Finite Group Databasebeta

← C3×#80128 #11884390

Subgroups — C3×#80128 #11884390

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C2×C3×#911C211yesmaximal, characteristic, complemented
4C3×#5599C211yesmaximal, characteristic, complemented
5C32×#449C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7C3×#5173C211yesmaximal, characteristic, complemented
8C3×#5150C211yesmaximal, characteristic, complemented
9C3×#5038C211yesmaximal, characteristic, complemented
10C3×#4812C211yesmaximal, characteristic, complemented
11C3×#4798C211yesmaximal, characteristic, complemented
12C3×#4773C211yesmaximal, characteristic, complemented
13C3×#4757C211yesmaximal, characteristic, complemented
14C3×#4734C211yesmaximal, characteristic, complemented
15C3×#4730C211yesmaximal, characteristic, complemented
16C3×#3268—31nomaximal
17#80128C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic, complemented
22C2×C32×SD16C2211yescharacteristic, complemented
23C2×C32×D8C2211yescharacteristic
24C32×#121C2211yescharacteristic, complemented
25C3×#950—24no—
26C3×#947C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#940—21no—
31C3×#940C2211yescharacteristic, complemented
32C3×#939—21no—
33C3×#939—21no—
34C3×#937—21no—
35C3×D4×Dic3C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic
38C2×C3×#213C2211yescharacteristic
39C3×#930C2211yescharacteristic
40C3×#929—21no—
41C3×C4×#67C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4—21no—
43C22×C3×C3⋊C8C2211yescharacteristic, complemented
44C3×#911—24no—
45C2×C3×D24C2211yescharacteristic
46C2×C3×#204C2211yescharacteristic
47C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
48C3×#895C2211yescharacteristic
49C3×#887C2211yescharacteristic, complemented
50C3×#884—21no—
51C3×#67⋊C4—21no—
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic
54C32×C22⋊C8C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×#816C2211yescharacteristic, complemented
59C3×#815C2211yescharacteristic, complemented
60C3×Dic3⋊C8C2211yescharacteristic, complemented
61C3×#809C2211yescharacteristic
62C3×#807C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65C3×#550—31no—
66C3×#546—31no—
67#5829C2×C311yescharacteristic, complemented
68C2×#950C2×C311yescharacteristic, complemented
69C2×#911C2×C311yescharacteristic, complemented
70#5599C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#468—31no—
73C3×#466—31no—
74C3×#464—31no—
75C3×#459—31no—
76C3×#452—31no—
77C3×#449—21no—
78C3×#449—31no—
79C3×#449D311yescharacteristic, complemented
80C3×#449C2×C311yescharacteristic, complemented
81C3×#447—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5176C2×C311yescharacteristic, complemented
85#5173C2×C311yescharacteristic, complemented
86#5150C2×C311yescharacteristic, complemented
87#5038C2×C311yescharacteristic, complemented
88#4812C2×C311yescharacteristic, complemented
89#4798C2×C311yescharacteristic, complemented
90#4773C2×C311yescharacteristic, complemented
91#4757C2×C311yescharacteristic, complemented
92#4734C2×C311yescharacteristic, complemented
93#4730C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4—21no—
100C2×C32×D4C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C22×C32×C4—21no—
103C22×C32×C4C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C22×C3×Dic3—21no—
112C22×C3×Dic3—21no—
113C3×#237—22no—
