Finite Group Databasebeta

← C3×#69958 #11787161

Subgroups — C3×#69958 #11787161

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 679 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×C3×#830C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#1870—31nomaximal
9#69958C311yesmaximal, characteristic, direct product factor
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67C411yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C3×#217C411yescharacteristic
16C3×C4×#67—22no—
17C3×C4×#67—22no—
18C2×C3×(C2×D3)⋊C4C411yescharacteristic
19C2×C3×Dic3⋊C4C411yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)—22no—
24C2×C3×ΓL(1,𝔽25)—22no—
25C2×C3×ΓL(1,𝔽25)—22no—
26C32×C22⋊C8—22no—
27C3×#830—22no—
28C3×(C2×D3)⋊C8—22no—
29C22×C3×M16—31no—
30C2×C3×C4×D4—31no—
31C2×C4×#67C2×C311yescharacteristic
32C22×ΓL(1,𝔽25)C2×C311yescharacteristic, complemented
33C2×C3×C22⋊C8—21no—
34C2×C3×C22⋊C8—31no—
35C2×C3×C22⋊C8—31no—
36C2×C3×C22⋊C8D311yescharacteristic, complemented
37C2×C3×C22⋊C8C2×C311yescharacteristic, complemented
38C2×#830C2×C311yescharacteristic, complemented
39C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
40C3×#336—31no—
41C3×#336—31no—
42#4550C2×C311yescharacteristic, complemented
43#4550C2×C311yescharacteristic, complemented
44C24×C32C2×C411yescharacteristic
45C23×C3×D3C2×C411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2×C411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C2×C3×#67—22no—
55C2×C3×#67—22no—
56C2×C3×#67—22no—
57C22×C3×Dic3C2×C411yescharacteristic
58C22×C3×Dic3C2×C411yescharacteristic
59C22×C3×Dic3C2×C411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×C4×D3D412yes—
65C2×C3×C4×D3D412yes—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C2×C32×C8—21no—
69C2×C32×C8—21no—
70C2×C32×C8—21no—
71C2×C32×C8D412yescomplemented
72C3×#217—22no—
73C3×(C2×D3)⋊C4—22no—
74C3×Dic3⋊C4—22no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8D412yescomplemented
83C3×ΓL(1,𝔽25)—28no—
84#1870—31noSylow
85C22×C3×D4—31no—
86C23×C3×C4—21no—
87C23×C3×C4—31no—
88C23×C3×C4C2×D311yescharacteristic
89C23×C3×C4C22×C311yescharacteristic
90C22×#67C3×C411yescharacteristic
91C22×C4×D3C22×C311yescharacteristic
92C2×C3×M16—62no—
93C2×C3×M16—62no—
94C2×C3×M16—62no—
95C22×C3×C8—21no—
96C22×C3×C8—21no—
97C22×C3×C8—31no—
98C22×C3×C8—31no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C22×C3×C8C22×C311yescharacteristic
102C22×C3×C8C22×C311yescharacteristic
103C3×C4×D4—62no—
104C3×C4×D4—62no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4—31no—
108C2×C3×C42—31no—
109C2×#217C3×C411yescharacteristic
110C4×#67—22no—
111C4×#67—22no—
112C2×(C2×D3)⋊C4C3×C411yescharacteristic
113C2×Dic3⋊C4C3×C411yescharacteristic
114C2×C4×Dic3C22×C311yescharacteristic
115C22×C3⋊C8C22×C311yescharacteristic
116C22×C3⋊C8C22×C311yescharacteristic
117C2×ΓL(1,𝔽25)—22no—
118C2×ΓL(1,𝔽25)—22no—
119C2×ΓL(1,𝔽25)—22no—
120C3×C22⋊C8—24no—
121C3×C22⋊C8—22no—
122C3×C22⋊C8—22no—
123C3×C22⋊C8—62no—
124C3×C22⋊C8—62no—
125#830—22no—
126(C2×D3)⋊C8—22no—
127C23×C32—21no—
128C23×C32—21no—
129C23×C32—21no—
130C23×C32—21no—
131C23×C32—21no—
132C23×C32—21no—
133C23×C32M1612yescomplemented
134C23×C32C22×C411yescharacteristic
135C22×C3×D3—21no—
136C22×C3×D3—21no—
137C22×C3×D3—21no—
138C22×C3×D3—21no—
139C22×C3×D3—21no—
140C22×C3×D3—21no—
141C22×C3×D3C22⋊C412yes—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—41no—
