Finite Group Databasebeta

← C3×#80540 #11878755

Subgroups — C3×#80540 #11878755

Order 1152.

938 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5668C211yesmaximal, characteristic, complemented
2C3×#5548C211yesmaximal, characteristic, complemented
3C32×#463C211yesmaximal, characteristic, complemented
4C3×#5175C211yesmaximal, characteristic, complemented
5C3×#5172C211yesmaximal, characteristic, complemented
6C3×#5158C211yesmaximal, characteristic, complemented
7C3×#5151C211yesmaximal, characteristic, complemented
8C3×#5057C211yesmaximal, characteristic, complemented
9C3×#5016C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×#4833C211yesmaximal, characteristic, complemented
12C3×#4810C211yesmaximal, characteristic, complemented
13C3×#4792C211yesmaximal, characteristic, complemented
14C3×#4781C211yesmaximal, characteristic, complemented
15C3×#4760C211yesmaximal, characteristic, complemented
16C3×#3207—31nomaximal
17#80540C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#235—21no—
21C2×C32×SD16C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic
23C32×#124C2211yescharacteristic
24C32×C4×D4C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#940C2211yescharacteristic
28C3×#940C2211yescharacteristic
29C3×#938C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×C4×#67—21no—
34C2×C3×D24C2211yescharacteristic
35C2×C3×#204C2211yescharacteristic
36C3×#895C2211yescharacteristic
37C3×#888C2211yescharacteristic
38C3×#885—21no—
39C3×#884—21no—
40C3×#884—21no—
41C3×#884—21no—
42C3×#67⋊C4—21no—
43C3×#67⋊C4—21no—
44C3×#875C2211yescharacteristic
45C3×C4×D12C2211yescharacteristic
46C3×C42×D3C2211yescharacteristic
47C32×C4⋊C8C2211yescharacteristic
48C32×#103C2211yescharacteristic
49C32×#102C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#809C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#532—31no—
62C3×#532—31no—
63#5668C2×C311yescharacteristic, complemented
64#5548C2×C311yescharacteristic, complemented
65C3×#493—31no—
66C3×#492—31no—
67C3×#487—31no—
68C3×#486—31no—
69C3×#463—21no—
70C3×#463—31no—
71C3×#463—31no—
72C3×#463—31no—
73C3×#463D311yescharacteristic, complemented
74C3×#463C2×C311yescharacteristic, complemented
75C3×#449—31no—
76C3×#449—31no—
77C3×#449—31no—
78C3×#449—31no—
79C3×#431—31no—
80#5175C2×C311yescharacteristic, complemented
81#5172C2×C311yescharacteristic, complemented
82#5158C2×C311yescharacteristic, complemented
83#5151C2×C311yescharacteristic, complemented
84#5057C2×C311yescharacteristic, complemented
85#5016C2×C311yescharacteristic, complemented
86#4844C2×C311yescharacteristic, complemented
87#4833C2×C311yescharacteristic, complemented
88#4810C2×C311yescharacteristic, complemented
89#4792C2×C311yescharacteristic, complemented
90#4781C2×C311yescharacteristic, complemented
91#4760C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#239—41no—
104C3×#239—41no—
105C3×#237—41no—
106C3×#237—41no—
107C3×#235—44no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3D411yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
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—
125C32×C22⋊C4—21no—
126C32×C22⋊C4—21no—
127C32×C42C2311yescharacteristic
128C3×#217—21no—
129C3×#215—41no—
130C3×#214—41no—
131C3×#213—41no—
