Finite Group Databasebeta

← C3×#80407 #11884828

Subgroups — C3×#80407 #11884828

Order 1152.

1040 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2C2×C3×#915C211yesmaximal, characteristic, complemented
3C3×#5718C211yesmaximal, characteristic, complemented
4C3×#5576C211yesmaximal, characteristic, complemented
5C32×#460C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic, complemented
7C3×#5170C211yesmaximal, characteristic, complemented
8C3×#5074C211yesmaximal, characteristic, complemented
9C3×#5030C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4836C211yesmaximal, characteristic, complemented
12C3×#4783C211yesmaximal, characteristic, complemented
13C3×#4782C211yesmaximal, characteristic, complemented
14C3×#4781C211yesmaximal, characteristic, complemented
15C3×#4778C211yesmaximal, characteristic, complemented
16C3×#3271—31nomaximal
17#80407C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×C3×#237C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic
24C32×#127C2211yescharacteristic
25C32×C4×Q8C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#940—21no—
28C3×#939—21no—
29C3×#939—21no—
30C3×#938C2211yescharacteristic
31C3×#938C2211yescharacteristic
32C3×D4×Dic3—21no—
33C2×C3×#214C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic
35C2×C3×#213C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C3×#916—24no—
38C3×#915—24no—
39C2×C3×Dic12C2211yescharacteristic
40C2×C3×#204C2211yescharacteristic
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
42C2×C3×D3×C8C2211yescharacteristic
43C3×#897—21no—
44C3×#897C2211yescharacteristic
45C3×#895—21no—
46C3×#895C2211yescharacteristic
47C3×#875—21no—
48C3×#875C2211yescharacteristic
49C3×C4×D12—21no—
50C3×C4×D12C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic
52C32×C4⋊C8C2211yescharacteristic
53C32×#102C2211yescharacteristic
54C32×#102C2211yescharacteristic
55C3×#835C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×#816C2211yescharacteristic
60C3×#810C2211yescharacteristic
61C3×#808C2211yescharacteristic
62C3×#803C2211yescharacteristic
63C2×C3×#137—31no—
64C2×C3×#135—31no—
65C3×#550—31no—
66C3×#548—31no—
67C2×#916C2×C311yescharacteristic, complemented
68C2×#915C2×C311yescharacteristic, complemented
69#5718C2×C311yescharacteristic, complemented
70#5576C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#469—31no—
73C3×#465—31no—
74C3×#464—31no—
75C3×#460—21no—
76C3×#460D311yescharacteristic, complemented
77C3×#460C2×C311yescharacteristic, complemented
78C3×#452—31no—
79C3×#449—31no—
80C3×#449—31no—
81C3×#448—31no—
82C3×#441—31no—
83C3×#435—31no—
84#5172C2×C311yescharacteristic, complemented
85#5170C2×C311yescharacteristic, complemented
86#5074C2×C311yescharacteristic, complemented
87#5030C2×C311yescharacteristic, complemented
88#4845C2×C311yescharacteristic, complemented
89#4836C2×C311yescharacteristic, complemented
90#4783C2×C311yescharacteristic, complemented
91#4782C2×C311yescharacteristic, complemented
92#4781C2×C311yescharacteristic, complemented
93#4778C2×C311yescharacteristic, complemented
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C3×#239—22no—
106C3×#239—41no—
107C3×D3×Q8—22no—
108C3×D3×Q8—41no—
109C3×#237—22no—
110C3×#237—22no—
111C3×#237—41no—
112C3×#237—41no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12D411yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124C32×SD16—22no—
