Finite Group Databasebeta

← C3×#83583 #11884831

Subgroups — C3×#83583 #11884831

Order 1152.

1132 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#550C211yesmaximal, characteristic, complemented
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×C3×#950C211yesmaximal, characteristic, complemented
4C3×#5552C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7C3×#5075C211yesmaximal, characteristic, complemented
8C3×#5074C211yesmaximal, characteristic, complemented
9C3×#5041C211yesmaximal, characteristic, complemented
10C3×#5040C211yesmaximal, characteristic, complemented
11C3×#5039C211yesmaximal, characteristic, complemented
12C3×#5037C211yesmaximal, characteristic, complemented
13C3×#5030C211yesmaximal, characteristic, complemented
14C3×#5028C211yesmaximal, characteristic, complemented
15C3×#5011C211yesmaximal, characteristic, complemented
16C3×#3271—31nomaximal
17#83583C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C32×#41C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C32×#127—21no—
23C32×#127C2211yescharacteristic
24C32×#121—21no—
25C32×#121—21no—
26C32×#121C2211yescharacteristic
27C32×#121C2211yescharacteristic
28C32×C4×Q8C2211yescharacteristic
29C32×C4×D4—21no—
30C32×C4×D4C2211yescharacteristic
31C3×#951—24no—
32C3×#950—24no—
33C2×C3×#216C2211yescharacteristic
34C2×C3×#216C2211yescharacteristic
35C2×C3×#215C2211yescharacteristic
36C3×#939—21no—
37C2×C3×#214C2211yescharacteristic
38C2×C3×#214C2211yescharacteristic
39C2×C3×#214C2211yescharacteristic
40C2×C3×#214C2211yescharacteristic
41C2×C3×#213C2211yescharacteristic
42C2×C3×#213C2211yescharacteristic
43C3×#930C2211yescharacteristic
44C3×#924C2211yescharacteristic
45C2×C3×#208C2211yescharacteristic
46C22×C3×C3⋊C8C2211yescharacteristic
47C3×#896—21no—
48C3×#885—21no—
49C3×#67⋊C4—21no—
50C3×#875C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic
52C3×#835C2211yescharacteristic
53C3×#832C2211yescharacteristic
54C3×#832C2211yescharacteristic
55C3×#830C2211yescharacteristic
56C3×#830C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#809C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×C4⋊(C3⋊C8)C2211yescharacteristic
62C3×#803C2211yescharacteristic
63C2×C3×#137—31no—
64C2×C3×#135—31no—
65C3×#550—21no—
66C3×#550D311yescharacteristic, complemented
67C3×#550C2×C311yescharacteristic, complemented
68C3×#548—31no—
69C2×#951C2×C311yescharacteristic, complemented
70C2×#950C2×C311yescharacteristic, complemented
71#5552C2×C311yescharacteristic, complemented
72C3×#496—31no—
73C3×#469—31no—
74C3×#465—31no—
75C3×#464—31no—
76C3×#460—31no—
77C3×#452—31no—
78C3×#449—31no—
79C3×#449—31no—
80C3×#448—31no—
81C3×#441—31no—
82C3×#435—31no—
83#5239C2×C311yescharacteristic, complemented
84#5238C2×C311yescharacteristic, complemented
85#5075C2×C311yescharacteristic, complemented
86#5074C2×C311yescharacteristic, complemented
87#5041C2×C311yescharacteristic, complemented
88#5040C2×C311yescharacteristic, complemented
89#5039C2×C311yescharacteristic, complemented
90#5037C2×C311yescharacteristic, complemented
91#5030C2×C311yescharacteristic, complemented
92#5028C2×C311yescharacteristic, complemented
93#5011C2×C311yescharacteristic, complemented
94C32×#41—22no—
95C32×#41—22no—
96C32×#41—41no—