132C3×#213—41no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×C4×Dic3D411yescharacteristic
142C3×C4×Dic3D411yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C3×D24—41no—
147C3×#204—41no—
148#3207—31noSylow
149C2×C3×#41—31no—
150C2×C3×#41—31no—
151C2×C3×#41—61no—
152C2×#239C22×C311yescharacteristic
153C2×#237C22×C311yescharacteristic
154C2×#235—21no—
155C2×C3×SD16—21no—
156C2×C3×SD16—31no—
157C2×C3×SD16—31no—
158C2×C3×SD16—31no—
159C2×C3×SD16C2×D311yescharacteristic
160C2×C3×SD16C22×C311yescharacteristic
161C2×C3×D8—21no—
162C2×C3×D8—31no—
163C2×C3×D8—31no—
164C2×C3×D8—31no—
165C2×C3×D8C2×D311yescharacteristic
166C2×C3×D8C22×C311yescharacteristic
167C3×C4⋊Q8—31no—
168C3×C4⋊Q8—31no—
169C3×#127—31no—
170C3×#127—31no—
171C3×#124—21no—
172C3×#124—31no—
173C3×#124—61no—
174C3×#124C2×D311yescharacteristic
175C3×#124C22×C311yescharacteristic
176C3×#121—31no—
177C3×#121—31no—
178C3×#121—61no—
179C3×#121—61no—
180C3×#121—61no—
181C3×C4×D4—21no—
182C3×C4×D4—31no—
183C3×C4×D4—61no—
184C3×C4×D4—61no—
185C3×C4×D4—61no—
186C3×C4×D4C2×D311yescharacteristic
187C3×C4×D4C22×C311yescharacteristic
188C2×C3×C42—31no—
189#944C22×C311yescharacteristic
190C2×#215C22×C311yescharacteristic
191#940C22×C311yescharacteristic
192#940C22×C311yescharacteristic
193#938C22×C311yescharacteristic
194C2×#214C22×C311yescharacteristic
195C2×#213C22×C311yescharacteristic
196C2×#213C22×C311yescharacteristic
197C4×#67—21no—
198C2×D24C22×C311yescharacteristic
199C2×#204C22×C311yescharacteristic
200#895C22×C311yescharacteristic
201#888C22×C311yescharacteristic
202#885—21no—
203#884—21no—
204#884—21no—
205#884—21no—
206#67⋊C4—21no—
207#67⋊C4—21no—
208#875C22×C311yescharacteristic
209C4×D12C22×C311yescharacteristic
210C42×D3C22×C311yescharacteristic
211C3×C4⋊C8—21no—
212C3×C4⋊C8—31no—
213C3×C4⋊C8C2×D311yescharacteristic
214C3×C4⋊C8C22×C311yescharacteristic
215C3×#103—21no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#103C2×D311yescharacteristic
220C3×#103C22×C311yescharacteristic
221C3×#102—21no—
222C3×#102—31no—
223C3×#102—31no—
224C3×#102—31no—
225C3×#102C2×D311yescharacteristic
226C3×#102C22×C311yescharacteristic
227C3×C22⋊C8—31no—
228C3×C22⋊C8—31no—
229C3×C4×C8—31no—
230C3×C4×C8—31no—
231#835C22×C311yescharacteristic
232#832C22×C311yescharacteristic
233#821C22×C311yescharacteristic
234(C2×D3)⋊C8C22×C311yescharacteristic
235(C2×D3)⋊C8C22×C311yescharacteristic
236#816C22×C311yescharacteristic
237C8×Dic3C22×C311yescharacteristic
238C8×Dic3C22×C311yescharacteristic
239#810C22×C311yescharacteristic
240#809C22×C311yescharacteristic
241C4⋊(C3⋊C8)C22×C311yescharacteristic
242C23×C32—21no—
243C23×C32—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3C2×D411yescharacteristic
247C32×Q8—21no—
248C32×Q8—21no—
249C32×D4—21no—
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—42no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C3×#67—42no—
260C3×#67—42no—
261C3×#67—42no—
262C3×#67—42no—
263C3×#67—42no—
264C3×#67—42no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—42no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—42no—
276C3×D12—42no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—22no—
280C3×C4×D3—22no—
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#463C3×D311yescharacteristic, complemented
300#449—31no—
