Finite Group Databasebeta

← C3×#81859 #11884840

Subgroups — C3×#81859 #11884840

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic, complemented
2C2×C3×#912C211yesmaximal, characteristic, complemented
3C3×#5718C211yesmaximal, characteristic, complemented
4C3×#5677C211yesmaximal, characteristic, complemented
5C32×#496C211yesmaximal, characteristic, complemented
6C3×#5173C211yesmaximal, characteristic, complemented
7C3×#5171C211yesmaximal, characteristic, complemented
8C3×#5170C211yesmaximal, characteristic, complemented
9C3×#5159C211yesmaximal, characteristic, complemented
10C3×#5158C211yesmaximal, characteristic, complemented
11C3×#5158C211yesmaximal, characteristic, complemented
12C3×#5075C211yesmaximal, characteristic, complemented
13C3×#5054C211yesmaximal, characteristic, complemented
14C3×#4716C211yesmaximal, characteristic, complemented
15C3×#4706C211yesmaximal, characteristic, complemented
16C3×#3271—31nomaximal
17#81859C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×C3×#237C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic
24C2×C32×D8C2211yescharacteristic
25C2×C32×D8C2211yescharacteristic
26C32×#127C2211yescharacteristic
27C32×#124C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C3×#940—21no—
31C3×#939—21no—
32C3×#939—21no—
33C3×#938C2211yescharacteristic
34C3×#938C2211yescharacteristic
35C3×#938C2211yescharacteristic
36C3×D4×Dic3—21no—
37C2×C3×#214C2211yescharacteristic
38C2×C3×#214C2211yescharacteristic
39C2×C3×#214C2211yescharacteristic
40C3×#915—24no—
41C3×#912—24no—
42C2×C3×Dic12C2211yescharacteristic
43C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
44C2×C3×D3×C8C2211yescharacteristic
45C3×#885—21no—
46C3×#884—21no—
47C3×#67⋊C4—21no—
48C3×#878—21no—
49C3×C4×D12C2211yescharacteristic
50C3×C4×Dic6C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic
52C32×#97C2211yescharacteristic
53C3×#835C2211yescharacteristic
54C3×#832C2211yescharacteristic
55C3×#832C2211yescharacteristic
56C3×#832C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×#817C2211yescharacteristic
60C3×#816C2211yescharacteristic
61C3×#816C2211yescharacteristic
62C3×C4⋊(C3⋊C8)C2211yescharacteristic
63C2×C3×#137—31no—
64C2×C3×#135—31no—
65C3×#550—31no—
66C3×#548—31no—
67C2×#915C2×C311yescharacteristic, complemented
68C2×#912C2×C311yescharacteristic, complemented
69#5718C2×C311yescharacteristic, complemented
70#5677C2×C311yescharacteristic, complemented
71C3×#496—21no—
72C3×#496D311yescharacteristic, complemented
73C3×#496C2×C311yescharacteristic, complemented
74C3×#469—31no—
75C3×#465—31no—
76C3×#464—31no—
77C3×#460—31no—
78C3×#452—31no—
79C3×#449—31no—
80C3×#449—31no—
81C3×#448—31no—
82C3×#441—31no—
83C3×#435—31no—
84#5173C2×C311yescharacteristic, complemented
85#5171C2×C311yescharacteristic, complemented
86#5170C2×C311yescharacteristic, complemented
87#5159C2×C311yescharacteristic, complemented
88#5158C2×C311yescharacteristic, complemented
89#5158C2×C311yescharacteristic, complemented
90#5075C2×C311yescharacteristic, complemented
91#5054C2×C311yescharacteristic, complemented
92#4716C2×C311yescharacteristic, complemented
93#4706C2×C311yescharacteristic, complemented
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C3×D3×Q8—22no—
110C3×D3×Q8—41no—
111C3×#237—22no—
112C3×#237—22no—
113C3×#237—22no—
114C3×#237—41no—
