Finite Group Databasebeta

← #11808455

Subgroups — #11808455

Order 1152.

1467 conjugacy classes of subgroups.

The subgroup lattice has 967 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2C2×#63879C211yesmaximal, characteristic, complemented
3C2×#63879C211yesmaximal, characteristic, complemented
4C2×#63841C211yesmaximal, characteristic, complemented
5#10592681C211yesmaximal, characteristic, complemented
6C3×#4994C211yesmaximal, characteristic, complemented
7#10591394C211yesmaximal, characteristic, complemented
8#10591390C211yesmaximal, characteristic, complemented
9#10591389C211yesmaximal, characteristic
10Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#10591308C211yesmaximal, characteristic, complemented
12#10591300C211yesmaximal, characteristic, complemented
13#10591298C211yesmaximal, characteristic, complemented
14Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#10591237C211yesmaximal, characteristic, complemented
16#82345—31nomaximal
17#77281—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C3×#893—24no—
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48#63879—24no—
49#63879—24no—
50#63841—24no—
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×C4×D4—31no—
58C2×C4×#67—31no—
59C2×C4×#67—31no—
60C2×#926—31no—
61C2×#893D311yescharacteristic, complemented
62C2×#892—31no—
63C2×#67⋊C4—31no—
64C2×#67⋊C4—31no—
65C3×#396—31no—
66#5223—31no—
67#5222—31no—
68C4×#217—31no—
69#4994—31no—
70#4994D311yescharacteristic, complemented
71#4991—31no—
72#4982—31no—
73#4982—31no—
74#4982—61no—
75Dic3×C4⋊C4—31no—
76#4961—31no—
77#4961—31no—
78#4961—31no—
79#4960—31no—
80#4959—31no—
81#4952—31no—
82#4948—31no—
83Dic3×C22⋊C4—31no—
84C4×(C2×D3)⋊C4—31no—
85C4×Dic3⋊C4—31no—
86#4675—31no—
87#4666—31no—
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×D12—22no—
104C2×C3×D12—22no—
105C2×C3×D12—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3D414yescomplemented
112C2×#625—22no—
113C2×#625—22no—
114C2×#625—22no—
115C2×#625—22no—
116C2×#625—22no—
117C2×#625—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C32×C4⋊C4—22no—
122C4⋊(C3⋊Dic3)—22no—
123#3750—22no—
124#3750—22no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×C4⋊Dic3—22no—
131C3×Dic3⋊C4—22no—
132C3×C4×Dic3—22no—
133Dic3⋊Dic3—22no—
134(C2×D3)⋊Dic3—22no—
135(C2×D3)⋊Dic3—22no—
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141Dic32—22no—
142Dic32—22no—
143Dic32D414yescomplemented
144#2392—91noSylow
145C22×C3×D4—31no—
146C23×C3×C4—31no—
147C23×C3×C4—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—31no—
152C23×Dic3—31no—
153C22×D12C2×D311yescharacteristic
154C22×C4×D3—31no—
155C22×C4×D3C2×D311yescharacteristic
156C22×C4×D3C2×D311yescharacteristic
157C3×C4×D4—64no—
158C2×C3×C4⋊C4—21no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4C2×D311yescharacteristic
162C2×C3×C4⋊C4C2×D311yescharacteristic
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C42—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C4×#67—64no—
177C4×#67—64no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×(C2×D3)⋊C4C2×D311yescharacteristic
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190#926—64no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—61no—
195C2×C4⋊Dic3C2×D311yescharacteristic
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—61no—
202C2×Dic3⋊C4—61no—
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3C2×D311yescharacteristic
211#893—24no—
212#892—64no—
213#67⋊C4—64no—
214#67⋊C4—64no—
215C3×#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—61no—
227C3⋊#95—61no—
228C3⋊#95—61no—
229C3⋊#95C2×D311yescharacteristic
230C23×C32C2411yescharacteristic
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
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—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3C2×D412yes—
250C22×C3×D3#4112yes—
251C22×C3×D3#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4C2×D412yes—
260C2×C32×C4#4112yes—
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⋊Dic3C2×D412yes—
272C2×C3⋊Dic3#4112yes—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—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×Dic3C2×D412yes—
285C2×C3×Dic3C2×D412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3#4112yes—
288C3×D12—28no—
289C3×C4×D3—28no—
290C3×C4×D3—44no—
