Finite Group Databasebeta

← C3×#80076 #11878752

Subgroups — C3×#80076 #11878752

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5832C211yesmaximal, characteristic, complemented
2C3×#5596C211yesmaximal, characteristic, complemented
3C32×#449C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5C3×#5175C211yesmaximal, characteristic, complemented
6C3×#5165C211yesmaximal, characteristic, complemented
7C3×#5153C211yesmaximal, characteristic, complemented
8C3×#5151C211yesmaximal, characteristic, complemented
9C3×#5037C211yesmaximal, characteristic, complemented
10C3×#4819C211yesmaximal, characteristic, complemented
11C3×#4792C211yesmaximal, characteristic, complemented
12C3×#4787C211yesmaximal, characteristic, complemented
13C3×#4760C211yesmaximal, characteristic, complemented
14C3×#4734C211yesmaximal, characteristic, complemented
15C3×#4718C211yesmaximal, characteristic, complemented
16C3×#3207—31nomaximal
17#80076C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237—21no—
20C2×C3×#235C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic
23C32×#121C2211yescharacteristic
24C3×#947C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#940C2211yescharacteristic
28C3×#940C2211yescharacteristic
29C3×#939—21no—
30C3×#939—21no—
31C3×#939—21no—
32C3×#936C2211yescharacteristic
33C3×D4×Dic3C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic
35C2×C3×#213C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C3×#930C2211yescharacteristic
38C3×C4×#67—21no—
39C3×C4×#67—21no—
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×D24C2211yescharacteristic
42C2×C3×#204C2211yescharacteristic
43C3×#893C2211yescharacteristic
44C3×#888C2211yescharacteristic
45C3×#885—21no—
46C3×#67⋊C4—21no—
47C32×#103C2211yescharacteristic
48C32×#102C2211yescharacteristic
49C32×C22⋊C8C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#830C2211yescharacteristic
53C3×#821C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×C8×Dic3C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#809C2211yescharacteristic
61C3×#532—31no—
62C3×#532—31no—
63#5832C2×C311yescharacteristic, complemented
64#5596C2×C311yescharacteristic, complemented
65C3×#493—31no—
66C3×#492—31no—
67C3×#487—31no—
68C3×#486—31no—
69C3×#463—31no—
70C3×#463—31no—
71C3×#463—31no—
72C3×#463—31no—
73C3×#449—21no—
74C3×#449—31no—
75C3×#449—31no—
76C3×#449—31no—
77C3×#449D311yescharacteristic, complemented
78C3×#449C2×C311yescharacteristic, complemented
79C3×#431—31no—
80#5238C2×C311yescharacteristic, complemented
81#5175C2×C311yescharacteristic, complemented
82#5165C2×C311yescharacteristic, complemented
83#5153C2×C311yescharacteristic, complemented
84#5151C2×C311yescharacteristic, complemented
85#5037C2×C311yescharacteristic, complemented
86#4819C2×C311yescharacteristic, complemented
87#4792C2×C311yescharacteristic, complemented
88#4787C2×C311yescharacteristic, complemented
89#4760C2×C311yescharacteristic, complemented
90#4734C2×C311yescharacteristic, complemented
91#4718C2×C311yescharacteristic, complemented
92C32×#41—41no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C22×C32×C4C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3D411yescharacteristic
109C22×C3×Dic3D411yescharacteristic
110C3×#237—44no—
111C3×#235—41no—
112C3×#235—41no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C32×SD16—41no—
