Finite Group Databasebeta

← C3×#81490 #11887603

Subgroups — C3×#81490 #11887603

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5632C211yesmaximal, characteristic
2C3×#5511C211yesmaximal, characteristic
3C32×#484C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C3×#4887C211yesmaximal, characteristic, complemented
7C3×#4884C211yesmaximal, characteristic, complemented
8C3×#4875C211yesmaximal, characteristic, complemented
9C3×#4873C211yesmaximal, characteristic, complemented
10C3×#4809C211yesmaximal, characteristic, complemented
11C3×D3×#103C211yesmaximal, characteristic, complemented
12C3×#4795C211yesmaximal, characteristic, complemented
13C3×#4792C211yesmaximal, characteristic, complemented
14C3×#4739C211yesmaximal, characteristic, complemented
15C3×#67⋊C8C211yesmaximal, characteristic
16C3×#3299—31nomaximal
17#81490C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C3×C4×#67—21no—
25C3×C4×#67C2211yescharacteristic
26C3×#924—21no—
27C3×#924C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29C2×C3×Dic12C2211yescharacteristic
30C2×C3×Dic12C2211yescharacteristic
31C2×C3×D3×C8C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#897C2211yescharacteristic
34C3×#896—21no—
35C3×#896—21no—
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×#889—21no—
38C3×#888—21no—
39C3×#888C2211yescharacteristic
40C3×#887C2211yescharacteristic
41C3×#887C2211yescharacteristic
42C3×#67⋊C4—21no—
43C3×#878—21no—
44C32×#107C2211yescharacteristic
45C32×#107C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×C22⋊C8C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#554—31no—
62C3×D4×Q8—31no—
63#5632C2×C311yescharacteristic
64#5511C2×C311yescharacteristic
65C3×#487—31no—
66C3×#484—21no—
67C3×#484—31no—
68C3×#484D311yescharacteristic, complemented
69C3×#484C2×C311yescharacteristic, complemented
70C3×#477—31no—
71C3×#467—31no—
72C3×#467—31no—
73C3×#462—31no—
74C3×#451—31no—
75C3×#451—31no—
76C3×C4×Q16—31no—
77C3×C8×D4—31no—
78C2×C3×#103—31no—
79C2×C3×#103—31no—
80#5051C2×C311yescharacteristic, complemented
81C2×#810C2×C311yescharacteristic, complemented
82#4887C2×C311yescharacteristic, complemented
83#4884C2×C311yescharacteristic, complemented
84#4875C2×C311yescharacteristic, complemented
85#4873C2×C311yescharacteristic, complemented
86#4809C2×C311yescharacteristic, complemented
87D3×#103C2×C311yescharacteristic, complemented
88#4795C2×C311yescharacteristic, complemented
89#4792C2×C311yescharacteristic, complemented
90#4739C2×C311yescharacteristic, complemented
91#67⋊C8C2×C311yescharacteristic
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C3×D3×Q8—22no—
98C3×D3×Q8—41no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—22no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6—41no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#216—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×Dic12—22no—
142C3×Dic12—41no—
143C3×D3×C8—41no—
144#3299—31noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C22×C311yescharacteristic
148C22×Dic6C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C22×C3×C8—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×C4⋊Q8—31no—
156C3×C4⋊Q8—61no—
157C3×#125—61no—
158C3×C22⋊Q8—21no—
159C3×C22⋊Q8—31no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—61no—
163C3×C22⋊Q8—61no—
164C3×C22⋊Q8—61no—
165C3×C22⋊Q8—61no—
166C3×C22⋊Q8C2×D311yescharacteristic
167C3×C22⋊Q8C22×C311yescharacteristic
168C3×C4×Q8—31no—
169C3×C4×Q8—31no—
170C3×C4×D4—31no—
171C3×C4×D4—61no—
172C3×C4×D4—61no—
173C2×C3×C4⋊C4—21no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4C2×D311yescharacteristic
176C2×C3×C4⋊C4C22×C311yescharacteristic
177#944C22×C311yescharacteristic
178C2×#216C22×C311yescharacteristic
179C4×#67—21no—
180C4×#67C22×C311yescharacteristic
181#924—21no—
182#924C22×C311yescharacteristic
183C22×C3⋊C8C22×C311yescharacteristic
184C2×Dic12C22×C311yescharacteristic
185C2×Dic12C22×C311yescharacteristic
186C2×D3×C8C22×C311yescharacteristic
187#897C22×C311yescharacteristic
188#897C22×C311yescharacteristic
189#896—21no—
190#896—21no—
191D3×C4⋊C4C22×C311yescharacteristic
192#889—21no—
193#888—21no—
194#888C22×C311yescharacteristic
195#887C22×C311yescharacteristic
196#887C22×C311yescharacteristic
197#67⋊C4—21no—
198#878—21no—
199C3×#107—21no—
200C3×#107—21no—
201C3×#107—31no—
202C3×#107C2×D311yescharacteristic
203C3×#107C2×D311yescharacteristic
204C3×#107C22×C311yescharacteristic
205C3×#107C22×C311yescharacteristic
206C3×C4⋊C8—31no—
207C3×#103—21no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103C2×D311yescharacteristic
218C3×#103C2×D311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×#103C22×C311yescharacteristic
221C3×C22⋊C8—21no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8C2×D311yescharacteristic
224C3×C22⋊C8C22×C311yescharacteristic
225C3×C4×C8—31no—
226#835C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231C8×Dic3C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#810C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—81no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C3×#67Q1614yescomplemented
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—42no—
263C3×C4×D3—81no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6—42no—
271C3×Dic6—81no—
272C3×Dic6#4112yes—
273C32×C8—21no—
274C32×C8—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—31no—
278D4×Q8—31no—
279#487—31no—
280#484—31no—
281#484C3×D311yescharacteristic, complemented
282#477—31no—
283#467—31no—
284#467—31no—
285#462—31no—
286#451—31no—
287#451—31no—
288C4×Q16—31no—
289C8×D4—31no—
290C2×#103—31no—
291C2×#103—31no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×Q8—61no—
297C2×C3×Q8—61no—
298C2×C3×Q8—62no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8—121no—
302C2×C3×Q8—121no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C23×C311yescharacteristic
305C2×C3×D4—31no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—41no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C23×C311yescharacteristic
316C2×#67C3×D411yescharacteristic
317C22×Dic3—21no—
318D3×Q8—22no—
319D3×Q8—41no—
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3C23×C311yescharacteristic
323C2×Dic6—22no—
324C2×Dic6—21no—
325C2×Dic6—21no—
326C2×Dic6—21no—
327C2×Dic6—41no—
328C2×Dic6C23×C311yescharacteristic
329C2×Dic6C23×C311yescharacteristic
330C2×Dic6C23×C311yescharacteristic
331C3×Q16—62no—
332C3×Q16—121no—
333C3×Q16—121no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—121no—
