Finite Group Databasebeta

← C3×#80348 #11884396

Subgroups — C3×#80348 #11884396

Order 1152.

1090 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic, complemented
2C2×C3×#911C211yesmaximal, characteristic, complemented
3C3×#5718C211yesmaximal, characteristic, complemented
4C3×#5554C211yesmaximal, characteristic, complemented
5C32×#459C211yesmaximal, characteristic, complemented
6C3×#5158C211yesmaximal, characteristic, complemented
7C3×#5156C211yesmaximal, characteristic, complemented
8C3×#5074C211yesmaximal, characteristic, complemented
9C3×#5018C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4836C211yesmaximal, characteristic, complemented
12C3×#4783C211yesmaximal, characteristic, complemented
13C3×#4781C211yesmaximal, characteristic, complemented
14C3×#4780C211yesmaximal, characteristic, complemented
15C3×#4775C211yesmaximal, characteristic, complemented
16C3×#3268—31nomaximal
17#80348C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic
23C2×C32×D8C2211yescharacteristic
24C32×#127C2211yescharacteristic, complemented
25C32×C4×D4C2211yescharacteristic
26C3×#940—21no—
27C3×#939—21no—
28C3×#939—21no—
29C3×#938C2211yescharacteristic
30C3×#938C2211yescharacteristic, complemented
31C3×D4×Dic3—21no—
32C2×C3×#214C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic, complemented
34C2×C3×#214C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C3×#930—21no—
38C2×C3×(C2×D3)⋊C4—21no—
39C3×#912—24no—
40C3×#911—24no—
41C2×C3×Dic12C2211yescharacteristic, complemented
42C2×C3×#204C2211yescharacteristic
43C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
44C2×C3×D3×C8C2211yescharacteristic, complemented
45C3×#897C2211yescharacteristic
46C3×#895C2211yescharacteristic
47C3×#886—21no—
48C3×#882—21no—
49C3×#875C2211yescharacteristic
50C3×C4×D12C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic, complemented
52C32×C4⋊C8C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C32×#102C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61C3×#807C2211yescharacteristic, complemented
62C3×#803C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65C3×#550—31no—
66C3×#546—31no—
67C2×#912C2×C311yescharacteristic, complemented
68C2×#911C2×C311yescharacteristic, complemented
69#5718C2×C311yescharacteristic, complemented
70#5554C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#468—31no—
73C3×#466—31no—
74C3×#464—31no—
75C3×#459—21no—
76C3×#459D311yescharacteristic, complemented
77C3×#459C2×C311yescharacteristic, complemented
78C3×#452—31no—
79C3×#449—31no—
80C3×#449—31no—
81C3×#447—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5158C2×C311yescharacteristic, complemented
85#5156C2×C311yescharacteristic, complemented
86#5074C2×C311yescharacteristic, complemented
87#5018C2×C311yescharacteristic, complemented
88#4845C2×C311yescharacteristic, complemented
89#4836C2×C311yescharacteristic, complemented
90#4783C2×C311yescharacteristic, complemented
91#4781C2×C311yescharacteristic, complemented
92#4780C2×C311yescharacteristic, complemented
93#4775C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×D4—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
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—
109C22×C3×Dic3—21no—
110C3×#237—22no—
111C3×#237—22no—
112C3×#237—22no—
113C3×#237—41no—
114C3×#237—41no—
115C3×#237—41no—
116C3×D3×D4—22no—
117C3×D3×D4—41no—
118C2×C3×D12—21no—
119C2×C3×D12D411yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic
125C32×D8—22no—
126C32×D8—22no—
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129C32×C4⋊C4C2311yescharacteristic
130C32×C22⋊C4—21no—
131C32×C42C2311yescharacteristic
132C3×#217—21no—
133C3×#217—21no—
134C3×#214—22no—
135C3×#214—41no—
136C3×#214D414yescomplemented
137C3×#213—22no—
138C3×#213—41no—