125C32×SD16—22no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C32×C4⋊C4—21no—
129C32×C4⋊C4C2311yescharacteristic
130C32×C42—21no—
131C32×C42C2311yescharacteristic
132C3×#217—21no—
133C3×#217—21no—
134C3×#216D414yescomplemented
135C3×#214—22no—
136C3×#214—41no—
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#3271—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×Q8—31no—
161C2×#239C22×C311yescharacteristic
162C2×D3×Q8C22×C311yescharacteristic
163C2×#237C22×C311yescharacteristic
164C2×#237C22×C311yescharacteristic
165C3×#137—64no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×SD16—21no—
170C2×C3×SD16—21no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16C2×D311yescharacteristic
175C2×C3×SD16C2×D311yescharacteristic
176C2×C3×SD16C22×C311yescharacteristic
177C2×C3×SD16C22×C311yescharacteristic
178C2×C3×D8—31no—
179C2×C3×D8—31no—
180C2×C3×M16—31no—
181C22×C3×C8—31no—
182C3×#127—21no—
183C3×#127—61no—
184C3×#127C2×D311yescharacteristic
185C3×#127C22×C311yescharacteristic
186C3×#124—31no—
187C3×#124—61no—
188C3×C22⋊Q8—31no—
189C3×C22⋊Q8—61no—
190C3×#121—31no—
191C3×#121—31no—
192C3×#121—31no—
193C3×#121—61no—
194C3×#121—61no—
195C3×#121—61no—
196C3×C4×Q8—21no—
197C3×C4×Q8—31no—
198C3×C4×Q8C2×D311yescharacteristic
199C3×C4×Q8C22×C311yescharacteristic
200C3×C4×D4—31no—
201C3×C4×D4—61no—
202C3×C4×D4—61no—
203C2×#216C22×C311yescharacteristic
204#940—21no—
205#939—21no—
206#939—21no—
207#938C22×C311yescharacteristic
208#938C22×C311yescharacteristic
209D4×Dic3—21no—
210C2×#214C22×C311yescharacteristic
211C2×#214C22×C311yescharacteristic
212C2×#213C22×C311yescharacteristic
213C2×#213C22×C311yescharacteristic
214#916—24no—
215#915—24no—
216C2×Dic12C22×C311yescharacteristic
217C2×#204C22×C311yescharacteristic
218C2×ΓL(1,𝔽25)C22×C311yescharacteristic
219C2×D3×C8C22×C311yescharacteristic
220#897—21no—
221#897C22×C311yescharacteristic
222#895—21no—
223#895C22×C311yescharacteristic
224#875—21no—
225#875C22×C311yescharacteristic
226C4×D12—21no—
227C4×D12C22×C311yescharacteristic
228C4×Dic6C22×C311yescharacteristic
229C3×#106—31no—
230C3×C4⋊C8—21no—
231C3×C4⋊C8C2×D311yescharacteristic
232C3×C4⋊C8C22×C311yescharacteristic
233C3×#103—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#102—21no—
237C3×#102—21no—
238C3×#102—31no—
239C3×#102C2×D311yescharacteristic
240C3×#102C2×D311yescharacteristic
241C3×#102C22×C311yescharacteristic
242C3×#102C22×C311yescharacteristic
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×#97—31no—
246#835C22×C311yescharacteristic
247#821C22×C311yescharacteristic
248(C2×D3)⋊C8C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic
250#816C22×C311yescharacteristic
251#810C22×C311yescharacteristic
252#808C22×C311yescharacteristic
253#803C22×C311yescharacteristic
254C23×C32—21no—
255C23×C32—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C22×C3×D3C2×D411yescharacteristic
259C32×Q8—21no—
260C32×Q8C2×D412yes—
261C32×D4—21no—
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—42no—
266C32×D4—81no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C3×#67—42no—
273C3×#67—42no—
274C3×#67—81no—
275C3×#67—81no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3—42no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—41no—
286C3×D12—42no—
287C3×D12—42no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—42no—
298C3×Dic6C2×D412yes—
299C32×C8—21no—
300C32×C8—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×#137—31no—
304C2×#135—31no—
