—
261C22×C3×D3C2×D412yes—
262C22×C3×D3C2×D412yes—
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—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4C2×D412yes—
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—
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×Dic3C2×D412yes—
305C3×D12—28no—
306C3×C4×D3—44no—
307C3×C4×D3—44no—
308#626—44no—
309#625—44no—
310D3×Dic3—44no—
311C2×#123—91no—
312C2×#120—91no—
313C2×C4×D4—31no—
314C22×C22⋊C4—91no—
315#399—91no—
316#397—31no—
317#394—91no—
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—31no—
327C24×C3—31no—
328C24×C3—31no—
329C23×D3—31no—
330C23×D3—31no—
331C23×D3—61no—
332C23×D3—62no—
333C23×D3—62no—
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—121no—
343C23×D3—121no—
344C23×D3—121no—
345C23×D3—121no—
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D311yescharacteristic
348C23×D3C22×D311yescharacteristic
349C2×C3×D4—34no—
350C2×C3×D4—62no—
351C2×C3×D4—62no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—62no—
361C22×C3×C4—62no—
362C22×C3×C4—62no—
363C22×C3×C4—62no—
364C22×C3×C4—121no—
365C22×C3×C4—121no—
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C2×#67—62no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—62no—
377C2×#67—62no—
378C2×#67—121no—
379C2×#67—121no—
380C2×#67—121no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—62no—
391C22×Dic3—62no—
392C22×Dic3—121no—
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C2×D12—22no—
399C2×D12—22no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—121no—
403C2×D12#6714yes—
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—22no—
414C3×C4⋊C4—22no—
415C3×C4⋊C4—42no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—62no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—62no—
421C3×C42—62no—
422#217—34no—
423#217—62no—
424#217—62no—
425#217—62no—
426#217—121no—
427#217—121no—
428(C2×D3)⋊C4—22no—
429(C2×D3)⋊C4—22no—
430(C2×D3)⋊C4—22no—
431(C2×D3)⋊C4—22no—
432(C2×D3)⋊C4—22no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
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—122no—
446(C2×D3)⋊C4—122no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—122no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4—121no—
452C4⋊Dic3—62no—
453Dic3⋊C4—62no—
454Dic3⋊C4—62no—
455Dic3⋊C4—62no—
456Dic3⋊C4—122no—
457Dic3⋊C4—121no—
458Dic3⋊C4—121no—
459Dic3⋊C4—121no—
460Dic3⋊C4—121no—
461Dic3⋊C4—122no—
462C4×Dic3—22no—
463C22×C32C22×D411yescharacteristic
464C22×C32C22×D411yescharacteristic
465C22×C32C2×#4111yescharacteristic
466C22×C32C2×#4111yescharacteristic
467C22×C32C2×#4111yescharacteristic
468C22×C32H(5,𝔽2)11yescharacteristic
469C22×C32H(5,𝔽2)11yescharacteristic
470C2×C3⋊D3—22no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3⋊D3—41no—
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—22no—
488C2×C3×D3—22no—
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—41no—
497C2×C3×D3#12314yescomplemented
498D32—416no—
499C32×C4—22no—
500C32×C4—41no—
501C32×C4—41no—
502C3⋊Dic3—22no—
503C3⋊Dic3—41no—
504C3⋊Dic3—41no—
505C3×Dic3—22no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C25—91no—
511C22×D4—31no—
512C22×D4—91no—
513C22×D4—91no—
514C23×C4—31no—
515C23×C4—31no—
516C23×C4—91no—
517#123—184no—
518#120—184no—
519C4×D4—64no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4D3211yescharacteristic, complemented
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
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⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—184no—
542C2×C42—31no—
543#95—31no—
544#95—31no—
545#95—31no—
546#95—91no—
547#95—91no—
548#95—91no—
549C23×C3—21no—
550C23×C3—32no—
551C23×C3—32no—
552C23×C3—32no—
553C23×C3—32no—
554C23×C3—32no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3C23×D311yescharacteristic
572C23×C3C23×D311yescharacteristic
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—32no—
590C22×D3—32no—
591C22×D3—62no—
592C22×D3—68no—
