Finite Group Databasebeta

← #11824453

Subgroups — #11824453

Order 1152.

2109 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64093C211yesmaximal, characteristic, complemented
2C2×#63979C211yesmaximal, characteristic, complemented
3C2×#63979C211yesmaximal, characteristic, complemented
4C2×#63971C211yesmaximal, characteristic, complemented
5C2×#63912C211yesmaximal, characteristic, complemented
6C2×#63911C211yesmaximal, characteristic, complemented
7C2×#63885C211yesmaximal, characteristic, complemented
8C2×#63881C211yesmaximal, characteristic, complemented
9C3×#4960C211yesmaximal, characteristic, complemented
10C3×#4957C211yesmaximal, characteristic, complemented
11#10591724C211yesmaximal, characteristic, complemented
12#10591395C211yesmaximal, characteristic, complemented
13#10591393C211yesmaximal, characteristic, complemented
14#10591384C211yesmaximal, characteristic, complemented
15#10591243C211yesmaximal, characteristic, complemented
16#76688—31nomaximal
17#76348—31nomaximal
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#625C2211yescharacteristic
33C22×#625C2211yescharacteristic
34C22×D3×Dic3C2211yescharacteristic
35C2×C32×C22⋊C4C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×#3750C2211yescharacteristic
38#64093—24no—
39C2×C3×#217C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46#63979—24no—
47#63979—24no—
48#63971—24no—
49C2×#3724C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×Dic32C2211yescharacteristic
54C2×Dic32C2211yescharacteristic
55#63912—24no—
56#63911—24no—
57#63885—24no—
58#63881—24no—
59C3×C3⋊#95C2211yescharacteristic
60#63579C2211yescharacteristic
61C2×#940—31no—
62C2×#940—31no—
63C2×#940—31no—
64C2×#940—31no—
65C2×#940—31no—
66C2×#939—31no—
67C2×#939—31no—
68C2×#893—31no—
69C2×#884—31no—
70C2×#884—31no—
71C2×#884—31no—
72C2×#884—31no—
73C2×#884—31no—
74C2×#884—31no—
75C2×#884—61no—
76C2×#67⋊C4—31no—
77C2×#874—31no—
78C3×#392—31no—
79C3×#390—31no—
80#5223—31no—
81#4988—31no—
82#4960—31no—
83#4960—31no—
84#4960—31no—
85#4960—31no—
86#4960D311yescharacteristic, complemented
87#4957—31no—
88#4957D311yescharacteristic, complemented
89C4×Dic3⋊C4—31no—
90#4671—31no—
91#4649—31no—
92C24×C32C2311yescharacteristic
93C23×C3⋊D3C2311yescharacteristic
94C23×C3⋊D3C2311yescharacteristic
95C23×C3×D3C2311yescharacteristic
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#638—22no—
101C2×#638—22no—
102C2×#638—22no—
103C2×#638—22no—
104C2×#638—22no—
105C2×#638—41no—
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C2×C4⋊(C3⋊D3)—22no—
109C2×C4⋊(C3⋊D3)—22no—
110C2×C4⋊(C3⋊D3)—41no—
111C2×C4×C3⋊D3—22no—
112C2×C4×C3⋊D3—22no—
113C2×C4×C3⋊D3—22no—
114C2×C3×#67—22no—
115C2×C3×#67—22no—
116C2×C3×#67—22no—
117C2×C3×#67—22no—
118C2×C3×#67—22no—
119C2×C3×#67—22no—
120C2×C3×#67—41no—
121C2×C3×#67—41no—
122C2×C3×#67—41no—
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C2×C3×D12—22no—
129C2×C3×D12—22no—
130C2×C3×D12—41no—
131C2×#626—22no—
132C2×#626—22no—
133C2×#626—22no—
134C2×#626—22no—
135C2×#626—22no—
136C2×#626—22no—
137C2×#626—22no—
138C2×#626—22no—
139C2×#626—22no—
140C2×#626—22no—
141C2×#626—22no—