120C32×D8—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125C3×#217—21no—
126C3×#217—21no—
127C3×#217—21no—
128C3×#215—41no—
129C3×#214—41no—
130C3×#213—41no—
131C3×#213—41no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3D411yescharacteristic
141C3×C4×Dic3D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C3×D24—41no—
147C3×#204—41no—
148#3207—31noSylow
149C2×C3×#41—21no—
150C2×C3×#41—31no—
151C2×C3×#41—61no—
152C2×C3×#41C2×D311yescharacteristic
153C2×C3×#41C22×C311yescharacteristic
154C2×#237—21no—
155C2×#235C22×C311yescharacteristic
156C2×C3×SD16—21no—
157C2×C3×SD16—31no—
158C2×C3×SD16—31no—
159C2×C3×SD16—31no—
160C2×C3×SD16C2×D311yescharacteristic
161C2×C3×SD16C22×C311yescharacteristic
162C2×C3×D8—21no—
163C2×C3×D8—31no—
164C2×C3×D8—31no—
165C2×C3×D8—31no—
166C2×C3×D8C2×D311yescharacteristic
167C2×C3×D8C22×C311yescharacteristic
168C3×C4⋊Q8—31no—
169C3×C4⋊Q8—31no—
170C3×#127—31no—
171C3×#127—31no—
172C3×#124—31no—
173C3×#124—31no—
174C3×#124—61no—
175C3×#121—21no—
176C3×#121—31no—
177C3×#121—61no—
178C3×#121—61no—
179C3×#121—61no—
180C3×#121C2×D311yescharacteristic
181C3×#121C22×C311yescharacteristic
182C3×C4×D4—31no—
183C3×C4×D4—31no—
184C3×C4×D4—61no—
185C3×C4×D4—61no—
186C3×C4×D4—61no—
187C2×C3×C42—31no—
188#947C22×C311yescharacteristic
189#944C22×C311yescharacteristic
190C2×#215C22×C311yescharacteristic
191#940C22×C311yescharacteristic
192#940C22×C311yescharacteristic
193#939—21no—
194#939—21no—
195#939—21no—
196#936C22×C311yescharacteristic
197D4×Dic3C22×C311yescharacteristic
198C2×#214C22×C311yescharacteristic
199C2×#213C22×C311yescharacteristic
200C2×#213C22×C311yescharacteristic
201#930C22×C311yescharacteristic
202C4×#67—21no—
203C4×#67—21no—
204C2×C4×Dic3C22×C311yescharacteristic
205C2×D24C22×C311yescharacteristic
206C2×#204C22×C311yescharacteristic
207#893C22×C311yescharacteristic
208#888C22×C311yescharacteristic
209#885—21no—
210#67⋊C4—21no—
211C3×C4⋊C8—31no—
212C3×C4⋊C8—31no—
213C3×#103—21no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103C2×D311yescharacteristic
218C3×#103C22×C311yescharacteristic
219C3×#102—21no—
220C3×#102—31no—
221C3×#102—31no—
222C3×#102—31no—
223C3×#102C2×D311yescharacteristic
224C3×#102C22×C311yescharacteristic
225C3×C22⋊C8—21no—
226C3×C22⋊C8—31no—
227C3×C22⋊C8C2×D311yescharacteristic
228C3×C22⋊C8C22×C311yescharacteristic
229C3×C4×C8—31no—
230C3×C4×C8—31no—
231#835C22×C311yescharacteristic
232#832C22×C311yescharacteristic
233#830C22×C311yescharacteristic
234#821C22×C311yescharacteristic
235#816C22×C311yescharacteristic
236Dic3⋊C8C22×C311yescharacteristic
237Dic3⋊C8C22×C311yescharacteristic
238C8×Dic3C22×C311yescharacteristic
239C8×Dic3C22×C311yescharacteristic
240#810C22×C311yescharacteristic
241#809C22×C311yescharacteristic
242C23×C32—21no—
243C23×C32—21no—
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C32×D4—21no—
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—21no—
253C32×D4—42no—
254C32×D4—42no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—42no—
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2411yescharacteristic
262C3×#67—42no—
263C3×#67—42no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—42no—
267C3×#67—42no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—42no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×C4×D3—42no—