114C3×#237—41no—
115C3×D3×D4—22no—
116C3×D3×D4—41no—
117C3×#235—22no—
118C3×#235—41no—
119C2×C3×D12—21no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic
125C32×SD16—41no—
126C32×D8—22no—
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129C32×C4⋊C4C2311yescharacteristic
130C32×C22⋊C4—21no—
131C3×#217—21no—
132C3×#217D411yescharacteristic
133C3×#216—22no—
134C3×#215—22no—
135C3×#214D414yescomplemented
136C3×#213—22no—
137C3×#213—22no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4D411yescharacteristic
144C3×C4⋊Dic3C2311yescharacteristic
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4D411yescharacteristic
148C3×C4×Dic3—21no—
149C3×C4×Dic3C2311yescharacteristic
150C2×C3×C3⋊C8—22no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×D24—41no—
154C3×#204—22no—
155C3×ΓL(1,𝔽25)—22no—
156#3268—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×C3×#41C2×D311yescharacteristic
161C2×C3×#41C22×C311yescharacteristic
162C22×C3×D4—31no—
163C2×#237C22×C311yescharacteristic
164C2×D3×D4C22×C311yescharacteristic
165C2×#235C22×C311yescharacteristic, complemented
166C3×AGL(1,ℤ/8)—64no—
167C3×#135—64no—
168C2×C3×Q16—31no—
169C2×C3×SD16—21no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16C2×D311yescharacteristic, complemented
174C2×C3×SD16C22×C311yescharacteristic, complemented
175C2×C3×D8—21no—
176C2×C3×D8—31no—
177C2×C3×D8—31no—
178C2×C3×D8—31no—
179C2×C3×D8C2×D311yescharacteristic
180C2×C3×D8C22×C311yescharacteristic
181C2×C3×M16—31no—
182C22×C3×C8—31no—
183C3×#127—31no—
184C3×#127—61no—
185C3×#124—31no—
186C3×#123—61no—
187C3×C22⋊Q8—31no—
188C3×#121—21no—
189C3×#121—31no—
190C3×#121—31no—
191C3×#121—61no—
192C3×#121—61no—
193C3×#121—61no—
194C3×#121C2×D311yescharacteristic, complemented
195C3×#121C22×C311yescharacteristic, complemented
196C3×#120—61no—
197C3×C4×Q8—31no—
198C3×C4×D4—31no—
199C3×C4×D4—31no—
200C3×C4×D4—61no—
201C2×C3×C22⋊C4—61no—
202#950—24no—
203#947C22×C311yescharacteristic
204#946C22×C311yescharacteristic
205C2×#216C22×C311yescharacteristic, complemented
206C2×#215C22×C311yescharacteristic, complemented
207#940—21no—
208#940C22×C311yescharacteristic, complemented
209#939—21no—
210#939—21no—
211#937—21no—
212D4×Dic3C22×C311yescharacteristic
213C2×#214C22×C311yescharacteristic
214C2×#213C22×C311yescharacteristic
215C2×#213C22×C311yescharacteristic
216#930C22×C311yescharacteristic
217#929—21no—
218C4×#67C22×C311yescharacteristic
219C2×(C2×D3)⋊C4—21no—
220C22×C3⋊C8C22×C311yescharacteristic, complemented
221#911—24no—
222C2×D24C22×C311yescharacteristic
223C2×#204C22×C311yescharacteristic
224C2×ΓL(1,𝔽25)C22×C311yescharacteristic
225#895C22×C311yescharacteristic
226#887C22×C311yescharacteristic, complemented
227#884—21no—
228#67⋊C4—21no—
229C3×#107—31no—
230C3×C4⋊C8—31no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103C2×D311yescharacteristic, complemented
234C3×#103C22×C311yescharacteristic, complemented
235C3×#102—21no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102C2×D311yescharacteristic
240C3×#102C22×C311yescharacteristic
241C3×C22⋊C8—21no—
242C3×C22⋊C8—31no—
243C3×C22⋊C8C2×D311yescharacteristic, complemented
244C3×C22⋊C8C22×C311yescharacteristic, complemented
245C3×#97—31no—
246#832C22×C311yescharacteristic, complemented
247#821C22×C311yescharacteristic, complemented