142C2×#626—22no—
143C2×#626—41no—
144C2×#626—41no—
145C2×#626—41no—
146C2×#626—41no—
147C2×#626—41no—
148C2×#626D414yescomplemented
149C2×#625—22no—
150C2×#625—22no—
151C2×#625—22no—
152C2×#625—22no—
153C2×#625—22no—
154C2×#625—41no—
155C2×D3×Dic3—22no—
156C2×D3×Dic3—22no—
157C2×D3×Dic3—22no—
158C32×C22⋊C4—22no—
159#3752—22no—
160#3750D414yescomplemented
161C3×#217—22no—
162C3×(C2×D3)⋊C4—22no—
163C3×(C2×D3)⋊C4—22no—
164C3×(C2×D3)⋊C4—22no—
165C3×(C2×D3)⋊C4—22no—
166C3×Dic3⋊C4—22no—
167C3×C4×Dic3—22no—
168#3724D414yescomplemented
169#3722—22no—
170#3722—22no—
171(C2×D3)⋊Dic3—22no—
172Dic32—22no—
173Dic32D414yescomplemented
174#2541—91noSylow
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—61no—
194C22×#67—61no—
195C22×#67C2×D311yescharacteristic
196C22×#67C2×D311yescharacteristic
197C22×#67C2×D311yescharacteristic
198C23×Dic3—31no—
199C22×D12—31no—
200C22×D12—31no—
201C22×D12—31no—
202C22×D12—31no—
203C22×D12—31no—
204C22×D12—31no—
205C22×D12—31no—
206C22×D12—31no—
207C22×D12—61no—
208C22×D12C2×D311yescharacteristic
209C22×C4×D3—31no—
210C22×C4×D3—31no—
211C22×C4×D3—31no—
212C22×C4×D3—61no—
213C2×C3×C4⋊C4—31no—
214C2×C3×C22⋊C4—21no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C22⋊C4—31no—
218C2×C3×C22⋊C4—31no—
219C2×C3×C22⋊C4—31no—
220C2×C3×C22⋊C4C2×D311yescharacteristic
221C2×C3×C22⋊C4C2×D311yescharacteristic
222C2×C3×C42—31no—
223C2×#217—31no—
224C2×#217C2×D311yescharacteristic
225#940—64no—
226#940—64no—
227#940—64no—
228#940—64no—
229#940—64no—
230#939—64no—
231#939—64no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—61no—
240C2×(C2×D3)⋊C4C2×D311yescharacteristic
241C2×(C2×D3)⋊C4C2×D311yescharacteristic
242C2×(C2×D3)⋊C4C2×D311yescharacteristic
243C2×(C2×D3)⋊C4C2×D311yescharacteristic
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—61no—
249C2×Dic3⋊C4C2×D311yescharacteristic
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3C2×D311yescharacteristic
255#893—64no—
256#884—64no—
257#884—64no—
258#884—64no—
259#884—64no—
260#884—64no—
261#884—64no—
262#884—68no—
263#67⋊C4—64no—
264#874—64no—
265C3×#95—31no—
266C3⋊#95—31no—
267C3⋊#95—31no—
268C3⋊#95C2×D311yescharacteristic
269C23×C32—21no—
270C23×C32—21no—
271C23×C32—21no—
272C23×C32—21no—
273C23×C32—21no—
274C23×C32—21no—
275C23×C32—21no—
276C23×C32C2411yescharacteristic
277C22×C3⋊D3—21no—
278C22×C3⋊D3—21no—
279C22×C3⋊D3—21no—
280C22×C3⋊D3—21no—
281C22×C3⋊D3—21no—
282C22×C3⋊D3—21no—
283C22×C3⋊D3—21no—
284C22×C3⋊D3—21no—
285C22×C3⋊D3—21no—
286C22×C3⋊D3—21no—
287C22×C3⋊D3—21no—
288C22×C3⋊D3—21no—
289C22×C3⋊D3—21no—
290C22×C3⋊D3C2×D412yes—
291C22×C3×D3—21no—
292C22×C3×D3—21no—
293C22×C3×D3—21no—
294C22×C3×D3—21no—
295C22×C3×D3—21no—
296C22×C3×D3—21no—
297C22×C3×D3—21no—
298C22×C3×D3—21no—
299C22×C3×D3—21no—
300C22×C3×D3—21no—
301C22×C3×D3—21no—
302C22×C3×D3—21no—
303C22×C3×D3—21no—
304C22×C3×D3—21no—
305C22×C3×D3—21no—
306C22×C3×D3—21no—
307C22×C3×D3—21no—
308C22×C3×D3—21no—
309C22×C3×D3—21no—
310C22×C3×D3—21no—
311C22×C3×D3C2×D412yes—
312C2×C32×C4—21no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4—21no—
317C2×C32×C4C2×D412yes—
318#638—44no—
