Finite Group Databasebeta

← #11808451

Subgroups — #11808451

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic, complemented
2C2×#63904C211yesmaximal, characteristic, complemented
3C2×#63880C211yesmaximal, characteristic, complemented
4C2×#63879C211yesmaximal, characteristic, complemented
5#10592693C211yesmaximal, characteristic, complemented
6C3×#4994C211yesmaximal, characteristic, complemented
7#10591394C211yesmaximal, characteristic, complemented
8#10591393C211yesmaximal, characteristic
9#10591392C211yesmaximal, characteristic, complemented
10#10591392C211yesmaximal, characteristic, complemented
11Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#10591342C211yesmaximal, characteristic, complemented
13#10591297C211yesmaximal, characteristic, complemented
14Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16#82273—31nomaximal
17#77281—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×#626C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C3×#892—24no—
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48#63904—24no—
49#63880—24no—
50#63879—24no—
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×#117—31no—
58C2×C4×#67—31no—
59C2×C4×#67—31no—
60C2×#893—31no—
61C2×#892D311yescharacteristic, complemented
62C2×#67⋊C4—31no—
63C2×#67⋊C4—31no—
64C2×C4×D12—31no—
65C3×#396—31no—
66#4994—31no—
67#4994—31no—
68#4994—61no—
69#4994D311yescharacteristic, complemented
70#4991—31no—
71#4991—31no—
72#4982—31no—
73#4981—31no—
74Dic3×C4⋊C4—31no—
75#4961—31no—
76#4961—31no—
77#4961—31no—
78#4961—31no—
79#4960—31no—
80#4960—31no—
81#4953—31no—
82Dic3×C22⋊C4—31no—
83C4×(C2×D3)⋊C4—31no—
84C4×(C2×D3)⋊C4—31no—
85C4×C4⋊Dic3—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×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3D414yescomplemented
106C2×#626—22no—
107C2×#626—22no—
108C2×#626—22no—
109C2×#626—22no—
110C2×#626—22no—
111C2×#626—22no—
112C2×#625—22no—
113C2×#625—22no—
114C2×#625—22no—
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C32×C4⋊C4—22no—
122#3752—22no—
123#3752—22no—
124#3752—22no—
125C4⋊(C3⋊Dic3)—22no—
126#3750—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×C4⋊Dic3—22no—
133C3×C4⋊Dic3—22no—
134C3×Dic3⋊C4—22no—
135C3×C4×Dic3—22no—
136C3×C4×Dic3D414yescomplemented
137Dic3⋊Dic3—22no—
138#3722—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142Dic32—22no—
143Dic32—22no—
144#2392—91noSylow
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C23×Dic3—31no—
151C22×D12—31no—
152C22×D12—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3C2×D311yescharacteristic
157C3×#117—64no—
158C2×C3×C4⋊C4—21no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4C2×D311yescharacteristic
163C2×C3×C4⋊C4C2×D311yescharacteristic
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C42—31no—
170C2×C3×C42—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C4×#67—64no—
175C4×#67—64no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
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)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—61no—
188C2×(C2×D3)⋊C4—61no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×(C2×D3)⋊C4C2×D311yescharacteristic
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—61no—
199C2×C4⋊Dic3C2×D311yescharacteristic
200C2×C4⋊Dic3C2×D311yescharacteristic
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—61no—
205C2×Dic3⋊C4C2×D311yescharacteristic
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3C2×D311yescharacteristic
211C2×C4×Dic3C2×D311yescharacteristic
212#893—64no—
213#892—24no—
214#67⋊C4—64no—
215#67⋊C4—64no—
216C4×D12—64no—
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—31no—
227C3⋊#95—31no—
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#4112yes—
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×D3—21no—
250C22×C3×D3C2×D412yes—
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×C4C2×D412yes—
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#4112yes—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D412yes—
284C2×C3×Dic3C2×D412yes—
285C2×C3×Dic3C2×D412yes—
286C2×C3×Dic3#4112yes—
287C2×C3×Dic3#4112yes—
288C3×C4×D3—28no—
289#626—28no—
290#626—28no—
291#625—28no—
292#624—44no—
293D3×Dic3—44no—
294C2×C4×D4—91no—
295C2×C4×D4—91no—
296C2×C4×D4—91no—
297C2×#117—31no—
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—
311C23×D3—31no—
312C23×D3—31no—
313C23×D3—61no—
314C23×D3C22×D311yescharacteristic
315C23×D3C22×D311yescharacteristic
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—34no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—62no—