248(C2×D3)⋊C8C22×C311yescharacteristic
249#816C22×C311yescharacteristic, complemented
250#815C22×C311yescharacteristic, complemented
251Dic3⋊C8C22×C311yescharacteristic, complemented
252#809C22×C311yescharacteristic
253#807C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—21no—
268C32×D4—42no—
269C32×D4—81no—
270C32×D4C2×D412yes—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—42no—
276C2×C32×C4C2×D411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278C3×#67—41no—
279C3×#67—42no—
280C3×#67—42no—
281C3×#67—42no—
282C3×#67—42no—
283C3×#67—81no—
284C3×#67—81no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—42no—
288C2×C3×Dic3—81no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—81no—
297C3×C4×D3—21no—
298C3×C4×D3—21no—
299C3×C4×D3—42no—
300C3×Dic6—21no—
301C3×Dic6C2×D412yes—
302C32×C8—21no—
303C32×C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—31no—
307C2×#135—31no—
308#550—31no—
309#546—31no—
310#496—31no—
311#468—31no—
312#466—31no—
313#464—31no—
314#459—31no—
315#452—31no—
316#449—31no—
317#449C3×D311yescharacteristic, complemented
318#447—31no—
319#440—31no—
320#435—31no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—22no—
324C3×#41—22no—
325C3×#41—42no—
326C3×#41—41no—
327C3×#41—41no—
328C3×#41—42no—
329C3×#41—62no—
330C3×#41—62no—
331C3×#41—121no—
332C3×#41—121no—
333C2×C3×Q8—21no—
334C2×C3×Q8—31no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C23×C311yescharacteristic
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—21no—
342C2×C3×D4—21no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—41no—
347C2×C3×D4—41no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C2×C3×D4—62no—
353C2×C3×D4—61no—
354C2×C3×D4—61no—
355C2×C3×D4—61no—
356C2×C3×D4—121no—
357C2×C3×D4C22×D311yescharacteristic
358C2×C3×D4C22×D311yescharacteristic
359C2×C3×D4C23×C311yescharacteristic
360C2×C3×D4C23×C311yescharacteristic
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—31no—
365C22×C3×C4—41no—
366C22×C3×C4—61no—
367C22×C3×C4—61no—
368C22×C3×C4—61no—
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C23×C311yescharacteristic
371C2×#67—21no—
372C2×#67—21no—
373C2×#67—21no—
374C2×#67—21no—
375C2×#67—21no—
376C2×#67—21no—
377C2×#67C3×D411yescharacteristic
378C22×Dic3—21no—
379C22×Dic3—21no—
380#237—22no—
381#237—41no—
382D3×D4—22no—
383D3×D4—41no—
384#235—22no—
385#235—41no—
386C2×D12—21no—
387C2×D12C23×C311yescharacteristic
388C2×D12C23×C311yescharacteristic
389C2×C4×D3—21no—
390C2×C4×D3C23×C311yescharacteristic
391C2×Dic6C23×C311yescharacteristic
392C3×Q16—62no—
393C3×SD16—34no—
394C3×SD16—41no—
395C3×SD16—41no—
396C3×SD16—42no—
397C3×SD16—62no—
398C3×SD16—62no—
399C3×D8—22no—
400C3×D8—22no—
401C3×D8—42no—
402C3×D8—62no—
403C3×D8—62no—
404C3×D8—121no—
405C3×M16—62no—
406C2×C3×C8—21no—
407C2×C3×C8—21no—
408C2×C3×C8—31no—
409C2×C3×C8—31no—
410C2×C3×C8—62no—
411C2×C3×C8C22×D311yescharacteristic
412C2×C3×C8C22×D311yescharacteristic
413C2×C3×C8C23×C311yescharacteristic
414C2×C3×C8C23×C311yescharacteristic
415C3×C4⋊C4—21no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—61no—
419C3×C4⋊C4—61no—
420C3×C4⋊C4C22×D311yescharacteristic
421C3×C4⋊C4C23×C311yescharacteristic
422C3×C22⋊C4—21no—
423C3×C22⋊C4—21no—
424C3×C22⋊C4—31no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—41no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C22⋊C4—61no—