146C2×C32×C4—41no—
147C2×C32×C4—41no—
148C2×C32×C4—41no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4#4111yescharacteristic
154C2×C32×C4#4111yescharacteristic
155C3×#67—28no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3C22⋊C412yes—
164C2×C3×Dic3M1612yescomplemented
165C3×C4×D3—22no—
166C3×C4×D3—22no—
167C3×C4×D3—22no—
168C3×C4×D3—22no—
169C32×C8—22no—
170C32×C8—41no—
171C3×C3⋊C8—22no—
172C3×C3⋊C8—41no—
173C22×M16—31no—
174C2×C4×D4—31no—
175C2×C22⋊C8—31no—
176C2×C22⋊C8—31no—
177C2×C22⋊C8C3×D311yescharacteristic, complemented
178#336—31no—
179#336—31no—
180C24×C3—21no—
181C24×C3—31no—
182C24×C3C4×D311yescharacteristic
183C24×C3C2×C3×C411yescharacteristic
184C23×D3C2×C3×C411yescharacteristic
185C2×C3×D4—62no—
186C2×C3×D4—62no—
187C2×C3×D4—62no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—31no—
209C22×C3×C4—41no—
210C22×C3×C4—41no—
211C22×C3×C4—41no—
212C22×C3×C4—41no—
213C22×C3×C4—61no—
214C22×C3×C4—61no—
215C22×C3×C4—61no—
216C22×C3×C4—61no—
217C22×C3×C4C4×D311yescharacteristic
218C22×C3×C4C2×C3×C411yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C23×C311yescharacteristic
221C2×#67—22no—
222C2×#67—22no—
223C2×#67—22no—
224C22×Dic3C2×C3×C411yescharacteristic
225C22×Dic3C2×C3×C411yescharacteristic
226C22×Dic3C2×C3×C411yescharacteristic
227C2×C4×D3—21no—
228C2×C4×D3—21no—
229C2×C4×D3—21no—
230C2×C4×D3—21no—
231C2×C4×D3C3×D412yes—
232C2×C4×D3C3×D412yes—
233C3×M16—68no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—22no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—22no—
246C2×C3×C8—32no—
247C2×C3×C8—41no—
248C2×C3×C8—41no—
249C2×C3×C8—41no—
250C2×C3×C8—41no—
251C2×C3×C8—61no—
252C2×C3×C8—61no—
253C2×C3×C8—61no—
254C2×C3×C8—61no—
255C2×C3×C8—61no—
256C2×C3×C8#6712yescomplemented
257C2×C3×C8C3×D412yescomplemented
258C3×C4⋊C4—62no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4—62no—
261C3×C42—61no—
262C3×C42—61no—
263#217—22no—
264(C2×D3)⋊C4—22no—
265Dic3⋊C4—22no—
266C4×Dic3—21no—
267C4×Dic3—21no—
268C2×C3⋊C8—21no—
269C2×C3⋊C8—21no—
270C2×C3⋊C8—21no—
271C2×C3⋊C8—21no—
272C2×C3⋊C8—21no—
273C2×C3⋊C8C3×D412yescomplemented
274ΓL(1,𝔽25)—28no—
275C22×C32—22no—
276C22×C32—22no—
277C22×C32—22no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C2×C22⋊C411yescharacteristic
283C22×C32C4×D411yescharacteristic
284C22×C32C4×D411yescharacteristic
285C22×C32C2×M1611yescharacteristic
286C22×C32C2×M1611yescharacteristic
287C22×C32#13111yescharacteristic
288C22×C32#13111yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—22no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C32×C4—41no—
297C32×C4#12011yescharacteristic
298C32×C4#12111yescharacteristic
299C32×C4#12111yescharacteristic
300C32×C4#12311yescharacteristic
301C3×Dic3—22no—
302C3×Dic3—22no—
303C3×Dic3—41no—
304C22×D4—31no—
305C23×C4—31no—
306C23×C4C2×C3×D311yescharacteristic
307C2×M16—62no—
308C2×M16—62no—
309C2×M16—62no—
310C22×C8—31no—
311C22×C8—31no—
312C22×C8C2×C3×D311yescharacteristic
313C22×C8C2×C3×D311yescharacteristic
314C4×D4—62no—
315C4×D4—62no—
316C2×C4⋊C4—31no—
317C2×C22⋊C4—31no—
318C2×C22⋊C4—31no—
319C2×C42—31no—
320C22⋊C8—22no—
321C22⋊C8—62no—
322C22⋊C8—62no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—22no—
338C23×C3—21no—
339C23×C3—32no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—61no—
345C23×C3—61no—