301#449—31no—
302#449—31no—
303#449—31no—
304#431—31no—
305C3×#41—124no—
306C3×#41—121no—
307C3×#41—121no—
308C3×#41—121no—
309C3×#41—121no—
310C2×C3×Q8—21no—
311C2×C3×Q8—31no—
312C2×C3×Q8—61no—
313C2×C3×Q8C22×D311yescharacteristic
314C2×C3×Q8C23×C311yescharacteristic
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4C22×D311yescharacteristic
328C2×C3×D4C22×D311yescharacteristic
329C2×C3×D4C23×C311yescharacteristic
330C2×C3×D4C23×C311yescharacteristic
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—41no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—21no—
346C22×Dic3—21no—
347#239—41no—
348#239—41no—
349#237—41no—
350#237—41no—
351#235—44no—
352C2×D12—21no—
353C2×D12—21no—
354C2×D12C23×C311yescharacteristic
355C2×D12C23×C311yescharacteristic
356C2×C4×D3—21no—
357C2×C4×D3—21no—
358C2×C4×D3C3×D411yescharacteristic
359C2×C4×D3C3×D411yescharacteristic
360C2×C4×D3C23×C311yescharacteristic
361C2×Dic6—21no—
362C2×Dic6C23×C311yescharacteristic
363C3×SD16—41no—
364C3×SD16—41no—
365C3×SD16—42no—
366C3×SD16—121no—
367C3×SD16—121no—
368C3×SD16—121no—
369C3×D8—41no—
370C3×D8—41no—
371C3×D8—42no—
372C3×D8—121no—
373C3×D8—121no—
374C3×D8—121no—
375C2×C3×C8—21no—
376C2×C3×C8—21no—
377C2×C3×C8—31no—
378C2×C3×C8—31no—
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C23×C311yescharacteristic
382C2×C3×C8C23×C311yescharacteristic
383C3×C4⋊C4—21no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C23×C311yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—41no—
397C3×C22⋊C4—41no—
398C3×C22⋊C4—41no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C42—21no—
405C3×C42—31no—
406C3×C42—31no—
407C3×C42—31no—
408C3×C42C22×D311yescharacteristic
409C3×C42C23×C311yescharacteristic
410#217—21no—
411#215—41no—
412#214—41no—
413#213—41no—
414#213—41no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419C4⋊Dic3C23×C311yescharacteristic
420Dic3⋊C4—21no—
421Dic3⋊C4—21no—
422Dic3⋊C4—21no—
423C4×Dic3C3×D411yescharacteristic
424C4×Dic3C3×D411yescharacteristic
425C4×Dic3C23×C311yescharacteristic
426C2×C3⋊C8C23×C311yescharacteristic
427C2×C3⋊C8C23×C311yescharacteristic
428D24—41no—
429#204—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32C22×D411yescharacteristic
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C32×C4—21no—
447C32×C4—21no—
448C32×C4—41no—
449C32×C4—41no—
450C32×C4H(5,𝔽2)11yescharacteristic
451C32×C4H(5,𝔽2)11yescharacteristic
452C3×Dic3—21no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3#13512yes—
456C3×Dic3AGL(1,ℤ/8)12yes—
457C2×#41—31no—
458C2×#41—31no—
459C2×#41—61no—
460C2×SD16—31no—
461C2×SD16—31no—
462C2×SD16—31no—
463C2×SD16C2×C3×D311yescharacteristic
464C2×D8—31no—
465C2×D8—31no—
466C2×D8—31no—
467C2×D8C2×C3×D311yescharacteristic
468C4⋊Q8—31no—
469C4⋊Q8—31no—
470#127—31no—
471#127—31no—
472#124—31no—
473#124—61no—
474#124C2×C3×D311yescharacteristic
475#121—31no—
476#121—31no—
477#121—61no—
478#121—61no—
479#121—61no—
480C4×D4—31no—
481C4×D4—61no—
482C4×D4—61no—
483C4×D4—61no—
484C4×D4C2×C3×D311yescharacteristic
485C2×C42—31no—
486C4⋊C8—31no—
487C4⋊C8C2×C3×D311yescharacteristic
488#103—31no—
489#103—31no—
490#103—31no—
491#103C2×C3×D311yescharacteristic
492#102—31no—
493#102—31no—
494#102—31no—
495#102C2×C3×D311yescharacteristic
496C22⋊C8—31no—