97C32×#41—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—21no—
100C2×C32×D4—21no—
101C2×C32×D4—21no—
102C2×C32×D4—21no—
103C2×C32×D4—21no—
104C2×C32×D4—21no—
105C2×C32×D4D411yescharacteristic
106C2×C32×D4C2311yescharacteristic
107C2×C32×D4C2311yescharacteristic
108C22×C32×C4—21no—
109C22×C32×C4—21no—
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C2×C3×#67—21no—
113C2×C3×#67—21no—
114C22×C3×Dic3—21no—
115C3×#235—22no—
116C3×#235—41no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×Dic6—22no—
120C2×C3×Dic6—21no—
121C2×C3×Dic6—41no—
122C2×C3×Dic6C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124C32×C4⋊C4—21no—
125C32×C4⋊C4D411yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128C32×C22⋊C4—21no—
129C32×C22⋊C4D411yescharacteristic
130C32×C22⋊C4D411yescharacteristic
131C32×C42—21no—
132C32×C42C2311yescharacteristic
133C3×#217—21no—
134C3×#216—22no—
135C3×#216D414yescomplemented
136C3×#215—22no—
137C3×#214—22no—
138C3×#214—22no—
139C3×#214—22no—
140C3×#214—41no—
141C3×#213—22no—
142C3×#213—41no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C3×#208—22no—
151C2×C3×C3⋊C8—22no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C2×C3×C3⋊C8C2311yescharacteristic
155C2×C3×C3⋊C8C2311yescharacteristic
156#3271—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41—21no—
159C2×C3×#41—31no—
160C2×C3×#41C2×D311yescharacteristic
161C2×C3×#41C2×D311yescharacteristic
162C2×C3×#41C22×C311yescharacteristic
163C2×C3×#41C22×C311yescharacteristic
164C22×C3×Q8—31no—
165C2×#235C22×C311yescharacteristic
166C22×Dic6C22×C311yescharacteristic
167C3×#137—64no—
168C3×#135—64no—
169C2×C3×Q16—31no—
170C2×C3×Q16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—31no—
176C2×C3×D8—31no—
177C2×C3×D8—31no—
178C2×C3×M16—31no—
179C22×C3×C8—31no—
180C3×#127—22no—
181C3×#127—21no—
182C3×#127—21no—
183C3×#127—21no—
184C3×#127C2×D311yescharacteristic
185C3×#127C22×C311yescharacteristic
186C3×#124—31no—
187C3×#124—61no—
188C3×C22⋊Q8—31no—
189C3×C22⋊Q8—61no—
190C3×#121—22no—
191C3×#121—22no—
192C3×#121—21no—
193C3×#121—21no—
194C3×#121—21no—
195C3×#121—21no—
196C3×#121—21no—
197C3×#121—21no—
198C3×#121—31no—
199C3×#121—61no—
200C3×#121C2×D311yescharacteristic
201C3×#121C2×D311yescharacteristic
202C3×#121C22×C311yescharacteristic
203C3×#121C22×C311yescharacteristic
204C3×C4×Q8—21no—
205C3×C4×Q8—31no—
206C3×C4×Q8C2×D311yescharacteristic
207C3×C4×Q8C22×C311yescharacteristic
208C3×C4×D4—22no—
209C3×C4×D4—21no—
210C3×C4×D4—21no—
211C3×C4×D4—21no—
212C3×C4×D4—61no—
213C3×C4×D4C2×D311yescharacteristic
214C3×C4×D4C22×C311yescharacteristic
215#951—24no—
216#950—24no—
217C2×#216C22×C311yescharacteristic
218C2×#216C22×C311yescharacteristic
219C2×#215C22×C311yescharacteristic
220#939—21no—
221C2×#214C22×C311yescharacteristic
222C2×#214C22×C311yescharacteristic
223C2×#214C22×C311yescharacteristic
224C2×#214C22×C311yescharacteristic
225C2×#213C22×C311yescharacteristic
226C2×#213C22×C311yescharacteristic
227#930C22×C311yescharacteristic
228#924C22×C311yescharacteristic
229C2×#208C22×C311yescharacteristic
230C22×C3⋊C8C22×C311yescharacteristic
231#896—21no—
232#885—21no—
233#67⋊C4—21no—
234#875C22×C311yescharacteristic
235C4×Dic6C22×C311yescharacteristic
236C3×#106—31no—
237C3×C4⋊C8—31no—
238C3×#103—31no—