339C2×C3×C8—121no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C23×C311yescharacteristic
343C2×C3×C8C23×C311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C23×C311yescharacteristic
368C3×C4⋊C4C23×C311yescharacteristic
369C3×C4⋊C4C23×C311yescharacteristic
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—31no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—41no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C42—31no—
379C3×C42—61no—
380C3×C42—61no—
381#217—21no—
382#217C3×D411yescharacteristic
383#216—41no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4C3×D411yescharacteristic
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3C23×C311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4C3×D411yescharacteristic
398C4×Dic3—21no—
399C4×Dic3—21no—
400C4×Dic3C23×C311yescharacteristic
401C2×C3⋊C8—41no—
402C2×C3⋊C8C23×C311yescharacteristic
403C2×C3⋊C8C23×C311yescharacteristic
404Dic12—22no—
405Dic12—41no—
406D3×C8—41no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32C2×Q1612yes—
410C22×C32C22×D411yescharacteristic
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3C2×Q1612yes—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4H(5,𝔽2)11yescharacteristic
421C3×Dic3—22no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×Q1612yes—
428C22×Q8—31no—
429C22×Q8—31no—
430C2×Q16—31no—
431C2×Q16—31no—
432C2×Q16—31no—
433C22×C8—31no—
434C22×C8—31no—
435C4⋊Q8—31no—
436C4⋊Q8—31no—
437C4⋊Q8—61no—
438#125—61no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—31no—
442C22⋊Q8—61no—
443C22⋊Q8—61no—
444C22⋊Q8—61no—
445C22⋊Q8—61no—
446C22⋊Q8C2×C3×D311yescharacteristic
447C4×Q8—31no—
448C4×Q8—31no—
449C4×D4—31no—
450C4×D4—61no—
451C4×D4—61no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4C2×C3×D311yescharacteristic
454#107—31no—
455#107C2×C3×D311yescharacteristic
456#107C2×C3×D311yescharacteristic
457C4⋊C8—31no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103C2×C3×D311yescharacteristic
467#103C2×C3×D311yescharacteristic
468C22⋊C8—31no—
469C22⋊C8C2×C3×D311yescharacteristic
470C4×C8—31no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3D3×D411yescharacteristic
474C23×C3C2×C3×D411yescharacteristic
475C22×D3C2×C3×D411yescharacteristic
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—32no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—122no—
489C3×Q8—122no—
490C3×Q8—241no—
491C3×D4—34no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—81no—
522C2×C3×C4—81no—
523C2×C3×C4—82no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4—241no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C2×C3×D411yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C24×C311yescharacteristic
531#67C3×Q1614yescomplemented
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—42no—
537C2×Dic3C2×C3×D411yescharacteristic
538C2×Dic3C2×C3×D411yescharacteristic
539C2×Dic3C2×C3×D411yescharacteristic
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—42no—
543C4×D3—81no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—21no—
548Dic6—21no—
549Dic6—42no—
550Dic6—42no—
551Dic6—81no—
552Dic6C3×#4112yes—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—41no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C2×C32—22no—
564C2×C32#54611yescharacteristic
565C2×C32C22×Q1611yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—22no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×Q8—61no—
573C2×Q8—62no—
574C2×Q8—61no—
575C2×Q8—62no—
576C2×Q8—121no—
577C2×Q8—121no—
578C2×Q8C22×C3×D311yescharacteristic
579C2×D4—31no—
580C22×C4—21no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4C22×C3×D311yescharacteristic
586Q16—62no—
587Q16—121no—
588Q16—121no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—121no—
592C2×C8—121no—
593C2×C8C22×C3×D311yescharacteristic
594C2×C8C22×C3×D311yescharacteristic
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4C22×C3×D311yescharacteristic
609C4⋊C4C22×C3×D311yescharacteristic
610C4⋊C4C22×C3×D311yescharacteristic
611C22⋊C4—21no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C42—31no—
618C42—61no—
619C42—61no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—32no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3D3×Q1612yes—
632C22×C3C2×C3×Q1612yes—
633C22×C3C2×D3×D411yescharacteristic
634C22×C3C22×C3×D411yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3C2×C3×Q1612yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—61no—
653C3×C4—62no—
654C3×C4—61no—
655C3×C4—81no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4—81no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4D3×#4111yescharacteristic
663C3×C4#100911yescharacteristic
664C3×C4C2×C3×#4111yescharacteristic
665C3×C4C3×H(5,𝔽2)11yescharacteristic
666Dic3—21no—
667Dic3—22no—
668Dic3—21no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3C2×C3×Q1612yes—
673C32#329911yescharacteristic, complemented, Sylow
674C23—31no—
675C23C3×D3×D411yescharacteristic
676Q8—21no—
677Q8—21no—
678Q8—32no—
679Q8—61no—
680Q8—61no—
681Q8—61no—
682Q8—61no—
683Q8—61no—
684Q8—122no—
685Q8—122no—
686Q8—241no—
687D4—34no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—81no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—241no—
707C2×C4C3×D3×D411yescharacteristic
708C2×C4C23×C3×D311yescharacteristic
709C8—21no—
710C8—21no—
711C8—61no—
712C8—61no—
713C2×C3—22no—
714C2×C3—22no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—42no—
719C2×C3—62no—
720C2×C3#565411yescharacteristic
721C2×C3C2×D3×Q1611yescharacteristic
722C2×C3#577511yescharacteristic
723C2×C3C3×#54611yescharacteristic
724C2×C3C22×C3×Q1611yescharacteristic
725C2×C3C3×#57711yescharacteristic
726D3—22no—
727C22—21no—
728C22—21no—
729C22—32no—
730C22—61no—
731C22—61no—
732C22C3×D3×Q1612yes—
733C22C2×C3×D3×D411yescharacteristic
734C4—21no—
735C4—32no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—61no—
741C4—61no—
742C4—62no—
743C4—121no—
744C4—121no—
745C4—121no—
746C4C3×D3×#4111yescharacteristic
747C4C3×#100911yescharacteristic
748C3—21no—
749C3#8149011yescharacteristic, direct product factor
750C3C3×#329911yescharacteristic, complemented
751C2—22no—
752C2—62no—
753C2C3×#565411yescharacteristic
754C2C2×C3×D3×Q1611yescharacteristic
755C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#484C2
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC3×#484D3
hypocenterC3C3×#3299
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#484