305#550—31no—
306#548—31no—
307#496—31no—
308#469—31no—
309#465—31no—
310#464—31no—
311#460C3×D311yescharacteristic, complemented
312#452—31no—
313#449—31no—
314#449—31no—
315#448—31no—
316#441—31no—
317#435—31no—
318C3×#41—62no—
319C3×#41—62no—
320C3×#41—62no—
321C3×#41—121no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—21no—
325C2×C3×Q8—31no—
326C2×C3×Q8—31no—
327C2×C3×Q8—61no—
328C2×C3×Q8—62no—
329C2×C3×Q8—121no—
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C23×C311yescharacteristic
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—61no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4C22×D311yescharacteristic
349C2×C3×D4C22×D311yescharacteristic
350C2×C3×D4C23×C311yescharacteristic
351C2×C3×D4C23×C311yescharacteristic
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C2×#67—21no—
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—21no—
362C22×Dic3—21no—
363C22×Dic3—21no—
364#239—22no—
365#239—41no—
366D3×Q8—22no—
367D3×Q8—41no—
368#237—22no—
369#237—22no—
370#237—41no—
371#237—41no—
372C2×D12—21no—
373C2×D12—21no—
374C2×D12C3×D411yescharacteristic
375C2×D12C23×C311yescharacteristic
376C2×C4×D3—21no—
377C2×C4×D3—21no—
378C2×C4×D3C23×C311yescharacteristic
379C2×C4×D3C23×C311yescharacteristic
380C2×Dic6—21no—
381C2×Dic6C23×C311yescharacteristic
382C2×Dic6C23×C311yescharacteristic
383C3×Q16—34no—
384C3×Q16—62no—
385C3×SD16—22no—
386C3×SD16—22no—
387C3×SD16—22no—
388C3×SD16—22no—
389C3×SD16—42no—
390C3×SD16—42no—
391C3×SD16—62no—
392C3×SD16—62no—
393C3×SD16—121no—
394C3×D8—62no—
395C3×D8—121no—
396C3×M16—62no—
397C2×C3×C8—21no—
398C2×C3×C8—21no—
399C2×C3×C8—31no—
400C2×C3×C8—31no—
401C2×C3×C8—62no—
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C23×C311yescharacteristic
405C2×C3×C8C23×C311yescharacteristic
406C3×C4⋊C4—21no—
407C3×C4⋊C4—21no—
408C3×C4⋊C4—21no—
409C3×C4⋊C4—31no—
410C3×C4⋊C4—31no—
411C3×C4⋊C4—41no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4—61no—
414C3×C4⋊C4C22×D311yescharacteristic
415C3×C4⋊C4C23×C311yescharacteristic
416C3×C22⋊C4—31no—
417C3×C22⋊C4—31no—
418C3×C22⋊C4—61no—
419C3×C22⋊C4—61no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C42—21no—
425C3×C42—21no—
426C3×C42—21no—
427C3×C42—41no—
428C3×C42—61no—
429C3×C42C22×D311yescharacteristic
430C3×C42C23×C311yescharacteristic
431#217—21no—
432#217—21no—
433#216C3×D414yescomplemented
434#214—22no—
435#214—41no—
436#213—22no—
437#213—41no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4C3×D411yescharacteristic
443(C2×D3)⋊C4C3×D411yescharacteristic
444C4⋊Dic3—21no—
445C4⋊Dic3C3×D411yescharacteristic
446C4⋊Dic3C23×C311yescharacteristic
447Dic3⋊C4—21no—
448C4×Dic3—21no—
449C2×C3⋊C8C23×C311yescharacteristic
450C2×C3⋊C8C23×C311yescharacteristic
451Dic12—22no—
452#204—22no—
453ΓL(1,𝔽25)—22no—
454D3×C8—22no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32C22×D411yescharacteristic
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C32×C4—21no—
472C32×C4—22no—
473C32×C4—21no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3×Dic3—22no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—31no—
483C2×#41—31no—
484C2×#41—31no—
485C22×Q8—31no—
486#137—64no—
487#135—64no—
488C2×Q16—31no—
489C2×Q16—31no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16C2×C3×D311yescharacteristic
494C2×SD16C2×C3×D311yescharacteristic
495C2×D8—31no—
496C2×D8—31no—
497C2×M16—31no—
498C22×C8—31no—
499#127—61no—