239C3×#103—31no—
240C3×#103—31no—
241C3×#102—31no—
242C3×#102—31no—
243C3×#102—31no—
244C3×C22⋊C8—31no—
245C3×C22⋊C8—31no—
246C3×#97—31no—
247#835C22×C311yescharacteristic
248#832C22×C311yescharacteristic
249#832C22×C311yescharacteristic
250#830C22×C311yescharacteristic
251#830C22×C311yescharacteristic
252#810C22×C311yescharacteristic
253#810C22×C311yescharacteristic
254#809C22×C311yescharacteristic
255#808C22×C311yescharacteristic
256C4⋊(C3⋊C8)C22×C311yescharacteristic
257#803C22×C311yescharacteristic
258C23×C32—21no—
259C23×C32—21no—
260C23×C32C2×D411yescharacteristic
261C23×C32C2×D411yescharacteristic
262C22×C3×D3—21no—
263C32×Q8—21no—
264C32×Q8C2×D412yes—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—21no—
268C32×D4—21no—
269C32×D4—41no—
270C32×D4—42no—
271C32×D4—42no—
272C32×D4—42no—
273C32×D4—81no—
274C32×D4—81no—
275C32×D4—81no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—42no—
283C2×C32×C4—42no—
284C2×C32×C4C2×D411yescharacteristic
285C2×C32×C4C2×D411yescharacteristic
286C2×C32×C4C2×D411yescharacteristic
287C2×C32×C4C2×D411yescharacteristic
288C2×C32×C4C2411yescharacteristic
289C3×#67—42no—
290C3×#67—42no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—42no—
295C3×D12—21no—
296C3×D12—21no—
297C3×C4×D3—42no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300C3×Dic6—21no—
301C3×Dic6—42no—
302C3×Dic6C2×D412yes—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C3×C3⋊C8C2×D412yes—
307C2×#137—31no—
308C2×#135—31no—
309#550C3×D311yescharacteristic, complemented
310#548—31no—
311#496—31no—
312#469—31no—
313#465—31no—
314#464—31no—
315#460—31no—
316#452—31no—
317#449—31no—
318#449—31no—
319#448—31no—
320#441—31no—
321#435—31no—
322C3×#41—22no—
323C3×#41—22no—
324C3×#41—22no—
325C3×#41—22no—
326C3×#41—42no—
327C3×#41—42no—
328C3×#41—41no—
329C3×#41—41no—
330C3×#41—41no—
331C3×#41—41no—
332C3×#41—42no—
333C3×#41—42no—
334C3×#41—62no—
335C3×#41—121no—
336C2×C3×Q8—21no—
337C2×C3×Q8—31no—
338C2×C3×Q8—31no—
339C2×C3×Q8—62no—
340C2×C3×Q8—61no—
341C2×C3×Q8—121no—
342C2×C3×Q8C22×D311yescharacteristic
343C2×C3×Q8C23×C311yescharacteristic
344C2×C3×D4—22no—
345C2×C3×D4—22no—
346C2×C3×D4—22no—
347C2×C3×D4—21no—
348C2×C3×D4—21no—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—22no—
352C2×C3×D4—22no—
353C2×C3×D4—22no—
354C2×C3×D4—21no—
355C2×C3×D4—21no—
356C2×C3×D4—21no—
357C2×C3×D4—21no—
358C2×C3×D4—21no—
359C2×C3×D4—21no—
360C2×C3×D4—21no—
361C2×C3×D4—21no—
362C2×C3×D4—21no—
363C2×C3×D4—21no—
364C2×C3×D4—21no—
365C2×C3×D4—31no—
366C2×C3×D4—61no—
367C2×C3×D4—61no—
368C2×C3×D4#6711yescharacteristic
369C2×C3×D4C3×D411yescharacteristic
370C2×C3×D4C22×D311yescharacteristic
371C2×C3×D4C22×D311yescharacteristic
372C2×C3×D4C23×C311yescharacteristic
373C2×C3×D4C23×C311yescharacteristic
374C22×C3×C4—22no—
375C22×C3×C4—22no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—21no—
381C22×C3×C4—21no—
382C22×C3×C4—61no—
383C22×C3×C4—61no—
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C23×C311yescharacteristic
387C22×C3×C4C23×C311yescharacteristic
388C2×#67—21no—
389C2×#67—21no—
390C22×Dic3—21no—
391#235—22no—
392#235—41no—
393C2×D12C23×C311yescharacteristic
394C2×C4×D3—21no—
395C2×Dic6—22no—
396C2×Dic6—21no—
397C2×Dic6—41no—
398C2×Dic6C23×C311yescharacteristic
