Finite Group Databasebeta

← #11803618

Subgroups — #11803618

Order 1152.

1431 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic, complemented
2C2×#63906C211yesmaximal, characteristic
3C2×#63880C211yesmaximal, characteristic, complemented
4#10592689C211yesmaximal, characteristic, complemented
5C3×#4990C211yesmaximal, characteristic, complemented
6#10591385C211yesmaximal, characteristic, complemented
7#10591383C211yesmaximal, characteristic, complemented
8#10591383C211yesmaximal, characteristic, complemented
9#10591378C211yesmaximal, characteristic, complemented
10#10591377C211yesmaximal, characteristic, complemented
11#10591363C211yesmaximal, characteristic, complemented
12C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
13#10591327C211yesmaximal, characteristic, complemented
14#10591295C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#82236—31nomaximal
17#75461—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⋊Dic3C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C3×#892—24no—
39C2×#3724C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48#63906C418yescomplemented
49#63880—24no—
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×#117—31no—
57C2×#930—31no—
58C2×#892D311yescharacteristic, complemented
59C2×#884—31no—
60C2×#67⋊C4—31no—
61C2×C4×D12—31no—
62C3×#388—31no—
63#5212—31no—
64#4990—31no—
65#4990—31no—
66#4990—61no—
67#4990D311yescharacteristic, complemented
68#4989—31no—
69#4989—31no—
70#4958—31no—
71#4957—31no—
72#4957—31no—
73#4957—31no—
74#4957—31no—
75#4956—31no—
76#4956—31no—
77#4950—31no—
78#4939—31no—
79#4939—31no—
80C4×C4⋊Dic3—31no—
81C4×Dic3⋊C4—31no—
82#4928—31no—
83#4668—31no—
84#4667—31no—
85#4665—31no—
86#4647—31no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3C2×C414yescomplemented
105C2×#626—22no—
106C2×#626—22no—
107C2×#626—41no—
108C2×#626—41no—
109C2×#626C2×C414yes—
110C2×#626C2×C414yescomplemented
111C2×#625—41no—
112C2×#625—41no—
113C2×#625C2×C414yescomplemented
114C2×#624—22no—
115C2×#624—41no—
116C2×#624—41no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—41no—
119C2×D3×Dic3—41no—
120C32×C4⋊C4—22no—
121#3752—22no—
122#3752—41no—
123#3752C2×C414yescomplemented
124C4×C3⋊Dic3—41no—
125C3×(C2×D3)⋊C4—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—41no—
129C3×(C2×D3)⋊C4C2×C414yescomplemented
130C3×C4⋊Dic3—22no—
131C3×C4×Dic3—22no—
132C3×C4×Dic3—41no—
133C3×C4×Dic3D414yescomplemented
134#3724—41no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—41no—
138Dic3⋊Dic3C2×C414yescomplemented
139#3722—41no—
140(C2×D3)⋊Dic3—41no—
141(C2×D3)⋊Dic3—41no—
142(C2×D3)⋊Dic3—41no—
143#2324—91noSylow
144C23×C3×C4—31no—
145C22×#67—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C23×Dic3—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3C2×D311yescharacteristic
156C3×#117—64no—
157C2×C3×C4⋊C4—21no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4C2×D311yescharacteristic
160C2×C3×C4⋊C4C2×D311yescharacteristic
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C42—31no—
167C2×C3×C42—31no—
168C2×C3×C42—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172#930—38no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
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—61no—
185C2×(C2×D3)⋊C4—61no—
186C2×(C2×D3)⋊C4—61no—
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3C2×D311yescharacteristic
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—61no—
206C2×C4×Dic3C2×D311yescharacteristic
207C2×C4×Dic3C2×D311yescharacteristic
208C2×C4×Dic3C2×D311yescharacteristic
209#892—24no—
210#884—38no—
211#67⋊C4—64no—
212C4×D12—64no—
213C3×#95—31no—
214C3×#95—31no—
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—61no—
224C3⋊#95—61no—
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C23×C32C2411yescharacteristic
