Finite Group Databasebeta

← #11824452

Subgroups — #11824452

Order 1152.

2057 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#884C211yesmaximal, characteristic, complemented
2C2×#63979C211yesmaximal, characteristic, complemented
3C2×#63979C211yesmaximal, characteristic, complemented
4C2×#63958C211yesmaximal, characteristic, complemented
5C2×#63911C211yesmaximal, characteristic, complemented
6C2×#63910C211yesmaximal, characteristic, complemented
7C2×#63906C211yesmaximal, characteristic, complemented
8C2×#63904C211yesmaximal, characteristic, complemented
9#10592659C211yesmaximal, characteristic, complemented
10C3×#4957C211yesmaximal, characteristic, complemented
11#10591724C211yesmaximal, characteristic, complemented
12#10591393C211yesmaximal, characteristic, complemented
13#10591389C211yesmaximal, characteristic, complemented
14#10591384C211yesmaximal, characteristic, complemented
15Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#82669—31nomaximal
17#76348—31nomaximal
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#625C2211yescharacteristic
33C22×#625C2211yescharacteristic
34C22×#624C2211yescharacteristic
35C2×C32×C22⋊C4C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37C2×#3752C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C3×#884—24no—
46#63979—24no—
47#63979—24no—
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×#3722C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52#63958—24no—
53C2×Dic32C2211yescharacteristic
54C2×Dic32C2211yescharacteristic
55#63911—24no—
56#63910—24no—
57#63906—24no—
58#63904—24no—
59#63658C2211yescharacteristic
60#63579C2211yescharacteristic
61C2×C3×#121—31no—
62C2×#940—31no—
63C2×#940—31no—
64C2×#940—31no—
65C2×#940—31no—
66C2×#940—31no—
67C2×#938—31no—
68C2×#930—31no—
69C2×C4×#67—31no—
70C2×#895—31no—
71C2×#893—31no—
72C2×#884—31no—
73C2×#884—31no—
74C2×#884—31no—
75C2×#884D311yescharacteristic, complemented
76C2×#874—31no—
77C3×#390—31no—
78#5223—31no—
79#5223—31no—
80#4988—31no—
81Dic3×C4⋊C4—31no—
82#4960—31no—
83#4960—31no—
84#4960—31no—
85#4960—31no—
86#4960—31no—
87#4960—31no—
88#4960—61no—
89#4957—31no—
90#4957D311yescharacteristic, complemented
91C4×Dic3⋊C4—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—41no—
104C2×#638—41no—
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×C3×#67—22no—
112C2×C3×#67—22no—
113C2×C3×#67—22no—
114C2×C3×#67—22no—
115C2×C3×#67—22no—
116C2×C3×#67—22no—
117C2×C3×#67—22no—
118C2×C3×#67—22no—
119C2×C3×#67—41no—
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×D12—22no—
126C2×C3×D12—22no—
127C2×C3×D12—41no—
128C2×C3×C4×D3—22no—
129C2×C3×C4×D3—22no—
130C2×C3×C4×D3—22no—
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—22no—
144C2×#626—22no—
145C2×#626—41no—
146C2×#626—41no—
147C2×#626—41no—
148C2×#626D414yescomplemented
149C2×#625—22no—
150C2×#625—22no—
151C2×#625—22no—
152C2×#625—41no—
153C2×#625—41no—
154C2×#625—41no—
155C2×#624—22no—
156C2×#624—22no—
157C2×#624—22no—
158C32×C22⋊C4—22no—
159#3752—22no—
160#3752—22no—