282C3×C4×D3—42no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285C3×Dic6—42no—
286C32×C8—21no—
287C32×C8—21no—
288C3×C3⋊C8—21no—
289C3×C3⋊C8—21no—
290#532—31no—
291#532—31no—
292#493—31no—
293#492—31no—
294#487—31no—
295#486—31no—
296#463—31no—
297#463—31no—
298#463—31no—
299#463—31no—
300#449—31no—
301#449—31no—
302#449—31no—
303#449C3×D311yescharacteristic, complemented
304#431—31no—
305C3×#41—41no—
306C3×#41—41no—
307C3×#41—41no—
308C3×#41—41no—
309C3×#41—42no—
310C3×#41—42no—
311C3×#41—121no—
312C3×#41—121no—
313C3×#41—124no—
314C2×C3×Q8—21no—
315C2×C3×Q8—31no—
316C2×C3×Q8—61no—
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C23×C311yescharacteristic
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—41no—
328C2×C3×D4—41no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C23×C311yescharacteristic
338C2×C3×D4C23×C311yescharacteristic
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—41no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C23×C311yescharacteristic
350C2×#67—21no—
351C2×#67—21no—
352C2×#67—21no—
353C2×#67—21no—
354C2×#67—21no—
355C2×#67—21no—
356C22×Dic3—21no—
357C22×Dic3C3×D411yescharacteristic
358C22×Dic3C3×D411yescharacteristic
359#237—44no—
360#235—41no—
361#235—41no—
362C2×D12C23×C311yescharacteristic
363C2×D12C23×C311yescharacteristic
364C2×C4×D3—21no—
365C2×C4×D3—21no—
366C2×Dic6—21no—
367C2×Dic6C23×C311yescharacteristic
368C3×SD16—41no—
369C3×SD16—41no—
370C3×SD16—42no—
371C3×SD16—121no—
372C3×SD16—121no—
373C3×SD16—121no—
374C3×D8—41no—
375C3×D8—41no—
376C3×D8—42no—
377C3×D8—121no—
378C3×D8—121no—
379C3×D8—121no—
380C2×C3×C8—21no—
381C2×C3×C8—21no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C23×C311yescharacteristic
387C2×C3×C8C23×C311yescharacteristic
388C3×C4⋊C4—21no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C4⋊C4C23×C311yescharacteristic
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—41no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C42—31no—
406C3×C42—31no—
407C3×C42—31no—
408C3×C42—31no—
409#217—21no—
410#217—21no—
411#217—21no—
412#215—41no—
413#214—41no—
414#213—41no—
415#213—41no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420C4⋊Dic3C23×C311yescharacteristic
421Dic3⋊C4—21no—
422Dic3⋊C4—21no—
423Dic3⋊C4—21no—
424C4×Dic3C3×D411yescharacteristic
425C4×Dic3C3×D411yescharacteristic
426C4×Dic3C23×C311yescharacteristic
427C4×Dic3C23×C311yescharacteristic
428C2×C3⋊C8C23×C311yescharacteristic
429C2×C3⋊C8C23×C311yescharacteristic
430D24—41no—
431#204—41no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32C22×D411yescharacteristic
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C32×C4—21no—
449C32×C4—41no—
450C32×C4—41no—
451C32×C4H(5,𝔽2)11yescharacteristic
452C32×C4H(5,𝔽2)11yescharacteristic
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3#13512yes—
458C3×Dic3AGL(1,ℤ/8)12yes—
459C2×#41—31no—
460C2×#41—61no—
461C2×#41C2×C3×D311yescharacteristic
462C2×SD16—31no—
463C2×SD16—31no—
464C2×SD16—31no—
465C2×SD16C2×C3×D311yescharacteristic
466C2×D8—31no—
467C2×D8—31no—
468C2×D8—31no—
469C2×D8C2×C3×D311yescharacteristic
470C4⋊Q8—31no—
471C4⋊Q8—31no—
472#127—31no—
473#127—31no—
474#124—31no—
475#124—31no—
476#124—61no—
477#121—31no—
478#121—61no—
479#121—61no—
480#121—61no—
481#121C2×C3×D311yescharacteristic
482C4×D4—31no—
483C4×D4—31no—
484C4×D4—61no—
485C4×D4—61no—
486C4×D4—61no—