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3C22×C412yes—
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×D3C22×C412yes—
248C22×C3×D3C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C22×C412yes—
257C2×C32×C4C2×D412yes—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C22×C412yes—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
281C2×C3×Dic3C22×C412yes—
282C2×C3×Dic3C2×D412yes—
283C2×C3×Dic3C2×D412yes—
284C2×C3×Dic3#4112yes—
285C3×C4×D3—28no—
286#626—28no—
287#626—44no—
288#625—44no—
289#624—44no—
290D3×Dic3—44no—
291C2×#121—91no—
292C2×C4×D4—91no—
293C2×#117—31no—
294#390—91no—
295#390—91no—
296#390—91no—
297#389—91no—
298#388—31no—
299#388—91no—
300#386—91no—
301#386—91no—
302#385—91no—
303#385—91no—
304#380—91no—
305C4×C4⋊C4—91no—
306C24×C3—31no—
307C24×C3—31no—
308C23×D3—31no—
309C23×D3—31no—
310C23×D3—61no—
311C23×D3C22×D311yescharacteristic
312C23×D3C22×D311yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—34no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—62no—
324C22×C3×C4—62no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C2×#67—34no—
332C2×#67—34no—
333C2×#67—34no—
334C2×#67—34no—
335C2×#67—62no—
336C2×#67—62no—
337C2×#67—121no—
338C2×#67—121no—
339C2×#67—121no—
340C2×#67—121no—
341C2×#67—121no—
342C2×#67—121no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—62no—
353C22×Dic3—121no—
354C22×Dic3—121no—
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C2×D12—34no—
362C2×D12—34no—
363C2×D12—62no—
364C2×D12—62no—
365C2×D12—121no—
366C2×D12—121no—
367C2×C4×D3—22no—
368C2×C4×D3—22no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—121no—
373C2×C4×D3—121no—
374C2×C4×D3—121no—
375C2×C4×D3—121no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3C4×D314yescomplemented
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—42no—
382C3×C4⋊C4—62no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—62no—
385C3×C22⋊C4—62no—
386C3×C22⋊C4—62no—
387C3×C22⋊C4—121no—
388C3×C42—34no—
389C3×C42—62no—
390C3×C42—121no—
391#217—121no—
392#217—121no—
393#217—121no—
394(C2×D3)⋊C4—22no—
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4—34no—
398(C2×D3)⋊C4—34no—
399(C2×D3)⋊C4—41no—
400(C2×D3)⋊C4—64no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—122no—
404(C2×D3)⋊C4—121no—
405(C2×D3)⋊C4—121no—
406(C2×D3)⋊C4—121no—
407(C2×D3)⋊C4—121no—
408(C2×D3)⋊C4—122no—
409(C2×D3)⋊C4—121no—
410(C2×D3)⋊C4—121no—
411(C2×D3)⋊C4—121no—
412(C2×D3)⋊C4C4×D314yescomplemented
413C4⋊Dic3—22no—
414C4⋊Dic3—34no—
415C4⋊Dic3—62no—
416C4⋊Dic3—62no—
417C4⋊Dic3—121no—
418Dic3⋊C4—34no—
419Dic3⋊C4—62no—
420Dic3⋊C4—62no—
421Dic3⋊C4—121no—
422Dic3⋊C4—121no—
423Dic3⋊C4—121no—
424C4×Dic3—22no—
425C4×Dic3—41no—
426C4×Dic3—121no—
427C4×Dic3—121no—
428C4×Dic3—122no—
429C4×Dic3#6714yescomplemented
430C22×C32C23×C411yescharacteristic
431C22×C32C22×D411yescharacteristic
432C22×C32C2×#4111yescharacteristic
433C22×C32H(5,𝔽2)11yescharacteristic
434C22×C32H(5,𝔽2)11yescharacteristic
435C22×C32H(5,𝔽2)11yescharacteristic
436C22×C322−1+411yescharacteristic
437C2×C3⋊D3—22no—
438C2×C3⋊D3—22no—
439C2×C3⋊D3—22no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—22no—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
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—
458C32×C4—22no—
459C32×C4—22no—
460C32×C4—41no—
461C3⋊Dic3—22no—
462C3⋊Dic3—41no—
463C3⋊Dic3—41no—
464C3×Dic3—22no—
465C3×Dic3—22no—
466C3×Dic3—41no—
467C3×Dic3—41no—
468C3×Dic3—41no—
469C3×Dic3C4×D414yes—
470C22×D4—91no—
471C22×D4—91no—
472C22×D4—91no—
473C23×C4—31no—
474C23×C4—91no—
475C23×C4—91no—
476#121—98no—
477C4×D4—184no—
478#117—64no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—91no—
481C2×C4⋊C4—91no—
482C2×C4⋊C4—91no—
483C2×C4⋊C4—91no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4D3211yescharacteristic
486C2×C22⋊C4—31no—
487C2×C22⋊C4—31no—