291#625—28no—
292#625—28no—
293D3×Dic3—44no—
294C2×C4×D4—31no—
295C2×C4×D4—91no—
296C2×C4×D4—91no—
297C2×#117—91no—
298#398—91no—
299#397—91no—
300#396—31no—
301#396—91no—
302#394—91no—
303#394—91no—
304#394—91no—
305#392—91no—
306C4×C4⋊C4—91no—
307C4×C22⋊C4—91no—
308C4×C22⋊C4—91no—
309C24×C3—31no—
310C24×C3—31no—
311C24×C3—31no—
312C23×D3C22×D311yescharacteristic
313C23×D3C22×D311yescharacteristic
314C23×D3C22×D311yescharacteristic
315C2×C3×D4—62no—
316C2×C3×D4—62no—
317C2×C3×D4—62no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—34no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—62no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—62no—
363C22×Dic3—62no—
364C22×Dic3—62no—
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C2×D12—22no—
371C2×D12—22no—
372C2×D12—22no—
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3#6714yescomplemented
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—42no—
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C22⋊C4—62no—
388C3×C22⋊C4—62no—
389C3×C22⋊C4—62no—
390C3×C22⋊C4—62no—
391C3×C22⋊C4—62no—
392C3×C42—62no—
393#217—62no—
394#217—62no—
395#217—62no—
396#217—62no—
397#217—62no—
398#217—62no—
399#217—62no—
400(C2×D3)⋊C4—22no—
401(C2×D3)⋊C4—22no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—22no—
404(C2×D3)⋊C4—22no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412C4⋊Dic3—22no—
413C4⋊Dic3—62no—
414C4⋊Dic3—62no—
415C4⋊Dic3—62no—
416C4⋊Dic3—122no—
417Dic3⋊C4—22no—
418Dic3⋊C4—62no—
419Dic3⋊C4—62no—
420Dic3⋊C4—62no—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—122no—
424Dic3⋊C4—122no—
425C4×Dic3—22no—
426C4×Dic3—34no—
427C4×Dic3—34no—
428C4×Dic3—62no—
429C4×Dic3—62no—
430C4×Dic3—62no—
431C4×Dic3—62no—
432C22×C32C22×D411yescharacteristic
433C22×C32C22×D411yescharacteristic
434C22×C32C2×#4111yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32C2×#4111yescharacteristic
438C22×C32C2×#4111yescharacteristic
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—22no—
447C2×C3×D3—22no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C32×C4—22no—
461C32×C4—22no—
462C32×C4—41no—
463C3⋊Dic3—22no—
464C3⋊Dic3—22no—
465C3⋊Dic3—41no—
466C3⋊Dic3—41no—
467C3×Dic3—22no—
468C3×Dic3—41no—
469C3×Dic3—41no—
470C3×Dic3—41no—
471C3×Dic3#12114yes—
472C22×D4—31no—
473C22×D4—91no—
474C22×D4—91no—
475C23×C4—31no—
476C23×C4—31no—
477C23×C4—91no—
478C4×D4—64no—
479C4×D4—184no—
480C4×D4—184no—
481#117—184no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4D3211yescharacteristic
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C42—31no—
502C2×C42—91no—
503C2×C42—91no—
504C2×C42—91no—
505#95—31no—
506#95—91no—
507#95—91no—
508#95—91no—
509#95—91no—
510#95—91no—
511C23×C3—21no—
512C23×C3—32no—
513C23×C3—32no—
514C23×C3—32no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3C23×D311yescharacteristic
534C23×C3C23×D311yescharacteristic
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3#23512yes—
554C22×D3#23912yes—
555C22×D3C2×#6712yes—
556C3×D4—68no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—68no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—124no—
597C2×C3×C4#23512yes—
598C2×C3×C4D3×D412yes—
599C2×C3×C4#23712yes—
600C2×C3×C4C2×#6712yes—
601#67—68no—
602#67—68no—
603#67—68no—
604#67—68no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—62no—
621C2×Dic3—62no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3—124no—
653C2×Dic3D3×D412yes—
654C2×Dic3D3×D412yes—
655C2×Dic3#23712yes—
656C2×Dic3C2×#6712yes—
657D12—28no—
658C4×D3—28no—
659C4×D3—44no—
660C4×D3—124no—
661C2×C32C2×#12111yescharacteristic
662C2×C32#52511yescharacteristic
663C2×C32#52511yescharacteristic
664C2×C32#52511yescharacteristic
665C2×C32#52911yescharacteristic
666C2×C32#52911yescharacteristic
667C2×C32#53211yescharacteristic
668C3×D3—42no—
669C3×D3—42no—
670C3×D3—42no—
671C24—31no—
672C24—31no—
673C24—31no—
674C2×D4—62no—
675C2×D4—62no—
676C2×D4—62no—
677C2×D4—182no—
678C2×D4—182no—
679C2×D4—182no—
680C2×D4—182no—
681C2×D4—182no—
682C2×D4—182no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—34no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—91no—
698C22×C4—182no—
699C22×C4—182no—
700C22×C4—182no—
701C22×C4C2×D3211yescharacteristic
702C22×C4C2×D3211yescharacteristic
703C22×C4C2×D3211yescharacteristic