161C3×#217—22no—
162C3×(C2×D3)⋊C4—22no—
163C3×(C2×D3)⋊C4—22no—
164C3×(C2×D3)⋊C4—22no—
165C3×Dic3⋊C4—22no—
166C3×Dic3⋊C4D414yescomplemented
167C3×C4×Dic3—22no—
168Dic3⋊Dic3D414yescomplemented
169#3722—22no—
170(C2×D3)⋊Dic3—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—
179C23×C3×C4—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—31no—
194C22×#67—61no—
195C22×#67—61no—
196C22×#67C2×D311yescharacteristic
197C22×#67C2×D311yescharacteristic
198C22×#67C2×D311yescharacteristic
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×D3C2×D311yescharacteristic
212C3×#121—64no—
213C2×C3×C4⋊C4—31no—
214C2×C3×C4⋊C4—31no—
215C2×C3×C22⋊C4—21no—
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×#217—31no—
225C2×#217C2×D311yescharacteristic
226#940—64no—
227#940—64no—
228#940—64no—
229#940—64no—
230#940—64no—
231#938—64no—
232#930—64no—
233C4×#67—64no—
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—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—61no—
243C2×(C2×D3)⋊C4—61no—
244C2×(C2×D3)⋊C4C2×D311yescharacteristic
245C2×(C2×D3)⋊C4C2×D311yescharacteristic
246C2×(C2×D3)⋊C4C2×D311yescharacteristic
247C2×C4⋊Dic3—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4C2×D311yescharacteristic
250C2×Dic3⋊C4C2×D311yescharacteristic
251C2×C4×Dic3—31no—
252C2×C4×Dic3—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3—31no—
255C2×C4×Dic3C2×D311yescharacteristic
256#895—64no—
257#893—64no—
258#884—24no—
259#884—64no—
260#884—64no—
261#884—64no—
262#874—64no—
263C3⋊#95—31no—
264C3⋊#95—31no—
265C3⋊#95—31no—
266C3⋊#95—31no—
267C3⋊#95—61no—
268C23×C32—21no—
269C23×C32—21no—
270C23×C32—21no—
271C23×C32—21no—
272C23×C32—21no—
273C23×C32—21no—
274C23×C32—21no—
275C23×C32C2411yescharacteristic
276C22×C3⋊D3—21no—
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⋊D3C2×D412yes—
290C22×C3×D3—21no—
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×D3C2×D412yes—
311C2×C32×C4—21no—
312C2×C32×C4—21no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4C2×D412yes—
317#638—44no—
318#638—44no—
319C2×C3⋊Dic3—21no—
320C2×C3⋊Dic3—21no—
321C2×C3⋊Dic3—21no—
322C2×C3⋊Dic3—21no—
323C2×C3⋊Dic3C2×D412yes—
324C2×C3⋊Dic3C2×D412yes—
325C4⋊(C3⋊D3)—44no—
326C3×#67—44no—
327C3×#67—44no—
328C3×#67—44no—
329C2×C3×Dic3—21no—
330C2×C3×Dic3—21no—
331C2×C3×Dic3—21no—
332C2×C3×Dic3—21no—
333C2×C3×Dic3—21no—
334C2×C3×Dic3—21no—
335C2×C3×Dic3—21no—
336C2×C3×Dic3C2×D412yes—
337C2×C3×Dic3C2×D412yes—
338C2×C3×Dic3C2×D412yes—
339C2×C3×Dic3C2×D412yes—
340C2×C3×Dic3C2×D412yes—
341C2×C3×Dic3C2×D412yes—
342C2×C3×Dic3C2×D412yes—
343C2×C3×Dic3#4112yes—
344C3×D12—44no—
345C3×C4×D3—44no—
346#626—28no—
347#626—44no—
348#626—44no—
349#626—44no—
350#626—44no—
351#626—44no—
352#625—44no—
353#625—44no—
354#624—44no—
355C2×#127—91no—
356C2×#127—91no—
357C2×#127—91no—
358C2×#121—31no—
359C2×#121—91no—
360C2×#121—91no—
361C2×#121—91no—
362C2×C4×D4—91no—
363#392—91no—
364#392—91no—
365#392—91no—
366#392—91no—
367#390—31no—
368#390—91no—
369C4×C4⋊C4—91no—
370C24×C3—21no—