346C23×C3—61no—
347C23×C3—61no—
348C23×C3—61no—
349C23×C3—61no—
350C23×C3ΓL(1,𝔽25)12yescomplemented
351C23×C3C3×M1612yescomplemented
352C23×C3C2×C4×D311yescharacteristic
353C23×C3C22×C3×C411yescharacteristic
354C22×D3—21no—
355C22×D3—21no—
356C22×D3—21no—
357C22×D3—21no—
358C22×D3—21no—
359C22×D3—21no—
360C22×D3C3×C22⋊C412yes—
361C3×D4—68no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—32no—
376C2×C3×C4—32no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—61no—
402C2×C3×C4#23511yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4#23711yescharacteristic
407C2×C3×C4C2×#6711yescharacteristic
408C2×C3×C4C2×C3×D411yescharacteristic
409C2×C3×C4C2×C3×D411yescharacteristic
410C2×C3×C4C2×C3×D411yescharacteristic
411C2×C3×C4C2×C3×D411yescharacteristic
412C2×C3×C4C3×#4111yescharacteristic
413C2×C3×C4C3×#4111yescharacteristic
414#67—28no—
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419C2×Dic3—21no—
420C2×Dic3—21no—
421C2×Dic3—21no—
422C2×Dic3C3×C22⋊C412yes—
423C2×Dic3C3×M1612yescomplemented
424C4×D3—22no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—22no—
428C3×C8—22no—
429C3×C8—22no—
430C3×C8—42no—
431C3×C8—42no—
432C3×C8—41no—
433C3×C8—41no—
434C3×C8—62no—
435C3×C8—121no—
436C3⋊C8—22no—
437C3⋊C8—41no—
438C2×C32—42no—
439C2×C32#38611yescharacteristic
440C2×C32#40711yescharacteristic
441C2×C32#40811yescharacteristic
442C2×C32#43511yescharacteristic
443C2×C32#43511yescharacteristic
444C2×C32#43611yescharacteristic
445C2×C32#43611yescharacteristic
446C3×D3—42no—
447C24—31no—
448C24C3×C4×D311yescharacteristic
449C2×D4—62no—
450C2×D4—62no—
451C2×D4—62no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—31no—
459C22×C4—31no—
460C22×C4—32no—
461C22×C4—32no—
462C22×C4—31no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4C3×C4×D311yescharacteristic
468C22×C4C22×C3×D311yescharacteristic
469M16—68no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—32no—
476C2×C8—61no—
477C2×C8—61no—
478C2×C8—61no—
479C2×C8—61no—
480C2×C8—61no—
481C2×C8C3×#6712yescomplemented
482C4⋊C4—62no—
483C22⋊C4—62no—
484C22⋊C4—62no—
485C42—61no—
486C42—61no—
487C22×C3—24no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—121no—
519C22×C3—121no—
520C22×C3—121no—
521C22×C3—121no—
522C22×C3D3×C22⋊C411yescharacteristic
523C22×C3#67⋊C411yescharacteristic
524C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
525C22×C3#90111yescharacteristic
526C22×C3D3×M1611yescharacteristic
527C22×C3#90711yescharacteristic
528C22×C3C4×#6711yescharacteristic
529C22×C3C2×C3×C22⋊C411yescharacteristic
530C22×C3C3×C4×D411yescharacteristic
531C22×C3C3×C4×D411yescharacteristic
532C22×C3C2×C3×M1611yescharacteristic
533C22×C3C2×C3×M1611yescharacteristic
534C22×C3C3×#13111yescharacteristic
535C22×C3C3×#13111yescharacteristic
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—22no—
539C2×D3—41no—
540C2×D3—41no—
541C2×D3—41no—
542C2×D3—41no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—42no—
548C3×C4—41no—
549C3×C4—41no—
550C3×C4—62no—
551C3×C4—62no—
552C3×C4—121no—
553C3×C4#88311yescharacteristic
554C3×C4#88411yescharacteristic
555C3×C4#93711yescharacteristic
556C3×C4#93811yescharacteristic
557C3×C4C3×#12011yescharacteristic
558C3×C4C3×#12111yescharacteristic
559C3×C4C3×#12111yescharacteristic
560C3×C4C3×#12311yescharacteristic
561Dic3—22no—
562Dic3—22no—
563Dic3—41no—