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×(C2×D3)⋊C4D411yescharacteristic
145C3×C4⋊Dic3—21no—
146C3×C4⋊Dic3D411yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×Dic12—22no—
153C3×#204—22no—
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×#237C22×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—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×D8—21no—
173C2×C3×D8—21no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8C2×D311yescharacteristic
177C2×C3×D8C2×D311yescharacteristic
178C2×C3×D8C22×C311yescharacteristic
179C2×C3×D8C22×C311yescharacteristic
180C2×C3×M16—31no—
181C22×C3×C8—31no—
182C3×#127—21no—
183C3×#127—61no—
184C3×#127C2×D311yescharacteristic, complemented
185C3×#127C22×C311yescharacteristic, complemented
186C3×#124—31no—
187C3×#123—61no—
188C3×C22⋊Q8—31no—
189C3×#121—31no—
190C3×#121—31no—
191C3×#121—31no—
192C3×#121—61no—
193C3×#121—61no—
194C3×#121—61no—
195C3×#120—61no—
196C3×C4×Q8—31no—
197C3×C4×D4—21no—
198C3×C4×D4—31no—
199C3×C4×D4—61no—
200C3×C4×D4C2×D311yescharacteristic
201C3×C4×D4C22×C311yescharacteristic
202C2×C3×C22⋊C4—61no—
203#940—21no—
204#939—21no—
205#939—21no—
206#938C22×C311yescharacteristic
207#938C22×C311yescharacteristic, complemented
208D4×Dic3—21no—
209C2×#214C22×C311yescharacteristic
210C2×#214C22×C311yescharacteristic, complemented
211C2×#214C22×C311yescharacteristic, complemented
212C2×#213C22×C311yescharacteristic
213C2×#213C22×C311yescharacteristic
214#930—21no—
215C2×(C2×D3)⋊C4—21no—
216#912—24no—
217#911—24no—
218C2×Dic12C22×C311yescharacteristic, complemented
219C2×#204C22×C311yescharacteristic
220C2×ΓL(1,𝔽25)C22×C311yescharacteristic
221C2×D3×C8C22×C311yescharacteristic, complemented
222#897C22×C311yescharacteristic
223#895C22×C311yescharacteristic
224#886—21no—
225#882—21no—
226#875C22×C311yescharacteristic
227C4×D12C22×C311yescharacteristic
228C4×Dic6C22×C311yescharacteristic, complemented
229C3×#107—31no—
230C3×C4⋊C8—21no—
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×C4⋊C8C22×C311yescharacteristic, complemented
233C3×#103—31no—
234C3×#103—31no—
235C3×#102—21no—
236C3×#102—21no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102C2×D311yescharacteristic, complemented
240C3×#102C2×D311yescharacteristic, complemented
241C3×#102C22×C311yescharacteristic, complemented
242C3×#102C22×C311yescharacteristic, complemented
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×#97—31no—
246#832C22×C311yescharacteristic
247#821C22×C311yescharacteristic
248(C2×D3)⋊C8C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic, complemented
250#816C22×C311yescharacteristic, complemented
251#810C22×C311yescharacteristic, complemented
252#807C22×C311yescharacteristic, complemented
253#803C22×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×D4—21no—
264C32×D4—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—81no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276C3×#67—42no—
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—42no—
280C3×#67—81no—
281C3×#67—81no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—42no—
286C2×C3×Dic3—42no—
287C2×C3×Dic3—42no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—41no—
293C3×D12—81no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—21no—
298C3×Dic6—21no—
299C3×Dic6—21no—
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#459C3×D311yescharacteristic, complemented
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—31no—
330C2×C3×Q8—31no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—41no—
341C2×C3×D4—41no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—62no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—121no—
351C2×C3×D4C22×D311yescharacteristic
352C2×C3×D4C22×D311yescharacteristic
353C2×C3×D4C22×D311yescharacteristic