319#638—44no—
320C2×C3⋊Dic3—21no—
321C2×C3⋊Dic3—21no—
322C2×C3⋊Dic3C2×D412yes—
323C2×C3⋊Dic3C2×D412yes—
324C2×C3⋊Dic3C2×D412yes—
325C2×C3⋊Dic3C2×D412yes—
326C4⋊(C3⋊D3)—44no—
327C4×C3⋊D3—44no—
328C3×#67—44no—
329C3×#67—44no—
330C3×#67—44no—
331C2×C3×Dic3—21no—
332C2×C3×Dic3—21no—
333C2×C3×Dic3—21no—
334C2×C3×Dic3—21no—
335C2×C3×Dic3—21no—
336C2×C3×Dic3—21no—
337C2×C3×Dic3—21no—
338C2×C3×Dic3—21no—
339C2×C3×Dic3—21no—
340C2×C3×Dic3C2×D412yes—
341C2×C3×Dic3C2×D412yes—
342C2×C3×Dic3C2×D412yes—
343C2×C3×Dic3C2×D412yes—
344C2×C3×Dic3C2×D412yes—
345C2×C3×Dic3#4112yes—
346C3×D12—44no—
347#626—28no—
348#626—44no—
349#626—44no—
350#626—44no—
351#626—44no—
352#626—44no—
353#625—44no—
354#625—44no—
355D3×Dic3—44no—
356C2×#127—91no—
357C2×#127—91no—
358C2×#127—91no—
359C2×#121—91no—
360C2×#121—91no—
361C2×#121—91no—
362C2×#121—91no—
363C2×C4×D4—91no—
364#392—31no—
365#392—91no—
366#392—91no—
367#392—91no—
368#390—31no—
369#390—91no—
370C4×C4⋊C4—91no—
371C24×C3—21no—
372C24×C3—31no—
373C24×C3—31no—
374C24×C3—31no—
375C24×C3C22×D311yescharacteristic
376C24×C3C22×D311yescharacteristic
377C23×D3—31no—
378C23×D3—31no—
379C23×D3—31no—
380C23×D3—31no—
381C23×D3—61no—
382C23×D3—61no—
383C23×D3C22×D311yescharacteristic
384C23×D3C22×D311yescharacteristic
385C23×D3C22×D311yescharacteristic
386C2×C3×D4—62no—
387C2×C3×D4—62no—
388C2×C3×D4—62no—
389C2×C3×D4—62no—
390C2×C3×D4—62no—
391C2×C3×D4—62no—
392C2×C3×D4—62no—
393C2×C3×D4—62no—
394C2×C3×D4—121no—
395C2×C3×D4—121no—
396C2×C3×D4—121no—
397C2×C3×D4—121no—
398C22×C3×C4—21no—
399C22×C3×C4—21no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—31no—
405C22×C3×C4C22×D311yescharacteristic
406C22×C3×C4C22×D311yescharacteristic
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C2×#67—22no—
410C2×#67—22no—
411C2×#67—22no—
412C2×#67—22no—
413C2×#67—22no—
414C2×#67—22no—
415C2×#67—34no—
416C2×#67—41no—
417C2×#67—41no—
418C2×#67—41no—
419C2×#67—62no—
420C2×#67—62no—
421C2×#67—62no—
422C2×#67—62no—
423C2×#67—62no—
424C2×#67—62no—
425C2×#67—62no—
426C2×#67—62no—
427C2×#67—62no—
428C2×#67—62no—
429C2×#67—62no—
430C2×#67—62no—
431C2×#67—62no—
432C2×#67—62no—
433C2×#67—62no—
434C2×#67—62no—
435C2×#67—62no—
436C2×#67—62no—
437C2×#67—62no—
438C2×#67—62no—
439C2×#67—62no—
440C2×#67—62no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—62no—
444C2×#67—62no—
445C2×#67—62no—
446C2×#67—62no—
447C2×#67—62no—
448C2×#67—62no—
449C2×#67—62no—
450C2×#67—62no—
451C2×#67—62no—
452C2×#67—62no—
453C2×#67—122no—
454C2×#67—122no—
455C2×#67—122no—
456C2×#67—121no—
457C2×#67—121no—
458C2×#67—121no—
459C2×#67—121no—
460C2×#67—121no—
461C2×#67—121no—
462C2×#67—121no—
463C2×#67—121no—
464C2×#67—121no—
465C2×#67—122no—
466C22×Dic3—31no—
467C22×Dic3—31no—
468C22×Dic3—31no—
469C22×Dic3—31no—
470C22×Dic3—61no—
471C22×Dic3—61no—
472C22×Dic3—62no—
473C22×Dic3—62no—
474C22×Dic3—62no—
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D311yescharacteristic
477C22×Dic3C22×D311yescharacteristic
478C22×Dic3C22×D311yescharacteristic
479C22×Dic3C22×D311yescharacteristic
480C2×D12—22no—
481C2×D12—22no—
482C2×D12—34no—
483C2×D12—41no—
484C2×D12—62no—
