Finite Group Databasebeta

← C3×#81858 #11884375

Subgroups — C3×#81858 #11884375

Order 1152.

1092 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2C2×C3×#911C211yesmaximal, characteristic, complemented
3C3×#5718C211yesmaximal, characteristic, complemented
4C3×#5676C211yesmaximal, characteristic, complemented
5C32×#496C211yesmaximal, characteristic, complemented
6C3×#5174C211yesmaximal, characteristic, complemented
7C3×#5173C211yesmaximal, characteristic, complemented
8C3×#5172C211yesmaximal, characteristic, complemented
9C3×#5158C211yesmaximal, characteristic, complemented
10C3×#5157C211yesmaximal, characteristic, complemented
11C3×#5156C211yesmaximal, characteristic, complemented
12C3×#5072C211yesmaximal, characteristic, complemented
13C3×#5054C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4706C211yesmaximal, characteristic, complemented
16C3×#3268—31nomaximal
17#81858C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic, complemented
24C2×C32×D8C2211yescharacteristic
25C2×C32×D8C2211yescharacteristic
26C32×#127C2211yescharacteristic, complemented
27C32×#124C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic, complemented
30C3×#940—21no—
31C3×#939—21no—
32C3×#939—21no—
33C3×#938C2211yescharacteristic
34C3×#938C2211yescharacteristic
35C3×#938C2211yescharacteristic, complemented
36C3×D4×Dic3—21no—
37C2×C3×#214C2211yescharacteristic
38C2×C3×#213C2211yescharacteristic
39C2×C3×#213C2211yescharacteristic
40C3×#916—24no—
41C3×#911—24no—
42C2×C3×#204C2211yescharacteristic
43C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
44C2×C3×D3×C8C2211yescharacteristic, complemented
45C3×#884—21no—
46C3×#883—21no—
47C3×#882—21no—
48C3×D3×C22⋊C4—21no—
49C3×C4×D12C2211yescharacteristic
50C3×C4×D12C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic, complemented
52C32×#97C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic
55C3×#832C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
60C3×#818C2211yescharacteristic, complemented
61C3×#816C2211yescharacteristic, complemented
62C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65C3×#550—31no—
66C3×#546—31no—
67C2×#916C2×C311yescharacteristic, complemented
68C2×#911C2×C311yescharacteristic, complemented
69#5718C2×C311yescharacteristic, complemented
70#5676C2×C311yescharacteristic, complemented
71C3×#496—21no—
72C3×#496D311yescharacteristic, complemented
73C3×#496C2×C311yescharacteristic, complemented
74C3×#468—31no—
75C3×#466—31no—
76C3×#464—31no—
77C3×#459—31no—
78C3×#452—31no—
79C3×#449—31no—
80C3×#449—31no—
81C3×#447—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5174C2×C311yescharacteristic, complemented
85#5173C2×C311yescharacteristic, complemented
86#5172C2×C311yescharacteristic, complemented
87#5158C2×C311yescharacteristic, complemented
88#5157C2×C311yescharacteristic, complemented
89#5156C2×C311yescharacteristic, complemented
90#5072C2×C311yescharacteristic, complemented
91#5054C2×C311yescharacteristic, complemented
92#4710C2×C311yescharacteristic, complemented
93#4706C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C3×#239—22no—
110C3×#239—41no—
111C3×#237—22no—
112C3×#237—22no—
113C3×#237—41no—
114C3×#237—41no—
115C3×D3×D4—22no—
116C3×D3×D4—41no—
117C2×C3×D12—21no—
118C2×C3×D12D411yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic
