Finite Group Databasebeta

← C3×#10591145 #13158322

Subgroups — C3×#10591145 #13158322

Order 1728.

950 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic
2C2×C3×#3711C211yesmaximal, characteristic, complemented
3C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C3×#63657C211yesmaximal, characteristic, complemented
5C32×#830C211yesmaximal, characteristic, complemented
6C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5234—31nomaximal
9C3×#4727—31nomaximal
10#10591145C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C2×C32×#67C411yescharacteristic
13C2×C32×#67C411yescharacteristic
14C32×#235—22no—
15C32×#235—22no—
16C2×C32×D12C411yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C411yescharacteristic
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C32×C3⋊C8C2211yescharacteristic
23C2×C32×C3⋊C8C2211yescharacteristic
24C3×#3711—22no—
25C3×D3×C3⋊C8—22no—
26C2×C32×#41—31no—
27C2×C3×#235—21no—
28C2×C3×#235D311yescharacteristic
29C2×C3×#235C2×C311yescharacteristic
30C2×C3×#208—31no—
31C22×C3×C3⋊C8—31no—
32C2×C3×ΓL(1,𝔽25)—31no—
33C2×C3×D3×C8—31no—
34C2×#3711C2×C311yescharacteristic, complemented
35C2×D3×C3⋊C8C2×C311yescharacteristic, complemented
36C32×C22⋊C8—31no—
37#63657C2×C311yescharacteristic, complemented
38C3×#830—21no—
39C3×#830—31no—
40C3×#830—31no—
41C3×#830—31no—
42C3×#830—31no—
43C3×#830—61no—
44C3×#830D311yescharacteristic, complemented
45C3×#830C2×C311yescharacteristic, complemented
46C3×(C2×D3)⋊C8—31no—
47C3×(C2×D3)⋊C8—31no—
48(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
49(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
50C23×C33C2×C411yescharacteristic
51C22×C32×D3C2×C411yescharacteristic
52C22×C32×D3C2×C411yescharacteristic
53C2×C33×C4—21no—
54C2×C33×C4—21no—
55C2×C33×C4C2×C411yescharacteristic
56C2×C33×C4C2311yescharacteristic
57C32×#67—22no—
58C32×#67—22no—
59C2×C32×Dic3C2×C411yescharacteristic
60C2×C32×Dic3C2×C411yescharacteristic
61C32×D12—22no—
62C32×C4×D3—21no—
63C32×C4×D3—21no—
64C32×C4×D3D412yes—
65C32×C4×D3D412yes—
66C32×Dic6—22no—
67C3×C3⋊(C3⋊C8)—21no—
68C3×C3⋊(C3⋊C8)—21no—
69C32×C3⋊C8—21no—
70C32×C3⋊C8—21no—
71C3×#408—91no—
72#5234—31no—
73#4727—31no—
74C32×#41—62no—
75C32×#41—62no—
76C2×C32×Q8—31no—
77C2×C32×D4—31no—
78C2×C32×D4—31no—
79C2×C32×D4—31no—
80C22×C32×C4—21no—
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4—31no—
84C22×C32×C4—31no—
85C22×C32×C4—41no—
86C22×C32×C4C2×D311yescharacteristic
87C22×C32×C4C2×D311yescharacteristic
88C22×C32×C4C22×C311yescharacteristic
89C2×C3×#67—21no—
90C2×C3×#67—21no—
91C2×C3×#67Dic311yescharacteristic
92C2×C3×#67Dic311yescharacteristic
93C2×C3×#67C3×C411yescharacteristic
94C2×C3×#67C3×C411yescharacteristic
95C3×#235—24no—
96C3×#235—24no—
97C3×#235—22no—
98C3×#235—22no—
99C3×#235—22no—
100C3×#235—22no—
101C2×C3×D12—21no—
102C2×C3×D12Dic311yescharacteristic
103C2×C3×D12C3×C411yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2×D311yescharacteristic
107C2×C3×C4×D3C2×D311yescharacteristic
108C2×C3×C4×D3C22×C311yescharacteristic
109C2×C3×C4×D3C22×C311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6Dic311yescharacteristic