354C2×C3×D4C23×C311yescharacteristic
355C2×C3×D4C23×C311yescharacteristic
356C2×C3×D4C23×C311yescharacteristic
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—41no—
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—
373C22×Dic3—21no—
374#237—22no—
375#237—22no—
376#237—22no—
377#237—41no—
378#237—41no—
379#237—41no—
380D3×D4—22no—
381D3×D4—41no—
382C2×D12—21no—
383C2×D12C3×D411yescharacteristic
384C2×D12C23×C311yescharacteristic
385C2×C4×D3C23×C311yescharacteristic
386C2×C4×D3C23×C311yescharacteristic
387C2×Dic6C23×C311yescharacteristic
388C2×Dic6C23×C311yescharacteristic
389C3×Q16—62no—
390C3×SD16—34no—
391C3×SD16—62no—
392C3×SD16—62no—
393C3×SD16—121no—
394C3×D8—22no—
395C3×D8—22no—
396C3×D8—22no—
397C3×D8—22no—
398C3×D8—42no—
399C3×D8—42no—
400C3×D8—62no—
401C3×D8—121no—
402C3×M16—62no—
403C2×C3×C8—21no—
404C2×C3×C8—21no—
405C2×C3×C8—31no—
406C2×C3×C8—31no—
407C2×C3×C8—62no—
408C2×C3×C8C22×D311yescharacteristic
409C2×C3×C8C22×D311yescharacteristic
410C2×C3×C8C23×C311yescharacteristic
411C2×C3×C8C23×C311yescharacteristic
412C3×C4⋊C4—21no—
413C3×C4⋊C4—31no—
414C3×C4⋊C4—31no—
415C3×C4⋊C4—61no—
416C3×C4⋊C4—61no—
417C3×C4⋊C4C22×D311yescharacteristic
418C3×C4⋊C4C23×C311yescharacteristic
419C3×C22⋊C4—21no—
420C3×C22⋊C4—21no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—41no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C42—21no—
431C3×C42—61no—
432C3×C42C22×D311yescharacteristic
433C3×C42C23×C311yescharacteristic
434#217—21no—
435#217—21no—
436#214—22no—
437#214—41no—
438#214C3×D414yescomplemented
439#213—22no—
440#213—41no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4C3×D411yescharacteristic
446(C2×D3)⋊C4C3×D411yescharacteristic
447C4⋊Dic3—21no—
448C4⋊Dic3C3×D411yescharacteristic
449C4⋊Dic3C23×C311yescharacteristic
450Dic3⋊C4—21no—
451C4×Dic3—21no—
452C2×C3⋊C8C23×C311yescharacteristic
453C2×C3⋊C8C23×C311yescharacteristic
454Dic12—22no—
455#204—22no—
456ΓL(1,𝔽25)—22no—
457D3×C8—22no—
458C22×C32—22no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32C22×D411yescharacteristic
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—84no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—41no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3×Dic3—22no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—31no—
491C22×D4—31no—
492AGL(1,ℤ/8)—64no—
493#135—64no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×D8—31no—
500C2×D8—31no—
501C2×D8C2×C3×D311yescharacteristic
502C2×D8C2×C3×D311yescharacteristic
503C2×M16—31no—
504C22×C8—31no—
505#127—61no—
506#127C2×C3×D311yescharacteristic, complemented
507#124—31no—
508#123—61no—
509C22⋊Q8—31no—
510#121—31no—
511#121—31no—
512#121—31no—
513#121—61no—
514#121—61no—
515#121—61no—
516#120—61no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—61no—
520C4×D4C2×C3×D311yescharacteristic
521C2×C22⋊C4—61no—
522#107—31no—
523C4⋊C8C2×C3×D311yescharacteristic, complemented
524#103—31no—
525#103—31no—
526#102—31no—
527#102—31no—
528#102C2×C3×D311yescharacteristic, complemented
529#102C2×C3×D311yescharacteristic, complemented
530C22⋊C8—31no—
531C22⋊C8—31no—
532#97—31no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—31no—
540C23×C3—31no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—61no—
545C23×C3—122no—
546C23×C3—122no—
547C23×C3—241no—
548C22×D3—21no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—81no—
552C22×D3C2×C3×D411yescharacteristic
553C22×D3C2×C3×D411yescharacteristic
554C3×Q8—32no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—22no—
569C3×D4—41no—
570C3×D4—41no—
571C3×D4—41no—
572C3×D4—41no—
573C3×D4—41no—
574C3×D4—42no—
575C3×D4—42no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—82no—
579C3×D4—81no—
580C3×D4—81no—
581C3×D4—82no—
582C3×D4—121no—
583C3×D4—122no—
584C3×D4—122no—
585C3×D4—122no—