327C22×C3×C4—62no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C2×#67—62no—
335C2×#67—62no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—62no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—62no—
356C22×Dic3—62no—
357C22×Dic3—62no—
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C2×D12—62no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—62no—
368C2×D12—62no—
369C2×D12—62no—
370C2×C4×D3—22no—
371C2×C4×D3—22no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3D1214yescomplemented
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—42no—
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C4⋊C4—62no—
388C3×C22⋊C4—62no—
389C3×C22⋊C4—62no—
390C3×C22⋊C4—62no—
391C3×C22⋊C4—62no—
392C3×C22⋊C4—62no—
393C3×C42—34no—
394C3×C42—62no—
395#217—62no—
396#217—62no—
397#217—62no—
398(C2×D3)⋊C4—22no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—22no—
401(C2×D3)⋊C4—22no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
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—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—122no—
415(C2×D3)⋊C4—122no—
416(C2×D3)⋊C4—122no—
417C4⋊Dic3—22no—
418C4⋊Dic3—22no—
419C4⋊Dic3—62no—
420C4⋊Dic3—62no—
421C4⋊Dic3—62no—
422C4⋊Dic3—122no—
423Dic3⋊C4—22no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—122no—
428C4×Dic3—22no—
429C4×Dic3—62no—
430C4×Dic3—62no—
431C4×Dic3—62no—
432C4×Dic3—62no—
433C4×Dic3#6714yescomplemented
434C22×C32C22×D411yescharacteristic
435C22×C32C22×D411yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32C2×#4111yescharacteristic
438C22×C32C2×#4111yescharacteristic
439C22×C32C2×#4111yescharacteristic
440C22×C32C2×#4111yescharacteristic
441C2×C3⋊D3—22no—
442C2×C3⋊D3—22no—
443C2×C3⋊D3—22no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3⋊D3—41no—
447C2×C3⋊D3—41no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—22no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—41no—
465C3⋊Dic3—22no—
466C3⋊Dic3—41no—
467C3⋊Dic3—41no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3#12114yes—
474C22×D4—91no—
475C22×D4—91no—
476C22×D4—91no—
477C23×C4—31no—
478C23×C4—91no—
479C23×C4—91no—
480C4×D4—184no—
481C4×D4—184no—
482C4×D4—184no—
483#117—64no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4D3211yescharacteristic
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C42—31no—
504C2×C42—31no—
505C2×C42—91no—
506C2×C42—91no—
507#95—31no—
508#95—91no—
509#95—91no—
510#95—91no—
511#95—91no—
512#95—91no—
513C23×C3—21no—
514C23×C3—32no—
515C23×C3—32no—
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×C3C23×D311yescharacteristic
529C23×C3C23×D311yescharacteristic
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—32no—
543C22×D3—32no—
544C22×D3—62no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3—121no—
562C22×D3—121no—
563C22×D3C2×D1212yes—
564C22×D3#23912yes—
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—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—68no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4C2×D1212yes—
608C2×C3×C4D3×D412yes—
609C2×C3×C4D3×D412yes—
610C2×C3×C4C2×#6712yes—
611#67—68no—
612#67—68no—
613#67—68no—
614#67—68no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—32no—
629C2×Dic3—32no—
630C2×Dic3—62no—
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—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3—124no—
656C2×Dic3C2×D1212yes—
657C2×Dic3#23512yes—
658C2×Dic3#23712yes—
659C2×Dic3C2×#6712yes—
660C2×Dic3C2×#6712yes—
661D12—68no—
662D12—68no—
663C4×D3—28no—
664C4×D3—124no—
665C4×D3—124no—
666C4×D3—124no—
667C2×C32C2×#12111yescharacteristic
668C2×C32#52511yescharacteristic
669C2×C32#52511yescharacteristic
670C2×C32#52511yescharacteristic
671C2×C32#52911yescharacteristic
672C2×C32#52911yescharacteristic
673C2×C32#53211yescharacteristic
674C3⋊D3—42no—
675C3×D3—42no—
676C3×D3—42no—
677C24—31no—
678C24—31no—
679C24—91no—
680C2×D4—182no—
681C2×D4—182no—
682C2×D4—182no—
683C2×D4—182no—
684C2×D4—182no—
685C2×D4—182no—
686C2×D4—182no—
687C2×D4—182no—
688C2×D4—182no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—34no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—91no—
699C22×C4—91no—
700C22×C4—91no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4—182no—
704C22×C4—182no—
705C22×C4—182no—
706C22×C4—182no—
707C22×C4C2×D3211yescharacteristic
708C22×C4C2×D3211yescharacteristic
709C22×C4C2×D3211yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—62no—
712C4⋊C4—62no—
713C4⋊C4—62no—
714C4⋊C4—182no—
715C4⋊C4—182no—
716C4⋊C4—182no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C22⋊C4—62no—
721C22⋊C4—62no—