704C4⋊C4—22no—
705C4⋊C4—62no—
706C4⋊C4—62no—
707C4⋊C4—182no—
708C4⋊C4—182no—
709C4⋊C4—182no—
710C4⋊C4—182no—
711C22⋊C4—62no—
712C22⋊C4—62no—
713C22⋊C4—62no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—182no—
717C22⋊C4—182no—
718C22⋊C4—182no—
719C22⋊C4—182no—
720C22⋊C4—182no—
721C22⋊C4—182no—
722C22⋊C4—182no—
723C42—62no—
724C42—94no—
725C42—182no—
726C42—182no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3C2×#23511yescharacteristic
756C22×C3C2×#23511yescharacteristic
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×#23711yescharacteristic
761C22×C3C2×#23711yescharacteristic
762C22×C3C2×#23911yescharacteristic
763C22×C3D3×#4111yescharacteristic
764C22×C3D3×#4111yescharacteristic
765C22×C3D3×#4111yescharacteristic
766C22×C3D3×#4111yescharacteristic
767C22×C3D3×#4111yescharacteristic
768C22×C3C22×#6711yescharacteristic
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C3×C4—22no—
791C3×C4—22no—
792C3×C4—22no—
793C3×C4—22no—
794C3×C4—34no—
795C3×C4—42no—
796C3×C4—42no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—62no—
800C3×C4—81no—
801C3×C4—121no—
802C3×C4—121no—
803C3×C4—121no—
804Dic3—22no—
805Dic3—41no—
806Dic3—41no—
807Dic3—41no—
808Dic3—62no—
809Dic3—62no—
810Dic3—62no—
811Dic3—62no—
812Dic3—122no—
813Dic3—122no—
814Dic3—121no—
815Dic3—121no—
816Dic3—121no—
817Dic3—121no—
818Dic3—241no—
819Dic3—241no—
820Dic3#93914yes—
821C32#239211yescharacteristic, complemented, Sylow
822C23—32no—
823C23—32no—
824C23—32no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23C22×D3211yescharacteristic
844D4—68no—
845D4—188no—
846D4—188no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—68no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—92no—
871C2×C4—92no—
872C2×C4—124no—
873C2×C4—181no—
874C2×C4—181no—
875C2×C4—181no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—364no—
884C2×C4#379512yes—
885C2×C4D3×#6712yes—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—122no—
894C2×C3—122no—
895C2×C3—122no—
896C2×C3#553811yescharacteristic
897C2×C3#554711yescharacteristic
898C2×C3#554811yescharacteristic
899C2×C3#555711yescharacteristic
900C2×C3#559611yescharacteristic
901C2×C3D3×#12111yescharacteristic
902C2×C3#560611yescharacteristic
903C2×C3#562411yescharacteristic
904C2×C3#562711yescharacteristic
905C2×C3#562711yescharacteristic
906C2×C3#570611yescharacteristic
907C2×C3#579111yescharacteristic
908C2×C3C2×#93911yescharacteristic
909C2×C3#582811yescharacteristic
910D3—42no—
911D3—42no—
912D3—42no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22—62no—
921C22—62no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22C2×#379511yescharacteristic
935C22D3×#23511yescharacteristic
936C22D32×D411yescharacteristic
937C22D3×#23711yescharacteristic
938C22D3×#23911yescharacteristic
939C22#6431911yescharacteristic
940C22C2×D3×#6711yescharacteristic
941C4—22no—
942C4—22no—
943C4—34no—
944C4—41no—
945C4—62no—
946C4—121no—
947C4—121no—
948C4—121no—
949C4—182no—
950C4—182no—
951C4—361no—
952C4—361no—
953C3—21no—
954C3#7728111yescharacteristic, complemented
955C3#8234511yescharacteristic, complemented
956C2—122no—
957C2—122no—
958C2—122no—
959C2#1059436711yescharacteristic
960C2#1059440511yescharacteristic
961C2#1059444411yescharacteristic
962C2#1059462311yescharacteristic
963C2#1059489211yescharacteristic
964C2D3×#93911yescharacteristic
965C2#1059542411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radical#10591389C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2392
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
2. C2×#63879C2semidirect
3. C2×#63879C2semidirect
4. C2×#63841C2semidirect
5. #10592681C2semidirect
6. C3×#4994C2semidirect
7. #10591394C2semidirect
8. #10591390C2semidirect
10. Dic3×(C2×D3)⋊C4C2semidirect
11. #10591308C2semidirect
12. #10591300C2semidirect
13. #10591298C2semidirect
14. Dic3×Dic3⋊C4C2semidirect
15. #10591237C2semidirect
61. C2×#893D3semidirect
70. #4994D3semidirect
111. C2×C3×C4×D3D4semidirect
143. Dic32D4semidirect
381. C2×C4×D3#67semidirect
821. C32#2392semidirect
954. C3#77281semidirect
955. C3#82345semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#638792
C2×#638412
#105926812
C3×#49942
#105913942
#105913902
#105913892
Dic3×(C2×D3)⋊C42
#105913082
#105913002
#105912982
Dic3×Dic3⋊C42
#105912372
#823453
#772813