Finite Group Databasebeta

← #11803615

Subgroups — #11803615

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×#63906C211yesmaximal, characteristic
2C2×#63904C211yesmaximal, characteristic, complemented
3C2×#63841C211yesmaximal, characteristic, complemented
4#10592369C211yesmaximal, characteristic, complemented
5C3×#4668C211yesmaximal, characteristic, complemented
6C3×#4667C211yesmaximal, characteristic, complemented
7#10591385C211yesmaximal, characteristic, complemented
8#10591384C211yesmaximal, characteristic, complemented
9#10591384C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591378C211yesmaximal, characteristic, complemented
12#10591316C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591246C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#74385—31nomaximal
17#73872—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63906C418yescomplemented
48#63904—24no—
49#63841—24no—
50C32×#95C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#930—31no—
57C2×C4×#67—31no—
58C2×#926—31no—
59C2×#893—31no—
60C2×#892—31no—
61C2×#884—31no—
62C3×#385—31no—
63C3×#380—31no—
64#5213—31no—
65#4989—31no—
66#4988—31no—
67#4988—31no—
68#4976—31no—
69Dic3×C4⋊C4—31no—
70#4972—31no—
71#4957—31no—
72#4957—31no—
73#4957—31no—
74#4957—31no—
75#4956—31no—
76#4956—31no—
77#4951—31no—
78#4670—31no—
79#4670—31no—
80#4670—31no—
81#4670—61no—
82#4668—31no—
83#4668D311yescharacteristic, complemented
84#4667D311yescharacteristic, complemented
85#4665—31no—
86#4649—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×D3—22no—
105C2×C3×C4×D3—41no—
106C2×C3×C4×D3—41no—
107C2×C3×C4×D3C2×C414yescomplemented
108C2×#626—22no—
109C2×#626—22no—
110C2×#626—41no—
111C2×#626—41no—
112C2×#626C2×C414yes—
113C2×#626C2×C414yescomplemented
114C2×#625—41no—
115C2×#625—41no—
116C2×#625C2×C414yescomplemented
117C2×#624—22no—
118C2×#624—41no—
119C2×#624—41no—
120#3752—22no—
121#3752—41no—
122#3752C2×C414yescomplemented
123C4⋊(C3⋊Dic3)—22no—
124C4×C3⋊Dic3—41no—
125C3×(C2×D3)⋊C4—41no—
126C3×(C2×D3)⋊C4—41no—
127C3×(C2×D3)⋊C4—41no—
128C3×(C2×D3)⋊C4C2×C414yescomplemented
129C3×C4⋊Dic3—22no—
130C3×Dic3⋊C4—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—41no—
133#3724—41no—
134Dic3⋊Dic3C2×C414yescomplemented
135#3722—41no—
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—41no—
140Dic32—22no—
141Dic32—41no—
142Dic32D414yescomplemented
143#2324—91noSylow
144C23×C3×C4—31no—
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3C2×D311yescharacteristic
155C22×C4×D3C2×D311yescharacteristic
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168#930—38no—
169C4×#67—64no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
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—61no—
183C2×(C2×D3)⋊C4—61no—
184C2×(C2×D3)⋊C4—61no—
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×(C2×D3)⋊C4C2×D311yescharacteristic
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189#926—64no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—61no—
194C2×C4⋊Dic3C2×D311yescharacteristic
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4C2×D311yescharacteristic
199C2×Dic3⋊C4C2×D311yescharacteristic
200C2×Dic3⋊C4C2×D311yescharacteristic
201C2×C4×Dic3—31no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—61no—
210#893—64no—
211#892—64no—
212#884—38no—
213C3×#95—21no—
214C3×#95—31no—
215C3×#95—31no—
216C3×#95C2×D311yescharacteristic
217C3×#95C2×D311yescharacteristic
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
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×C4—21no—
257C2×C32×C4C22×C412yes—
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⋊Dic3C22×C412yes—
266C2×C3⋊Dic3C2×D412yes—
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—
286C3×C4×D3—44no—