433C3×C42—31no—
434C3×C42—61no—
435#217—21no—
436#217C3×D411yescharacteristic
437#216—22no—
438#215—22no—
439#214C3×D414yescomplemented
440#213—22no—
441#213—22no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4—21no—
447(C2×D3)⋊C4C3×D411yescharacteristic
448C4⋊Dic3C23×C311yescharacteristic
449Dic3⋊C4—21no—
450Dic3⋊C4—21no—
451Dic3⋊C4C3×D411yescharacteristic
452C4×Dic3—21no—
453C4×Dic3C23×C311yescharacteristic
454C2×C3⋊C8—22no—
455C2×C3⋊C8C23×C311yescharacteristic
456C2×C3⋊C8C23×C311yescharacteristic
457D24—41no—
458#204—22no—
459ΓL(1,𝔽25)—22no—
460C22×C32—21no—
461C22×C32—22no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—84no—
480C32×C4—21no—
481C32×C4—41no—
482C32×C4—41no—
483C32×C4C22×D411yescharacteristic
484C32×C4H(5,𝔽2)11yescharacteristic
485C3×Dic3—22no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—31no—
492C2×#41C2×C3×D311yescharacteristic
493C22×D4—31no—
494AGL(1,ℤ/8)—64no—
495#135—64no—
496C2×Q16—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16—31no—
500C2×SD16C2×C3×D311yescharacteristic, complemented
501C2×D8—31no—
502C2×D8—31no—
503C2×D8—31no—
504C2×D8C2×C3×D311yescharacteristic
505C2×M16—31no—
506C22×C8—31no—
507#127—31no—
508#127—61no—
509#124—31no—
510#123—61no—
511C22⋊Q8—31no—
512#121—31no—
513#121—31no—
514#121—61no—
515#121—61no—
516#121—61no—
517#121C2×C3×D311yescharacteristic, complemented
518#120—61no—
519C4×Q8—31no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—61no—
523C2×C22⋊C4—61no—
524#107—31no—
525C4⋊C8—31no—
526#103—31no—
527#103C2×C3×D311yescharacteristic, complemented
528#102—31no—
529#102—31no—
530#102—31no—
531#102C2×C3×D311yescharacteristic
532C22⋊C8—31no—
533C22⋊C8C2×C3×D311yescharacteristic, complemented
534#97—31no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—122no—
546C23×C3—122no—
547C23×C3—241no—
548C23×C3D3×D411yescharacteristic
549C23×C3C2×C3×D411yescharacteristic
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—81no—
555C22×D3C2×C3×D411yescharacteristic
556C3×Q8—22no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—21no—
561C3×Q8—32no—
562C3×Q8—41no—
563C3×Q8—61no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—22no—
571C3×D4—41no—
572C3×D4—41no—
573C3×D4—41no—
574C3×D4—42no—
575C3×D4—42no—
576C3×D4—44no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—81no—
582C3×D4—81no—
583C3×D4—82no—
584C3×D4—121no—
585C3×D4—122no—
586C3×D4—122no—
587C3×D4—122no—
588C3×D4—122no—
589C3×D4—241no—
590C3×D4—241no—
591C3×D4—241no—
592C3×D4D3×D412yes—
593C3×D4C2×C3×D412yes—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—31no—
605C2×C3×C4—31no—
606C2×C3×C4—31no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—42no—
612C2×C3×C4—42no—
613C2×C3×C4—44no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—122no—
619C2×C3×C4—122no—
620C2×C3×C4—241no—
621C2×C3×C4D3×D411yescharacteristic
622C2×C3×C4C2×C3×D411yescharacteristic
623C2×C3×C4C23×D311yescharacteristic
624C2×C3×C4C24×C311yescharacteristic
625#67—41no—
626#67—42no—
627#67—42no—
628#67—42no—
629#67—42no—
630#67—81no—
631#67—81no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—42no—
635C2×Dic3—81no—
636C2×Dic3C2×C3×D411yescharacteristic
637C2×Dic3C2×C3×D411yescharacteristic
638C2×Dic3C2×C3×D411yescharacteristic
