Finite Group Databasebeta

← C3×#81551 #11878414

Subgroups — C3×#81551 #11878414

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5628C211yesmaximal, characteristic
2C3×#5526C211yesmaximal, characteristic
3C32×#485C211yesmaximal, characteristic, complemented
4C3×#5050C211yesmaximal, characteristic, complemented
5C3×#4996C211yesmaximal, characteristic, complemented
6C3×#4888C211yesmaximal, characteristic, complemented
7C3×#4887C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic, complemented
9C3×#4867C211yesmaximal, characteristic, complemented
10C3×#4816C211yesmaximal, characteristic, complemented
11C3×#4813C211yesmaximal, characteristic, complemented
12C3×#4809C211yesmaximal, characteristic, complemented
13C3×#4809C211yesmaximal, characteristic, complemented
14C3×#4739C211yesmaximal, characteristic, complemented
15C3×#4727C211yesmaximal, characteristic
16C3×#3202—31nomaximal
17#81551C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C32×#117C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic
28C2×C3×Dic12C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#897C2211yescharacteristic
34C3×#897C2211yescharacteristic
35C3×#897C2211yescharacteristic
36C3×#894—21no—
37C3×#892C2211yescharacteristic
38C3×#888—21no—
39C3×#886—21no—
40C3×#886—21no—
41C3×#885—21no—
42C3×#883—21no—
43C3×#875—21no—
44C3×#869—21no—
45C32×#107C2211yescharacteristic
46C32×#106C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×#103C2211yescharacteristic
49C32×C22⋊C8C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#536—31no—
62C3×#536—31no—
63#5628C2×C311yescharacteristic
64#5526C2×C311yescharacteristic
65C3×#485—21no—
66C3×#485—31no—
67C3×#485—31no—
68C3×#485—31no—
69C3×#485D311yescharacteristic, complemented
70C3×#485C2×C311yescharacteristic, complemented
71C3×#470—31no—
72C3×#470—31no—
73C3×#467—31no—
74C3×#467—31no—
75C3×#451—31no—
76C3×#451—31no—
77C3×#451—31no—
78C3×#451—31no—
79C3×#408—31no—
80#5050C2×C311yescharacteristic, complemented
81#4996C2×C311yescharacteristic, complemented
82#4888C2×C311yescharacteristic, complemented
83#4887C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic, complemented
85#4867C2×C311yescharacteristic, complemented
86#4816C2×C311yescharacteristic, complemented
87#4813C2×C311yescharacteristic, complemented
88#4809C2×C311yescharacteristic, complemented
89#4809C2×C311yescharacteristic, complemented
90#4739C2×C311yescharacteristic, complemented
91#4727C2×C311yescharacteristic
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67D411yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C3×D3×Q8—41no—
98C3×D3×Q8—41no—
99C3×#235—41no—
100C3×#235—41no—
101C2×C3×D12D411yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6—41no—
108C2×C3×Dic6—41no—
109C2×C3×Dic6D411yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4—21no—
120C32×C22⋊C4—21no—
121C32×C42—21no—
122C3×#217—21no—
123C3×#216—41no—
124C3×#216—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—21no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×Dic12—41no—
144C3×Dic12—41no—
145C3×ΓL(1,𝔽25)—41no—
146C3×D3×C8—41no—
147#3202—31noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—31no—
150C22×C3×Q8—31no—
151C2×D3×Q8C22×C311yescharacteristic
152C2×#235C22×C311yescharacteristic
153C22×Dic6C22×C311yescharacteristic
154C2×C3×Q16—31no—
155C2×C3×Q16—31no—
156C2×C3×Q16—31no—
157C2×C3×Q16—31no—
158C2×C3×M16—31no—
159C22×C3×C8—31no—
160C3×C4⋊Q8—61no—
161C3×C4⋊Q8—61no—
162C3×#124—61no—
163C3×#124—61no—
164C3×#123—61no—
165C3×#123—61no—
166C3×#123—61no—
167C3×#123—61no—
168C3×C22⋊Q8—21no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—31no—
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8C2×D311yescharacteristic
177C3×C22⋊Q8C22×C311yescharacteristic
178C3×#117—21no—
179C3×#117—31no—
180C3×#117C2×D311yescharacteristic
181C3×#117C22×C311yescharacteristic
182#946C22×C311yescharacteristic
183C2×#216C22×C311yescharacteristic
184C2×#216C22×C311yescharacteristic
185#924C22×C311yescharacteristic
186C2×Dic12C22×C311yescharacteristic
187C2×Dic12C22×C311yescharacteristic
188C2×ΓL(1,𝔽25)C22×C311yescharacteristic
189C2×D3×C8C22×C311yescharacteristic
190#897C22×C311yescharacteristic
191#897C22×C311yescharacteristic
192#897C22×C311yescharacteristic
193#897C22×C311yescharacteristic
194#897C22×C311yescharacteristic
195#894—21no—
196#892C22×C311yescharacteristic
197#888—21no—
198#886—21no—
199#886—21no—
200#885—21no—
201#883—21no—
202#875—21no—
203#869—21no—
204C3×#107—21no—
205C3×#107—31no—
206C3×#107C2×D311yescharacteristic
207C3×#107C22×C311yescharacteristic
208C3×#106—21no—
209C3×#106—31no—
210C3×#106C2×D311yescharacteristic
211C3×#106C22×C311yescharacteristic
212C3×#103—21no—
213C3×#103—21no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#103—31no—
220C3×#103C2×D311yescharacteristic
221C3×#103C2×D311yescharacteristic
222C3×#103C22×C311yescharacteristic
223C3×#103C22×C311yescharacteristic
224C3×C22⋊C8—21no—
225C3×C22⋊C8—31no—
226C3×C22⋊C8—31no—
227C3×C22⋊C8—31no—
228C3×C22⋊C8C2×D311yescharacteristic
229C3×C22⋊C8C22×C311yescharacteristic
230#830C22×C311yescharacteristic
231(C2×D3)⋊C8C22×C311yescharacteristic
232(C2×D3)⋊C8C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#810C22×C311yescharacteristic
237#810C22×C311yescharacteristic
238#810C22×C311yescharacteristic
239#808C22×C311yescharacteristic
240#807C22×C311yescharacteristic
241C23×C32C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C3×#67—41no—
255C3×#67—41no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—41no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—41no—
276C3×Dic6—42no—
277C3×Dic6—42no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#536—31no—
283#536—31no—
284#485—31no—
285#485—31no—
286#485—31no—
287#485C3×D311yescharacteristic, complemented
288#470—31no—
289#470—31no—
290#467—31no—
291#467—31no—
292#451—31no—
293#451—31no—
294#451—31no—
295#451—31no—
296#408—31no—
297C3×#41—121no—
298C3×#41—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8—31no—
303C2×C3×Q8—31no—
304C2×C3×Q8—61no—
305C2×C3×Q8—61no—
306C2×C3×Q8—121no—
307C2×C3×Q8—121no—
308C2×C3×Q8—121no—
309C2×C3×Q8—121no—
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×Q8C23×C311yescharacteristic
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C23×C311yescharacteristic
