Finite Group Databasebeta

← C3×#80013 #11884372

Subgroups — C3×#80013 #11884372

Order 1152.

1119 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C2×C3×#912C211yesmaximal, characteristic, complemented
4C3×#5599C211yesmaximal, characteristic, complemented
5C32×#447C211yesmaximal, characteristic, complemented
6C3×#5158C211yesmaximal, characteristic, complemented
7C3×#5154C211yesmaximal, characteristic, complemented
8C3×#5150C211yesmaximal, characteristic, complemented
9C3×#5042C211yesmaximal, characteristic, complemented
10C3×#4781C211yesmaximal, characteristic, complemented
11C3×#4775C211yesmaximal, characteristic, complemented
12C3×#4767C211yesmaximal, characteristic, complemented
13C3×#4757C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic, complemented
15C3×#4728C211yesmaximal, characteristic, complemented
16C3×#3268—31nomaximal
17#80013C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic, complemented
21C2×C3×#235C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic
23C2×C32×D8C2211yescharacteristic
24C32×#121C2211yescharacteristic
25C3×#953—21no—
26C2×C3×#217—21no—
27C3×#940—21no—
28C3×#940C2211yescharacteristic, complemented
29C3×#939—21no—
30C3×#939—21no—
31C3×#938C2211yescharacteristic
32C3×#936C2211yescharacteristic
33C3×#935—21no—
34C3×D4×Dic3C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C2×C3×#214C2211yescharacteristic, complemented
38C3×#932—24no—
39C2×C3×#213C2211yescharacteristic
40C2×C3×#213C2211yescharacteristic
41C3×C4×#67C2211yescharacteristic
42C3×#924C2211yescharacteristic
43C2×C3×#208C2211yescharacteristic
44C3×#912—24no—
45C2×C3×Dic12C2211yescharacteristic, complemented
46C2×C3×#204C2211yescharacteristic, complemented
47C2×C3×D3×C8C2211yescharacteristic, complemented
48C3×#895C2211yescharacteristic, complemented
49C3×#887C2211yescharacteristic, complemented
50C3×#884—21no—
51C3×#67⋊C4—21no—
52C32×#102C2211yescharacteristic
53C32×#102C2211yescharacteristic
54C32×C22⋊C8C2211yescharacteristic
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#815C2211yescharacteristic, complemented
60C3×Dic3⋊C8C2211yescharacteristic, complemented
61C3×#810C2211yescharacteristic, complemented
62C3×#807C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65C3×#550—31no—
66C3×#546—31no—
67#5806C2×C311yescharacteristic, complemented
68C2×#932C2×C311yescharacteristic, complemented
69C2×#912C2×C311yescharacteristic, complemented
70#5599C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#468—31no—
73C3×#466—31no—
74C3×#464—31no—
75C3×#459—31no—
76C3×#452—31no—
77C3×#449—31no—
78C3×#449—31no—
79C3×#447—21no—
80C3×#447D311yescharacteristic, complemented
81C3×#447C2×C311yescharacteristic, complemented
82C3×#440—31no—
83C3×#435—31no—
84#5158C2×C311yescharacteristic, complemented
85#5154C2×C311yescharacteristic, complemented
86#5150C2×C311yescharacteristic, complemented
87#5042C2×C311yescharacteristic, complemented
88#4781C2×C311yescharacteristic, complemented
89#4775C2×C311yescharacteristic, complemented
90#4767C2×C311yescharacteristic, complemented
91#4757C2×C311yescharacteristic, complemented
92#4733C2×C311yescharacteristic, complemented
93#4728C2×C311yescharacteristic, complemented
94C24×C32—21no—
95C2×C32×D4—22no—
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4—41no—
99C2×C32×D4C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C22×C3×Dic3—21no—
113C3×#237—22no—
114C3×#237—22no—
115C3×#237—41no—
116C3×#237—41no—
117C3×#235—22no—
118C3×#235—41no—