112C2×C3×Dic6C3×C411yescharacteristic
113C2×C32×C8—31no—
114C2×C32×C8—31no—
115C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
116C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
117C3×#208—62no—
118C2×C3×C3⋊C8—21no—
119C2×C3×C3⋊C8—21no—
120C2×C3×C3⋊C8—31no—
121C2×C3×C3⋊C8—31no—
122C2×C3×C3⋊C8—31no—
123C2×C3×C3⋊C8—31no—
124C2×C3×C3⋊C8—62no—
125C2×C3×C3⋊C8—61no—
126C2×C3×C3⋊C8—61no—
127C2×C3×C3⋊C8C2×D311yescharacteristic
128C2×C3×C3⋊C8C2×D311yescharacteristic
129C2×C3×C3⋊C8C22×C311yescharacteristic
130C2×C3×C3⋊C8C22×C311yescharacteristic
131C3×ΓL(1,𝔽25)—62no—
132C3×D3×C8—62no—
133#3711—22no—
134D3×C3⋊C8—22no—
135C22×C33—21no—
136C22×C33—21no—
137C22×C33—21no—
138C22×C33C22×C411yescharacteristic
139C2×C32×D3—21no—
140C2×C32×D3—21no—
141C2×C32×D3—21no—
142C2×C32×D3—21no—
143C2×C32×D3—21no—
144C2×C32×D3C22⋊C412yes—
145C33×C4—21no—
146C33×C4C2×D411yescharacteristic
147C33×C4C2×D411yescharacteristic
148C32×Dic3—21no—
149C32×Dic3C22⋊C412yes—
150C2×C3×#41—31no—
151C2×C3×#41—31no—
152C2×C3×#41—61no—
153C2×#235C3×D311yescharacteristic
154C2×C3×M16—91no—
155C22×C3×C8—91no—
156C2×#208—31no—
157C22×C3⋊C8—31no—
158C2×ΓL(1,𝔽25)—31no—
159C2×D3×C8—31no—
160C3×C22⋊C8—31no—
161C3×C22⋊C8—31no—
162C3×C22⋊C8—61no—
163C3×C22⋊C8—91no—
164C3×C22⋊C8—91no—
165C3×C22⋊C8—91no—
166#830—31no—
167#830—31no—
168#830—31no—
169#830—31no—
170#830—61no—
171#830C3×D311yescharacteristic, complemented
172(C2×D3)⋊C8—31no—
173(C2×D3)⋊C8—31no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—31no—
178C23×C32—31no—
179C23×C32—41no—
180C23×C32C4×D311yescharacteristic
181C23×C32C2×Dic311yescharacteristic
182C23×C32C2×C3×C411yescharacteristic
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C22×C3×D3C2×Dic311yescharacteristic
186C22×C3×D3C2×Dic311yescharacteristic
187C22×C3×D3C2×C3×C411yescharacteristic
188C22×C3×D3C2×C3×C411yescharacteristic
189C32×Q8—62no—
190C32×D4—62no—
191C32×D4—62no—
192C32×D4—62no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—22no—
196C2×C32×C4—22no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—31no—
208C2×C32×C4—32no—
209C2×C32×C4—32no—
210C2×C32×C4—31no—
211C2×C32×C4—41no—
212C2×C32×C4—41no—
213C2×C32×C4—41no—
214C2×C32×C4—41no—
215C2×C32×C4—41no—
216C2×C32×C4—41no—
217C2×C32×C4—42no—
218C2×C32×C4—42no—
219C2×C32×C4—61no—
220C2×C32×C4—61no—
221C2×C32×C4C4×D311yescharacteristic
222C2×C32×C4C2×Dic311yescharacteristic
223C2×C32×C4C2×C3×C411yescharacteristic
224C2×C32×C4C22×D311yescharacteristic
225C2×C32×C4C22×D311yescharacteristic
226C2×C32×C4C23×C311yescharacteristic
227C3×#67—24no—
228C3×#67—24no—
229C3×#67—22no—
230C3×#67—22no—
231C3×#67—22no—
232C3×#67—22no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3C2×Dic311yescharacteristic
236C2×C3×Dic3C2×Dic311yescharacteristic
237C2×C3×Dic3C2×C3×C411yescharacteristic
238C2×C3×Dic3C2×C3×C411yescharacteristic
239C3×D12—24no—
240C3×D12—22no—
241C3×D12—22no—
242C3×C4×D3—22no—
243C3×C4×D3—22no—
244C3×C4×D3—21no—
245C3×C4×D3—21no—
246C3×C4×D3—21no—
247C3×C4×D3—21no—
248C3×C4×D3—22no—
249C3×C4×D3—22no—
250C3×C4×D3#6712yes—
251C3×C4×D3#6712yes—
252C3×C4×D3C3×D412yes—