586C3×D4—122no—
587C3×D4—241no—
588C3×D4—241no—
589C3×D4—241no—
590C3×D4D3×D412yes—
591C3×D4C2×C3×D412yes—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—41no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—81no—
608C2×C3×C4—81no—
609C2×C3×C4—82no—
610C2×C3×C4—122no—
611C2×C3×C4—122no—
612C2×C3×C4—122no—
613C2×C3×C4D3×D411yescharacteristic
614C2×C3×C4D3×D411yescharacteristic
615C2×C3×C4C2×C3×D411yescharacteristic
616C2×C3×C4C2×C3×D411yescharacteristic
617C2×C3×C4C23×D311yescharacteristic
618C2×C3×C4C24×C311yescharacteristic
619#67—42no—
620#67—42no—
621#67—42no—
622#67—42no—
623#67—81no—
624#67—81no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—42no—
629C2×Dic3—42no—
630C2×Dic3—42no—
631C2×Dic3C2×C3×D411yescharacteristic
632C2×Dic3C2×C3×D411yescharacteristic
633D12—21no—
634D12—21no—
635D12—41no—
636D12—81no—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—21no—
641Dic6—21no—
642Dic6—21no—
643Dic6—21no—
644Dic6C2×C3×D412yes—
645C3×C8—21no—
646C3×C8—21no—
647C3×C8—21no—
648C3×C8—21no—
649C3×C8—32no—
650C3×C8—41no—
651C3×C8—41no—
652C3×C8—61no—
653C3⋊C8—21no—
654C3⋊C8C2×C3×D412yes—
655C2×C32—42no—
656C2×C32—81no—
657C2×C32—81no—
658C2×C32D4211yescharacteristic
659C2×C32#57511yescharacteristic
660C2×C32#57611yescharacteristic
661C3×D3—41no—
662C3×D3—41no—
663C3×D3—81no—
664C24—61no—
665#41—62no—
666#41—62no—
667#41—62no—
668#41—121no—
669#41—121no—
670#41—121no—
671C2×Q8—31no—
672C2×Q8—31no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—62no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—121no—
686C2×D4C22×C3×D311yescharacteristic
687C2×D4C22×C3×D311yescharacteristic
688C2×D4C22×C3×D311yescharacteristic
689C22×C4—21no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—61no—
695Q16—62no—
696SD16—34no—
697SD16—62no—
698SD16—62no—
699SD16—121no—
700D8—22no—
701D8—22no—
702D8—62no—
703D8—121no—
704M16—62no—
705C2×C8—31no—
706C2×C8—31no—
707C2×C8—62no—
708C2×C8C22×C3×D311yescharacteristic
709C2×C8C22×C3×D311yescharacteristic
710C4⋊C4—31no—
711C4⋊C4—31no—
712C4⋊C4—61no—
713C4⋊C4—61no—
714C4⋊C4C22×C3×D311yescharacteristic
715C22⋊C4—21no—
716C22⋊C4—31no—
717C22⋊C4—31no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C42—61no—
725C42C22×C3×D311yescharacteristic
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—21no—
729C22×C3—42no—
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—61no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—61no—
752C22×C3—81no—
753C22×C3—81no—
754C22×C3—81no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3—81no—
758C22×C3—81no—
759C22×C3—81no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—244no—
764C22×C3C2×D3×D411yescharacteristic
765C22×C3C22×C3×D411yescharacteristic
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—21no—
769C2×D3—21no—
770C2×D3—21no—
771C2×D3—21no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—84no—
776C3×C4—22no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—61no—
787C3×C4—61no—
788C3×C4—62no—
789C3×C4—81no—
790C3×C4—121no—
791C3×C4—121no—
792C3×C4C2×D3×D411yescharacteristic
793C3×C4#100911yescharacteristic
794C3×C4C22×C3×D411yescharacteristic
795C3×C4C3×H(5,𝔽2)11yescharacteristic
796Dic3—22no—
797Dic3—21no—
798Dic3—21no—
799Dic3—41no—
800Dic3—41no—
801C32#326811yescharacteristic, complemented, Sylow
802C23—21no—
803C23—21no—
804C23—21no—
805C23—31no—
806C23—31no—
807C23—61no—
808C23—122no—
809C23—122no—
810C23—241no—
811Q8—32no—
812Q8—61no—
813Q8—61no—
814Q8—61no—
815D4—21no—
816D4—21no—
817D4—21no—
818D4—21no—
819D4—21no—
820D4—42no—
821D4—61no—
822D4—61no—
823D4—81no—
824D4—121no—
825D4—122no—
826D4—122no—
827D4—122no—
828D4—122no—
829D4—241no—
830D4—241no—
831D4—241no—
832D4C3×D3×D412yes—
833C2×C4—21no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—81no—
