Finite Group Databasebeta

← #11803881

Subgroups — #11803881

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1075 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63979C211yesmaximal, characteristic
2C2×#63952C211yesmaximal, characteristic, complemented
3C2×#63879C211yesmaximal, characteristic, complemented
4#10592656C211yesmaximal, characteristic, complemented
5C3×#4958C211yesmaximal, characteristic, complemented
6C3×#4956C211yesmaximal, characteristic, complemented
7#10591721C211yesmaximal, characteristic, complemented
8#10591710C211yesmaximal, characteristic, complemented
9#10591385C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11#10591364C211yesmaximal, characteristic, complemented
12#10591275C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591252C211yesmaximal, characteristic, complemented
15#10591247C211yesmaximal, characteristic, complemented
16#74667—31nomaximal
17#74667—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38#63979C418yescomplemented
39C2×#3724C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46#63952—24no—
47#63879—24no—
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#940—31no—
57C2×#940—31no—
58C2×C4×#67—31no—
59C2×C4×#67—31no—
60C2×#67⋊C4—31no—
61C2×#67⋊C4—31no—
62C3×#386—31no—
63C3×#386—31no—
64#5220—31no—
65#5220—31no—
66#5213—31no—
67#5213—31no—
68#4958—31no—
69#4958D311yescharacteristic, complemented
70#4957—31no—
71#4957—31no—
72#4957—31no—
73#4957—31no—
74#4957—61no—
75#4956—31no—
76#4956—31no—
77#4956—31no—
78#4956D311yescharacteristic, complemented
79#4665—31no—
80#4665—31no—
81#4665—31no—
82#4665—31no—
83#4650—31no—
84#4650—31no—
85#4648—31no—
86#4648—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C2×#638—22no—
94C2×#638—22no—
95C2×#638C2×C414yescomplemented
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C2×C3×#67—41no—
100C2×C3×#67—41no—
101C2×C3×#67—41no—
102C2×C3×#67—41no—
103C2×C3×#67C2×C414yescomplemented
104C2×C3×#67C2×C414yescomplemented
105C22×C3×Dic3—22no—
106C22×C3×Dic3—41no—
107C22×C3×Dic3—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×#626—41no—
118C2×#626—41no—
119C2×#626—41no—
120C2×#626—41no—
121C2×#626C2×C414yescomplemented
122C2×#626C2×C414yescomplemented
123C2×#625—22no—
124C2×#625—22no—
125C2×#625C2×C414yescomplemented
126C2×#624—22no—
127C2×#624—41no—
128C2×#624—41no—
129C2×D3×Dic3—22no—
130C2×D3×Dic3—41no—
131C2×D3×Dic3—41no—
132C32×C22⋊C4—41no—
133#3757—41no—
134#3752—41no—
135#3752—41no—
136#3750—22no—
137C4×C3⋊Dic3—22no—
138C3×#217—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×(C2×D3)⋊C4—41no—
141C3×(C2×D3)⋊C4—41no—
142#3724—22no—
143#3722—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—41no—
146(C2×D3)⋊Dic3—41no—
147Dic32C2×C414yescomplemented
148Dic32D414yescomplemented
149#2328—91noSylow
150C22×C3×D4—31no—
151C22×C3×D4—31no—
152C23×C3×C4—31no—
153C23×C3×C4—31no—
154C22×#67—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—31no—
160C22×#67—61no—
161C22×#67C2×D311yescharacteristic
162C22×#67C2×D311yescharacteristic
163C23×Dic3—31no—
164C23×Dic3C2×D311yescharacteristic
165C22×D12—31no—
166C22×D12—31no—
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C22×C4×D3—31no—
170C22×C4×D3C2×D311yescharacteristic
171C2×C3×C22⋊C4—21no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4C2×D311yescharacteristic
177C2×C3×C22⋊C4C2×D311yescharacteristic
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—61no—
184C2×#217C2×D311yescharacteristic
185#940—38no—
186#940—38no—
187C4×#67—64no—
188C4×#67—64no—
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—61no—
199C2×(C2×D3)⋊C4—61no—
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—61no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3—61no—
215#67⋊C4—64no—
216#67⋊C4—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—31no—
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C3⋊#95C2×D311yescharacteristic
232C3⋊#95C2×D311yescharacteristic