253C3×C4×D3C3×D412yes—
254C3×Dic6—24no—
255C3×Dic6—22no—
256C3×Dic6—22no—
257C32×C8—61no—
258C32×C8—61no—
259C3⋊(C3⋊C8)—21no—
260C3⋊(C3⋊C8)—21no—
261C3×C3⋊C8—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—41no—
266C3×C3⋊C8—41no—
267C3×C3⋊C8—61no—
268C3×C3⋊C8—61no—
269C3×C3⋊C8—61no—
270C3×C3⋊C8—61no—
271C3×C3⋊C8—121no—
272C3×C3⋊C8—121no—
273#408—91noSylow
274C2×C33—41no—
275C2×C33C2×C22⋊C411yescharacteristic
276C2×C33#13111yescharacteristic
277C2×C33#13111yescharacteristic
278C32×D3—22no—
279C32×D3—41no—
280C3×#41—62no—
281C3×#41—62no—
282C3×#41—62no—
283C3×#41—62no—
284C3×#41—64no—
285C3×#41—64no—
286C2×C3×Q8—31no—
287C2×C3×Q8—31no—
288C2×C3×Q8—61no—
289C2×C3×D4—31no—
290C2×C3×D4—31no—
291C2×C3×D4—31no—
292C2×C3×D4—31no—
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—41no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4D3211yescharacteristic
309C22×C3×C4C2×C3×D311yescharacteristic
310C22×C3×C4C2×C3×D311yescharacteristic
311C2×#67C3×Dic311yescharacteristic
312C2×#67C3×Dic311yescharacteristic
313#235—22no—
314#235—22no—
315C2×D12C3×Dic311yescharacteristic
316C2×C4×D3C2×C3×D311yescharacteristic
317C2×C4×D3C2×C3×D311yescharacteristic
318C2×Dic6C3×Dic311yescharacteristic
319C3×M16—182no—
320C2×C3×C8—31no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8—61no—
325C2×C3×C8—61no—
326C2×C3×C8—91no—
327C2×C3×C8—91no—
328C2×C3×C8—182no—
329#208—62no—
330C2×C3⋊C8—31no—
331C2×C3⋊C8—31no—
332C2×C3⋊C8—31no—
333C2×C3⋊C8—31no—
334C2×C3⋊C8—61no—
335C2×C3⋊C8—61no—
336C2×C3⋊C8—62no—
337C2×C3⋊C8C2×C3×D311yescharacteristic
338C2×C3⋊C8C2×C3×D311yescharacteristic
339ΓL(1,𝔽25)—62no—
340D3×C8—62no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—22no—
345C22×C32—22no—
346C22×C32—22no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—21no—
356C22×C32—32no—
357C22×C32—41no—
358C22×C32—41no—
359C22×C32—41no—
360C22×C32—41no—
361C22×C32—41no—
362C22×C32—41no—
363C22×C32—41no—
364C22×C32—42no—
365C22×C32—42no—
366C22×C32—42no—
367C22×C32—61no—
368C22×C32—61no—
369C22×C32—61no—
370C22×C32—61no—
371C22×C32—61no—
372C22×C32C2×C4×D311yescharacteristic
373C22×C32C22×Dic311yescharacteristic
374C22×C32C22×C3×C411yescharacteristic
375C2×C3×D3—21no—
376C2×C3×D3—21no—
377C2×C3×D3—21no—
378C2×C3×D3—21no—
379C2×C3×D3—22no—
380C2×C3×D3—21no—
381C2×C3×D3—21no—
382C2×C3×D3—21no—
383C2×C3×D3—21no—
384C2×C3×D3—21no—
385C2×C3×D3—21no—
386C2×C3×D3—22no—
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3#21712yes—
392C2×C3×D3C3×C22⋊C412yes—
393C32×C4—21no—
394C32×C4—22no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—21no—
399C32×C4—21no—
400C32×C4—21no—
401C32×C4—21no—
402C32×C4—21no—
403C32×C4—32no—
404C32×C4—41no—
405C32×C4—41no—
406C32×C4—41no—
407C32×C4—41no—
408C32×C4—42no—
409C32×C4—61no—
410C32×C4D3×D411yescharacteristic
411C32×C4D3×D411yescharacteristic
412C32×C4C2×#6711yescharacteristic
413C32×C4C2×#6711yescharacteristic
414C32×C4C2×C3×D411yescharacteristic
415C32×C4C2×C3×D411yescharacteristic
416C3×Dic3—22no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—22no—
420C3×Dic3#21712yes—
421C3×Dic3C3×C22⋊C412yes—
422C2×#41—31no—
423C2×M16—91no—