371C24×C3—31no—
372C24×C3—31no—
373C24×C3—31no—
374C24×C3C22×D311yescharacteristic
375C24×C3C22×D311yescharacteristic
376C23×D3—31no—
377C23×D3—31no—
378C23×D3—31no—
379C23×D3—31no—
380C23×D3—61no—
381C23×D3—61no—
382C23×D3C22×D311yescharacteristic
383C23×D3C22×D311yescharacteristic
384C23×D3C22×D311yescharacteristic
385C2×C3×D4—62no—
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—62no—
395C2×C3×D4—121no—
396C2×C3×D4—121no—
397C22×C3×C4—21no—
398C22×C3×C4—21no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—62no—
405C22×C3×C4—62no—
406C22×C3×C4—62no—
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C22×C3×C4C22×D311yescharacteristic
410C22×C3×C4C22×D311yescharacteristic
411C2×#67—22no—
412C2×#67—22no—
413C2×#67—22no—
414C2×#67—22no—
415C2×#67—22no—
416C2×#67—22no—
417C2×#67—22no—
418C2×#67—22no—
419C2×#67—34no—
420C2×#67—41no—
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—62no—
442C2×#67—62no—
443C2×#67—62no—
444C2×#67—62no—
445C2×#67—62no—
446C2×#67—62no—
447C2×#67—122no—
448C2×#67—122no—
449C2×#67—122no—
450C2×#67—121no—
451C2×#67—121no—
452C2×#67—121no—
453C2×#67—121no—
454C2×#67—121no—
455C2×#67—121no—
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—
466C2×#67—122no—
467C2×#67—122no—
468C22×Dic3—31no—
469C22×Dic3—31no—
470C22×Dic3—31no—
471C22×Dic3—31no—
472C22×Dic3—61no—
473C22×Dic3—61no—
474C22×Dic3C22×D311yescharacteristic
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D311yescharacteristic
477C22×Dic3C22×D311yescharacteristic
478C22×Dic3C22×D311yescharacteristic
479C2×D12—22no—
480C2×D12—22no—
481C2×D12—34no—
482C2×D12—41no—
483C2×D12—62no—
484C2×D12—62no—
485C2×D12—62no—
486C2×D12—62no—
487C2×D12—62no—
488C2×D12—62no—
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—122no—
503C2×D12—121no—
504C2×D12—121no—
505C2×D12—122no—
506C2×D12—121no—
507C2×D12—121no—
508C2×D12—121no—
509C2×C4×D3—22no—
510C2×C4×D3—22no—
511C2×C4×D3—22no—
512C2×C4×D3—62no—
513C2×C4×D3—62no—
514C2×C4×D3—62no—
515C2×C4×D3—62no—
516C2×C4×D3—62no—
517C2×C4×D3—62no—
518C3×C4⋊C4—34no—
519C3×C4⋊C4—62no—
520C3×C22⋊C4—22no—
521C3×C22⋊C4—22no—
522C3×C22⋊C4—42no—
523C3×C22⋊C4—62no—
524C3×C22⋊C4—62no—
525C3×C22⋊C4—62no—
526C3×C22⋊C4—62no—
527C3×C42—62no—
528#217—22no—
529#217—62no—
530#217—62no—
531(C2×D3)⋊C4—22no—
532(C2×D3)⋊C4—22no—
533(C2×D3)⋊C4—22no—
534(C2×D3)⋊C4—62no—
535(C2×D3)⋊C4—62no—
536(C2×D3)⋊C4—62no—
537(C2×D3)⋊C4—62no—
538(C2×D3)⋊C4—62no—
539(C2×D3)⋊C4—62no—
540(C2×D3)⋊C4—62no—
541(C2×D3)⋊C4—62no—
542(C2×D3)⋊C4—122no—
543(C2×D3)⋊C4—122no—
544C4⋊Dic3—34no—
545Dic3⋊C4—22no—
546Dic3⋊C4—34no—
547Dic3⋊C4#6714yescomplemented
548C4×Dic3—22no—
549C4×Dic3—34no—
550C4×Dic3—34no—
551C4×Dic3—62no—
552C4×Dic3—62no—
553C22×C32—41no—
554C22×C32—41no—
555C22×C32—41no—
556C22×C32—41no—
557C22×C32—41no—
558C22×C32—41no—
559C22×C32—41no—
560C22×C32C22×D411yescharacteristic
561C22×C32C22×D411yescharacteristic
562C22×C32C22×D411yescharacteristic
563C22×C32C22×D411yescharacteristic
564C22×C32C2×#4111yescharacteristic
565C22×C32H(5,𝔽2)11yescharacteristic