399C2×Dic6C23×C311yescharacteristic
400C3×Q16—34no—
401C3×Q16—62no—
402C3×SD16—62no—
403C3×SD16—62no—
404C3×SD16—62no—
405C3×SD16—62no—
406C3×SD16—121no—
407C3×D8—62no—
408C3×D8—121no—
409C3×M16—62no—
410C2×C3×C8—31no—
411C2×C3×C8—31no—
412C2×C3×C8—31no—
413C2×C3×C8—31no—
414C2×C3×C8—62no—
415C3×C4⋊C4—22no—
416C3×C4⋊C4—21no—
417C3×C4⋊C4—21no—
418C3×C4⋊C4—21no—
419C3×C4⋊C4—21no—
420C3×C4⋊C4—31no—
421C3×C4⋊C4—61no—
422C3×C4⋊C4—61no—
423C3×C4⋊C4#6711yescharacteristic
424C3×C4⋊C4C3×D411yescharacteristic
425C3×C4⋊C4C22×D311yescharacteristic
426C3×C4⋊C4C23×C311yescharacteristic
427C3×C22⋊C4—22no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—21no—
430C3×C22⋊C4—21no—
431C3×C22⋊C4—21no—
432C3×C22⋊C4—21no—
433C3×C22⋊C4—21no—
434C3×C22⋊C4—21no—
435C3×C22⋊C4—61no—
436C3×C22⋊C4—61no—
437C3×C22⋊C4—61no—
438C3×C22⋊C4—61no—
439C3×C22⋊C4#6711yescharacteristic
440C3×C22⋊C4#6711yescharacteristic
441C3×C22⋊C4C3×D411yescharacteristic
442C3×C22⋊C4C3×D411yescharacteristic
443C3×C42—22no—
444C3×C42—21no—
445C3×C42—21no—
446C3×C42—21no—
447C3×C42—61no—
448C3×C42C22×D311yescharacteristic
449C3×C42C23×C311yescharacteristic
450#217—21no—
451#216—22no—
452#216C3×D414yescomplemented
453#215—22no—
454#214—22no—
455#214—22no—
456#214—22no—
457#214—41no—
458#213—22no—
459#213—41no—
460(C2×D3)⋊C4—21no—
461(C2×D3)⋊C4—21no—
462(C2×D3)⋊C4—21no—
463C4⋊Dic3C23×C311yescharacteristic
464Dic3⋊C4—21no—
465Dic3⋊C4—21no—
466C4×Dic3—21no—
467#208—22no—
468C2×C3⋊C8—22no—
469C2×C3⋊C8C23×C311yescharacteristic
470C2×C3⋊C8C23×C311yescharacteristic
471C2×C3⋊C8C23×C311yescharacteristic
472C2×C3⋊C8C23×C311yescharacteristic
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32—41no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32C22×D411yescharacteristic
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C32×C4—22no—
490C32×C4—21no—
491C32×C4—21no—
492C32×C4—21no—
493C32×C4—21no—
494C32×C4—41no—
495C32×C4C22×D411yescharacteristic
496C32×C4H(5,𝔽2)11yescharacteristic
497C3×Dic3—22no—
498C3×Dic3—41no—
499C3×Dic3—41no—
500C2×#41—31no—
501C2×#41C2×C3×D311yescharacteristic
502C2×#41C2×C3×D311yescharacteristic
503C22×Q8—31no—
504#137—64no—
505#135—64no—
506C2×Q16—31no—
507C2×Q16—31no—
508C2×SD16—31no—
509C2×SD16—31no—
510C2×SD16—31no—
511C2×SD16—31no—
512C2×SD16—31no—
513C2×D8—31no—
514C2×D8—31no—
515C2×M16—31no—
516C22×C8—31no—
517#127—21no—
518#127C2×C3×D311yescharacteristic
519#124—31no—
520#124—61no—
521C22⋊Q8—31no—
522C22⋊Q8—61no—
523#121—21no—
524#121—21no—
525#121—31no—
526#121—61no—
527#121C2×C3×D311yescharacteristic
528#121C2×C3×D311yescharacteristic
529C4×Q8—31no—
530C4×Q8C2×C3×D311yescharacteristic
531C4×D4—21no—
532C4×D4—61no—
533C4×D4C2×C3×D311yescharacteristic
534#106—31no—
535C4⋊C8—31no—
536#103—31no—
537#103—31no—
538#103—31no—
539#102—31no—
540#102—31no—
541#102—31no—
542C22⋊C8—31no—
543C22⋊C8—31no—
544#97—31no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—61no—
554C23×C3C2×#6711yescharacteristic
555C23×C3C2×#6711yescharacteristic
556C23×C3C2×C3×D411yescharacteristic
557C23×C3C2×C3×D411yescharacteristic
558C22×D3—21no—
559C3×Q8—22no—
560C3×Q8—21no—
561C3×Q8—21no—
562C3×Q8—22no—
563C3×Q8—32no—
564C3×Q8—61no—
565C3×Q8—61no—
566C3×Q8—61no—
567C3×Q8—122no—
568C3×Q8D3×D412yes—