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32C22×C412yes—
240C23×C32C2411yescharacteristic
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×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×D3C22×C412yes—
261C22×C3×D3C22×C412yes—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268#638—28no—
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⋊Dic3C22×C412yes—
276C2×C3⋊Dic3C2×D412yes—
277C2×C3⋊Dic3#4112yes—
278C3×#67—44no—
279C3×#67—44no—
280C2×C3×Dic3—21no—
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×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—44no—
295C2×C3×Dic3C22×C412yes—
296C2×C3×Dic3C22×C412yes—
297C2×C3×Dic3C2×D412yes—
298C2×C3×Dic3C2×D412yes—
299C3×C4×D3—44no—
300#626—44no—
301#626—44no—
302#625—28no—
303#624—44no—
304D3×Dic3—44no—
305C2×#127—91no—
306C2×C4×D4—91no—
307C2×C4×D4—91no—
308#390—91no—
309#390—91no—
310#386—31no—
311#386—31no—
312#386—91no—
313#386—91no—
314#386—91no—
315#386—91no—
316#386—91no—
317#386—91no—
318#382—91no—
319#376—91no—
320C24×C3—21no—
321C24×C3—31no—
322C24×C3—31no—
323C24×C3C22×D311yescharacteristic
324C24×C3C22×D311yescharacteristic
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—61no—
328C23×D3C22×D311yescharacteristic
329C23×D3C22×D311yescharacteristic
330C2×C3×D4—34no—
331C2×C3×D4—34no—
332C2×C3×D4—121no—
333C2×C3×D4—121no—
334C2×C3×D4—121no—
335C2×C3×D4—121no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4—121no—
347C22×C3×C4—121no—
348C22×C3×C4—121no—
349C22×C3×C4—121no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—34no—
357C2×#67—34no—
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—41no—
361C2×#67—41no—
362C2×#67—41no—
363C2×#67—41no—
364C2×#67—64no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—62no—
370C2×#67—62no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—122no—
374C2×#67—122no—
375C2×#67—121no—
376C2×#67—121no—
377C2×#67—121no—
378C2×#67—121no—
379C2×#67C4×D314yescomplemented
380C2×#67C4×D314yescomplemented
381C22×Dic3—22no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—41no—
389C22×Dic3—41no—
390C22×Dic3—61no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—62no—
394C22×Dic3—121no—
395C22×Dic3—121no—
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C2×D12—34no—
403C2×D12—34no—
404C2×D12—121no—
405C2×D12—121no—
406C2×D12—121no—
407C2×D12—121no—
408C2×C4×D3—22no—
409C2×C4×D3—41no—
410C2×C4×D3—41no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—121no—
415C2×C4×D3—121no—
416C2×C4×D3—121no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—121no—
420C3×C22⋊C4—41no—
421C3×C22⋊C4—41no—
422C3×C22⋊C4—42no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—121no—
426C3×C22⋊C4—121no—
427#217—22no—
428#217—62no—
429#217—121no—
430#217—121no—
431#217—121no—
432#217—121no—
433#217—122no—
434(C2×D3)⋊C4—22no—
435(C2×D3)⋊C4—41no—
436(C2×D3)⋊C4—41no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—121no—
441(C2×D3)⋊C4—121no—
442(C2×D3)⋊C4—121no—
443(C2×D3)⋊C4—121no—
444(C2×D3)⋊C4—122no—
445(C2×D3)⋊C4—121no—
446(C2×D3)⋊C4—121no—
447(C2×D3)⋊C4—122no—
448Dic3⋊C4—62no—
449Dic3⋊C4—62no—
450Dic3⋊C4—62no—
451Dic3⋊C4—62no—
452Dic3⋊C4—122no—
453C4×Dic3—34no—
454C4×Dic3—34no—
455C4×Dic3—34no—
456C4×Dic3—34no—
457C4×Dic3—62no—
458C4×Dic3—62no—
459C4×Dic3—122no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32C23×C411yescharacteristic
468C22×C32C22×D411yescharacteristic
469C22×C32C2×#4111yescharacteristic
470C22×C32H(5,𝔽2)11yescharacteristic
471C22×C32H(5,𝔽2)11yescharacteristic
472C22×C32H(5,𝔽2)11yescharacteristic
473C22×C32H(5,𝔽2)11yescharacteristic
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—41no—
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—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C32×C4—41no—
496C32×C4—41no—
497C3⋊Dic3—41no—
498C3⋊Dic3—41no—
499C3⋊Dic3C4×D414yes—
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—22no—
503C3×Dic3—22no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C22×D4—31no—