287#626—28no—
288#626—44no—
289#625—44no—
290#624—44no—
291C2×#121—91no—
292C2×C4×D4—91no—
293C2×#117—91no—
294#390—91no—
295#390—91no—
296#390—91no—
297#389—91no—
298#388—91no—
299#388—91no—
300#386—91no—
301#386—91no—
302#385—31no—
303#385—91no—
304#380—31no—
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×C4—62no—
326C22×C3×C4—121no—
327C22×C3×C4—121no—
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—34no—
335C2×#67—34no—
336C2×#67—34no—
337C2×#67—34no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—121no—
341C2×#67—121no—
342C2×#67—121no—
343C2×#67—121no—
344C2×#67—121no—
345C2×#67—121no—
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×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—22no—
370C2×C4×D3—41no—
371C2×C4×D3—41no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—121no—
375C2×C4×D3—121no—
376C2×C4×D3—121no—
377C2×C4×D3—121no—
378C2×C4×D3C4×D314yescomplemented
379C3×C4⋊C4—62no—
380C3×C4⋊C4—62no—
381C3×C4⋊C4—62no—
382C3×C4⋊C4—121no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—121no—
385C3×C22⋊C4—121no—
386C3×C22⋊C4—121no—
387#217—62no—
388#217—62no—
389#217—62no—
390#217—121no—
391(C2×D3)⋊C4—34no—
392(C2×D3)⋊C4—34no—
393(C2×D3)⋊C4—41no—
394(C2×D3)⋊C4—41no—
395(C2×D3)⋊C4—41no—
396(C2×D3)⋊C4—64no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—122no—
403(C2×D3)⋊C4—121no—
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)⋊C4C4×D314yescomplemented
410C4⋊Dic3—22no—
411C4⋊Dic3—34no—
412C4⋊Dic3—62no—
413C4⋊Dic3—62no—
414C4⋊Dic3—122no—
415Dic3⋊C4—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4—34no—
418Dic3⋊C4—41no—
419Dic3⋊C4—121no—
420Dic3⋊C4—121no—
421C4×Dic3—34no—
422C4×Dic3—34no—
423C4×Dic3—62no—
424C4×Dic3—62no—
425C4×Dic3—121no—
426C4×Dic3—121no—
427C4×Dic3—121no—
428C4×Dic3—121no—
429C4×Dic3—122no—
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—41no—
460C32×C4—41no—
461C3⋊Dic3—22no—
462C3⋊Dic3—22no—
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—31no—
475C23×C4—91no—
476#121—98no—
477C4×D4—184no—
478#117—184no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—91no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4—91no—
486C2×C22⋊C4—31no—
487C2×C22⋊C4—31no—
488C2×C22⋊C4—31no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—91no—
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—91no—
499C2×C42—91no—
500C2×C42—91no—
501C2×C42—91no—
502#95—31no—
503#95—31no—
504#95—91no—
505#95—91no—
506#95—91no—
507#95D3211yescharacteristic
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—22no—
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—22no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—68no—
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×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—124no—
605C2×C3×C4C2×C4×D312yes—
606C2×C3×C4C2×C4×D312yes—
607#67—68no—
608#67—124no—
609#67—124no—
610#67—124no—
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—21no—
624C2×Dic3—32no—
625C2×Dic3—32no—
626C2×Dic3—32no—
627C2×Dic3—32no—
628C2×Dic3—62no—
629C2×Dic3—62no—
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—61no—
643C2×Dic3—61no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3C2×C4×D312yes—
652C2×Dic3C2×C4×D312yes—
653C2×Dic3D3×D412yes—
654C2×Dic3D3×D412yes—
655C2×Dic3#23712yes—
656D12—68no—
657D12—124no—
658C4×D3—28no—
659C4×D3—44no—
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—62no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—121no—
698C22×C4—121no—
699C22×C4—182no—
700C22×C4—361no—
701C22×C4—361no—
702C22×C4C2×D3211yescharacteristic
703C22×C4C2×D3211yescharacteristic
704C22×C4C2×D3211yescharacteristic
705C4⋊C4—62no—
706C4⋊C4—62no—
707C4⋊C4—62no—
708C4⋊C4—94no—
709C4⋊C4—121no—
710C4⋊C4—182no—
711C4⋊C4—361no—