485C2×D12—62no—
486C2×D12—62no—
487C2×D12—62no—
488C2×D12—64no—
489C2×D12—62no—
490C2×D12—62no—
491C2×D12—62no—
492C2×D12—62no—
493C2×D12—62no—
494C2×D12—62no—
495C2×D12—62no—
496C2×D12—62no—
497C2×D12—62no—
498C2×D12—62no—
499C2×D12—62no—
500C2×D12—62no—
501C2×D12—122no—
502C2×D12—121no—
503C2×D12—121no—
504C2×D12—122no—
505C2×D12—121no—
506C2×D12—121no—
507C2×D12—121no—
508C2×D12—121no—
509C2×D12—121no—
510C2×C4×D3—62no—
511C2×C4×D3—62no—
512C2×C4×D3—62no—
513C2×C4×D3—62no—
514C2×C4×D3—62no—
515C2×C4×D3—62no—
516C2×C4×D3—62no—
517C2×C4×D3—62no—
518C2×C4×D3—62no—
519C2×C4×D3—64no—
520C2×C4×D3—122no—
521C2×C4×D3—122no—
522C3×C4⋊C4—62no—
523C3×C22⋊C4—24no—
524C3×C22⋊C4—22no—
525C3×C22⋊C4—22no—
526C3×C22⋊C4—62no—
527C3×C22⋊C4—62no—
528C3×C22⋊C4—62no—
529C3×C22⋊C4—62no—
530C3×C22⋊C4—62no—
531C3×C42—62no—
532#217—22no—
533#217—62no—
534(C2×D3)⋊C4—22no—
535(C2×D3)⋊C4—22no—
536(C2×D3)⋊C4—22no—
537(C2×D3)⋊C4—22no—
538(C2×D3)⋊C4—62no—
539(C2×D3)⋊C4—62no—
540(C2×D3)⋊C4—62no—
541(C2×D3)⋊C4—62no—
542(C2×D3)⋊C4—62no—
543(C2×D3)⋊C4—64no—
544(C2×D3)⋊C4—62no—
545(C2×D3)⋊C4—62no—
546Dic3⋊C4—22no—
547Dic3⋊C4—34no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—34no—
551Dic3⋊C4—64no—
552C4×Dic3—22no—
553C4×Dic3—34no—
554C4×Dic3—34no—
555C4×Dic3—62no—
556C4×Dic3—62no—
557C22×C32—41no—
558C22×C32—41no—
559C22×C32—41no—
560C22×C32—41no—
561C22×C32—41no—
562C22×C32—41no—
563C22×C32—41no—
564C22×C32C22×D411yescharacteristic
565C22×C32C22×D411yescharacteristic
566C22×C32C22×D411yescharacteristic
567C22×C32C22×D411yescharacteristic
568C22×C32C2×#4111yescharacteristic
569C22×C32H(5,𝔽2)11yescharacteristic
570C22×C32H(5,𝔽2)11yescharacteristic
571C2×C3⋊D3—22no—
572C2×C3⋊D3—22no—
573C2×C3⋊D3—22no—
574C2×C3⋊D3—41no—
575C2×C3⋊D3—41no—
576C2×C3⋊D3—41no—
577C2×C3⋊D3—41no—
578C2×C3⋊D3—41no—
579C2×C3⋊D3—41no—
580C2×C3⋊D3—41no—
581C2×C3⋊D3—41no—
582C2×C3⋊D3—41no—
583C2×C3⋊D3—41no—
584C2×C3⋊D3—41no—
585C2×C3×D3—22no—
586C2×C3×D3—22no—
587C2×C3×D3—22no—
588C2×C3×D3—41no—
589C2×C3×D3—41no—
590C2×C3×D3—41no—
591C2×C3×D3—41no—
592C2×C3×D3—41no—
593C2×C3×D3—41no—
594C2×C3×D3—41no—
595C2×C3×D3—41no—
596C2×C3×D3—41no—
597C2×C3×D3—41no—
598C2×C3×D3—41no—
599C2×C3×D3—41no—
600C2×C3×D3—41no—
601C2×C3×D3—41no—
602C2×C3×D3—41no—
603C2×C3×D3—41no—
604C2×C3×D3—41no—
605C2×C3×D3—41no—
606C32×C4—22no—
607C32×C4—41no—
608C3⋊Dic3—22no—
609C3⋊Dic3#12714yescomplemented
610C3×Dic3—22no—
611C3×Dic3—22no—
612C3×Dic3—22no—
613C3×Dic3—41no—
614C3×Dic3#12114yescomplemented
615C22×D4—31no—
616C22×D4—31no—
617C22×D4—31no—
618C22×D4—31no—
619C22×D4—91no—
620C22×D4—91no—
621C22×D4—91no—
622C22×D4—91no—
623C22×D4—91no—
624C22×D4—91no—
625C22×D4—91no—
626C22×D4—91no—
627C22×D4—91no—
628C22×D4—91no—
629C22×D4—91no—
630C23×C4—91no—
631C23×C4—91no—
632#127—184no—
633#127—184no—
634#127—184no—
635#121—184no—
636#121—184no—
637#121—184no—
638#121—184no—
639C4×D4—184no—
640C2×C4⋊C4—31no—
641C2×C4⋊C4—91no—
642C2×C4⋊C4—91no—
643C2×C22⋊C4—31no—
644C2×C22⋊C4—31no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—31no—
647C2×C22⋊C4—31no—
648C2×C22⋊C4—91no—
649C2×C22⋊C4—91no—
650C2×C22⋊C4—91no—