497C22⋊C8—31no—
498C4×C8—31no—
499C4×C8—31no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—31no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—61no—
508C23×C3—61no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3C2×C3×D411yescharacteristic
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—41no—
517C3×Q8—41no—
518C3×Q8—61no—
519C3×Q8—61no—
520C3×Q8—122no—
521C3×D4—22no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—41no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—122no—
538C3×D4—122no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—122no—
543C3×D4—122no—
544C3×D4—122no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—42no—
558C2×C3×C4—42no—
559C2×C3×C4—62no—
560C2×C3×C4—62no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—82no—
566C2×C3×C4—122no—
567C2×C3×C4—122no—
568C2×C3×C4—122no—
569C2×C3×C4D3×D411yescharacteristic
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4C2×C3×D411yescharacteristic
572C2×C3×C4C2×C3×D411yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574C2×C3×C4C24×C311yescharacteristic
575#67—42no—
576#67—42no—
577#67—42no—
578#67—42no—
579#67—42no—
580#67—42no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—42no—
584C2×Dic3C2×C3×D411yescharacteristic
585C2×Dic3C2×C3×D411yescharacteristic
586C2×Dic3C2×C3×D411yescharacteristic
587D12—21no—
588D12—21no—
589D12—21no—
590D12—21no—
591D12—42no—
592D12—42no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—22no—
596C4×D3—22no—
597C4×D3—42no—
598C4×D3—42no—
599Dic6—21no—
600Dic6—21no—
601Dic6—42no—
602C3×C8—21no—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—41no—
607C3×C8—41no—
608C3×C8—61no—
609C3×C8—61no—
610C3⋊C8—21no—
611C3⋊C8—21no—
612C2×C32—81no—
613C2×C32—81no—
614C2×C32#53511yescharacteristic
615C2×C32C2×#13511yescharacteristic
616C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
617C3×D3—41no—
618C3×D3—81no—
619C3×D3—81no—
620#41—124no—
621#41—121no—
622#41—121no—
623#41—121no—
624#41—121no—
625C2×Q8—31no—
626C2×Q8—61no—
627C2×Q8C22×C3×D311yescharacteristic
628C2×D4—31no—
629C2×D4—31no—
630C2×D4—61no—
631C2×D4—61no—
632C2×D4—61no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4C22×C3×D311yescharacteristic
639C2×D4C22×C3×D311yescharacteristic
640C22×C4—21no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647SD16—41no—
648SD16—121no—
649SD16—121no—
650SD16—121no—
651D8—41no—
652D8—121no—
653D8—121no—
654D8—121no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8C22×C3×D311yescharacteristic
658C2×C8C22×C3×D311yescharacteristic
659C4⋊C4—31no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4C22×C3×D311yescharacteristic
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C42—31no—
673C42—31no—
674C42—31no—
675C42C22×C3×D311yescharacteristic
676C22×C3—21no—
677C22×C3—42no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—61no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—121no—
704C22×C3C2×D3×D411yescharacteristic
705C22×C3C22×C3×D411yescharacteristic
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—32no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—61no—
730C3×C4—81no—
731C3×C4—81no—
732C3×C4—121no—
733C3×C4—121no—
734C3×C4#100411yescharacteristic
735C3×C4#100911yescharacteristic