569C3×Q8C2×C3×D412yes—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—41no—
581C3×D4—41no—
582C3×D4—41no—
583C3×D4—41no—
584C3×D4—42no—
585C3×D4—42no—
586C3×D4—42no—
587C3×D4—42no—
588C3×D4—42no—
589C3×D4—44no—
590C3×D4—42no—
591C3×D4—42no—
592C3×D4—44no—
593C3×D4—44no—
594C3×D4—61no—
595C3×D4—61no—
596C3×D4—81no—
597C3×D4—81no—
598C3×D4—81no—
599C3×D4—81no—
600C3×D4—81no—
601C3×D4—81no—
602C3×D4—82no—
603C3×D4—82no—
604C3×D4—82no—
605C3×D4—122no—
606C3×D4—122no—
607C2×C3×C4—22no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—22no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—42no—
631C2×C3×C4—42no—
632C2×C3×C4—42no—
633C2×C3×C4—42no—
634C2×C3×C4—44no—
635C2×C3×C4—44no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—122no—
640C2×C3×C4—122no—
641C2×C3×C4C2×#6711yescharacteristic
642C2×C3×C4C2×#6711yescharacteristic
643C2×C3×C4C2×#6711yescharacteristic
644C2×C3×C4C2×#6711yescharacteristic
645C2×C3×C4C2×C3×D411yescharacteristic
646C2×C3×C4C2×C3×D411yescharacteristic
647C2×C3×C4C2×C3×D411yescharacteristic
648C2×C3×C4C2×C3×D411yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C24×C311yescharacteristic
651#67—42no—
652#67—42no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—42no—
657D12—21no—
658D12—21no—
659C4×D3—42no—
660Dic6—21no—
661Dic6—21no—
662Dic6—21no—
663Dic6—42no—
664Dic6C2×C3×D412yes—
665C3×C8—32no—
666C3×C8—61no—
667C3×C8—61no—
668C3×C8—61no—
669C3⋊C8—21no—
670C3⋊C8—21no—
671C3⋊C8—21no—
672C3⋊C8C2×C3×D412yes—
673C2×C32—41no—
674C2×C32—41no—
675C2×C32—81no—
676C2×C32—81no—
677C2×C32D4211yescharacteristic
678C2×C32#57511yescharacteristic
679C2×C32#57711yescharacteristic
680C3×D3—81no—
681#41—22no—
682#41—22no—
683#41—41no—
684#41—41no—
685#41—62no—
686#41—121no—
687C2×Q8—31no—
688C2×Q8—31no—
689C2×Q8—62no—
690C2×Q8—61no—
691C2×Q8—121no—
692C2×Q8C22×C3×D311yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—31no—
700C2×D4—61no—
701C2×D4—61no—
702C2×D4C3×#6711yescharacteristic
703C2×D4C22×C3×D311yescharacteristic
704C2×D4C22×C3×D311yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4C22×C3×D311yescharacteristic
710C22×C4C22×C3×D311yescharacteristic
711Q16—34no—
712Q16—62no—
713SD16—62no—
714SD16—62no—
715SD16—62no—
716SD16—62no—
717SD16—121no—
718D8—62no—
719D8—121no—
720M16—62no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—31no—
724C2×C8—31no—
725C2×C8—62no—
726C4⋊C4—21no—
727C4⋊C4—31no—
728C4⋊C4—61no—
729C4⋊C4—61no—
730C4⋊C4C3×#6711yescharacteristic
731C4⋊C4C22×C3×D311yescharacteristic
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4C3×#6711yescharacteristic
739C22⋊C4C3×#6711yescharacteristic
740C42—21no—
741C42—61no—
742C42C22×C3×D311yescharacteristic
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3—121no—
783C22×C3C22×#6711yescharacteristic
784C22×C3C22×C3×D411yescharacteristic
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C3×C4—24no—
789C3×C4—22no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—22no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—22no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—42no—
806C3×C4—41no—
807C3×C4—41no—
808C3×C4—62no—
809C3×C4—121no—
810C3×C4—121no—
811C3×C4C2×D3×D411yescharacteristic
812C3×C4#100411yescharacteristic
813C3×C4C22×C3×D411yescharacteristic