651C2×C22⋊C4—91no—
652C2×C22⋊C4D3211yescharacteristic
653C2×C42—31no—
654C2×C42—91no—
655C2×C42—91no—
656#95—31no—
657#95—91no—
658C23×C3—22no—
659C23×C3—21no—
660C23×C3—21no—
661C23×C3—21no—
662C23×C3—21no—
663C23×C3—21no—
664C23×C3—21no—
665C23×C3—21no—
666C23×C3—21no—
667C23×C3—21no—
668C23×C3—21no—
669C23×C3—21no—
670C23×C3—21no—
671C23×C3—21no—
672C23×C3—21no—
673C23×C3—21no—
674C23×C3—32no—
675C23×C3—41no—
676C23×C3—41no—
677C23×C3—41no—
678C23×C3—41no—
679C23×C3—41no—
680C23×C3—41no—
681C23×C3—61no—
682C23×C3—61no—
683C23×C3—61no—
684C23×C3—61no—
685C23×C3—61no—
686C23×C3—61no—
687C23×C3—61no—
688C23×C3—61no—
689C23×C3—61no—
690C23×C3—61no—
691C23×C3—61no—
692C23×C3—61no—
693C23×C3—61no—
694C23×C3—61no—
695C23×C3—61no—
696C23×C3—61no—
697C23×C3—61no—
698C23×C3—61no—
699C23×C3—61no—
700C23×C3—61no—
701C23×C3C23×D311yescharacteristic
702C23×C3C23×D311yescharacteristic
703C22×D3—21no—
704C22×D3—21no—
705C22×D3—21no—
706C22×D3—21no—
707C22×D3—21no—
708C22×D3—21no—
709C22×D3—21no—
710C22×D3—21no—
711C22×D3—21no—
712C22×D3—21no—
713C22×D3—21no—
714C22×D3—21no—
715C22×D3—21no—
716C22×D3—21no—
717C22×D3—21no—
718C22×D3—21no—
719C22×D3—21no—
720C22×D3—21no—
721C22×D3—21no—
722C22×D3—21no—
723C22×D3—32no—
724C22×D3—32no—
725C22×D3—62no—
726C22×D3—62no—
727C22×D3—62no—
728C22×D3—61no—
729C22×D3—61no—
730C22×D3—61no—
731C22×D3—61no—
732C22×D3—61no—
733C22×D3—61no—
734C22×D3—61no—
735C22×D3—61no—
736C22×D3—61no—
737C22×D3—61no—
738C22×D3—61no—
739C22×D3—61no—
740C22×D3—62no—
741C22×D3—61no—
742C22×D3—61no—
743C22×D3—61no—
744C22×D3—61no—
745C22×D3—61no—
746C22×D3—61no—
747C22×D3—61no—
748C22×D3—61no—
749C22×D3—61no—
750C22×D3—61no—
751C22×D3—61no—
752C22×D3—61no—
753C22×D3—61no—
754C22×D3—61no—
755C22×D3—121no—
756C22×D3—121no—
757C22×D3—121no—
758C22×D3—121no—
759C22×D3—121no—
760C22×D3—121no—
761C22×D3—121no—
762C22×D3—121no—
763C22×D3—121no—
764C22×D3—121no—
765C22×D3D3×D412yes—
766C3×D4—124no—
767C3×D4—124no—
768C3×D4—124no—
769C3×D4—124no—
770C2×C3×C4—21no—
771C2×C3×C4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—22no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—21no—
781C2×C3×C4—22no—
782C2×C3×C4—32no—
783C2×C3×C4—32no—
784C2×C3×C4—32no—
785C2×C3×C4—32no—
786C2×C3×C4—32no—
787C2×C3×C4—32no—
788C2×C3×C4—41no—
789C2×C3×C4—41no—
790C2×C3×C4—41no—
791C2×C3×C4—41no—
792C2×C3×C4—61no—
793C2×C3×C4—61no—
794C2×C3×C4—61no—
795C2×C3×C4—61no—
796C2×C3×C4—61no—
797C2×C3×C4—61no—
798C2×C3×C4—61no—
799C2×C3×C4—61no—
800C2×C3×C4—61no—
801C2×C3×C4D3×D412yes—
802C2×C3×C4D3×D412yes—
803#67—44no—
804#67—44no—
805#67—44no—
806#67—68no—
807#67—124no—
808#67—124no—
809#67—124no—
810#67—124no—
811#67—124no—
812#67—124no—
813#67—124no—
814#67—124no—
815#67—124no—
816#67—124no—
817#67—124no—
818#67—124no—
819#67—128no—
820#67—128no—
821#67—124no—
822C2×Dic3—21no—
823C2×Dic3—21no—
824C2×Dic3—21no—
825C2×Dic3—21no—
826C2×Dic3—21no—
827C2×Dic3—21no—
828C2×Dic3—21no—
829C2×Dic3—21no—
830C2×Dic3—21no—
831C2×Dic3—32no—
832C2×Dic3—32no—
833C2×Dic3—32no—
834C2×Dic3—32no—
835C2×Dic3—32no—
836C2×Dic3—32no—
837C2×Dic3—32no—
838C2×Dic3—32no—