487C2×C42—31no—
488C4⋊C8—31no—
489C4⋊C8—31no—
490#103—31no—
491#103—31no—
492#103—31no—
493#103C2×C3×D311yescharacteristic
494#102—31no—
495#102—31no—
496#102—31no—
497#102C2×C3×D311yescharacteristic
498C22⋊C8—31no—
499C22⋊C8C2×C3×D311yescharacteristic
500C4×C8—31no—
501C4×C8—31no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—61no—
510C23×C3—61no—
511C23×C3D3×D411yescharacteristic
512C23×C3C2×C3×D411yescharacteristic
513C22×D3—21no—
514C22×D3—21no—
515C3×Q8—22no—
516C3×Q8—21no—
517C3×Q8—21no—
518C3×Q8—21no—
519C3×Q8—21no—
520C3×Q8—41no—
521C3×Q8—61no—
522C3×Q8—61no—
523C3×Q8—122no—
524C3×D4—22no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4—21no—
533C3×D4—41no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—42no—
537C3×D4—42no—
538C3×D4—42no—
539C3×D4—42no—
540C3×D4—44no—
541C3×D4—61no—
542C3×D4—61no—
543C3×D4—61no—
544C3×D4—61no—
545C3×D4—82no—
546C3×D4—122no—
547C3×D4—122no—
548C3×D4—122no—
549C3×D4—122no—
550C3×D4—122no—
551C3×D4—122no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—42no—
571C2×C3×C4—42no—
572C2×C3×C4—44no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—122no—
578C2×C3×C4—122no—
579C2×C3×C4—122no—
580C2×C3×C4D3×D411yescharacteristic
581C2×C3×C4C2×C3×D411yescharacteristic
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C24×C311yescharacteristic
584#67—42no—
585#67—42no—
586#67—42no—
587#67—42no—
588#67—42no—
589#67—42no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—42no—
595C2×Dic3C2×C3×D411yescharacteristic
596C2×Dic3C2×C3×D411yescharacteristic
597C2×Dic3C2×C3×D411yescharacteristic
598C2×Dic3C2×C3×D411yescharacteristic
599D12—21no—
600D12—21no—
601D12—21no—
602D12—21no—
603C4×D3—42no—
604C4×D3—42no—
605Dic6—21no—
606Dic6—21no—
607Dic6—42no—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—41no—
613C3×C8—41no—
614C3×C8—61no—
615C3×C8—61no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618C2×C32—41no—
619C2×C32—81no—
620C2×C32—81no—
621C2×C32#53511yescharacteristic
622C2×C32C2×#13511yescharacteristic
623C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
624C3×D3—81no—
625C3×D3—81no—
626#41—41no—
627#41—41no—
628#41—121no—
629#41—121no—
630#41—124no—
631C2×Q8—31no—
632C2×Q8—61no—
633C2×Q8C22×C3×D311yescharacteristic
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—31no—
637C2×D4—31no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—61no—
643C2×D4—61no—
644C2×D4C22×C3×D311yescharacteristic
645C2×D4C22×C3×D311yescharacteristic
646C22×C4—21no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4C22×C3×D311yescharacteristic
653SD16—41no—
654SD16—121no—
655SD16—121no—
656SD16—121no—
657D8—41no—
658D8—121no—
659D8—121no—
660D8—121no—
661C2×C8—31no—
662C2×C8—31no—
663C2×C8C22×C3×D311yescharacteristic
664C2×C8C22×C3×D311yescharacteristic
665C4⋊C4—31no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4C22×C3×D311yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C42—31no—
679C42—31no—
680C42—31no—
681C42—31no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—42no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—121no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3C2×D3×D411yescharacteristic
717C22×C3C22×C3×D411yescharacteristic
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—32no—
729C3×C4—32no—
730C3×C4—41no—
731C3×C4—42no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—41no—