125C32×SD16—22no—
126C32×SD16—41no—
127C32×D8—22no—
128C32×D8—41no—
129C2×C32×C8C2311yescharacteristic
130C2×C32×C8C2311yescharacteristic
131C32×C22⋊C4—21no—
132C32×C22⋊C4—21no—
133C32×C42C2311yescharacteristic
134C3×#217—21no—
135C3×#217—21no—
136C3×#217—21no—
137C3×#216—22no—
138C3×#214—22no—
139C3×#213—22no—
140C3×#213—22no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4D411yescharacteristic
144C3×(C2×D3)⋊C4D411yescharacteristic
145C3×C4⋊Dic3D411yescharacteristic
146C3×C4⋊Dic3C2311yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×Dic3⋊C4—21no—
149C3×Dic3⋊C4—21no—
150C3×C4×Dic3—21no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×#204D414yescomplemented
154C3×ΓL(1,𝔽25)—22no—
155C3×D3×C8—22no—
156#3268—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×D4—31no—
161C2×#239C22×C311yescharacteristic
162C2×#237C22×C311yescharacteristic
163C2×#237C22×C311yescharacteristic, complemented
164C2×D3×D4C22×C311yescharacteristic
165C3×AGL(1,ℤ/8)—64no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—21no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16C2×D311yescharacteristic, complemented
173C2×C3×SD16C2×D311yescharacteristic, complemented
174C2×C3×SD16C22×C311yescharacteristic, complemented
175C2×C3×SD16C22×C311yescharacteristic, complemented
176C2×C3×D8—21no—
177C2×C3×D8—21no—
178C2×C3×D8—31no—
179C2×C3×D8—31no—
180C2×C3×D8C2×D311yescharacteristic
181C2×C3×D8C2×D311yescharacteristic
182C2×C3×D8C22×C311yescharacteristic
183C2×C3×D8C22×C311yescharacteristic
184C2×C3×M16—31no—
185C22×C3×C8—31no—
186C3×#127—21no—
187C3×#127—61no—
188C3×#127C2×D311yescharacteristic, complemented
189C3×#127C22×C311yescharacteristic, complemented
190C3×#124—21no—
191C3×#124C2×D311yescharacteristic
192C3×#124C22×C311yescharacteristic
193C3×#123—61no—
194C3×C22⋊Q8—31no—
195C3×#121—31no—
196C3×#121—31no—
197C3×#121—31no—
198C3×#121—61no—
199C3×#121—61no—
200C3×#121—61no—
201C3×#120—61no—
202C3×C4×Q8—31no—
203C3×C4×D4—31no—
204C3×C4×D4—31no—
205C3×C4×D4—61no—
206C2×C3×C22⋊C4—61no—
207#946C22×C311yescharacteristic
208C2×#216C22×C311yescharacteristic, complemented
209#940—21no—
210#939—21no—
211#939—21no—
212#938C22×C311yescharacteristic
213#938C22×C311yescharacteristic
214#938C22×C311yescharacteristic, complemented
215D4×Dic3—21no—
216C2×#214C22×C311yescharacteristic
217C2×#213C22×C311yescharacteristic
218C2×#213C22×C311yescharacteristic
219#916—24no—
220#911—24no—
221C2×#204C22×C311yescharacteristic
222C2×ΓL(1,𝔽25)C22×C311yescharacteristic
223C2×D3×C8C22×C311yescharacteristic, complemented
224#884—21no—
225#883—21no—
226#882—21no—
227D3×C22⋊C4—21no—
228C4×D12C22×C311yescharacteristic
229C4×D12C22×C311yescharacteristic
230C4×Dic6C22×C311yescharacteristic, complemented
231C3×#107—31no—
232C3×C4⋊C8—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×C22⋊C8—31no—
240C3×C22⋊C8—31no—
241C3×#97—21no—
242C3×#97C2×D311yescharacteristic, complemented
243C3×#97C22×C311yescharacteristic, complemented
244#835C22×C311yescharacteristic, complemented
245#832C22×C311yescharacteristic
246#832C22×C311yescharacteristic, complemented
247#832C22×C311yescharacteristic, complemented
248#821C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic
250(C2×D3)⋊C8C22×C311yescharacteristic, complemented
251#818C22×C311yescharacteristic, complemented