424C22×C8—91no—
425C22⋊C8—31no—
426C22⋊C8—91no—
427C22⋊C8—91no—
428C22⋊C8—91no—
429C33#40811yescharacteristic, complemented, Sylow
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—31no—
434C23×C3—31no—
435C23×C3—31no—
436C23×C3—31no—
437C23×C3—41no—
438C23×C3—61no—
439C23×C3—61no—
440C23×C3D3×Dic311yescharacteristic
441C23×C3C3×C4×D311yescharacteristic
442C23×C3C2×C3×Dic311yescharacteristic
443C22×D3C2×C3×Dic311yescharacteristic
444C22×D3C2×C3×Dic311yescharacteristic
445C3×Q8—62no—
446C3×Q8—62no—
447C3×Q8—64no—
448C3×D4—62no—
449C3×D4—62no—
450C3×D4—64no—
451C3×D4—62no—
452C3×D4—62no—
453C3×D4—62no—
454C3×D4—62no—
455C3×D4—64no—
456C3×D4—64no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—32no—
474C2×C3×C4—32no—
475C2×C3×C4—32no—
476C2×C3×C4—32no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—62no—
488C2×C3×C4—62no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—62no—
492C2×C3×C4—62no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4D3×Dic311yescharacteristic
498C2×C3×C4C3×C4×D311yescharacteristic
499C2×C3×C4C2×C3×Dic311yescharacteristic
500C2×C3×C4C2×D3211yescharacteristic
501C2×C3×C4C22×C3×D311yescharacteristic
502C2×C3×C4C22×C3×D311yescharacteristic
503#67—22no—
504#67—22no—
505C2×Dic3C2×C3×Dic311yescharacteristic
506C2×Dic3C2×C3×Dic311yescharacteristic
507D12—22no—
508C4×D3—21no—
509C4×D3—21no—
510C4×D3C3×#6712yes—
511C4×D3C3×#6712yes—
512Dic6—22no—
513C3×C8—61no—
514C3×C8—61no—
515C3×C8—61no—
516C3×C8—61no—
517C3×C8—121no—
518C3×C8—121no—
519C3×C8—181no—
520C3×C8—181no—
521C3⋊C8—21no—
522C3⋊C8—21no—
523C3⋊C8—61no—
524C3⋊C8—61no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—121no—
528C3⋊C8—121no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—41no—
539C2×C32—41no—
540C2×C32—41no—
541C2×C32—42no—
542C2×C32—42no—
543C2×C32—42no—
544C2×C32—44no—
545C2×C32—41no—
546C2×C32—41no—
547C2×C32—41no—
548C2×C32—62no—
549C2×C32—121no—
550C2×C32D3×C22⋊C411yescharacteristic
551C2×C32#90111yescharacteristic
552C2×C32#90711yescharacteristic
553C2×C32#94811yescharacteristic
554C2×C32#94811yescharacteristic
555C2×C32C2×#21711yescharacteristic
556C2×C32C2×C3×C22⋊C411yescharacteristic
557C2×C32C3×#13111yescharacteristic
558C2×C32C3×#13111yescharacteristic
559C3×D3—22no—
560C3×D3—22no—
561C3×D3—42no—
562C3×D3—42no—
563C3×D3—41no—
564C3×D3—41no—
565#41—62no—
566#41—62no—
567C2×Q8—31no—
568C2×D4—31no—
569C2×D4—31no—
570C2×D4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4C3×D3211yescharacteristic
574M16—182no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8—91no—
578C2×C8—91no—
579C2×C8—182no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—32no—
596C22×C3—32no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—41no—
607C22×C3—62no—
608C22×C3—62no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3C2×D3×Dic311yescharacteristic
624C22×C3C2×C3×C4×D311yescharacteristic
625C22×C3C22×C3×Dic311yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3C3×#21712yes—
632C3×C4—22no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—32no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—42no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—62no—