814C3×C4C3×H(5,𝔽2)11yescharacteristic
815Dic3—22no—
816Dic3—41no—
817Dic3—41no—
818C32#327111yescharacteristic, complemented, Sylow
819C23—21no—
820C23—21no—
821C23—61no—
822C23C2×C3×#6711yescharacteristic
823C23C2×C3×#6711yescharacteristic
824Q8—21no—
825Q8—32no—
826Q8—61no—
827Q8—61no—
828Q8—61no—
829Q8—122no—
830Q8C3×D3×D412yes—
831D4—21no—
832D4—21no—
833D4—21no—
834D4—21no—
835D4—41no—
836D4—42no—
837D4—42no—
838D4—42no—
839D4—61no—
840D4—61no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—122no—
845D4—122no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4C2×C3×#6711yescharacteristic
860C2×C4C2×C3×#6711yescharacteristic
861C2×C4C2×C3×#6711yescharacteristic
862C2×C4C2×C3×#6711yescharacteristic
863C2×C4C23×C3×D311yescharacteristic
864C8—32no—
865C8—61no—
866C8—61no—
867C8—61no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—41no—
872C2×C3—41no—
873C2×C3—41no—
874C2×C3—41no—
875C2×C3—81no—
876C2×C3—81no—
877C2×C3—82no—
878C2×C3—82no—
879C2×C3—81no—
880C2×C3—81no—
881C2×C3—81no—
882C2×C3—81no—
883C2×C3—241no—
884C2×C3D4×#6711yescharacteristic
885C2×C3#582211yescharacteristic
886C2×C3#583611yescharacteristic
887C2×C3C3×D4211yescharacteristic
888C2×C3C3×#57511yescharacteristic
889C2×C3C3×#57711yescharacteristic
890D3—81no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22C22×C3×#6711yescharacteristic
907C4—21no—
908C4—21no—
909C4—22no—
910C4—21no—
911C4—21no—
912C4—41no—
913C4—62no—
914C4—121no—
915C4—121no—
916C4C2×C3×D3×D411yescharacteristic
917C4C3×#100411yescharacteristic
918C3—21no—
919C3#8358311yescharacteristic, direct product factor
920C3C3×#327111yescharacteristic, complemented
921C2—41no—
922C2—41no—
923C2—81no—
924C2—81no—
925C2—241no—
926C2C3×D4×#6711yescharacteristic
927C2C3×#582211yescharacteristic
928C2C3×#583611yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#550C2
socleC22×C32C22×D4
hypercenterC3×#550D3
hypocenterC3C3×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#550

Complements

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

NH ≅ G/Ntype
1. C32×#550C2semidirect
2. C2×C3×#951C2semidirect
3. C2×C3×#950C2semidirect
4. C3×#5552C2semidirect
5. C3×#5239C2semidirect
6. C3×#5238C2semidirect
7. C3×#5075C2semidirect
8. C3×#5074C2semidirect
9. C3×#5041C2semidirect
10. C3×#5040C2semidirect
11. C3×#5039C2semidirect
12. C3×#5037C2semidirect
13. C3×#5030C2semidirect
14. C3×#5028C2semidirect
15. C3×#5011C2semidirect
17. #83583C3direct (N × H)
66. C3×#550D3semidirect
67. C3×#550C2×C3semidirect
69. C2×#951C2×C3semidirect
70. C2×#950C2×C3semidirect
71. #5552C2×C3semidirect
83. #5239C2×C3semidirect
84. #5238C2×C3semidirect
85. #5075C2×C3semidirect
86. #5074C2×C3semidirect
87. #5041C2×C3semidirect
88. #5040C2×C3semidirect
89. #5039C2×C3semidirect
90. #5037C2×C3semidirect
91. #5030C2×C3semidirect
92. #5028C2×C3semidirect
93. #5011C2×C3semidirect
135. C3×#216D4semidirect
309. #550C3×D3semidirect
452. #216C3×D4semidirect
818. C32#3271semidirect
919. C3#83583direct (N × H)
920. C3C3×#3271semidirect

Maximal subgroups

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

subgroupindex
C32×#5502
C2×C3×#9512
C2×C3×#9502
C3×#55522
C3×#52392
C3×#52382
C3×#50752
C3×#50742
C3×#50412
C3×#50402
C3×#50392
C3×#50372
C3×#50302
C3×#50282
C3×#50112
C3×#32713
#835833