Complements

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

NH ≅ G/Ntype
3. C32×#484C2semidirect
4. C3×#5051C2semidirect
5. C2×C3×#810C2semidirect
6. C3×#4887C2semidirect
7. C3×#4884C2semidirect
8. C3×#4875C2semidirect
9. C3×#4873C2semidirect
10. C3×#4809C2semidirect
11. C3×D3×#103C2semidirect
12. C3×#4795C2semidirect
13. C3×#4792C2semidirect
14. C3×#4739C2semidirect
17. #81490C3direct (N × H)
68. C3×#484D3semidirect
69. C3×#484C2×C3semidirect
80. #5051C2×C3semidirect
81. C2×#810C2×C3semidirect
82. #4887C2×C3semidirect
83. #4884C2×C3semidirect
84. #4875C2×C3semidirect
85. #4873C2×C3semidirect
86. #4809C2×C3semidirect
87. D3×#103C2×C3semidirect
88. #4795C2×C3semidirect
89. #4792C2×C3semidirect
90. #4739C2×C3semidirect
251. C3×#67Q16semidirect
281. #484C3×D3semidirect
531. #67C3×Q16semidirect
673. C32#3299semidirect
749. C3#81490direct (N × H)
750. C3C3×#3299semidirect

Maximal subgroups

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

subgroupindex
C3×#56322
C3×#55112
C32×#4842
C3×#50512
C2×C3×#8102
C3×#48872
C3×#48842
C3×#48752
C3×#48732
C3×#48092
C3×D3×#1032
C3×#47952
C3×#47922
C3×#47392
C3×#67⋊C82
C3×#32993
#814903