500#127C2×C3×D311yescharacteristic
501#124—31no—
502#124—61no—
503C22⋊Q8—31no—
504C22⋊Q8—61no—
505#121—31no—
506#121—31no—
507#121—31no—
508#121—61no—
509#121—61no—
510#121—61no—
511C4×Q8—31no—
512C4×Q8C2×C3×D311yescharacteristic
513C4×D4—31no—
514C4×D4—61no—
515C4×D4—61no—
516#106—31no—
517C4⋊C8C2×C3×D311yescharacteristic
518#103—31no—
519#103—31no—
520#103—31no—
521#102—31no—
522#102C2×C3×D311yescharacteristic
523#102C2×C3×D311yescharacteristic
524C22⋊C8—31no—
525C22⋊C8—31no—
526#97—31no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—31no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—61no—
536C22×D3—21no—
537C22×D3C2×C3×D411yescharacteristic
538C22×D3C2×C3×D411yescharacteristic
539C3×Q8—21no—
540C3×Q8—21no—
541C3×Q8—22no—
542C3×Q8—32no—
543C3×Q8—41no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—122no—
548C3×Q8D3×D412yes—
549C3×Q8C2×C3×D412yes—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—41no—
561C3×D4—41no—
562C3×D4—42no—
563C3×D4—42no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—82no—
567C3×D4—81no—
568C3×D4—81no—
569C3×D4—82no—
570C3×D4—121no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—122no—
575C3×D4—241no—
576C3×D4—241no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—122no—
596C2×C3×C4—122no—
597C2×C3×C4—122no—
598C2×C3×C4—122no—
599C2×C3×C4D3×D411yescharacteristic
600C2×C3×C4D3×D411yescharacteristic
601C2×C3×C4C2×C3×D411yescharacteristic
602C2×C3×C4C2×C3×D411yescharacteristic
603C2×C3×C4C23×D311yescharacteristic
604C2×C3×C4C24×C311yescharacteristic
605#67—42no—
606#67—42no—
607#67—81no—
608#67—81no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—42no—
613C2×Dic3—42no—
614C2×Dic3C2×C3×D411yescharacteristic
615C2×Dic3C2×C3×D411yescharacteristic
616D12—21no—
617D12—21no—
618D12—41no—
619D12—42no—
620D12—42no—
621C4×D3—21no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—42no—
626C4×D3—42no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630Dic6—42no—
631Dic6C2×C3×D412yes—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—32no—
637C3×C8—41no—
638C3×C8—41no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8C2×C3×D412yes—
642C2×C32—81no—
643C2×C32—81no—
644C2×C32D4211yescharacteristic
645C2×C32#57511yescharacteristic
646C2×C32#57711yescharacteristic
647C3×D3—41no—
648C3×D3—41no—
649C3×D3—81no—
650#41—62no—
651#41—62no—
652#41—62no—
653#41—121no—
654#41—121no—
655#41—121no—
656C2×Q8—31no—
657C2×Q8—31no—
658C2×Q8—61no—
659C2×Q8—62no—
660C2×Q8—121no—
661C2×Q8C22×C3×D311yescharacteristic
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—31no—
665C2×D4—31no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4C22×C3×D311yescharacteristic
673C2×D4C22×C3×D311yescharacteristic
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680Q16—34no—
681Q16—62no—
682SD16—22no—
683SD16—22no—
684SD16—62no—
685SD16—62no—
686SD16—121no—
687D8—62no—
688D8—121no—
689M16—62no—
690C2×C8—31no—
691C2×C8—31no—
692C2×C8—62no—
693C2×C8C22×C3×D311yescharacteristic
694C2×C8C22×C3×D311yescharacteristic
695C4⋊C4—21no—
696C4⋊C4—31no—
697C4⋊C4—31no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4C22×C3×D311yescharacteristic
701C22⋊C4—31no—
702C22⋊C4—31no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C42—21no—
710C42—61no—
711C42C22×C3×D311yescharacteristic
712C22×C3—21no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3C2×D3×D411yescharacteristic
741C22×C3C22×C3×D411yescharacteristic