593C22×D3—68no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—121no—
607C22×D3—121no—
608C22×D3—121no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—124no—
613C22×D3—124no—
614C22×D3—124no—
615C22×D3—124no—
616C22×D3—124no—
617C22×D3—124no—
618C22×D3—124no—
619C22×D3—124no—
620C22×D3—124no—
621C22×D3—124no—
622C22×D3—124no—
623C22×D3—124no—
624C22×D3#23512yes—
625C22×D3#23512yes—
626C22×D3D3×D412yes—
627C22×D3C2×#6712yes—
628C22×D3C2×#6712yes—
629C3×D4—68no—
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—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—22no—
647C2×C3×C4—32no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
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—124no—
671C2×C3×C4—124no—
672C2×C3×C4D3×D412yes—
673C2×C3×C4C2×#6712yes—
674#67—124no—
675#67—124no—
676#67—124no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
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—32no—
692C2×Dic3—32no—
693C2×Dic3—62no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—62no—
699C2×Dic3—61no—
700C2×Dic3—61no—
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—121no—
712C2×Dic3—121no—
713C2×Dic3—121no—
714C2×Dic3—121no—
715C2×Dic3—121no—
716C2×Dic3—121no—
717C2×Dic3—121no—
718C2×Dic3—124no—
719C2×Dic3D3×D412yes—
720D12—28no—
721D12—124no—
722C4×D3—44no—
723C4×D3—44no—
724C4×D3—124no—
725C2×C32C2×#12311yescharacteristic
726C2×C32#52511yescharacteristic
727C2×C32#53811yescharacteristic
728C2×C32D4211yescharacteristic
729C2×C32#54611yescharacteristic
730C2×C32#54611yescharacteristic
731C2×C32#55111yescharacteristic
732C3⋊D3—42no—
733C3×D3—24no—
734C3×D3—42no—
735C3×D3—42no—
736C24—31no—
737C24—31no—
738C24—31no—
739C24—91no—
740C24—182no—
741C24—182no—
742C24—182no—
743C24—182no—
744C24—182no—
745C24—361no—
746C24—361no—
747C2×D4—34no—
748C2×D4—62no—
749C2×D4—62no—
750C2×D4—182no—
751C2×D4—182no—
752C2×D4—182no—
753C2×D4—182no—
754C2×D4—361no—
755C2×D4—361no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—62no—
762C22×C4—62no—
763C22×C4—62no—
764C22×C4—62no—
765C22×C4—91no—
766C22×C4—91no—
767C22×C4—91no—
768C22×C4—121no—
769C22×C4—121no—
770C22×C4—182no—
771C22×C4—182no—
772C22×C4—361no—
773C22×C4C2×D3211yescharacteristic
774C22×C4C2×D3211yescharacteristic
775C22×C4C2×D3211yescharacteristic
776C4⋊C4—22no—
777C4⋊C4—182no—
778C4⋊C4—182no—
779C4⋊C4—361no—
780C4⋊C4—361no—
781C22⋊C4—62no—
782C22⋊C4—62no—
783C22⋊C4—62no—
784C22⋊C4—62no—
785C22⋊C4—62no—
786C22⋊C4—94no—
787C22⋊C4—182no—
788C22⋊C4—182no—
789C22⋊C4—182no—
790C22⋊C4—182no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—361no—
795C22⋊C4—361no—
796C22⋊C4—361no—
797C42—62no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—34no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3—121no—
825C22×C3—121no—
826C22×C3C2×#23511yescharacteristic
827C22×C3C2×#23511yescharacteristic
828C22×C3C2×D3×D411yescharacteristic
829C22×C3C2×D3×D411yescharacteristic
830C22×C3C2×D3×D411yescharacteristic
831C22×C3#100411yescharacteristic
832C22×C3D3×#4111yescharacteristic
833C22×C3D3×#4111yescharacteristic
834C22×C3D3×#4111yescharacteristic
835C22×C3D3×#4111yescharacteristic
836C22×C3#100911yescharacteristic
837C22×C3#100911yescharacteristic
838C22×C3#100911yescharacteristic
839C22×C3C22×#6711yescharacteristic
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—122no—
867C2×D3—122no—
868C2×D3—122no—
869C2×D3—1216no—
870C2×D3—1216no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—241no—
880C2×D3—241no—
881C2×D3—241no—
882C2×D3—241no—
883C2×D3#92914yescomplemented
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—42no—
887C3×C4—41no—
888C3×C4—41no—
889C3×C4—41no—
890C3×C4—41no—
891C3×C4—62no—
892C3×C4—81no—
893C3×C4—81no—
894C3×C4—121no—
895C3×C4—121no—
896C3×C4—121no—
897C3×C4—121no—
898Dic3—22no—
899Dic3—41no—
900Dic3—41no—
901Dic3—41no—
902Dic3—41no—
903Dic3—62no—
904Dic3—62no—
905Dic3—122no—
906Dic3—122no—
907Dic3—121no—
908Dic3—121no—
909Dic3—121no—