712C22⋊C4—34no—
713C22⋊C4—94no—
714C22⋊C4—121no—
715C22⋊C4—121no—
716C22⋊C4—121no—
717C22⋊C4—182no—
718C22⋊C4—182no—
719C22⋊C4—182no—
720C22⋊C4—182no—
721C22⋊C4—361no—
722C22⋊C4—361no—
723C22⋊C4—361no—
724C42—94no—
725C42—182no—
726C42—361no—
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×D3×D411yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C22×C3C2×#23711yescharacteristic
754C22×C3#100411yescharacteristic
755C22×C3#100411yescharacteristic
756C22×C3#100411yescharacteristic
757C22×C3#100711yescharacteristic
758C22×C3#100711yescharacteristic
759C22×C3D3×#4111yescharacteristic
760C22×C3#100911yescharacteristic
761C22×C3#100911yescharacteristic
762C22×C3#100911yescharacteristic
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—34no—
801C3×C4—42no—
802C3×C4—42no—
803C3×C4—41no—
804C3×C4—41no—
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—62no—
821Dic3—62no—
822Dic3—122no—
823Dic3—122no—
824Dic3—121no—
825Dic3—121no—
826Dic3—241no—
827Dic3#67⋊C414yes—
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—21no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—68no—
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—61no—
881C2×C4—92no—
882C2×C4—92no—
883C2×C4—124no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4—364no—
892C2×C4C4×D3212yes—
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×C3C2×#67⋊C411yescharacteristic
903C2×C3#550411yescharacteristic
904C2×C3#550411yescharacteristic
905C2×C3#552111yescharacteristic
906C2×C3C4×D3×D411yescharacteristic
907C2×C3#554511yescharacteristic
908C2×C3#559211yescharacteristic
909C2×C3#560711yescharacteristic
910C2×C3#561911yescharacteristic
911C2×C3#562911yescharacteristic
912C2×C3#562911yescharacteristic
913C2×C3#564011yescharacteristic
914C2×C3#564311yescharacteristic
915C2×C3#566311yescharacteristic
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
943C22#6430711yescharacteristic
944C22#6430811yescharacteristic
945C22D32×D411yescharacteristic
946C22D3×#23711yescharacteristic
947C22#6431311yescharacteristic
948C22#6431611yescharacteristic
949C4—22no—
950C4—34no—
951C4—41no—
952C4—41no—
953C4—62no—
954C4—62no—
955C4—121no—
956C4—121no—
957C4—121no—
958C4—182no—
959C4—182no—
960C4—361no—
961C3—21no—
962C3#7387211yescharacteristic, complemented
963C3#7438511yescharacteristic, complemented
964C2—122no—
965C2—122no—
966C2—362no—
967C2#1059399411yescharacteristic
968C2#1059422011yescharacteristic
969C2D3×#67⋊C411yescharacteristic
970C2#1059426911yescharacteristic
971C2#1059450911yescharacteristic
972C2#1059451911yescharacteristic
973C2#1059455811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63906C2
hypercenter#95D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63904C2semidirect
3. C2×#63841C2semidirect
4. #10592369C2semidirect
5. C3×#4668C2semidirect
6. C3×#4667C2semidirect
7. #10591385C2semidirect
8. #10591384C2semidirect
9. #10591384C2semidirect
10. #10591381C2semidirect
11. #10591378C2semidirect
12. #10591316C2semidirect
13. #10591275C2semidirect
14. #10591246C2semidirect
15. #10591241C2semidirect
47. #63906C4semidirect
83. #4668D3semidirect
84. #4667D3semidirect
107. C2×C3×C4×D3C2×C4semidirect
113. C2×#626C2×C4semidirect
116. C2×#625C2×C4semidirect
122. #3752C2×C4semidirect
128. C3×(C2×D3)⋊C4C2×C4semidirect
134. Dic3⋊Dic3C2×C4semidirect
142. Dic32D4semidirect
378. C2×C4×D3C4×D3semidirect
409. (C2×D3)⋊C4C4×D3semidirect
828. C32#2324semidirect
962. C3#73872semidirect
963. C3#74385semidirect

Maximal subgroups

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

subgroupindex
C2×#639062
C2×#639042
C2×#638412
#105923692
C3×#46682
C3×#46672
#105913852
#105913842
#105913812
#105913782
#105913162
#105912752
#105912462
#105912412
#743853
#738723