639D12—21no—
640D12—21no—
641D12—21no—
642D12—21no—
643D12—81no—
644C4×D3—21no—
645C4×D3—21no—
646C4×D3—42no—
647Dic6—21no—
648Dic6C2×C3×D412yes—
649C3×C8—21no—
650C3×C8—21no—
651C3×C8—21no—
652C3×C8—21no—
653C3×C8—32no—
654C3×C8—41no—
655C3×C8—41no—
656C3×C8—61no—
657C3⋊C8—21no—
658C3⋊C8C2×C3×D412yes—
659C2×C32—42no—
660C2×C32—41no—
661C2×C32—81no—
662C2×C32D4211yescharacteristic
663C2×C32#57511yescharacteristic
664C2×C32#57611yescharacteristic
665C3×D3—41no—
666C3×D3—81no—
667C3×D3—81no—
668C24—61no—
669#41—22no—
670#41—41no—
671#41—62no—
672#41—62no—
673#41—121no—
674#41—121no—
675C2×Q8—31no—
676C2×Q8C22×C3×D311yescharacteristic
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—62no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—121no—
691C2×D4C22×C3×D311yescharacteristic
692C2×D4C22×C3×D311yescharacteristic
693C22×C4—21no—
694C22×C4—31no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4C22×C3×D311yescharacteristic
699Q16—62no—
700SD16—34no—
701SD16—41no—
702SD16—62no—
703SD16—62no—
704D8—22no—
705D8—62no—
706D8—62no—
707D8—121no—
708M16—62no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—62no—
712C2×C8C22×C3×D311yescharacteristic
713C2×C8C22×C3×D311yescharacteristic
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—61no—
717C4⋊C4—61no—
718C4⋊C4C22×C3×D311yescharacteristic
719C22⋊C4—21no—
720C22⋊C4—31no—
721C22⋊C4—31no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C42—31no—
729C42—61no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—22no—
738C22×C3—21no—
739C22×C3—42no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—61no—
754C22×C3—61no—
755C22×C3—61no—
756C22×C3—81no—
757C22×C3—81no—
758C22×C3—81no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—244no—
768C22×C3C2×D3×D411yescharacteristic
769C22×C3C22×C3×D411yescharacteristic
770C2×D3—21no—
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—84no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—41no—
785C3×C4—42no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—61no—
793C3×C4—62no—
794C3×C4—81no—
795C3×C4—121no—
796C3×C4C2×D3×D411yescharacteristic
797C3×C4#100411yescharacteristic
798C3×C4C22×C3×D411yescharacteristic
799C3×C4C3×H(5,𝔽2)11yescharacteristic
800Dic3—21no—
801Dic3—21no—
802Dic3—22no—
803Dic3—21no—
804Dic3—41no—
805C32#326811yescharacteristic, complemented, Sylow
806C23—21no—
807C23—21no—
808C23—31no—
809C23—61no—
810C23—61no—
811C23—122no—
812C23—122no—
813C23—241no—
814C23C3×D3×D411yescharacteristic
815Q8—21no—
816Q8—21no—
817Q8—32no—
818Q8—61no—
819D4—21no—
820D4—21no—
821D4—21no—
822D4—42no—
823D4—61no—
824D4—61no—
825D4—61no—
826D4—61no—
827D4—81no—
828D4—121no—
829D4—122no—
830D4—122no—
831D4—122no—
832D4—122no—
833D4—241no—
834D4—241no—
835D4—241no—
836D4C3×D3×D412yes—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—31no—
844C2×C4—42no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—122no—
850C2×C4—122no—
851C2×C4—241no—
852C2×C4C3×D3×D411yescharacteristic
853C2×C4C23×C3×D311yescharacteristic
854C8—21no—
855C8—21no—
856C8—32no—
857C8—61no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—41no—
862C2×C3—42no—
863C2×C3—42no—
864C2×C3—41no—
865C2×C3—81no—
866C2×C3—82no—
867C2×C3—81no—
868C2×C3—81no—
869C2×C3—121no—
870C2×C3—161no—
871C2×C3—241no—
872C2×C3—241no—
873C2×C3#559011yescharacteristic