910Dic3—121no—
911Dic3—241no—
912C32#241811yescharacteristic, complemented, Sylow
913C23—32no—
914C23—32no—
915C23—32no—
916C23—32no—
917C23—32no—
918C23—61no—
919C23—61no—
920C23—61no—
921C23—61no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—92no—
935C23—188no—
936C23—181no—
937C23—181no—
938C23—181no—
939C23—181no—
940C23—181no—
941C23—181no—
942C23—364no—
943C23—364no—
944C23—364no—
945C23—364no—
946C23—364no—
947C23—364no—
948C23C22×D3211yescharacteristic
949D4—68no—
950D4—364no—
951D4—364no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—32no—
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—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—92no—
976C2×C4—124no—
977C2×C4—124no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—181no—
982C2×C4—181no—
983C2×C4—181no—
984C2×C4—181no—
985C2×C4—181no—
986C2×C4—364no—
987C2×C4D3×#6712yes—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—64no—
996C2×C3—122no—
997C2×C3—122no—
998C2×C3#554711yescharacteristic
999C2×C3#555011yescharacteristic
1000C2×C3#555611yescharacteristic
1001C2×C3#556011yescharacteristic
1002C2×C3#560911yescharacteristic
1003C2×C3D3×#12311yescharacteristic
1004C2×C3#565411yescharacteristic
1005C2×C3#565611yescharacteristic
1006C2×C3#567611yescharacteristic
1007C2×C3#570411yescharacteristic
1008C2×C3#570511yescharacteristic
1009C2×C3C2×#92911yescharacteristic
1010C2×C3D4×#6711yescharacteristic
1011C2×C3#582911yescharacteristic
1012D3—24no—
1013D3—42no—
1014D3—42no—
1015D3—122no—
1016D3—122no—
1017D3—242no—
1018C22—34no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—121no—
1036C22—121no—
1037C22—121no—
1038C22—121no—
1039C22—182no—
1040C22—182no—
1041C22—182no—
1042C22—3616no—
1043C22—361no—
1044C22—361no—
1045C22—361no—
1046C22—361no—
1047C22D3×#23511yescharacteristic
1048C22D3×#23511yescharacteristic
1049C22D32×D411yescharacteristic
1050C22#6431411yescharacteristic
1051C22#6431911yescharacteristic
1052C22#6432011yescharacteristic
1053C22C2×D3×#6711yescharacteristic
1054C4—22no—
1055C4—41no—
1056C4—41no—
1057C4—62no—
1058C4—121no—
1059C4—121no—
1060C4—121no—
1061C4—121no—
1062C4—182no—
1063C4—361no—
1064C4—361no—
1065C3—21no—
1066C3#7766911yescharacteristic, complemented
1067C3#8240411yescharacteristic, complemented
1068C2—64no—
1069C2—122no—
1070C2—122no—
1071C2—362no—
1072C2#1059461411yescharacteristic
1073C2#1059461911yescharacteristic
1074C2#1059463811yescharacteristic
1075C2#1059464511yescharacteristic
1076C2D3×#92911yescharacteristic
1077C2#1059528811yescharacteristic
1078C2#1059542811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63922C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2418
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
3. C2×D3×(C2×D3)⋊C4C2semidirect
4. C2×#63905C2semidirect
5. #10592692C2semidirect
6. C3×#4992C2semidirect
7. #10591399C2semidirect
8. #10591388C2semidirect
9. #10591382C2semidirect
10. #10591376C2semidirect
11. #10591369C2semidirect
12. #10591292C2semidirect
13. #10591279C2semidirect
14. #10591278C2semidirect
15. #10591194C2semidirect
21. C22×C3×C4×D3C22semidirect
25. C2×C32×C4⋊C4C22semidirect
29. C2×#3750C22semidirect
30. C2×#3750C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×C4×Dic3C22semidirect
38. C2×#3724C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
61. C2×#893D3semidirect
72. #4992D3semidirect
149. (C2×D3)⋊Dic3D4semidirect
164. C22×C4×D3C2×D3semidirect
167. C2×C3×C4⋊C4C2×D3semidirect
168. C2×C3×C4⋊C4C2×D3semidirect
207. C2×(C2×D3)⋊C4C2×D3semidirect
218. C2×C4×Dic3C2×D3semidirect
233. C3⋊#95C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
497. C2×C3×D3#123semidirect
524. C2×C4⋊C4D32semidirect
883. C2×D3#929semidirect
912. C32#2418semidirect
1066. C3#77669semidirect
1067. C3#82404semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639052
#105926922
C3×#49922
#105913992
#105913882
#105913822
#105913762
#105913692
#105912922
#105912792
#105912782
#105911942
#824043
#776693