722C22⋊C4—182no—
723C22⋊C4—182no—
724C22⋊C4—182no—
725C22⋊C4—182no—
726C22⋊C4—182no—
727C22⋊C4—182no—
728C22⋊C4—182no—
729C42—34no—
730C42—62no—
731C42—182no—
732C42—182no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—62no—
745C22×C3—62no—
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×C3C22×D1211yescharacteristic
755C22×C3C2×#23511yescharacteristic
756C22×C3C2×D3×D411yescharacteristic
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C2×#23711yescharacteristic
759C22×C3C2×#23911yescharacteristic
760C22×C3D3×#4111yescharacteristic
761C22×C3D3×#4111yescharacteristic
762C22×C3D3×#4111yescharacteristic
763C22×C3D3×#4111yescharacteristic
764C22×C3D3×#4111yescharacteristic
765C22×C3D3×#4111yescharacteristic
766C22×C3D3×#4111yescharacteristic
767C22×C3C22×#6711yescharacteristic
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—122no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—241no—
800C2×D3—241no—
801C2×D3—241no—
802C2×D3—241no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—34no—
808C3×C4—42no—
809C3×C4—42no—
810C3×C4—41no—
811C3×C4—41no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—81no—
815C3×C4—121no—
816C3×C4—121no—
817C3×C4—121no—
818Dic3—22no—
819Dic3—22no—
820Dic3—41no—
821Dic3—41no—
822Dic3—41no—
823Dic3—62no—
824Dic3—62no—
825Dic3—122no—
826Dic3—121no—
827Dic3—121no—
828Dic3—121no—
829Dic3—121no—
830Dic3—241no—
831Dic3—241no—
832Dic3#93014yes—
833C32#239211yescharacteristic, complemented, Sylow
834C23—32no—
835C23—32no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—92no—
849C23—181no—
850C23—181no—
851C23—181no—
852C23—181no—
853C23—181no—
854C23—181no—
855C23C22×D3211yescharacteristic
856D4—188no—
857D4—188no—
858D4—188no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—32no—
869C2×C4—32no—
870C2×C4—32no—
871C2×C4—68no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—92no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—364no—
895C2×C4—364no—
896C2×C4D3×D1212yes—
897C2×C4D3×#6712yes—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—122no—
906C2×C3—122no—
907C2×C3#552411yescharacteristic
908C2×C3#552411yescharacteristic
909C2×C3#552811yescharacteristic
910C2×C3#552811yescharacteristic
911C2×C3#559611yescharacteristic
912C2×C3D3×#12111yescharacteristic
913C2×C3#560611yescharacteristic
914C2×C3#562411yescharacteristic
915C2×C3#562711yescharacteristic
916C2×C3#562711yescharacteristic
917C2×C3#570611yescharacteristic
918C2×C3C2×#93011yescharacteristic
919C2×C3#582811yescharacteristic
920C2×C3#583211yescharacteristic
921D3—42no—
922D3—42no—
923D3—122no—
924D3—122no—
925D3—242no—
926C22—62no—
927C22—62no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—62no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22—121no—
937C22—121no—
938C22—121no—
939C22—121no—
940C22—182no—
941C22—182no—
942C22—182no—
943C22—361no—
944C22—361no—
945C22—361no—
946C22—361no—
947C22C2×D3×D1211yescharacteristic
948C22D3×#23511yescharacteristic
949C22D3×#23711yescharacteristic
950C22#6431211yescharacteristic
951C22D3×#23911yescharacteristic
952C22#6431911yescharacteristic
953C22C2×D3×#6711yescharacteristic
954C4—22no—
955C4—22no—
956C4—34no—
957C4—41no—
958C4—62no—
959C4—62no—
960C4—121no—
961C4—121no—
962C4—121no—
963C4—182no—
964C4—361no—
965C4—361no—
966C3—21no—
967C3#7728111yescharacteristic, complemented
968C3#8227311yescharacteristic, complemented
969C2—122no—
970C2—122no—
971C2—362no—
972C2#1059440211yescharacteristic
973C2#1059441711yescharacteristic
974C2#1059462611yescharacteristic
975C2#1059462711yescharacteristic
976C2D3×#93011yescharacteristic
977C2#1059515511yescharacteristic
978C2#1059542411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radical#10591393C2
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×#892C2semidirect
2. C2×#63904C2semidirect
3. C2×#63880C2semidirect
4. C2×#63879C2semidirect
5. #10592693C2semidirect
6. C3×#4994C2semidirect
7. #10591394C2semidirect
9. #10591392C2semidirect
10. #10591392C2semidirect
11. Dic3×(C2×D3)⋊C4C2semidirect
12. #10591342C2semidirect
13. #10591297C2semidirect
14. Dic3×C4⋊Dic3C2semidirect
15. #10591233C2semidirect
61. C2×#892D3semidirect
69. #4994D3semidirect
105. C2×C3×C4×D3D4semidirect
136. C3×C4×Dic3D4semidirect
381. C2×C4×D3D12semidirect
433. C4×Dic3#67semidirect
833. C32#2392semidirect
967. C3#77281semidirect
968. C3#82273semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×#639042
C2×#638802
C2×#638792
#105926932
C3×#49942
#105913942
#105913932
#105913922
Dic3×(C2×D3)⋊C42
#105913422
#105912972
Dic3×C4⋊Dic32
#105912332
#822733
#772813