736C3×C4—61no—
737C3×C4—61no—
738C3×C4—81no—
739C3×C4—121no—
740C3×C4—121no—
741C3×C4#100411yescharacteristic
742C3×C4#100411yescharacteristic
743C3×C4C3×H(5,𝔽2)11yescharacteristic
744C3×C4C3×H(5,𝔽2)11yescharacteristic
745Dic3—21no—
746Dic3—21no—
747Dic3—41no—
748Dic3—41no—
749Dic3C3×#13512yes—
750Dic3C3×AGL(1,ℤ/8)12yes—
751C32#320711yescharacteristic, complemented, Sylow
752C23—21no—
753C23—21no—
754C23—61no—
755C23—61no—
756C23C3×D3×D411yescharacteristic
757Q8—21no—
758Q8—21no—
759Q8—61no—
760Q8—61no—
761Q8—122no—
762D4—21no—
763D4—21no—
764D4—21no—
765D4—21no—
766D4—42no—
767D4—42no—
768D4—61no—
769D4—61no—
770D4—61no—
771D4—61no—
772D4—122no—
773D4—122no—
774D4—122no—
775D4—122no—
776D4—122no—
777D4—122no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—31no—
786C2×C4—42no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—122no—
792C2×C4—122no—
793C2×C4—122no—
794C2×C4C3×D3×D411yescharacteristic
795C2×C4C23×C3×D311yescharacteristic
796C8—21no—
797C8—21no—
798C8—61no—
799C8—61no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—41no—
804C2×C3—41no—
805C2×C3—81no—
806C2×C3—82no—
807C2×C3—81no—
808C2×C3—81no—
809C2×C3—81no—
810C2×C3—81no—
811C2×C3—161no—
812C2×C3—241no—
813C2×C3—241no—
814C2×C3#559211yescharacteristic
815C2×C3D3×#13511yescharacteristic
816C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
817C2×C3C3×#53511yescharacteristic
818C2×C3C2×C3×#13511yescharacteristic
819C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
820D3—81no—
821D3—81no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22C2×C3×D3×D411yescharacteristic
838C4—21no—
839C4—32no—
840C4—32no—
841C4—41no—
842C4—41no—
843C4—61no—
844C4—61no—
845C4—121no—
846C4—121no—
847C4C3×#100411yescharacteristic
848C4C3×#100411yescharacteristic
849C3—21no—
850C3#8007611yescharacteristic, direct product factor
851C3C3×#320711yescharacteristic, complemented
852C2—41no—
853C2—81no—
854C2—81no—
855C2—241no—
856C2—241no—
857C2C3×#559211yescharacteristic
858C2C3×D3×#13511yescharacteristic
859C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenterC3×#449D3
hypocenterC3C3×#3207
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C3×#5832C2semidirect
2. C3×#5596C2semidirect
3. C32×#449C2semidirect
4. C3×#5238C2semidirect
5. C3×#5175C2semidirect
6. C3×#5165C2semidirect
7. C3×#5153C2semidirect
8. C3×#5151C2semidirect
9. C3×#5037C2semidirect
10. C3×#4819C2semidirect
11. C3×#4792C2semidirect
12. C3×#4787C2semidirect
13. C3×#4760C2semidirect
14. C3×#4734C2semidirect
15. C3×#4718C2semidirect
17. #80076C3direct (N × H)
63. #5832C2×C3semidirect
64. #5596C2×C3semidirect
77. C3×#449D3semidirect
78. C3×#449C2×C3semidirect
80. #5238C2×C3semidirect
81. #5175C2×C3semidirect
82. #5165C2×C3semidirect
83. #5153C2×C3semidirect
84. #5151C2×C3semidirect
85. #5037C2×C3semidirect
86. #4819C2×C3semidirect
87. #4792C2×C3semidirect
88. #4787C2×C3semidirect
89. #4760C2×C3semidirect
90. #4734C2×C3semidirect
91. #4718C2×C3semidirect
303. #449C3×D3semidirect
751. C32#3207semidirect
850. C3#80076direct (N × H)
851. C3C3×#3207semidirect

Maximal subgroups

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

subgroupindex
C3×#58322
C3×#55962
C32×#4492
C3×#52382
C3×#51752
C3×#51652
C3×#51532
C3×#51512
C3×#50372
C3×#48192
C3×#47922
C3×#47872
C3×#47602
C3×#47342
C3×#47182
C3×#32073
#800763