115C3×#237—41no—
116C3×#237—41no—
117C2×C3×D12D411yescharacteristic
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—41no—
126C32×D8—22no—
127C32×D8—41no—
128C2×C32×C8C2311yescharacteristic
129C2×C32×C8C2311yescharacteristic
130C32×C22⋊C4—21no—
131C32×C22⋊C4—21no—
132C32×C42C2311yescharacteristic
133C3×#217—21no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#216—22no—
137C3×#214—22no—
138C3×#214—22no—
139C3×#214—22no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×(C2×D3)⋊C4D411yescharacteristic
143C3×C4⋊Dic3D411yescharacteristic
144C3×C4⋊Dic3C2311yescharacteristic
145C3×C4⋊Dic3C2311yescharacteristic
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C3×C4×Dic3—21no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×Dic12D414yescomplemented
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×D3×Q8C22×C311yescharacteristic
162C2×#237C22×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—21no—
179C2×C3×D8—21no—
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
189C3×#127C22×C311yescharacteristic
190C3×#124—21no—
191C3×#124—61no—
192C3×#124C2×D311yescharacteristic
193C3×#124C22×C311yescharacteristic
194C3×C22⋊Q8—31no—
195C3×C22⋊Q8—61no—
196C3×#121—31no—
197C3×#121—31no—
198C3×#121—31no—
199C3×#121—61no—
200C3×#121—61no—
201C3×#121—61no—
202C3×C4×Q8—31no—
203C3×C4×Q8—31no—
204C3×C4×D4—31no—
205C3×C4×D4—61no—
206C3×C4×D4—61no—
207#946C22×C311yescharacteristic
208C2×#216C22×C311yescharacteristic
209#940—21no—
210#939—21no—
211#939—21no—
212#938C22×C311yescharacteristic
213#938C22×C311yescharacteristic
214#938C22×C311yescharacteristic
215D4×Dic3—21no—
216C2×#214C22×C311yescharacteristic
217C2×#214C22×C311yescharacteristic
218C2×#214C22×C311yescharacteristic
219#915—24no—
220#912—24no—
221C2×Dic12C22×C311yescharacteristic
222C2×ΓL(1,𝔽25)C22×C311yescharacteristic
223C2×D3×C8C22×C311yescharacteristic
224#885—21no—
225#884—21no—
226#67⋊C4—21no—
227#878—21no—
228C4×D12C22×C311yescharacteristic
229C4×Dic6C22×C311yescharacteristic
230C4×Dic6C22×C311yescharacteristic
231C3×#106—31no—
232C3×C4⋊C8—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×C22⋊C8—31no—
240C3×C22⋊C8—31no—
241C3×#97—21no—
242C3×#97C2×D311yescharacteristic
243C3×#97C22×C311yescharacteristic
244#835C22×C311yescharacteristic
245#832C22×C311yescharacteristic
246#832C22×C311yescharacteristic
247#832C22×C311yescharacteristic
248(C2×D3)⋊C8C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic
250#817C22×C311yescharacteristic
251#816C22×C311yescharacteristic
252#816C22×C311yescharacteristic
253C4⋊(C3⋊C8)C22×C311yescharacteristic
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—21no—
257C22×C3×D3C2×D411yescharacteristic
258C22×C3×D3C2×D411yescharacteristic
259C32×Q8—21no—
260C32×Q8—21no—
261C32×D4—21no—
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—42no—
268C32×D4—81no—
269C2×C32×C4—21no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—42no—
276C3×#67—42no—
277C3×#67—81no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3—42no—
285C2×C3×Dic3—42no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—41no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yes—
298C3×Dic6C2×D412yes—
299C32×C8—21no—
300C32×C8C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×#137—31no—
304C2×#135—31no—
305#550—31no—
306#548—31no—
307#496C3×D311yescharacteristic, complemented