488C2×C22⋊C4—31no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—91no—
492C2×C22⋊C4—91no—
493C2×C22⋊C4—91no—
494C2×C22⋊C4—91no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C42—31no—
499C2×C42—31no—
500C2×C42—31no—
501C2×C42—91no—
502#95—31no—
503#95—31no—
504#95—91no—
505#95—91no—
506#95—91no—
507#95—91no—
508C23×C3—21no—
509C23×C3—32no—
510C23×C3—32no—
511C23×C3—61no—
512C23×C3—61no—
513C23×C3—61no—
514C23×C3—61no—
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×C3C23×D311yescharacteristic
524C23×C3C23×D311yescharacteristic
525C22×D3—21no—
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—32no—
538C22×D3—32no—
539C22×D3—62no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—121no—
553C22×D3—121no—
554C22×D3—121no—
555C22×D3—121no—
556C22×D3—121no—
557C22×D3—121no—
558C22×D3C2×C4×D312yes—
559C22×D3C2×C4×D312yes—
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—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—68no—
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—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4C2×C4×D312yes—
603C2×C3×C4C2×C4×D312yes—
604C2×C3×C4D3×D412yes—
605C2×C3×C4C2×#6712yes—
606#67—68no—
607#67—124no—
608#67—124no—
609#67—124no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
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—32no—
624C2×Dic3—32no—
625C2×Dic3—62no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
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—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—124no—
651C2×Dic3C2×C4×D312yes—
652C2×Dic3C2×C4×D312yes—
653C2×Dic3#23512yes—
654C2×Dic3C2×#6712yes—
655C2×Dic3C2×#6712yes—
656D12—68no—
657D12—124no—
658C4×D3—28no—
659C4×D3—124no—
660C4×D3—124no—
661C4×D3—124no—
662C2×C32C2×C4×D411yescharacteristic
663C2×C32#51811yescharacteristic
664C2×C32#52011yescharacteristic
665C2×C32#53511yescharacteristic
666C2×C32#53711yescharacteristic
667C2×C32#54011yescharacteristic
668C2×C32#54211yescharacteristic
669C3⋊D3—42no—
670C3×D3—42no—
671C3×D3—42no—
672C24—31no—
673C24—31no—
674C24—91no—
675C2×D4—94no—
676C2×D4—94no—
677C2×D4—94no—
678C2×D4—182no—
679C2×D4—182no—
680C2×D4—361no—
681C2×D4—361no—
682C2×D4—361no—
683C2×D4—361no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—34no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—91no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—182no—
697C22×C4—182no—
698C22×C4—361no—
699C22×C4—361no—
700C22×C4—361no—
701C22×C4—361no—
702C22×C4C2×D3211yescharacteristic
703C22×C4C2×D3211yescharacteristic
704C22×C4C2×D3211yescharacteristic
705C4⋊C4—22no—
706C4⋊C4—62no—
707C4⋊C4—94no—
708C4⋊C4—182no—
709C4⋊C4—182no—
710C4⋊C4—361no—
711C4⋊C4—361no—
712C22⋊C4—34no—
713C22⋊C4—62no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—94no—
717C22⋊C4—121no—
718C22⋊C4—182no—
719C22⋊C4—361no—
720C22⋊C4—361no—
721C22⋊C4—361no—
722C22⋊C4—361no—
723C22⋊C4—361no—
724C42—34no—
725C42—62no—
726C42—121no—
727C42—361no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3C22×C4×D311yescharacteristic
750C22×C3C22×C4×D311yescharacteristic
751C22×C3C2×#23511yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C22×C3#100411yescharacteristic
754C22×C3D3×#4111yescharacteristic
755C22×C3#100911yescharacteristic
756C22×C3#100911yescharacteristic
757C22×C3#100911yescharacteristic
758C22×C3#100911yescharacteristic
759C22×C3#100911yescharacteristic
760C22×C3#101011yescharacteristic
761C22×C3#101011yescharacteristic
762C22×C3C22×#6711yescharacteristic
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—22no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—62no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—62no—
781C2×D3—62no—
782C2×D3—62no—
783C2×D3—122no—
784C2×D3—122no—
785C2×D3—122no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—241no—
795C2×D3—241no—