650C3×C4—62no—
651C3×C4—61no—
652C3×C4—61no—
653C3×C4D3×#6711yescharacteristic
654C3×C4D3×#6711yescharacteristic
655C3×C4C3×D3×D411yescharacteristic
656C3×C4C3×D3×D411yescharacteristic
657C3×C4C2×C3×#6711yescharacteristic
658C3×C4C2×C3×#6711yescharacteristic
659Dic3—21no—
660Dic3C3×#21712yes—
661C32—21no—
662C32—21no—
663C32—21no—
664C32—41no—
665C32#472711yescharacteristic, complemented
666C32#523411yescharacteristic, complemented
667C32C3×#40811yescharacteristic, complemented
668C23—31no—
669C23—31no—
670C23C3×D3×Dic311yescharacteristic
671Q8—62no—
672D4—62no—
673D4—62no—
674D4—62no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—31no—
678C2×C4—32no—
679C2×C4—32no—
680C2×C4—31no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4C3×D3×Dic311yescharacteristic
684C2×C4C2×C3×D3211yescharacteristic
685C8—61no—
686C8—61no—
687C8—181no—
688C8—181no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—42no—
699C2×C3—42no—
700C2×C3—42no—
701C2×C3—44no—
702C2×C3—41no—
703C2×C3—41no—
704C2×C3—41no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—62no—
709C2×C3—62no—
710C2×C3—122no—
711C2×C3—122no—
712C2×C3—121no—
713C2×C3—121no—
714C2×C3#6381411yescharacteristic
715C2×C3#6381511yescharacteristic
716C2×C3D3×#21711yescharacteristic
717C2×C3C3×D3×C22⋊C411yescharacteristic
718C2×C3C3×#90111yescharacteristic
719C2×C3C3×#90711yescharacteristic
720C2×C3C3×#94811yescharacteristic
721C2×C3C3×#94811yescharacteristic
722C2×C3C2×C3×#21711yescharacteristic
723D3—22no—
724D3—41no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22—61no—
734C22C2×C3×D3×Dic311yescharacteristic
735C4—21no—
736C4—32no—
737C4—61no—
738C4C3×D3×#6711yescharacteristic
739C4C3×D3×#6711yescharacteristic
740C3—21no—
741C3—21no—
742C3—21no—
743C3—41no—
744C3#1059114511yescharacteristic, direct product factor
745C3C3×#472711yescharacteristic, complemented
746C3C3×#523411yescharacteristic, complemented
747C2—41no—
748C2—62no—
749C2—121no—
750C2C3×#6381411yescharacteristic
751C2C3×#6381511yescharacteristic
752C2C3×D3×#21711yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC22×C33×C4C22
socleC22×C33C22×C4
prime radicalC2×C32×#235C2
cosocleC2×C32×C4C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#408
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3711C2semidirect
3. C2×C3×D3×C3⋊C8C2semidirect
4. C3×#63657C2semidirect
5. C32×#830C2semidirect
6. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10591145C3direct (N × H)
34. C2×#3711C2×C3semidirect
35. C2×D3×C3⋊C8C2×C3semidirect
37. #63657C2×C3semidirect
44. C3×#830D3semidirect
45. C3×#830C2×C3semidirect
48. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
49. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
171. #830C3×D3semidirect
429. C33#408semidirect
665. C32#4727semidirect
666. C32#5234semidirect
667. C32C3×#408semidirect
744. C3#10591145direct (N × H)
745. C3C3×#4727semidirect
746. C3C3×#5234semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C2×C3×#37112
C2×C3×D3×C3⋊C82
C3×#636572
C32×#8302
C3×(C2×D3)⋊(C3⋊C8)2
C3×#52343
C3×#47273
#105911453