564C32#187011yescharacteristic, complemented, Sylow
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—32no—
572C23—61no—
573C23—61no—
574C23—61no—
575C23—61no—
576C23—61no—
577C23—61no—
578C23C3×ΓL(1,𝔽25)12yescomplemented
579C23C2×C3×C4×D311yescharacteristic
580D4—68no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—61no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4C3×#23511yescharacteristic
602C2×C4C3×D3×D411yescharacteristic
603C2×C4C3×D3×D411yescharacteristic
604C2×C4C3×D3×D411yescharacteristic
605C2×C4C3×#23711yescharacteristic
606C2×C4C2×C3×#6711yescharacteristic
607C8—22no—
608C8—41no—
609C8—62no—
610C8—121no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—44no—
619C2×C3—42no—
620C2×C3—42no—
621C2×C3—122no—
622C2×C3#472611yescharacteristic
623C2×C3#472711yescharacteristic
624C2×C3#472911yescharacteristic
625C2×C3#473011yescharacteristic
626C2×C3#495611yescharacteristic
627C2×C3#511111yescharacteristic
628C2×C3#512811yescharacteristic
629C2×C3C3×#38611yescharacteristic
630C2×C3C3×#40711yescharacteristic
631C2×C3C3×#40811yescharacteristic
632C2×C3C3×#43511yescharacteristic
633C2×C3C3×#43511yescharacteristic
634C2×C3C3×#43611yescharacteristic
635C2×C3C3×#43611yescharacteristic
636D3—42no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—62no—
645C22—62no—
646C22—62no—
647C22—121no—
648C22—121no—
649C22—121no—
650C22—121no—
651C22C3×D3×C22⋊C411yescharacteristic
652C22C3×#67⋊C411yescharacteristic
653C22C2×C3×ΓL(1,𝔽25)11yescharacteristic
654C22C3×#90111yescharacteristic
655C22C3×D3×M1611yescharacteristic
656C22C3×#90711yescharacteristic
657C22C3×C4×#6711yescharacteristic
658C4—41no—
659C4—62no—
660C4—62no—
661C4—121no—
662C4C3×#88311yescharacteristic
663C4C3×#88411yescharacteristic
664C4C3×#93711yescharacteristic
665C4C3×#93811yescharacteristic
666C3—21no—
667C3#6995811yescharacteristic, direct product factor
668C3C3×#187011yescharacteristic, complemented
669C2—42no—
670C2—122no—
671C2C3×#472611yescharacteristic
672C2C3×#472711yescharacteristic
673C2C3×#472911yescharacteristic
674C2C3×#473011yescharacteristic
675C2C3×#495611yescharacteristic
676C2C3×#511111yescharacteristic
677C2C3×#512811yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C22×C4
prime radicalC22×C3×#67C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×#1870
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×C3×ΓL(1,𝔽25)C2semidirect
3. C2×C32×C22⋊C8C2semidirect
4. C2×C3×#830C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C3×#4550C2semidirect
7. C3×#4550C2semidirect
9. #69958C3direct (N × H)
32. C22×ΓL(1,𝔽25)C2×C3semidirect
36. C2×C3×C22⋊C8D3semidirect
37. C2×C3×C22⋊C8C2×C3semidirect
38. C2×#830C2×C3semidirect
39. C2×(C2×D3)⋊C8C2×C3semidirect
42. #4550C2×C3semidirect
43. #4550C2×C3semidirect
71. C2×C32×C8D4semidirect
82. C2×C3×C3⋊C8D4semidirect
133. C23×C32M16semidirect
164. C2×C3×Dic3M16semidirect
177. C2×C22⋊C8C3×D3semidirect
256. C2×C3×C8#67semidirect
257. C2×C3×C8C3×D4semidirect
273. C2×C3⋊C8C3×D4semidirect
350. C23×C3ΓL(1,𝔽25)semidirect
351. C23×C3C3×M16semidirect
423. C2×Dic3C3×M16semidirect
481. C2×C8C3×#67semidirect
564. C32#1870semidirect
578. C23C3×ΓL(1,𝔽25)semidirect
667. C3#69958direct (N × H)
668. C3C3×#1870semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C22×C3×ΓL(1,𝔽25)2
C2×C32×C22⋊C82
C2×C3×#8302
C2×C3×(C2×D3)⋊C82
C3×#45502
C3×#18703
#699583