252#816C22×C311yescharacteristic, complemented
253C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—21no—
268C32×D4—21no—
269C32×D4—21no—
270C32×D4—21no—
271C32×D4—42no—
272C32×D4—81no—
273C2×C32×C4—21no—
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—42no—
280C3×#67—81no—
281C3×#67—81no—
282C3×#67—81no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—42no—
287C2×C3×Dic3—42no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×D12—21no—
291C3×D12—41no—
292C3×D12—42no—
293C3×D12C2×D412yes—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—21no—
298C3×C4×D3—42no—
299C3×C4×D3—81no—
300C3×Dic6—21no—
301C3×Dic6C2×D412yes—
302C32×C8—21no—
303C32×C8C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—31no—
307C2×#135—31no—
308#550—31no—
309#546—31no—
310#496C3×D311yescharacteristic, complemented
311#468—31no—
312#466—31no—
313#464—31no—
314#459—31no—
315#452—31no—
316#449—31no—
317#449—31no—
318#447—31no—
319#440—31no—
320#435—31no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—62no—
326C3×#41—121no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C23×C311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—31no—
341C2×C3×D4—31no—
342C2×C3×D4—41no—
343C2×C3×D4—41no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—62no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C2×C3×D4—121no—
353C2×C3×D4C22×D311yescharacteristic
354C2×C3×D4C22×D311yescharacteristic
355C2×C3×D4C22×D311yescharacteristic
356C2×C3×D4C23×C311yescharacteristic
357C2×C3×D4C23×C311yescharacteristic
358C2×C3×D4C23×C311yescharacteristic
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—61no—
362C22×C3×C4—61no—
363C22×C3×C4—61no—
364C22×C3×C4—61no—
365C2×#67—21no—
366C2×#67—21no—
367C2×#67—21no—
368C2×#67—21no—
369C2×#67—21no—
370C2×#67—21no—
371C22×Dic3—21no—
372C22×Dic3—21no—
373#239—22no—
374#239—41no—
375#237—22no—
376#237—22no—
377#237—41no—
378#237—41no—
379D3×D4—22no—
380D3×D4—41no—
381C2×D12—21no—
382C2×D12C3×D411yescharacteristic
383C2×D12C23×C311yescharacteristic
384C2×C4×D3—21no—
385C2×C4×D3—21no—
386C2×C4×D3C23×C311yescharacteristic
387C2×C4×D3C23×C311yescharacteristic
388C2×Dic6C23×C311yescharacteristic
389C3×Q16—62no—
390C3×SD16—22no—
391C3×SD16—22no—
392C3×SD16—34no—
393C3×SD16—42no—
394C3×SD16—41no—
395C3×SD16—41no—
396C3×SD16—42no—
397C3×SD16—62no—
398C3×D8—22no—
399C3×D8—22no—
400C3×D8—42no—
401C3×D8—41no—
402C3×D8—41no—
403C3×D8—42no—
404C3×D8—62no—
405C3×D8—62no—
406C3×M16—62no—
407C2×C3×C8—21no—
408C2×C3×C8—21no—
409C2×C3×C8—31no—
410C2×C3×C8—31no—
411C2×C3×C8—62no—
412C2×C3×C8C22×D311yescharacteristic
413C2×C3×C8C22×D311yescharacteristic
414C2×C3×C8C23×C311yescharacteristic
415C2×C3×C8C23×C311yescharacteristic
416C3×C4⋊C4—31no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—31no—
419C3×C4⋊C4—61no—
420C3×C4⋊C4—61no—
421C3×C22⋊C4—21no—
422C3×C22⋊C4—21no—
423C3×C22⋊C4—21no—
424C3×C22⋊C4—21no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—41no—
428C3×C22⋊C4—41no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C22⋊C4—61no—
433C3×C22⋊C4—61no—
434C3×C42—21no—
435C3×C42—61no—
436C3×C42C22×D311yescharacteristic
437C3×C42C23×C311yescharacteristic
438#217—21no—
439#217—21no—
440#217—21no—
441#216—22no—
442#214—22no—
443#213—22no—
444#213—22no—
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4—21no—