308#469—31no—
309#465—31no—
310#464—31no—
311#460—31no—
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—21no—
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×D4C22×D311yescharacteristic
351C2×C3×D4C23×C311yescharacteristic
352C2×C3×D4C23×C311yescharacteristic
353C2×C3×D4C23×C311yescharacteristic
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C22×C3×C4—61no—
359C22×C3×C4—61no—
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—21no—
365C2×#67—21no—
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—21no—
369D3×Q8—22no—
370D3×Q8—41no—
371#237—22no—
372#237—22no—
373#237—22no—
374#237—41no—
375#237—41no—
376#237—41no—
377C2×D12C3×D411yescharacteristic
378C2×C4×D3—21no—
379C2×C4×D3C23×C311yescharacteristic
380C2×C4×D3C23×C311yescharacteristic
381C2×Dic6—21no—
382C2×Dic6C23×C311yescharacteristic
383C2×Dic6C23×C311yescharacteristic
384C3×Q16—34no—
385C3×Q16—62no—
386C3×SD16—22no—
387C3×SD16—22no—
388C3×SD16—42no—
389C3×SD16—41no—
390C3×SD16—41no—
391C3×SD16—42no—
392C3×SD16—62no—
393C3×SD16—62no—
394C3×SD16—62no—
395C3×D8—22no—
396C3×D8—22no—
397C3×D8—42no—
398C3×D8—41no—
399C3×D8—41no—
400C3×D8—42no—
401C3×M16—62no—
402C2×C3×C8—21no—
403C2×C3×C8—21no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C2×C3×C8—62no—
407C2×C3×C8C22×D311yescharacteristic
408C2×C3×C8C22×D311yescharacteristic
409C2×C3×C8C23×C311yescharacteristic
410C2×C3×C8C23×C311yescharacteristic
411C3×C4⋊C4—31no—
412C3×C4⋊C4—31no—
413C3×C4⋊C4—31no—
414C3×C4⋊C4—61no—
415C3×C4⋊C4—61no—
416C3×C4⋊C4—61no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—21no—
420C3×C22⋊C4—21no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—41no—
424C3×C22⋊C4—41no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C42—21no—
430C3×C42—61no—
431C3×C42—61no—
432C3×C42C22×D311yescharacteristic
433C3×C42C23×C311yescharacteristic
434#217—21no—
435#217—21no—
436#217—21no—
437#216—22no—
438#214—22no—
439#214—22no—
440#214—22no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4C3×D411yescharacteristic
443(C2×D3)⋊C4C3×D411yescharacteristic
444C4⋊Dic3C3×D411yescharacteristic
445C4⋊Dic3C23×C311yescharacteristic
446C4⋊Dic3C23×C311yescharacteristic
447Dic3⋊C4—21no—
448Dic3⋊C4—21no—
449Dic3⋊C4—21no—
450C4×Dic3—21no—
451C4×Dic3—21no—
452C2×C3⋊C8C23×C311yescharacteristic
453C2×C3⋊C8C23×C311yescharacteristic
454Dic12C3×D414yescomplemented
455ΓL(1,𝔽25)—22no—
456D3×C8—22no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C32×C4—21no—
474C32×C4—21no—
475C32×C4—41no—
476C32×C4C22×D411yescharacteristic
477C32×C4H(5,𝔽2)11yescharacteristic
478C3×Dic3—22no—
479C3×Dic3—22no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C2×#41—31no—
485C2×#41—31no—
486C2×#41—31no—
487C22×Q8—31no—
488#137—64no—
489#135—64no—
490C2×Q16—31no—
491C2×Q16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16C2×C3×D311yescharacteristic
496C2×SD16C2×C3×D311yescharacteristic
497C2×D8C2×C3×D311yescharacteristic
498C2×D8C2×C3×D311yescharacteristic
499C2×M16—31no—
500C22×C8—31no—
501#127—61no—
502#127C2×C3×D311yescharacteristic
503#124—61no—
504#124C2×C3×D311yescharacteristic
505C22⋊Q8—31no—
506C22⋊Q8—61no—
507#121—31no—
508#121—31no—
509#121—31no—
510#121—61no—
511#121—61no—
512#121—61no—
513C4×Q8—31no—
514C4×Q8—31no—
515C4×D4—31no—
516C4×D4—61no—
517C4×D4—61no—
518#106—31no—
519C4⋊C8—31no—