507C22×D4—31no—
508C22×D4—91no—
509C22×D4—91no—
510C22×D4—91no—
511C22×D4—91no—
512C23×C4—31no—
513C23×C4—31no—
514C23×C4—91no—
515C23×C4—91no—
516#127—98no—
517C4×D4—184no—
518C4×D4—184no—
519C2×C4⋊C4—91no—
520C2×C4⋊C4—91no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—91no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4D3211yescharacteristic
533C2×C42—91no—
534C2×C42—91no—
535C2×C42—91no—
536#95—31no—
537#95—31no—
538#95—31no—
539#95—31no—
540#95—91no—
541#95—91no—
542#95—91no—
543#95—91no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—22no—
558C23×C3—32no—
559C23×C3—32no—
560C23×C3—41no—
561C23×C3—41no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3C2×C4×D312yes—
579C23×C3C2×C4×D312yes—
580C23×C3C23×D311yescharacteristic
581C23×C3C23×D311yescharacteristic
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—32no—
595C22×D3—32no—
596C22×D3—62no—
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—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3C2×C4×D312yes—
616C22×D3C2×C4×D312yes—
617C3×D4—124no—
618C3×D4—124no—
619C2×C3×C4—22no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—124no—
656C2×C3×C4—124no—
657#67—44no—
658#67—44no—
659#67—68no—
660#67—68no—
661#67—68no—
662#67—68no—
663#67—128no—
664#67—124no—
665#67—124no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—44no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—121no—
704C2×Dic3—121no—
705C2×Dic3—121no—
706C2×Dic3—121no—
707C2×Dic3—121no—
708C2×Dic3—124no—
709C2×Dic3C2×C4×D312yes—
710C2×Dic3C2×C4×D312yes—
711C2×Dic3D3×D412yes—
712C2×Dic3D3×D412yes—
713D12—124no—
714D12—124no—
715C4×D3—44no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—124no—
719C2×C32—42no—
720C2×C32C2×C4×D411yescharacteristic
721C2×C32#51811yescharacteristic
722C2×C32#51811yescharacteristic
723C2×C32#53511yescharacteristic
724C2×C32#53511yescharacteristic
725C2×C32#54011yescharacteristic
726C2×C32#54011yescharacteristic
727C3⋊D3—42no—
728C3×D3—42no—
729C3×D3—42no—
730C24—31no—
731C24—31no—
732C24—91no—
733C24C2×D3211yescharacteristic
734C2×D4—34no—
735C2×D4—34no—
736C2×D4—94no—
737C2×D4—94no—
738C2×D4—94no—
739C2×D4—94no—
740C2×D4—121no—
741C2×D4—121no—
742C2×D4—121no—
743C2×D4—121no—
744C2×D4—182no—
745C2×D4—182no—
746C2×D4—182no—
747C2×D4—182no—
748C2×D4—361no—
749C2×D4—361no—
750C2×D4—361no—
751C2×D4—361no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—62no—
759C22×C4—62no—
760C22×C4—91no—
761C22×C4—91no—
762C22×C4—91no—
763C22×C4—121no—
764C22×C4—121no—
765C22×C4—121no—
766C22×C4—121no—
767C22×C4—182no—
768C22×C4—182no—
769C22×C4—361no—
770C22×C4—361no—
771C22×C4—361no—
772C22×C4—361no—
773C22×C4C2×D3211yescharacteristic
774C22×C4C2×D3211yescharacteristic
775C4⋊C4—182no—
776C4⋊C4—182no—
777C22⋊C4—41no—
778C22⋊C4—62no—
779C22⋊C4—62no—
780C22⋊C4—121no—
781C22⋊C4—121no—
782C22⋊C4—182no—
783C22⋊C4—182no—
784C22⋊C4—361no—
785C22⋊C4—361no—
786C22⋊C4—361no—
787C22⋊C4—361no—
788C22⋊C4—361no—
789C42—94no—
790C42—94no—
791C42—182no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—41no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—81no—
823C22×C3—81no—
824C22×C3—81no—
825C22×C3—81no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3C22×C4×D311yescharacteristic
835C22×C3C22×C4×D311yescharacteristic
836C22×C3C2×D3×D411yescharacteristic
837C22×C3C2×D3×D411yescharacteristic
838C22×C3#100411yescharacteristic
839C22×C3#100411yescharacteristic
840C22×C3#100411yescharacteristic
841C22×C3#100411yescharacteristic
842C22×C3#100411yescharacteristic
843C22×C3#100411yescharacteristic
844C22×C3D3×#4111yescharacteristic
845C22×C3D3×#4111yescharacteristic
846C22×C3#100911yescharacteristic
847C22×C3#100911yescharacteristic
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—122no—
869C2×D3—122no—
870C2×D3—122no—
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—
883C3×C4—42no—
884C3×C4—41no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—41no—