566C22×C32H(5,𝔽2)11yescharacteristic
567C2×C3⋊D3—22no—
568C2×C3⋊D3—22no—
569C2×C3⋊D3—22no—
570C2×C3⋊D3—41no—
571C2×C3⋊D3—41no—
572C2×C3⋊D3—41no—
573C2×C3⋊D3—41no—
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—22no—
582C2×C3×D3—22no—
583C2×C3×D3—22no—
584C2×C3×D3—41no—
585C2×C3×D3—41no—
586C2×C3×D3—41no—
587C2×C3×D3—41no—
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—
602C32×C4—22no—
603C32×C4—41no—
604C3⋊Dic3—22no—
605C3⋊Dic3—22no—
606C3×Dic3—22no—
607C3×Dic3—22no—
608C3×Dic3—41no—
609C3×Dic3#12114yescomplemented
610C3×Dic3#12714yescomplemented
611C22×D4—31no—
612C22×D4—31no—
613C22×D4—31no—
614C22×D4—31no—
615C22×D4—91no—
616C22×D4—91no—
617C22×D4—91no—
618C22×D4—91no—
619C22×D4—91no—
620C22×D4—91no—
621C22×D4—91no—
622C22×D4—91no—
623C22×D4—91no—
624C22×D4—91no—
625C22×D4—91no—
626C23×C4—31no—
627C23×C4—91no—
628#127—184no—
629#127—184no—
630#127—184no—
631#121—64no—
632#121—184no—
633#121—184no—
634#121—184no—
635C4×D4—184no—
636C2×C4⋊C4—31no—
637C2×C4⋊C4—31no—
638C2×C4⋊C4—91no—
639C2×C22⋊C4—31no—
640C2×C22⋊C4—31no—
641C2×C22⋊C4—31no—
642C2×C22⋊C4—31no—
643C2×C22⋊C4—91no—
644C2×C22⋊C4—91no—
645C2×C22⋊C4—91no—
646C2×C22⋊C4—91no—
647C2×C22⋊C4—91no—
648C2×C22⋊C4D3211yescharacteristic
649C2×C42—31no—
650C2×C42—91no—
651C2×C42—91no—
652#95—91no—
653#95—91no—
654C23×C3—22no—
655C23×C3—21no—
656C23×C3—21no—
657C23×C3—21no—
658C23×C3—21no—
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—32no—
671C23×C3—41no—
672C23×C3—41no—
673C23×C3—41no—
674C23×C3—41no—
675C23×C3—41no—
676C23×C3—41no—
677C23×C3—61no—
678C23×C3—61no—
679C23×C3—61no—
680C23×C3—61no—
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×C3C23×D311yescharacteristic
698C23×C3C23×D311yescharacteristic
699C22×D3—21no—
700C22×D3—21no—
701C22×D3—21no—
702C22×D3—21no—
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—32no—
720C22×D3—32no—
721C22×D3—62no—
722C22×D3—61no—
723C22×D3—61no—
724C22×D3—61no—
725C22×D3—61no—
726C22×D3—61no—
727C22×D3—61no—
728C22×D3—61no—
729C22×D3—61no—
730C22×D3—61no—
731C22×D3—61no—
732C22×D3—61no—
733C22×D3—61no—
734C22×D3—62no—
735C22×D3—61no—
736C22×D3—61no—
737C22×D3—61no—
738C22×D3—61no—
739C22×D3—61no—
740C22×D3—61no—
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—121no—
750C22×D3—121no—
751C22×D3—121no—
752C22×D3—121no—
753C22×D3—121no—
754C22×D3—121no—
755C22×D3—121no—
756C22×D3—121no—
757C22×D3—121no—
758C22×D3—121no—
759C22×D3—121no—
760C22×D3—121no—
761C22×D3D3×D412yes—
762C3×D4—124no—
763C3×D4—124no—
764C3×D4—124no—
765C3×D4—124no—
766C2×C3×C4—21no—
767C2×C3×C4—21no—
768C2×C3×C4—21no—
769C2×C3×C4—21no—
770C2×C3×C4—21no—
771C2×C3×C4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—21no—
775C2×C3×C4—21no—
776C2×C3×C4—22no—
777C2×C3×C4—32no—
778C2×C3×C4—32no—
779C2×C3×C4—32no—
780C2×C3×C4—32no—
781C2×C3×C4—32no—
782C2×C3×C4—32no—
783C2×C3×C4—32no—
784C2×C3×C4—32no—
785C2×C3×C4—41no—
786C2×C3×C4—41no—
787C2×C3×C4—41no—
788C2×C3×C4—41no—
789C2×C3×C4—41no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—61no—