322C2×#67C3×D411yescharacteristic
323C2×#67C3×D411yescharacteristic
324C22×Dic3—21no—
325D3×Q8—41no—
326D3×Q8—41no—
327#235—41no—
328#235—41no—
329C2×D12C3×D411yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3C23×C311yescharacteristic
332C2×C4×D3C23×C311yescharacteristic
333C2×Dic6—21no—
334C2×Dic6—21no—
335C2×Dic6—41no—
336C2×Dic6—41no—
337C2×Dic6C3×D411yescharacteristic
338C2×Dic6C23×C311yescharacteristic
339C2×Dic6C23×C311yescharacteristic
340C2×Dic6C23×C311yescharacteristic
341C3×Q16—121no—
342C3×Q16—121no—
343C3×Q16—121no—
344C3×Q16—121no—
345C3×M16—121no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—121no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C23×C311yescharacteristic
354C2×C3×C8C23×C311yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—41no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C23×C311yescharacteristic
373C3×C4⋊C4C23×C311yescharacteristic
374C3×C4⋊C4C23×C311yescharacteristic
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—41no—
380C3×C22⋊C4—41no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C42—21no—
390C3×C42—21no—
391C3×C42—41no—
392C3×C42—61no—
393#217—21no—
394#216—41no—
395#216—41no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—21no—
403C4⋊Dic3—21no—
404C4⋊Dic3—21no—
405C4⋊Dic3—21no—
406C4⋊Dic3—21no—
407C4⋊Dic3—21no—
408C4⋊Dic3C23×C311yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411C4×Dic3—21no—
412C2×C3⋊C8C23×C311yescharacteristic
413C2×C3⋊C8C23×C311yescharacteristic
414Dic12—41no—
415Dic12—41no—
416ΓL(1,𝔽25)—41no—
417D3×C8—41no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32C22×D411yescharacteristic
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4H(5,𝔽2)11yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—31no—
442C22×Q8—31no—
443C22×Q8—31no—
444C2×Q16—31no—
445C2×Q16—31no—
446C2×Q16—31no—
447C2×Q16—31no—
448C2×M16—31no—
449C22×C8—31no—
450C4⋊Q8—61no—
451C4⋊Q8—61no—
452#124—61no—
453#124—61no—
454#123—61no—
455#123—61no—
456#123—61no—
457#123—61no—
458C22⋊Q8—31no—
459C22⋊Q8—31no—
460C22⋊Q8—31no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464C22⋊Q8—31no—
465C22⋊Q8C2×C3×D311yescharacteristic
466#117—31no—
467#117C2×C3×D311yescharacteristic
468#107—31no—
469#107C2×C3×D311yescharacteristic
470#106—31no—
471#106C2×C3×D311yescharacteristic
472#103—31no—
473#103—31no—
474#103—31no—
475#103—31no—
476#103—31no—
477#103—31no—
478#103C2×C3×D311yescharacteristic
479#103C2×C3×D311yescharacteristic
480C22⋊C8—31no—
481C22⋊C8—31no—
482C22⋊C8—31no—
483C22⋊C8C2×C3×D311yescharacteristic
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—31no—
487C23×C3D3×D411yescharacteristic
488C23×C3C2×C3×D411yescharacteristic
489C22×D3C2×C3×D411yescharacteristic
490C22×D3C2×C3×D411yescharacteristic
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—41no—
496C3×Q8—41no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—121no—
504C3×Q8—122no—
505C3×Q8—122no—
506C3×D4—121no—
507C3×D4—121no—
508C3×D4—121no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—122no—
540C2×C3×C4—122no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×C3×D411yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C24×C311yescharacteristic
545#67—41no—
546#67—41no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—42no—
552C2×Dic3C2×C3×D411yescharacteristic
553C2×Dic3C2×C3×D411yescharacteristic
554D12—41no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—42no—
560Dic6—21no—
561Dic6—21no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566Dic6—41no—
567Dic6—42no—
568Dic6—42no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—41no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C2×C32—41no—
580C2×C32#53411yescharacteristic
581C2×C32#57811yescharacteristic
582C2×C32#57811yescharacteristic
583C3×D3—41no—
584C3×D3—41no—
585#41—121no—
586#41—121no—
587C2×Q8—31no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×Q8—31no—
591C2×Q8—61no—
592C2×Q8—61no—
593C2×Q8—121no—
594C2×Q8—121no—
595C2×Q8—121no—
596C2×Q8—121no—
597C2×Q8C22×C3×D311yescharacteristic
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4C22×C3×D311yescharacteristic
606Q16—121no—
607Q16—121no—
608Q16—121no—
609Q16—121no—
610M16—121no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—121no—
614C2×C8C22×C3×D311yescharacteristic
615C2×C8C22×C3×D311yescharacteristic
616C4⋊C4—21no—
617C4⋊C4—31no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4C22×C3×D311yescharacteristic
626C4⋊C4C22×C3×D311yescharacteristic
627C4⋊C4C22×C3×D311yescharacteristic
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C42—21no—
639C42—61no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C22×C3×D411yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4#100911yescharacteristic
688C3×C4#100911yescharacteristic
689C3×C4C3×H(5,𝔽2)11yescharacteristic
690C3×C4C3×H(5,𝔽2)11yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697C32#320211yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23C3×D3×D411yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—121no—
710Q8—122no—
711Q8—122no—
712D4—121no—
713D4—121no—
714D4—121no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4C3×D3×D411yescharacteristic
734C2×C4C23×C3×D311yescharacteristic
735C8—21no—
736C8—21no—
737C8—61no—
738C8—61no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—41no—
743C2×C3—41no—
744C2×C3—81no—
745C2×C3—121no—
746C2×C3—121no—
747C2×C3#565311yescharacteristic
748C2×C3#577111yescharacteristic
749C2×C3#577911yescharacteristic
750C2×C3C3×#53411yescharacteristic
751C2×C3C3×#57811yescharacteristic
752C2×C3C3×#57811yescharacteristic
753D3—41no—
754D3—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22C2×C3×D3×D411yescharacteristic
765C4—21no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—61no—
771C4—61no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4C3×#100911yescharacteristic
777C4C3×#100911yescharacteristic
778C3—21no—
779C3#8155111yescharacteristic, direct product factor
780C3C3×#320211yescharacteristic, complemented
781C2—41no—
782C2—121no—
783C2—121no—
784C2C3×#565311yescharacteristic
785C2C3×#577111yescharacteristic
786C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC3×#485D3
hypocenterC3C3×#3202
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#485