839C2×Dic3—62no—
840C2×Dic3—62no—
841C2×Dic3—62no—
842C2×Dic3—62no—
843C2×Dic3—61no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—61no—
847C2×Dic3—121no—
848C2×Dic3—121no—
849C2×Dic3—124no—
850C2×Dic3#23512yes—
851C2×Dic3D3×D412yes—
852C2×Dic3D3×D412yes—
853C2×Dic3D3×D412yes—
854C2×Dic3D3×D412yes—
855C2×Dic3D3×D412yes—
856D12—44no—
857D12—68no—
858D12—124no—
859D12—124no—
860D12—124no—
861D12—128no—
862D12—124no—
863D12—124no—
864D12—124no—
865D12—124no—
866C4×D3—124no—
867C4×D3—124no—
868C4×D3—124no—
869C4×D3—128no—
870C2×C32—81no—
871C2×C32C2×#12111yescharacteristic
872C2×C32C2×#12711yescharacteristic
873C2×C32#53511yescharacteristic
874C2×C32D4211yescharacteristic
875C2×C32D4211yescharacteristic
876C2×C32#55011yescharacteristic
877C2×C32#55011yescharacteristic
878C3⋊D3—42no—
879C3⋊D3—81no—
880C3×D3—42no—
881C3×D3—81no—
882C3×D3—81no—
883C24—31no—
884C24—31no—
885C24—31no—
886C24—91no—
887C24—91no—
888C24C2×D3211yescharacteristic
889C2×D4—62no—
890C2×D4—62no—
891C2×D4—62no—
892C2×D4—62no—
893C2×D4—62no—
894C2×D4—62no—
895C2×D4—62no—
896C2×D4—62no—
897C2×D4—94no—
898C2×D4—121no—
899C2×D4—121no—
900C2×D4—121no—
901C2×D4—121no—
902C2×D4—182no—
903C2×D4—182no—
904C2×D4—182no—
905C2×D4—182no—
906C2×D4—182no—
907C2×D4—182no—
908C2×D4—182no—
909C2×D4—182no—
910C2×D4—182no—
911C2×D4—182no—
912C2×D4—182no—
913C2×D4—182no—
914C2×D4—182no—
915C2×D4—182no—
916C2×D4—182no—
917C2×D4—182no—
918C2×D4—182no—
919C2×D4—182no—
920C2×D4—182no—
921C2×D4—182no—
922C2×D4—182no—
923C2×D4—182no—
924C2×D4—182no—
925C2×D4—182no—
926C2×D4—361no—
927C2×D4—361no—
928C2×D4—361no—
929C2×D4—361no—
930C2×D4—361no—
931C2×D4—361no—
932C2×D4—361no—
933C2×D4—361no—
934C22×C4—31no—
935C22×C4—31no—
936C22×C4—31no—
937C22×C4—31no—
938C22×C4—31no—
939C22×C4—91no—
940C22×C4—91no—
941C22×C4—182no—
942C22×C4—182no—
943C22×C4—182no—
944C22×C4—182no—
945C22×C4—182no—
946C22×C4—182no—
947C22×C4C2×D3211yescharacteristic
948C22×C4C2×D3211yescharacteristic
949C4⋊C4—62no—
950C4⋊C4—94no—
951C4⋊C4—94no—
952C22⋊C4—22no—
953C22⋊C4—62no—
954C22⋊C4—62no—
955C22⋊C4—62no—
956C22⋊C4—62no—
957C22⋊C4—62no—
958C22⋊C4—182no—
959C22⋊C4—182no—
960C22⋊C4—182no—
961C22⋊C4—182no—
962C42—62no—
963C42—94no—
964C42—182no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—42no—
973C22×C3—42no—
974C22×C3—42no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3—41no—
979C22×C3—41no—
980C22×C3—41no—
981C22×C3—41no—
982C22×C3—41no—
983C22×C3—41no—
984C22×C3—41no—
985C22×C3—41no—
986C22×C3—41no—
987C22×C3—41no—
988C22×C3—41no—
989C22×C3—62no—
990C22×C3—62no—
991C22×C3—62no—
992C22×C3—81no—
993C22×C3—81no—
994C22×C3—81no—
995C22×C3—81no—
996C22×C3—121no—
997C22×C3—121no—
998C22×C3—121no—
999C22×C3—121no—
1000C22×C3—121no—
1001C22×C3—121no—
1002C22×C3—121no—
1003C22×C3—121no—
1004C22×C3—121no—
1005C22×C3—121no—
1006C22×C3—121no—
1007C22×C3—121no—
1008C22×C3—121no—
1009C22×C3—121no—
1010C22×C3—121no—
1011C22×C3—121no—
1012C22×C3—121no—
1013C22×C3—121no—
1014C22×C3C2×#23511yescharacteristic
1015C22×C3C2×D3×D411yescharacteristic
1016C22×C3C2×D3×D411yescharacteristic
1017C22×C3C2×D3×D411yescharacteristic