447(C2×D3)⋊C4C3×D411yescharacteristic
448(C2×D3)⋊C4C3×D411yescharacteristic
449C4⋊Dic3C3×D411yescharacteristic
450C4⋊Dic3C23×C311yescharacteristic
451C4⋊Dic3C23×C311yescharacteristic
452Dic3⋊C4—21no—
453Dic3⋊C4—21no—
454C4×Dic3—21no—
455C2×C3⋊C8C23×C311yescharacteristic
456C2×C3⋊C8C23×C311yescharacteristic
457#204C3×D414yescomplemented
458ΓL(1,𝔽25)—22no—
459D3×C8—22no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
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—22no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—84no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—41no—
483C32×C4C22×D411yescharacteristic
484C32×C4H(5,𝔽2)11yescharacteristic
485C3×Dic3—22no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—31no—
492C2×#41—31no—
493C22×D4—31no—
494AGL(1,ℤ/8)—64no—
495#135—64no—
496C2×Q16—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16C2×C3×D311yescharacteristic, complemented
500C2×SD16C2×C3×D311yescharacteristic, complemented
501C2×D8—31no—
502C2×D8—31no—
503C2×D8C2×C3×D311yescharacteristic
504C2×D8C2×C3×D311yescharacteristic
505C2×M16—31no—
506C22×C8—31no—
507#127—61no—
508#127C2×C3×D311yescharacteristic, complemented
509#124C2×C3×D311yescharacteristic
510#123—61no—
511C22⋊Q8—31no—
512#121—31no—
513#121—31no—
514#121—31no—
515#121—61no—
516#121—61no—
517#121—61no—
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#103—31no—
528#102—31no—
529#102—31no—
530#102—31no—
531#102—31no—
532C22⋊C8—31no—
533C22⋊C8—31no—
534#97C2×C3×D311yescharacteristic, complemented
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—61no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—241no—
550C22×D3—21no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—81no—
554C22×D3C2×C3×D411yescharacteristic
555C22×D3C2×C3×D411yescharacteristic
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—32no—
561C3×Q8—41no—
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—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—32no—
577C3×D4—41no—
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—41no—
581C3×D4—41no—
582C3×D4—41no—
583C3×D4—42no—
584C3×D4—42no—
585C3×D4—61no—
586C3×D4—82no—
587C3×D4—81no—
588C3×D4—81no—
589C3×D4—82no—
590C3×D4—121no—
591C3×D4—122no—
592C3×D4—122no—
593C3×D4—122no—
594C3×D4—122no—
595C3×D4—241no—
596C3×D4—241no—
597C3×D4—241no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—31no—
604C2×C3×C4—31no—
605C2×C3×C4—41no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—122no—
614C2×C3×C4—122no—
615C2×C3×C4—122no—
616C2×C3×C4—241no—
617C2×C3×C4D3×D411yescharacteristic
618C2×C3×C4D3×D411yescharacteristic
619C2×C3×C4C2×C3×D411yescharacteristic
620C2×C3×C4C2×C3×D411yescharacteristic
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C24×C311yescharacteristic
623#67—42no—
624#67—42no—
625#67—42no—
626#67—81no—
627#67—81no—
628#67—81no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—42no—
633C2×Dic3—42no—
634C2×Dic3C2×C3×D411yescharacteristic
635C2×Dic3C2×C3×D411yescharacteristic
636D12—21no—
637D12—41no—
638D12—42no—
639D12C2×C3×D412yes—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—21no—
643C4×D3—21no—
644C4×D3—42no—
645C4×D3—81no—
646Dic6—21no—
647Dic6C2×C3×D412yes—
648C3×C8—22no—
649C3×C8—21no—
650C3×C8—21no—
651C3×C8—22no—
652C3×C8—61no—