736C3×C4C3×H(5,𝔽2)11yescharacteristic
737C3×C4C3×H(5,𝔽2)11yescharacteristic
738Dic3—21no—
739Dic3—41no—
740Dic3—41no—
741Dic3C3×#13512yes—
742Dic3C3×AGL(1,ℤ/8)12yes—
743C32#320711yescharacteristic, complemented, Sylow
744C23—21no—
745C23—21no—
746C23—31no—
747C23—61no—
748C23—61no—
749Q8—21no—
750Q8—21no—
751Q8—61no—
752Q8—61no—
753Q8—122no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—61no—
759D4—61no—
760D4—61no—
761D4—61no—
762D4—122no—
763D4—122no—
764D4—122no—
765D4—122no—
766D4—122no—
767D4—122no—
768D4—122no—
769D4—122no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—31no—
775C2×C4—42no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—122no—
783C2×C4—122no—
784C2×C4—122no—
785C2×C4C3×D3×D411yescharacteristic
786C2×C4C3×D3×D411yescharacteristic
787C2×C4C23×C3×D311yescharacteristic
788C8—21no—
789C8—21no—
790C8—61no—
791C8—61no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—82no—
796C2×C3—81no—
797C2×C3—81no—
798C2×C3—81no—
799C2×C3—81no—
800C2×C3—121no—
801C2×C3—161no—
802C2×C3—241no—
803C2×C3—241no—
804C2×C3#560711yescharacteristic
805C2×C3D3×#13511yescharacteristic
806C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
807C2×C3C3×#53511yescharacteristic
808C2×C3C2×C3×#13511yescharacteristic
809C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
810D3—41no—
811D3—81no—
812D3—81no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—61no—
820C22—61no—
821C22—61no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22C2×C3×D3×D411yescharacteristic
829C4—21no—
830C4—21no—
831C4—32no—
832C4—32no—
833C4—41no—
834C4—41no—
835C4—61no—
836C4—121no—
837C4—121no—
838C4C3×#100411yescharacteristic
839C4C3×#100911yescharacteristic
840C3—21no—
841C3#8054011yescharacteristic, direct product factor
842C3C3×#320711yescharacteristic, complemented
843C2—81no—
844C2—81no—
845C2—121no—
846C2—241no—
847C2—241no—
848C2C3×#560711yescharacteristic
849C2C3×D3×#13511yescharacteristic
850C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#463C2
socleC22×C32C22×D4
hypercenterC3×#463D3
hypocenterC3C3×#3207
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C3×#5668C2semidirect
2. C3×#5548C2semidirect
3. C32×#463C2semidirect
4. C3×#5175C2semidirect
5. C3×#5172C2semidirect
6. C3×#5158C2semidirect
7. C3×#5151C2semidirect
8. C3×#5057C2semidirect
9. C3×#5016C2semidirect
10. C3×#4844C2semidirect
11. C3×#4833C2semidirect
12. C3×#4810C2semidirect
13. C3×#4792C2semidirect
14. C3×#4781C2semidirect
15. C3×#4760C2semidirect
17. #80540C3direct (N × H)
63. #5668C2×C3semidirect
64. #5548C2×C3semidirect
73. C3×#463D3semidirect
74. C3×#463C2×C3semidirect
80. #5175C2×C3semidirect
81. #5172C2×C3semidirect
82. #5158C2×C3semidirect
83. #5151C2×C3semidirect
84. #5057C2×C3semidirect
85. #5016C2×C3semidirect
86. #4844C2×C3semidirect
87. #4833C2×C3semidirect
88. #4810C2×C3semidirect
89. #4792C2×C3semidirect
90. #4781C2×C3semidirect
91. #4760C2×C3semidirect
299. #463C3×D3semidirect
743. C32#3207semidirect
841. C3#80540direct (N × H)
842. C3C3×#3207semidirect

Maximal subgroups

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

subgroupindex
C3×#56682
C3×#55482
C32×#4632
C3×#51752
C3×#51722
C3×#51582
C3×#51512
C3×#50572
C3×#50162
C3×#48442
C3×#48332
C3×#48102
C3×#47922
C3×#47812
C3×#47602
C3×#32073
#805403