Complements

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

NH ≅ G/Ntype
3. C32×#485C2semidirect
4. C3×#5050C2semidirect
5. C3×#4996C2semidirect
6. C3×#4888C2semidirect
7. C3×#4887C2semidirect
8. C3×#4868C2semidirect
9. C3×#4867C2semidirect
10. C3×#4816C2semidirect
11. C3×#4813C2semidirect
12. C3×#4809C2semidirect
13. C3×#4809C2semidirect
14. C3×#4739C2semidirect
17. #81551C3direct (N × H)
69. C3×#485D3semidirect
70. C3×#485C2×C3semidirect
80. #5050C2×C3semidirect
81. #4996C2×C3semidirect
82. #4888C2×C3semidirect
83. #4887C2×C3semidirect
84. #4868C2×C3semidirect
85. #4867C2×C3semidirect
86. #4816C2×C3semidirect
87. #4813C2×C3semidirect
88. #4809C2×C3semidirect
89. #4809C2×C3semidirect
90. #4739C2×C3semidirect
287. #485C3×D3semidirect
697. C32#3202semidirect
779. C3#81551direct (N × H)
780. C3C3×#3202semidirect

Maximal subgroups

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

subgroupindex
C3×#56282
C3×#55262
C32×#4852
C3×#50502
C3×#49962
C3×#48882
C3×#48872
C3×#48682
C3×#48672
C3×#48162
C3×#48132
C3×#48092
C3×#47392
C3×#47272
C3×#32023
#815513