793C2×C3×C4—61no—
794C2×C3×C4—61no—
795C2×C3×C4—61no—
796C2×C3×C4—61no—
797C2×C3×C4—124no—
798C2×C3×C4D3×D412yes—
799C2×C3×C4C2×#6712yes—
800#67—44no—
801#67—44no—
802#67—44no—
803#67—68no—
804#67—124no—
805#67—124no—
806#67—124no—
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—128no—
816#67—128no—
817#67—124no—
818#67—124no—
819C2×Dic3—21no—
820C2×Dic3—21no—
821C2×Dic3—21no—
822C2×Dic3—21no—
823C2×Dic3—21no—
824C2×Dic3—21no—
825C2×Dic3—21no—
826C2×Dic3—32no—
827C2×Dic3—32no—
828C2×Dic3—32no—
829C2×Dic3—32no—
830C2×Dic3—62no—
831C2×Dic3—62no—
832C2×Dic3—61no—
833C2×Dic3—61no—
834C2×Dic3—61no—
835C2×Dic3—61no—
836C2×Dic3—61no—
837C2×Dic3—61no—
838C2×Dic3—61no—
839C2×Dic3—61no—
840C2×Dic3—121no—
841C2×Dic3—121no—
842C2×Dic3—121no—
843C2×Dic3—121no—
844C2×Dic3#23512yes—
845C2×Dic3D3×D412yes—
846C2×Dic3D3×D412yes—
847C2×Dic3D3×D412yes—
848C2×Dic3D3×D412yes—
849C2×Dic3D3×D412yes—
850C2×Dic3C2×#6712yes—
851C2×Dic3C2×#6712yes—
852D12—44no—
853D12—68no—
854D12—124no—
855D12—124no—
856D12—124no—
857D12—124no—
858D12—128no—
859D12—124no—
860D12—124no—
861D12—124no—
862C4×D3—44no—
863C4×D3—124no—
864C4×D3—124no—
865C2×C32—81no—
866C2×C32C2×#12111yescharacteristic
867C2×C32C2×#12711yescharacteristic
868C2×C32#53511yescharacteristic
869C2×C32D4211yescharacteristic
870C2×C32D4211yescharacteristic
871C2×C32#55011yescharacteristic
872C2×C32#55011yescharacteristic
873C3⋊D3—42no—
874C3⋊D3—81no—
875C3×D3—42no—
876C3×D3—81no—
877C3×D3—81no—
878C24—31no—
879C24—31no—
880C24—31no—
881C24—91no—
882C24—91no—
883C24C2×D3211yescharacteristic
884C2×D4—62no—
885C2×D4—62no—
886C2×D4—62no—
887C2×D4—62no—
888C2×D4—62no—
889C2×D4—62no—
890C2×D4—62no—
891C2×D4—62no—
892C2×D4—62no—
893C2×D4—62no—
894C2×D4—94no—
895C2×D4—121no—
896C2×D4—121no—
897C2×D4—182no—
898C2×D4—182no—
899C2×D4—182no—
900C2×D4—182no—
901C2×D4—182no—
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—361no—
920C2×D4—361no—
921C2×D4—361no—
922C2×D4—361no—
923C2×D4—361no—
924C2×D4—361no—
925C2×D4—361no—
926C2×D4—361no—
927C2×D4—361no—
928C2×D4—361no—
929C22×C4—31no—
930C22×C4—31no—
931C22×C4—31no—
932C22×C4—31no—
933C22×C4—31no—
934C22×C4—62no—
935C22×C4—62no—
936C22×C4—62no—
937C22×C4—91no—
938C22×C4—91no—
939C22×C4—182no—
940C22×C4—182no—
941C22×C4—182no—
942C22×C4C2×D3211yescharacteristic
943C22×C4C2×D3211yescharacteristic
944C4⋊C4—34no—
945C4⋊C4—62no—
946C4⋊C4—94no—
947C22⋊C4—22no—
948C22⋊C4—62no—
949C22⋊C4—62no—
950C22⋊C4—62no—
951C22⋊C4—62no—
952C22⋊C4—182no—
953C22⋊C4—182no—
954C22⋊C4—182no—
955C22⋊C4—182no—
956C22⋊C4—182no—
957C42—62no—
958C42—94no—
959C42—182no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—42no—
968C22×C3—42no—
969C22×C3—42no—
970C22×C3—41no—
971C22×C3—41no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
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—62no—
985C22×C3—62no—
986C22×C3—62no—
987C22×C3—81no—
988C22×C3—81no—
989C22×C3—81no—
990C22×C3—81no—
991C22×C3—121no—
992C22×C3—121no—
993C22×C3—121no—
994C22×C3—121no—