520#103—31no—
521#103—31no—
522#103—31no—
523#102—31no—
524#102—31no—
525#102—31no—
526C22⋊C8—31no—
527C22⋊C8—31no—
528#97C2×C3×D311yescharacteristic
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C22×D3C2×C3×D411yescharacteristic
541C22×D3C2×C3×D411yescharacteristic
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—32no—
547C3×Q8—32no—
548C3×Q8—41no—
549C3×Q8—41no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×Q8—122no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—41no—
569C3×D4—41no—
570C3×D4—41no—
571C3×D4—42no—
572C3×D4—42no—
573C3×D4—82no—
574C3×D4—81no—
575C3×D4—81no—
576C3×D4—82no—
577C3×D4—121no—
578C3×D4—122no—
579C3×D4—122no—
580C3×D4—122no—
581C3×D4—122no—
582C3×D4—241no—
583C3×D4—241no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—41no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—122no—
601C2×C3×C4—122no—
602C2×C3×C4—122no—
603C2×C3×C4—122no—
604C2×C3×C4D3×D411yescharacteristic
605C2×C3×C4D3×D411yescharacteristic
606C2×C3×C4C2×C3×D411yescharacteristic
607C2×C3×C4C2×C3×D411yescharacteristic
608C2×C3×C4C23×D311yescharacteristic
609C2×C3×C4C24×C311yescharacteristic
610#67—42no—
611#67—42no—
612#67—42no—
613#67—42no—
614#67—81no—
615#67—81no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—42no—
621C2×Dic3—42no—
622C2×Dic3—42no—
623C2×Dic3C2×C3×D411yescharacteristic
624C2×Dic3C2×C3×D411yescharacteristic
625D12—41no—
626C4×D3—21no—
627C4×D3—21no—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—42no—
631Dic6—21no—
632Dic6—21no—
633Dic6—42no—
634Dic6C2×C3×D412yes—
635Dic6C2×C3×D412yes—
636C3×C8—22no—
637C3×C8—21no—
638C3×C8—21no—
639C3×C8—22no—
640C3×C8—61no—
641C3×C8—61no—
642C3×C8D3×D412yes—
643C3×C8C2×C3×D412yes—
644C3⋊C8—21no—
645C3⋊C8—21no—
646C2×C32—81no—
647C2×C32—81no—
648C2×C32—81no—
649C2×C32D4211yescharacteristic
650C2×C32#57511yescharacteristic
651C2×C32#57711yescharacteristic
652C3×D3—41no—
653C3×D3—41no—
654#41—62no—
655#41—62no—
656#41—62no—
657#41—121no—
658#41—121no—
659#41—121no—
660C2×Q8—31no—
661C2×Q8—31no—
662C2×Q8—61no—
663C2×Q8—62no—
664C2×Q8—121no—
665C2×Q8C22×C3×D311yescharacteristic
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—31no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4C22×C3×D311yescharacteristic
676C2×D4C22×C3×D311yescharacteristic
677C2×D4C22×C3×D311yescharacteristic
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684Q16—34no—
685Q16—62no—
686SD16—22no—
687SD16—41no—
688SD16—62no—
689SD16—62no—
690SD16—62no—
691D8—22no—
692D8—41no—
693M16—62no—
694C2×C8—31no—
695C2×C8—31no—
696C2×C8—62no—
697C2×C8C22×C3×D311yescharacteristic
698C2×C8C22×C3×D311yescharacteristic
699C4⋊C4—31no—
700C4⋊C4—31no—
701C4⋊C4—31no—
702C4⋊C4—61no—
703C4⋊C4—61no—
704C4⋊C4—61no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—31no—
708C22⋊C4—31no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C42—61no—
714C42—61no—
715C42C22×C3×D311yescharacteristic
716C22×C3—21no—
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—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3C2×D3×D411yescharacteristic
751C22×C3C22×C3×D411yescharacteristic
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—21no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—41no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—62no—
771C3×C4—62no—
772C3×C4—81no—
773C3×C4—121no—