844C2×C4—122no—
845C2×C4—122no—
846C2×C4—122no—
847C2×C4C3×D3×D411yescharacteristic
848C2×C4C3×D3×D411yescharacteristic
849C2×C4C23×C3×D311yescharacteristic
850C8—21no—
851C8—21no—
852C8—32no—
853C8—61no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—42no—
858C2×C3—42no—
859C2×C3—82no—
860C2×C3—81no—
861C2×C3—81no—
862C2×C3—81no—
863C2×C3—81no—
864C2×C3—121no—
865C2×C3—121no—
866C2×C3—161no—
867C2×C3—161no—
868C2×C3—241no—
869C2×C3#560911yescharacteristic
870C2×C3#575711yescharacteristic
871C2×C3#577311yescharacteristic
872C2×C3C3×D4211yescharacteristic
873C2×C3C3×#57511yescharacteristic
874C2×C3C3×#57611yescharacteristic
875D3—41no—
876D3—41no—
877D3—81no—
878C22—22no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—61no—
888C22—61no—
889C22—61no—
890C22—61no—
891C22—61no—
892C22—61no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—244no—
897C22C2×C3×D3×D411yescharacteristic
898C4—21no—
899C4—21no—
900C4—41no—
901C4—61no—
902C4—61no—
903C4—62no—
904C4—121no—
905C4—121no—
906C4C2×C3×D3×D411yescharacteristic
907C4C3×#100911yescharacteristic
908C3—21no—
909C3#8034811yescharacteristic, direct product factor
910C3C3×#326811yescharacteristic, complemented
911C2—42no—
912C2—81no—
913C2—81no—
914C2—121no—
915C2—121no—
916C2—241no—
917C2C3×#560911yescharacteristic
918C2C3×#575711yescharacteristic
919C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenterC3×#459D3
hypocenterC3C3×#3268
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C2×C3×#912C2semidirect
2. C2×C3×#911C2semidirect
3. C3×#5718C2semidirect
4. C3×#5554C2semidirect
5. C32×#459C2semidirect
6. C3×#5158C2semidirect
7. C3×#5156C2semidirect
8. C3×#5074C2semidirect
9. C3×#5018C2semidirect
10. C3×#4845C2semidirect
11. C3×#4836C2semidirect
12. C3×#4783C2semidirect
13. C3×#4781C2semidirect
14. C3×#4780C2semidirect
15. C3×#4775C2semidirect
17. #80348C3direct (N × H)
20. C2×C3×#237C22semidirect
24. C32×#127C22semidirect
30. C3×#938C22semidirect
33. C2×C3×#214C22semidirect
34. C2×C3×#214C22semidirect
41. C2×C3×Dic12C22semidirect
44. C2×C3×D3×C8C22semidirect
51. C3×C4×Dic6C22semidirect
52. C32×C4⋊C8C22semidirect
53. C32×#102C22semidirect
54. C32×#102C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#816C22semidirect
60. C3×#810C22semidirect
61. C3×#807C22semidirect
62. C3×#803C22semidirect
67. C2×#912C2×C3semidirect
68. C2×#911C2×C3semidirect
69. #5718C2×C3semidirect
70. #5554C2×C3semidirect
76. C3×#459D3semidirect
77. C3×#459C2×C3semidirect
84. #5158C2×C3semidirect
85. #5156C2×C3semidirect
86. #5074C2×C3semidirect
87. #5018C2×C3semidirect
88. #4845C2×C3semidirect
89. #4836C2×C3semidirect
90. #4783C2×C3semidirect
91. #4781C2×C3semidirect
92. #4780C2×C3semidirect
93. #4775C2×C3semidirect
136. C3×#214D4semidirect
163. C2×#237C22×C3semidirect
184. C3×#127C2×D3semidirect
185. C3×#127C22×C3semidirect
207. #938C22×C3semidirect
210. C2×#214C22×C3semidirect
211. C2×#214C22×C3semidirect
218. C2×Dic12C22×C3semidirect
221. C2×D3×C8C22×C3semidirect
228. C4×Dic6C22×C3semidirect
231. C3×C4⋊C8C2×D3semidirect
232. C3×C4⋊C8C22×C3semidirect
239. C3×#102C2×D3semidirect
240. C3×#102C2×D3semidirect
241. C3×#102C22×C3semidirect
242. C3×#102C22×C3semidirect
249. (C2×D3)⋊C8C22×C3semidirect
250. #816C22×C3semidirect
251. #810C22×C3semidirect
252. #807C22×C3semidirect
253. #803C22×C3semidirect
314. #459C3×D3semidirect
438. #214C3×D4semidirect
506. #127C2×C3×D3semidirect
523. C4⋊C8C2×C3×D3semidirect
528. #102C2×C3×D3semidirect
529. #102C2×C3×D3semidirect
801. C32#3268semidirect
909. C3#80348direct (N × H)
910. C3C3×#3268semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
C2×C3×#9112
C3×#57182
C3×#55542
C32×#4592
C3×#51582
C3×#51562
C3×#50742
C3×#50182
C3×#48452
C3×#48362
C3×#47832
C3×#47812
C3×#47802
C3×#47752
C3×#32683
#803483