995C22×C3—121no—
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×C3C2×#23511yescharacteristic
1010C22×C3C2×D3×D411yescharacteristic
1011C22×C3C2×D3×D411yescharacteristic
1012C22×C3C2×D3×D411yescharacteristic
1013C22×C3C2×D3×D411yescharacteristic
1014C22×C3C2×D3×D411yescharacteristic
1015C22×C3C2×D3×D411yescharacteristic
1016C22×C3C2×D3×D411yescharacteristic
1017C22×C3#100411yescharacteristic
1018C22×C3D3×#4111yescharacteristic
1019C22×C3#100911yescharacteristic
1020C22×C3#100911yescharacteristic
1021C22×C3#100911yescharacteristic
1022C22×C3C22×#6711yescharacteristic
1023C2×D3—22no—
1024C2×D3—22no—
1025C2×D3—22no—
1026C2×D3—41no—
1027C2×D3—41no—
1028C2×D3—41no—
1029C2×D3—41no—
1030C2×D3—41no—
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—62no—
1045C2×D3—62no—
1046C2×D3—62no—
1047C2×D3—62no—
1048C2×D3—62no—
1049C2×D3—62no—
1050C2×D3—122no—
1051C2×D3—122no—
1052C2×D3—122no—
1053C2×D3—121no—
1054C2×D3—121no—
1055C2×D3—121no—
1056C2×D3—121no—
1057C2×D3—121no—
1058C2×D3—121no—
1059C2×D3—121no—
1060C2×D3—121no—
1061C2×D3—122no—
1062C2×D3—122no—
1063C2×D3—122no—
1064C2×D3—121no—
1065C2×D3—121no—
1066C2×D3—121no—
1067C2×D3—121no—
1068C2×D3—121no—
1069C2×D3—121no—
1070C2×D3—121no—
1071C2×D3—121no—
1072C2×D3—121no—
1073C2×D3—121no—
1074C2×D3—121no—
1075C2×D3—121no—
1076C2×D3—121no—
1077C2×D3—121no—
1078C2×D3—241no—
1079C2×D3—241no—
1080C2×D3—241no—
1081C2×D3—241no—
1082C2×D3—241no—
1083C2×D3—241no—
1084C2×D3—241no—
1085C2×D3—241no—
1086C3×C4—22no—
1087C3×C4—22no—
1088C3×C4—34no—
1089C3×C4—34no—
1090C3×C4—42no—
1091C3×C4—41no—
1092C3×C4—41no—
1093C3×C4—62no—
1094C3×C4—62no—
1095C3×C4—81no—
1096C3×C4—121no—
1097Dic3—22no—
1098Dic3—22no—
1099Dic3—41no—
1100Dic3—62no—
1101Dic3—62no—
1102Dic3—62no—
1103Dic3—62no—
1104Dic3—122no—
1105Dic3—122no—
1106Dic3#88414yescomplemented
1107Dic3#94014yescomplemented
1108C32#254111yescharacteristic, complemented, Sylow
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—32no—
1117C23—61no—
1118C23—61no—
1119C23—61no—
1120C23—61no—
1121C23—61no—
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—92no—
1138C23—181no—
1139C23—181no—
1140C23—181no—
1141C23—181no—
1142C23—181no—
1143C23—181no—
1144C23—181no—
1145C23—181no—
1146C23—181no—
1147C23—181no—
1148C23—181no—
1149C23—181no—
1150C23—181no—
1151C23C22×D3211yescharacteristic
1152D4—124no—
1153D4—124no—
1154D4—124no—
1155D4—124no—
1156D4—188no—
1157D4—364no—
1158D4—364no—
1159D4—364no—
1160D4—364no—
1161D4—364no—
1162D4—364no—
1163D4—364no—
1164D4—364no—
1165D4—364no—
1166D4—364no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—32no—
1173C2×C4—32no—
1174C2×C4—32no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—32no—
1178C2×C4—32no—
1179C2×C4—32no—
1180C2×C4—61no—
1181C2×C4—61no—
1182C2×C4—61no—
1183C2×C4—61no—
1184C2×C4—61no—
1185C2×C4—61no—
1186C2×C4—61no—
1187C2×C4—92no—
1188C2×C4—92no—
1189C2×C4—124no—
1190C2×C4—181no—
1191C2×C4—181no—
1192C2×C4—181no—
1193C2×C4—181no—
1194C2×C4—364no—
1195C2×C4D3×#6712yes—
1196C2×C3—21no—
1197C2×C3—21no—