653C3×C8—61no—
654C3×C8D3×D412yes—
655C3×C8C2×C3×D412yes—
656C3⋊C8—21no—
657C3⋊C8—21no—
658C2×C32—81no—
659C2×C32—81no—
660C2×C32—81no—
661C2×C32D4211yescharacteristic
662C2×C32#57511yescharacteristic
663C2×C32#57611yescharacteristic
664C3×D3—41no—
665C3×D3—41no—
666C3×D3—42no—
667C24—61no—
668#41—62no—
669#41—62no—
670#41—62no—
671#41—121no—
672#41—121no—
673#41—121no—
674C2×Q8—31no—
675C2×Q8C22×C3×D311yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—62no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—121no—
689C2×D4C22×C3×D311yescharacteristic
690C2×D4C22×C3×D311yescharacteristic
691C2×D4C22×C3×D311yescharacteristic
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698Q16—62no—
699SD16—22no—
700SD16—34no—
701SD16—41no—
702SD16—62no—
703D8—22no—
704D8—41no—
705D8—62no—
706D8—62no—
707M16—62no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—62no—
711C2×C8C22×C3×D311yescharacteristic
712C2×C8C22×C3×D311yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—61no—
717C4⋊C4—61no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—31no—
721C22⋊C4—31no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C42—61no—
728C42C22×C3×D311yescharacteristic
729C22×C3—21no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
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—61no—
749C22×C3—61no—
750C22×C3—62no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—61no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3—81no—
758C22×C3—81no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—81no—
763C22×C3—81no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—244no—
767C22×C3C2×D3×D411yescharacteristic
768C22×C3C22×C3×D411yescharacteristic
769C2×D3—21no—
770C2×D3—21no—
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—22no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—84no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—61no—
790C3×C4—61no—
791C3×C4—62no—
792C3×C4—81no—
793C3×C4—121no—
794C3×C4—121no—
795C3×C4C2×D3×D411yescharacteristic
796C3×C4#100411yescharacteristic
797C3×C4C22×C3×D411yescharacteristic
798C3×C4C3×H(5,𝔽2)11yescharacteristic
799Dic3—22no—
800Dic3—21no—
801Dic3—21no—
802Dic3—41no—
803Dic3—41no—
804C32#326811yescharacteristic, complemented, Sylow
805C23—21no—
806C23—21no—
807C23—21no—
808C23—31no—
809C23—31no—
810C23—61no—
811C23—122no—
812C23—122no—
813C23—241no—
814Q8—21no—
815Q8—21no—
816Q8—32no—
817Q8—61no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—21no—
822D4—21no—
823D4—21no—
824D4—32no—
825D4—42no—
826D4—61no—
827D4—81no—
828D4—121no—
829D4—122no—
830D4—122no—
831D4—122no—
832D4—122no—
833D4—241no—
834D4—241no—
835D4—241no—
836C2×C4—21no—
837C2×C4—31no—
838C2×C4—31no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—122no—
847C2×C4—122no—
848C2×C4—122no—
849C2×C4—241no—
850C2×C4C3×D3×D411yescharacteristic
851C2×C4C3×D3×D411yescharacteristic
852C2×C4C23×C3×D311yescharacteristic
853C8—21no—
854C8—61no—
855C8—61no—
856C8C3×D3×D412yes—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—81no—
861C2×C3—81no—
862C2×C3—81no—
863C2×C3—81no—
864C2×C3—81no—
865C2×C3—81no—
866C2×C3—121no—
867C2×C3—121no—
868C2×C3—122no—
869C2×C3—161no—
870C2×C3—161no—
871C2×C3—161no—
872C2×C3#571711yescharacteristic
873C2×C3#577311yescharacteristic
874C2×C3#577411yescharacteristic