796C2×D3—241no—
797C2×D3—241no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—34no—
803C3×C4—42no—
804C3×C4—42no—
805C3×C4—41no—
806C3×C4—41no—
807C3×C4—62no—
808C3×C4—62no—
809C3×C4—81no—
810C3×C4—121no—
811C3×C4—121no—
812C3×C4—121no—
813Dic3—22no—
814Dic3—22no—
815Dic3—41no—
816Dic3—41no—
817Dic3—41no—
818Dic3—62no—
819Dic3—62no—
820Dic3—122no—
821Dic3—122no—
822Dic3—121no—
823Dic3—121no—
824Dic3—121no—
825Dic3—121no—
826Dic3—241no—
827Dic3C4×#6714yes—
828C32#232411yescharacteristic, complemented, Sylow
829C23—32no—
830C23—32no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—92no—
844C23—181no—
845C23—181no—
846C23—181no—
847C23—181no—
848C23—181no—
849C23—181no—
850C23C22×D3211yescharacteristic
851D4—188no—
852D4—364no—
853D4—364no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—68no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
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—92no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—364no—
890C2×C4—364no—
891C2×C4C4×D3212yes—
892C2×C4D3×#6712yes—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—122no—
901C2×C3—122no—
902C2×C3#552111yescharacteristic
903C2×C3#552311yescharacteristic
904C2×C3#552311yescharacteristic
905C2×C3#553411yescharacteristic
906C2×C3#553511yescharacteristic
907C2×C3C4×D3×D411yescharacteristic
908C2×C3#554511yescharacteristic
909C2×C3#559711yescharacteristic
910C2×C3#566311yescharacteristic
911C2×C3#567411yescharacteristic
912C2×C3#571011yescharacteristic
913C2×C3C2×C4×#6711yescharacteristic
914C2×C3#583011yescharacteristic
915C2×C3#583311yescharacteristic
916D3—42no—
917D3—42no—
918D3—122no—
919D3—122no—
920D3—242no—
921C22—62no—
922C22—62no—
923C22—62no—
924C22—62no—
925C22—62no—
926C22—62no—
927C22—121no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—182no—
936C22—182no—
937C22—182no—
938C22—361no—
939C22—361no—
940C22—361no—
941C22—361no—
942C22C2×C4×D3211yescharacteristic
943C22D3×#23511yescharacteristic
944C22#6430911yescharacteristic
945C22#6431411yescharacteristic
946C22#6432011yescharacteristic
947C22#6432011yescharacteristic
948C22C2×D3×#6711yescharacteristic
949C4—22no—
950C4—22no—
951C4—34no—
952C4—41no—
953C4—62no—
954C4—62no—
955C4—121no—
956C4—121no—
957C4—121no—
958C4—182no—
959C4—361no—
960C4—361no—
961C3—21no—
962C3#7546111yescharacteristic, complemented
963C3#8223611yescharacteristic, complemented
964C2—122no—
965C2—122no—
966C2—362no—
967C2#1059451111yescharacteristic
968C2#1059454611yescharacteristic
969C2#1059454811yescharacteristic
970C2#1059460411yescharacteristic
971C2C4×D3×#6711yescharacteristic
972C2#1059515611yescharacteristic
973C2#1059542611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63906C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2324
LCSG ▷ C22×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
3. C2×#63880C2semidirect
4. #10592689C2semidirect
5. C3×#4990C2semidirect
6. #10591385C2semidirect
7. #10591383C2semidirect
8. #10591383C2semidirect
9. #10591378C2semidirect
10. #10591377C2semidirect
11. #10591363C2semidirect
12. C4×Dic3⋊Dic3C2semidirect
13. #10591327C2semidirect
14. #10591295C2semidirect
15. #10591275C2semidirect
48. #63906C4semidirect
58. C2×#892D3semidirect
67. #4990D3semidirect
104. C2×C3×C4×D3C2×C4semidirect
110. C2×#626C2×C4semidirect
113. C2×#625C2×C4semidirect
123. #3752C2×C4semidirect
129. C3×(C2×D3)⋊C4C2×C4semidirect
133. C3×C4×Dic3D4semidirect
138. Dic3⋊Dic3C2×C4semidirect
378. C2×C4×D3C4×D3semidirect
412. (C2×D3)⋊C4C4×D3semidirect
429. C4×Dic3#67semidirect
828. C32#2324semidirect
962. C3#75461semidirect
963. C3#82236semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×#639062
C2×#638802
#105926892
C3×#49902
#105913852
#105913832
#105913782
#105913772
#105913632
C4×Dic3⋊Dic32
#105913272
#105912952
#105912752
#822363
#754613