1018C22×C3C2×D3×D411yescharacteristic
1019C22×C3C2×D3×D411yescharacteristic
1020C22×C3C2×D3×D411yescharacteristic
1021C22×C3C2×D3×D411yescharacteristic
1022C22×C3C2×D3×D411yescharacteristic
1023C22×C3#100411yescharacteristic
1024C22×C3#100411yescharacteristic
1025C22×C3D3×#4111yescharacteristic
1026C22×C3#100911yescharacteristic
1027C22×C3#100911yescharacteristic
1028C2×D3—22no—
1029C2×D3—22no—
1030C2×D3—22no—
1031C2×D3—41no—
1032C2×D3—41no—
1033C2×D3—41no—
1034C2×D3—41no—
1035C2×D3—41no—
1036C2×D3—41no—
1037C2×D3—41no—
1038C2×D3—41no—
1039C2×D3—41no—
1040C2×D3—41no—
1041C2×D3—41no—
1042C2×D3—41no—
1043C2×D3—41no—
1044C2×D3—41no—
1045C2×D3—41no—
1046C2×D3—41no—
1047C2×D3—41no—
1048C2×D3—41no—
1049C2×D3—64no—
1050C2×D3—62no—
1051C2×D3—62no—
1052C2×D3—62no—
1053C2×D3—62no—
1054C2×D3—62no—
1055C2×D3—62no—
1056C2×D3—122no—
1057C2×D3—122no—
1058C2×D3—122no—
1059C2×D3—122no—
1060C2×D3—122no—
1061C2×D3—122no—
1062C2×D3—121no—
1063C2×D3—121no—
1064C2×D3—121no—
1065C2×D3—121no—
1066C2×D3—121no—
1067C2×D3—121no—
1068C2×D3—121no—
1069C2×D3—121no—
1070C2×D3—122no—
1071C2×D3—122no—
1072C2×D3—122no—
1073C2×D3—121no—
1074C2×D3—121no—
1075C2×D3—121no—
1076C2×D3—121no—
1077C2×D3—121no—
1078C2×D3—121no—
1079C2×D3—121no—
1080C2×D3—121no—
1081C2×D3—121no—
1082C2×D3—121no—
1083C2×D3—121no—
1084C2×D3—121no—
1085C2×D3—121no—
1086C2×D3—121no—
1087C2×D3—241no—
1088C2×D3—241no—
1089C2×D3—241no—
1090C2×D3—241no—
1091C3×C4—22no—
1092C3×C4—22no—
1093C3×C4—34no—
1094C3×C4—42no—
1095C3×C4—42no—
1096C3×C4—41no—
1097C3×C4—41no—
1098C3×C4—62no—
1099C3×C4—62no—
1100C3×C4—62no—
1101C3×C4—121no—
1102Dic3—22no—
1103Dic3—22no—
1104Dic3—22no—
1105Dic3—34no—
1106Dic3—34no—
1107Dic3—41no—
1108Dic3—64no—
1109Dic3—62no—
1110Dic3—62no—
1111Dic3—122no—
1112Dic3#88414yescomplemented
1113C32#254111yescharacteristic, complemented, Sylow
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—32no—
1122C23—61no—
1123C23—61no—
1124C23—61no—
1125C23—61no—
1126C23—61no—
1127C23—61no—
1128C23—61no—
1129C23—61no—
1130C23—61no—
1131C23—61no—
1132C23—61no—
1133C23—61no—
1134C23—61no—
1135C23—61no—
1136C23—61no—
1137C23—61no—
1138C23—61no—
1139C23—61no—
1140C23—61no—
1141C23—61no—
1142C23—92no—
1143C23—181no—
1144C23—181no—
1145C23—181no—
1146C23—181no—
1147C23—181no—
1148C23—181no—
1149C23—181no—
1150C23—181no—
1151C23—181no—
1152C23—181no—
1153C23—181no—
1154C23—181no—
1155C23—181no—
1156C23C22×D3211yescharacteristic
1157D4—124no—
1158D4—124no—
1159D4—124no—
1160D4—124no—
1161D4—188no—
1162D4—364no—
1163D4—364no—
1164D4—364no—
1165D4—364no—
1166D4—364no—
1167D4—364no—
1168D4—364no—
1169D4—364no—
1170D4—364no—
1171D4—364no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—32no—
1178C2×C4—32no—
1179C2×C4—32no—
1180C2×C4—32no—
1181C2×C4—32no—
1182C2×C4—32no—
1183C2×C4—61no—
1184C2×C4—61no—
1185C2×C4—61no—
1186C2×C4—61no—
1187C2×C4—61no—
1188C2×C4—61no—
1189C2×C4—61no—
1190C2×C4—61no—
1191C2×C4—61no—
1192C2×C4—92no—
1193C2×C4—92no—
1194C2×C4—92no—
1195C2×C4—92no—
1196C2×C4—181no—
1197C2×C4—181no—
1198C2×C4—364no—
1199C2×C4—364no—
1200C2×C4#381112yes—
1201C2×C3—21no—
1202C2×C3—21no—