875C2×C3C3×D4211yescharacteristic
876C2×C3C3×#57511yescharacteristic
877C2×C3C3×#57611yescharacteristic
878D3—41no—
879D3—41no—
880D3—42no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—61no—
891C22—61no—
892C22—61no—
893C22—61no—
894C22—61no—
895C22—61no—
896C22—62no—
897C22—121no—
898C22—121no—
899C22—244no—
900C22C2×C3×D3×D411yescharacteristic
901C4—21no—
902C4—21no—
903C4—41no—
904C4—61no—
905C4—61no—
906C4—62no—
907C4—121no—
908C4—121no—
909C4C2×C3×D3×D411yescharacteristic
910C4C3×#100411yescharacteristic
911C3—21no—
912C3#8185811yescharacteristic, direct product factor
913C3C3×#326811yescharacteristic, complemented
914C2—81no—
915C2—81no—
916C2—81no—
917C2—121no—
918C2—121no—
919C2—122no—
920C2C3×#571711yescharacteristic
921C2C3×#577311yescharacteristic
922C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#496C2
socleC22×C32C22×D4
hypercenterC3×#496D3
hypocenterC3C3×#3268
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#496

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. C2×C3×#911C2semidirect
3. C3×#5718C2semidirect
4. C3×#5676C2semidirect
5. C32×#496C2semidirect
6. C3×#5174C2semidirect
7. C3×#5173C2semidirect
8. C3×#5172C2semidirect
9. C3×#5158C2semidirect
10. C3×#5157C2semidirect
11. C3×#5156C2semidirect
12. C3×#5072C2semidirect
13. C3×#5054C2semidirect
14. C3×#4710C2semidirect
15. C3×#4706C2semidirect
17. #81858C3direct (N × H)
20. C2×C3×#237C22semidirect
22. C2×C32×SD16C22semidirect
23. C2×C32×SD16C22semidirect
26. C32×#127C22semidirect
29. C2×C3×#216C22semidirect
35. C3×#938C22semidirect
44. C2×C3×D3×C8C22semidirect
51. C3×C4×Dic6C22semidirect
52. C32×#97C22semidirect
53. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×#832C22semidirect
59. C3×(C2×D3)⋊C8C22semidirect
60. C3×#818C22semidirect
61. C3×#816C22semidirect
62. C3×C4⋊(C3⋊C8)C22semidirect
67. C2×#916C2×C3semidirect
68. C2×#911C2×C3semidirect
69. #5718C2×C3semidirect
70. #5676C2×C3semidirect
72. C3×#496D3semidirect
73. C3×#496C2×C3semidirect
84. #5174C2×C3semidirect
85. #5173C2×C3semidirect
86. #5172C2×C3semidirect
87. #5158C2×C3semidirect
88. #5157C2×C3semidirect
89. #5156C2×C3semidirect
90. #5072C2×C3semidirect
91. #5054C2×C3semidirect
92. #4710C2×C3semidirect
93. #4706C2×C3semidirect
153. C3×#204D4semidirect
163. C2×#237C22×C3semidirect
172. C2×C3×SD16C2×D3semidirect
173. C2×C3×SD16C2×D3semidirect
174. C2×C3×SD16C22×C3semidirect
175. C2×C3×SD16C22×C3semidirect
188. C3×#127C2×D3semidirect
189. C3×#127C22×C3semidirect
208. C2×#216C22×C3semidirect
214. #938C22×C3semidirect
223. C2×D3×C8C22×C3semidirect
230. C4×Dic6C22×C3semidirect
242. C3×#97C2×D3semidirect
243. C3×#97C22×C3semidirect
244. #835C22×C3semidirect
246. #832C22×C3semidirect
247. #832C22×C3semidirect
250. (C2×D3)⋊C8C22×C3semidirect
251. #818C22×C3semidirect
252. #816C22×C3semidirect
253. C4⋊(C3⋊C8)C22×C3semidirect
310. #496C3×D3semidirect
457. #204C3×D4semidirect
499. C2×SD16C2×C3×D3semidirect
500. C2×SD16C2×C3×D3semidirect
508. #127C2×C3×D3semidirect
534. #97C2×C3×D3semidirect
804. C32#3268semidirect
912. C3#81858direct (N × H)
913. C3C3×#3268semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
C2×C3×#9112
C3×#57182
C3×#56762
C32×#4962
C3×#51742
C3×#51732
C3×#51722
C3×#51582
C3×#51572
C3×#51562
C3×#50722
C3×#50542
C3×#47102
C3×#47062
C3×#32683
#818583