774C3×C4—121no—
775C3×C4C2×D3×D411yescharacteristic
776C3×C4#100411yescharacteristic
777C3×C4C22×C3×D411yescharacteristic
778C3×C4C3×H(5,𝔽2)11yescharacteristic
779Dic3—22no—
780Dic3—22no—
781Dic3—21no—
782Dic3—21no—
783Dic3—41no—
784Dic3—41no—
785C32#327111yescharacteristic, complemented, Sylow
786C23—21no—
787C23—21no—
788C23—21no—
789C23—31no—
790C23—31no—
791Q8—21no—
792Q8—21no—
793Q8—32no—
794Q8—32no—
795Q8—61no—
796Q8—61no—
797Q8—122no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—21no—
803D4—21no—
804D4—42no—
805D4—81no—
806D4—121no—
807D4—122no—
808D4—122no—
809D4—122no—
810D4—122no—
811D4—241no—
812D4—241no—
813C2×C4—21no—
814C2×C4—31no—
815C2×C4—31no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—122no—
825C2×C4—122no—
826C2×C4—122no—
827C2×C4—122no—
828C2×C4C3×D3×D411yescharacteristic
829C2×C4C3×D3×D411yescharacteristic
830C2×C4C23×C3×D311yescharacteristic
831C8—21no—
832C8—61no—
833C8—61no—
834C8C3×D3×D412yes—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—81no—
839C2×C3—81no—
840C2×C3—81no—
841C2×C3—81no—
842C2×C3—81no—
843C2×C3—81no—
844C2×C3—121no—
845C2×C3—121no—
846C2×C3—161no—
847C2×C3—161no—
848C2×C3—161no—
849C2×C3#571711yescharacteristic
850C2×C3#577311yescharacteristic
851C2×C3#577511yescharacteristic
852C2×C3C3×D4211yescharacteristic
853C2×C3C3×#57511yescharacteristic
854C2×C3C3×#57711yescharacteristic
855D3—41no—
856D3—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—61no—
867C22—61no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—61no—
872C22C2×C3×D3×D411yescharacteristic
873C4—21no—
874C4—21no—
875C4—41no—
876C4—61no—
877C4—61no—
878C4—62no—
879C4—62no—
880C4—121no—
881C4—121no—
882C4C2×C3×D3×D411yescharacteristic
883C4C3×#100411yescharacteristic
884C3—21no—
885C3#8185911yescharacteristic, direct product factor
886C3C3×#327111yescharacteristic, complemented
887C2—81no—
888C2—81no—
889C2—81no—
890C2—121no—
891C2—121no—
892C2C3×#571711yescharacteristic
893C2C3×#577311yescharacteristic
894C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#496C2
socleC22×C32C22×D4
hypercenterC3×#496D3
hypocenterC3C3×#3271
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×#915C2semidirect
2. C2×C3×#912C2semidirect
3. C3×#5718C2semidirect
4. C3×#5677C2semidirect
5. C32×#496C2semidirect
6. C3×#5173C2semidirect
7. C3×#5171C2semidirect
8. C3×#5170C2semidirect
9. C3×#5159C2semidirect
10. C3×#5158C2semidirect
11. C3×#5158C2semidirect
12. C3×#5075C2semidirect
13. C3×#5054C2semidirect
14. C3×#4716C2semidirect
15. C3×#4706C2semidirect
17. #81859C3direct (N × H)
67. C2×#915C2×C3semidirect
68. C2×#912C2×C3semidirect
69. #5718C2×C3semidirect
70. #5677C2×C3semidirect
72. C3×#496D3semidirect
73. C3×#496C2×C3semidirect
84. #5173C2×C3semidirect
85. #5171C2×C3semidirect
86. #5170C2×C3semidirect
87. #5159C2×C3semidirect
88. #5158C2×C3semidirect
89. #5158C2×C3semidirect
90. #5075C2×C3semidirect
91. #5054C2×C3semidirect
92. #4716C2×C3semidirect
93. #4706C2×C3semidirect
153. C3×Dic12D4semidirect
307. #496C3×D3semidirect
454. Dic12C3×D4semidirect
785. C32#3271semidirect
885. C3#81859direct (N × H)
886. C3C3×#3271semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9152
C2×C3×#9122
C3×#57182
C3×#56772
C32×#4962
C3×#51732
C3×#51712
C3×#51702
C3×#51592
C3×#51582
C3×#50752
C3×#50542
C3×#47162
C3×#47062
C3×#32713
#818593