1203C2×C3—21no—
1204C2×C3—21no—
1205C2×C3—21no—
1206C2×C3—21no—
1207C2×C3—21no—
1208C2×C3—82no—
1209C2×C3—81no—
1210C2×C3—81no—
1211C2×C3—122no—
1212C2×C3—241no—
1213C2×C3—241no—
1214C2×C3C2×#88411yescharacteristic
1215C2×C3#555311yescharacteristic
1216C2×C3#555311yescharacteristic
1217C2×C3#559011yescharacteristic
1218C2×C3#559011yescharacteristic
1219C2×C3#559211yescharacteristic
1220C2×C3#559911yescharacteristic
1221C2×C3#559911yescharacteristic
1222C2×C3D3×#12111yescharacteristic
1223C2×C3#560911yescharacteristic
1224C2×C3#560911yescharacteristic
1225C2×C3#567411yescharacteristic
1226C2×C3D3×#12711yescharacteristic
1227C2×C3D3×#12711yescharacteristic
1228D3—42no—
1229D3—81no—
1230D3—81no—
1231D3—124no—
1232D3—122no—
1233D3—122no—
1234D3—242no—
1235D3—241no—
1236D3—241no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—62no—
1245C22—62no—
1246C22—62no—
1247C22—121no—
1248C22—121no—
1249C22—121no—
1250C22—121no—
1251C22—121no—
1252C22—121no—
1253C22—121no—
1254C22—121no—
1255C22—121no—
1256C22—121no—
1257C22—121no—
1258C22—121no—
1259C22—121no—
1260C22—121no—
1261C22—121no—
1262C22—121no—
1263C22—121no—
1264C22—121no—
1265C22—182no—
1266C22—182no—
1267C22—182no—
1268C22—361no—
1269C22—361no—
1270C22—361no—
1271C22—361no—
1272C22—361no—
1273C22—361no—
1274C22—361no—
1275C22—361no—
1276C22—361no—
1277C22—361no—
1278C22—361no—
1279C22D3×#23511yescharacteristic
1280C22#6430711yescharacteristic
1281C22D32×D411yescharacteristic
1282C22D32×D411yescharacteristic
1283C22D32×D411yescharacteristic
1284C22#6431411yescharacteristic
1285C22C2×#381111yescharacteristic
1286C4—22no—
1287C4—34no—
1288C4—41no—
1289C4—62no—
1290C4—62no—
1291C4—62no—
1292C4—94no—
1293C4—121no—
1294C4—182no—
1295C3—21no—
1296C3#7634811yescharacteristic, complemented
1297C3#7668811yescharacteristic, complemented
1298C2—81no—
1299C2—122no—
1300C2—241no—
1301C2—241no—
1302C2—362no—
1303C2—721no—
1304C2#1059424611yescharacteristic
1305C2D3×#88411yescharacteristic
1306C2#1059427011yescharacteristic
1307C2#1059427511yescharacteristic
1308C2#1059491911yescharacteristic
1309C2#1059529211yescharacteristic
1310C2#1059530011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64093C2semidirect
2. C2×#63979C2semidirect
3. C2×#63979C2semidirect
4. C2×#63971C2semidirect
5. C2×#63912C2semidirect
6. C2×#63911C2semidirect
7. C2×#63885C2semidirect
8. C2×#63881C2semidirect
9. C3×#4960C2semidirect
10. C3×#4957C2semidirect
11. #10591724C2semidirect
12. #10591395C2semidirect
13. #10591393C2semidirect
14. #10591384C2semidirect
15. #10591243C2semidirect
86. #4960D3semidirect
88. #4957D3semidirect
148. C2×#626D4semidirect
160. #3750D4semidirect
168. #3724D4semidirect
173. Dic32D4semidirect
609. C3⋊Dic3#127semidirect
614. C3×Dic3#121semidirect
1112. Dic3#884semidirect
1113. C32#2541semidirect
1296. C3#76348semidirect
1297. C3#76688semidirect

Maximal subgroups

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

subgroupindex
C2×#640932
C2×#639792
C2×#639712
C2×#639122
C2×#639112
C2×#638852
C2×#638812
C3×#49602
C3×#49572
#105917242
#105913952
#105913932
#105913842
#105912432
#766883
#763483