888C3×C4—62no—
889C3×C4—62no—
890C3×C4—62no—
891C3×C4—62no—
892C3×C4—81no—
893C3×C4—121no—
894C3×C4—121no—
895Dic3—22no—
896Dic3—22no—
897Dic3—22no—
898Dic3—22no—
899Dic3—34no—
900Dic3—34no—
901Dic3—41no—
902Dic3—41no—
903Dic3—64no—
904Dic3—122no—
905Dic3—121no—
906Dic3—121no—
907Dic3—121no—
908Dic3—121no—
909Dic3—241no—
910C32#232811yescharacteristic, complemented, Sylow
911C23—21no—
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—32no—
918C23—32no—
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—92no—
932C23—181no—
933C23—181no—
934C23—181no—
935C23—181no—
936C23—181no—
937C23—181no—
938C23C4×D3212yes—
939C23C22×D3211yescharacteristic
940D4—124no—
941D4—124no—
942D4—188no—
943D4—188no—
944D4—364no—
945D4—364no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—32no—
953C2×C4—32no—
954C2×C4—32no—
955C2×C4—32no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
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—92no—
971C2×C4—92no—
972C2×C4—92no—
973C2×C4—124no—
974C2×C4—124no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—364no—
982C2×C4—364no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—42no—
991C2×C3—42no—
992C2×C3—82no—
993C2×C3—122no—
994C2×C3—122no—
995C2×C3#548611yescharacteristic
996C2×C3#548611yescharacteristic
997C2×C3C4×D3×D411yescharacteristic
998C2×C3C4×D3×D411yescharacteristic
999C2×C3#554511yescharacteristic
1000C2×C3#554511yescharacteristic
1001C2×C3#559211yescharacteristic
1002C2×C3#559211yescharacteristic
1003C2×C3#560711yescharacteristic
1004C2×C3#560711yescharacteristic
1005C2×C3#561511yescharacteristic
1006C2×C3#561511yescharacteristic
1007C2×C3#566311yescharacteristic
1008C2×C3#566311yescharacteristic
1009D3—42no—
1010D3—42no—
1011D3—122no—
1012D3—122no—
1013D3—242no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—121no—
1028C22—121no—
1029C22—121no—
1030C22—121no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—182no—
1036C22—182no—
1037C22—182no—
1038C22—361no—
1039C22—361no—
1040C22—361no—
1041C22—361no—
1042C22C2×C4×D3211yescharacteristic
1043C22#6430711yescharacteristic
1044C22D32×D411yescharacteristic
1045C22#6431211yescharacteristic
1046C22#6431311yescharacteristic
1047C22#6431411yescharacteristic
1048C22#6433011yescharacteristic
1049C4—41no—
1050C4—41no—
1051C4—62no—
1052C4—62no—
1053C4—62no—
1054C4—62no—
1055C4—94no—
1056C4—121no—
1057C4—121no—
1058C4—361no—
1059C4—361no—
1060C3—21no—
1061C3#7466711yescharacteristic, complemented
1062C3#7466711yescharacteristic, complemented
1063C2—42no—
1064C2—122no—
1065C2—122no—
1066C2—362no—
1067C2#1059416111yescharacteristic
1068C2#1059425411yescharacteristic
1069C2#1059425511yescharacteristic
1070C2#1059426911yescharacteristic
1071C2#1059505611yescharacteristic
1072C2#1059520511yescharacteristic
1073C2#1059528511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63979C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63952C2semidirect
3. C2×#63879C2semidirect
4. #10592656C2semidirect
5. C3×#4958C2semidirect
6. C3×#4956C2semidirect
7. #10591721C2semidirect
8. #10591710C2semidirect
9. #10591385C2semidirect
10. #10591382C2semidirect
11. #10591364C2semidirect
12. #10591275C2semidirect
13. #10591275C2semidirect
14. #10591252C2semidirect
15. #10591247C2semidirect
38. #63979C4semidirect
69. #4958D3semidirect
78. #4956D3semidirect
95. C2×#638C2×C4semidirect
103. C2×C3×#67C2×C4semidirect
104. C2×C3×#67C2×C4semidirect
121. C2×#626C2×C4semidirect
122. C2×#626C2×C4semidirect
125. C2×#625C2×C4semidirect
147. Dic32C2×C4semidirect
148. Dic32D4semidirect
379. C2×#67C4×D3semidirect
380. C2×#67C4×D3semidirect
910. C32#2328semidirect
1061. C3#74667semidirect
1062. C3#74667semidirect

Maximal subgroups

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

subgroupindex
C2×#639792
C2×#639522
C2×#638792
#105926562
C3×#49582
C3×#49562
#105917212
#105917102
#105913852
#105913822
#105913642
#105912752
#105912522
#105912472
#746673