874C2×C3#576811yescharacteristic
875C2×C3#577411yescharacteristic
876C2×C3C3×D4211yescharacteristic
877C2×C3C3×#57511yescharacteristic
878C2×C3C3×#57611yescharacteristic
879D3—41no—
880D3—81no—
881D3—81no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—22no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—61no—
892C22—61no—
893C22—61no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—244no—
901C22C2×C3×D3×D411yescharacteristic
902C4—21no—
903C4—41no—
904C4—41no—
905C4—61no—
906C4—61no—
907C4—61no—
908C4—62no—
909C4—121no—
910C4C2×C3×D3×D411yescharacteristic
911C4C3×#100411yescharacteristic
912C3—21no—
913C3#8012811yescharacteristic, direct product factor
914C3C3×#326811yescharacteristic, complemented
915C2—41no—
916C2—42no—
917C2—81no—
918C2—121no—
919C2—241no—
920C2—241no—
921C2C3×#559011yescharacteristic
922C2C3×#576811yescharacteristic
923C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenterC3×#449D3
hypocenterC3C3×#3268
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C3×#5829C2semidirect
2. C2×C3×#950C2semidirect
3. C2×C3×#911C2semidirect
4. C3×#5599C2semidirect
5. C32×#449C2semidirect
6. C3×#5176C2semidirect
7. C3×#5173C2semidirect
8. C3×#5150C2semidirect
9. C3×#5038C2semidirect
10. C3×#4812C2semidirect
11. C3×#4798C2semidirect
12. C3×#4773C2semidirect
13. C3×#4757C2semidirect
14. C3×#4734C2semidirect
15. C3×#4730C2semidirect
17. #80128C3direct (N × H)
21. C2×C3×#235C22semidirect
22. C2×C32×SD16C22semidirect
24. C32×#121C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#215C22semidirect
31. C3×#940C22semidirect
43. C22×C3×C3⋊C8C22semidirect
49. C3×#887C22semidirect
52. C32×#103C22semidirect
54. C32×C22⋊C8C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
58. C3×#816C22semidirect
59. C3×#815C22semidirect
60. C3×Dic3⋊C8C22semidirect
62. C3×#807C22semidirect
67. #5829C2×C3semidirect
68. C2×#950C2×C3semidirect
69. C2×#911C2×C3semidirect
70. #5599C2×C3semidirect
79. C3×#449D3semidirect
80. C3×#449C2×C3semidirect
84. #5176C2×C3semidirect
85. #5173C2×C3semidirect
86. #5150C2×C3semidirect
87. #5038C2×C3semidirect
88. #4812C2×C3semidirect
89. #4798C2×C3semidirect
90. #4773C2×C3semidirect
91. #4757C2×C3semidirect
92. #4734C2×C3semidirect
93. #4730C2×C3semidirect
135. C3×#214D4semidirect
165. C2×#235C22×C3semidirect
173. C2×C3×SD16C2×D3semidirect
174. C2×C3×SD16C22×C3semidirect
194. C3×#121C2×D3semidirect
195. C3×#121C22×C3semidirect
205. C2×#216C22×C3semidirect
206. C2×#215C22×C3semidirect
208. #940C22×C3semidirect
220. C22×C3⋊C8C22×C3semidirect
226. #887C22×C3semidirect
233. C3×#103C2×D3semidirect
234. C3×#103C22×C3semidirect
243. C3×C22⋊C8C2×D3semidirect
244. C3×C22⋊C8C22×C3semidirect
246. #832C22×C3semidirect
247. #821C22×C3semidirect
249. #816C22×C3semidirect
250. #815C22×C3semidirect
251. Dic3⋊C8C22×C3semidirect
253. #807C22×C3semidirect
317. #449C3×D3semidirect
439. #214C3×D4semidirect
500. C2×SD16C2×C3×D3semidirect
517. #121C2×C3×D3semidirect
527. #103C2×C3×D3semidirect
533. C22⋊C8C2×C3×D3semidirect
805. C32#3268semidirect
913. C3#80128direct (N × H)
914. C3C3×#3268semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
C2×C3×#9502
C2×C3×#9112
C3×#55992
C32×#4492
C3×#51762
C3×#51732
C3×#51502
C3×#50382
C3×#48122
C3×#47982
C3×#47732
C3×#47572
C3×#47342
C3×#47302
C3×#32683
#801283