1198C2×C3—21no—
1199C2×C3—21no—
1200C2×C3—21no—
1201C2×C3—21no—
1202C2×C3—21no—
1203C2×C3—82no—
1204C2×C3—81no—
1205C2×C3—81no—
1206C2×C3—122no—
1207C2×C3—241no—
1208C2×C3—241no—
1209C2×C3C2×#88411yescharacteristic
1210C2×C3#555311yescharacteristic
1211C2×C3#555311yescharacteristic
1212C2×C3#559911yescharacteristic
1213C2×C3D3×#12111yescharacteristic
1214C2×C3#560711yescharacteristic
1215C2×C3#560911yescharacteristic
1216C2×C3#560911yescharacteristic
1217C2×C3#560911yescharacteristic
1218C2×C3#567411yescharacteristic
1219C2×C3D3×#12711yescharacteristic
1220C2×C3D4×#6711yescharacteristic
1221C2×C3C2×#94011yescharacteristic
1222C2×C3#583411yescharacteristic
1223D3—42no—
1224D3—81no—
1225D3—81no—
1226D3—122no—
1227D3—122no—
1228D3—242no—
1229D3—242no—
1230D3—241no—
1231D3—241no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—62no—
1240C22—62no—
1241C22—62no—
1242C22—121no—
1243C22—121no—
1244C22—121no—
1245C22—121no—
1246C22—121no—
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—182no—
1261C22—182no—
1262C22—182no—
1263C22—361no—
1264C22—361no—
1265C22—361no—
1266C22—361no—
1267C22—361no—
1268C22—361no—
1269C22—361no—
1270C22—361no—
1271C22—361no—
1272C22—361no—
1273C22—361no—
1274C22D3×#23511yescharacteristic
1275C22#6430811yescharacteristic
1276C22D32×D411yescharacteristic
1277C22D32×D411yescharacteristic
1278C22D32×D411yescharacteristic
1279C22#6431411yescharacteristic
1280C22C2×D3×#6711yescharacteristic
1281C4—22no—
1282C4—34no—
1283C4—34no—
1284C4—41no—
1285C4—62no—
1286C4—62no—
1287C4—121no—
1288C4—182no—
1289C4—182no—
1290C3—21no—
1291C3#7634811yescharacteristic, complemented
1292C3#8266911yescharacteristic, complemented
1293C2—81no—
1294C2—122no—
1295C2—241no—
1296C2—241no—
1297C2—362no—
1298C2—721no—
1299C2#1059424611yescharacteristic
1300C2D3×#88411yescharacteristic
1301C2#1059428411yescharacteristic
1302C2#1059428711yescharacteristic
1303C2#1059500711yescharacteristic
1304C2D3×#94011yescharacteristic
1305C2#1059529111yescharacteristic
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×C3×#884C2semidirect
2. C2×#63979C2semidirect
3. C2×#63979C2semidirect
4. C2×#63958C2semidirect
5. C2×#63911C2semidirect
6. C2×#63910C2semidirect
7. C2×#63906C2semidirect
8. C2×#63904C2semidirect
9. #10592659C2semidirect
10. C3×#4957C2semidirect
11. #10591724C2semidirect
12. #10591393C2semidirect
13. #10591389C2semidirect
14. #10591384C2semidirect
15. Dic3×Dic3⋊C4C2semidirect
75. C2×#884D3semidirect
90. #4957D3semidirect
148. C2×#626D4semidirect
166. C3×Dic3⋊C4D4semidirect
168. Dic3⋊Dic3D4semidirect
173. Dic32D4semidirect
547. Dic3⋊C4#67semidirect
609. C3×Dic3#121semidirect
610. C3×Dic3#127semidirect
1106. Dic3#884semidirect
1107. Dic3#940semidirect
1108. C32#2541semidirect
1291. C3#76348semidirect
1292. C3#82669semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8842
C2×#639792
C2×#639582
C2×#639112
C2×#639102
C2×#639062
C2×#639042
#105926592
C3×#49572
#105917242
#105913932
#105913892
#105913842
Dic3×Dic3⋊C42
#826693
#763483