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—21no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C3×C4—22no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—41no—
761C3×C4—42no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—62no—
767C3×C4—81no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4C2×D3×D411yescharacteristic
771C3×C4#100911yescharacteristic
772C3×C4C22×C3×D411yescharacteristic
773C3×C4C3×H(5,𝔽2)11yescharacteristic
774Dic3—22no—
775Dic3—21no—
776Dic3—21no—
777Dic3—41no—
778Dic3—41no—
779C32#327111yescharacteristic, complemented, Sylow
780C23—21no—
781C23—21no—
782C23—31no—
783C23—31no—
784C23—61no—
785Q8—21no—
786Q8—32no—
787Q8—61no—
788Q8—61no—
789Q8—61no—
790Q8—122no—
791Q8C3×D3×D412yes—
792D4—21no—
793D4—21no—
794D4—21no—
795D4—21no—
796D4—42no—
797D4—61no—
798D4—61no—
799D4—81no—
800D4—121no—
801D4—122no—
802D4—122no—
803D4—122no—
804D4—122no—
805D4—241no—
806D4—241no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4C3×D3×D411yescharacteristic
823C2×C4C3×D3×D411yescharacteristic
824C2×C4C23×C3×D311yescharacteristic
825C8—21no—
826C8—21no—
827C8—32no—
828C8—61no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—81no—
833C2×C3—81no—
834C2×C3—81no—
835C2×C3—81no—
836C2×C3—121no—
837C2×C3—121no—
838C2×C3—161no—
839C2×C3—161no—
840C2×C3—241no—
841C2×C3#560911yescharacteristic
842C2×C3#576211yescharacteristic
843C2×C3#577311yescharacteristic
844C2×C3C3×D4211yescharacteristic
845C2×C3C3×#57511yescharacteristic
846C2×C3C3×#57711yescharacteristic
847D3—41no—
848D3—41no—
849D3—81no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—121no—
863C22—121no—
864C22—121no—
865C22C2×C3×D3×D411yescharacteristic
866C4—21no—
867C4—21no—
868C4—22no—
869C4—41no—
870C4—61no—
871C4—61no—
872C4—62no—
873C4—121no—
874C4—121no—
875C4C2×C3×D3×D411yescharacteristic
876C4C3×#100911yescharacteristic
877C3—21no—
878C3#8040711yescharacteristic, direct product factor
879C3C3×#327111yescharacteristic, complemented
880C2—81no—
881C2—81no—
882C2—121no—
883C2—121no—
884C2—241no—
885C2C3×#560911yescharacteristic
886C2C3×#576211yescharacteristic
887C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#460C2
socleC22×C32C22×D4
hypercenterC3×#460D3
hypocenterC3C3×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. C2×C3×#915C2semidirect
3. C3×#5718C2semidirect
4. C3×#5576C2semidirect
5. C32×#460C2semidirect
6. C3×#5172C2semidirect
7. C3×#5170C2semidirect
8. C3×#5074C2semidirect
9. C3×#5030C2semidirect
10. C3×#4845C2semidirect
11. C3×#4836C2semidirect
12. C3×#4783C2semidirect
13. C3×#4782C2semidirect
14. C3×#4781C2semidirect
15. C3×#4778C2semidirect
17. #80407C3direct (N × H)
67. C2×#916C2×C3semidirect
68. C2×#915C2×C3semidirect
69. #5718C2×C3semidirect
70. #5576C2×C3semidirect
76. C3×#460D3semidirect
77. C3×#460C2×C3semidirect
84. #5172C2×C3semidirect
85. #5170C2×C3semidirect
86. #5074C2×C3semidirect
87. #5030C2×C3semidirect
88. #4845C2×C3semidirect
89. #4836C2×C3semidirect
90. #4783C2×C3semidirect
91. #4782C2×C3semidirect
92. #4781C2×C3semidirect
93. #4778C2×C3semidirect
134. C3×#216D4semidirect
311. #460C3×D3semidirect
433. #216C3×D4semidirect
779. C32#3271semidirect
878. C3#80407direct (N × H)
879. C3C3×#3271semidirect

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×#9152
C3×#57182
C3×#55762
C32×#4602
C3×#51722
C3×#51702
C3×#50742
C3×#50302
C3×#48452
C3×#48362
C3×#47832
C3×#47822
C3×#47812
C3×#47782
C3×#32713
#804073