119C2×C3×D12—21no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic
125C32×D8—22no—
126C32×D8—41no—
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129C32×C4⋊C4C2311yescharacteristic
130C32×C22⋊C4—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#217D411yescharacteristic
137C3×#214—22no—
138C3×#214—22no—
139C3×#214D414yescomplemented
140C3×#213—22no—
141C3×#213—22no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4D411yescharacteristic
144C3×C4⋊Dic3C2311yescharacteristic
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4D411yescharacteristic
148C3×C4×Dic3—21no—
149C3×C4×Dic3C2311yescharacteristic
150C3×#208—22no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×Dic12—22no—
154C3×#204—41no—
155C3×D3×C8—22no—
156#3268—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×D4—21no—
161C22×C3×D4C2×D311yescharacteristic
162C22×C3×D4C22×C311yescharacteristic
163C2×#237C22×C311yescharacteristic
164C2×#237C22×C311yescharacteristic, complemented
165C2×#235C22×C311yescharacteristic
166C3×AGL(1,ℤ/8)—64no—
167C3×#135—64no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×D8—21no—
174C2×C3×D8—21no—
175C2×C3×D8—31no—
176C2×C3×D8—31no—
177C2×C3×D8C2×D311yescharacteristic
178C2×C3×D8C2×D311yescharacteristic
179C2×C3×D8C22×C311yescharacteristic
180C2×C3×D8C22×C311yescharacteristic
181C2×C3×M16—31no—
182C22×C3×C8—31no—
183C3×#127—31no—
184C3×#127—61no—
185C3×#124—31no—
186C3×#123—61no—
187C3×C22⋊Q8—31no—
188C3×#121—21no—
189C3×#121—31no—
190C3×#121—31no—
191C3×#121—61no—
192C3×#121—61no—
193C3×#121—61no—
194C3×#121C2×D311yescharacteristic
195C3×#121C22×C311yescharacteristic
196C3×#120—61no—
197C3×C4×Q8—31no—
198C3×C4×D4—31no—
199C3×C4×D4—31no—
200C3×C4×D4—61no—
201C2×C3×C22⋊C4—61no—
202#953—21no—
203C2×#217—21no—
204#940—21no—
205#940C22×C311yescharacteristic, complemented
206#939—21no—
207#939—21no—
208#938C22×C311yescharacteristic
209#936C22×C311yescharacteristic
210#935—21no—
211D4×Dic3C22×C311yescharacteristic
212C2×#214C22×C311yescharacteristic
213C2×#214C22×C311yescharacteristic
214C2×#214C22×C311yescharacteristic, complemented
215#932—24no—
216C2×#213C22×C311yescharacteristic
217C2×#213C22×C311yescharacteristic
218C4×#67C22×C311yescharacteristic
219#924C22×C311yescharacteristic
220C2×#208C22×C311yescharacteristic
221#912—24no—
222C2×Dic12C22×C311yescharacteristic, complemented
223C2×#204C22×C311yescharacteristic, complemented
224C2×D3×C8C22×C311yescharacteristic, complemented
225#895C22×C311yescharacteristic, complemented
226#887C22×C311yescharacteristic, complemented
227#884—21no—
228#67⋊C4—21no—
229C3×#107—31no—
230C3×C4⋊C8—31no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#102—21no—
234C3×#102—21no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102C2×D311yescharacteristic
238C3×#102C2×D311yescharacteristic
239C3×#102C22×C311yescharacteristic
240C3×#102C22×C311yescharacteristic
241C3×C22⋊C8—21no—
242C3×C22⋊C8—31no—
243C3×C22⋊C8C2×D311yescharacteristic
244C3×C22⋊C8C22×C311yescharacteristic
245C3×#97—31no—
246#832C22×C311yescharacteristic, complemented
247#821C22×C311yescharacteristic, complemented
248(C2×D3)⋊C8C22×C311yescharacteristic, complemented
249#816C22×C311yescharacteristic, complemented
250#815C22×C311yescharacteristic, complemented
251Dic3⋊C8C22×C311yescharacteristic, complemented
252#810C22×C311yescharacteristic, complemented
253#807C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—42no—
258C23×C32—42no—
259C23×C32—81no—
260C23×C32C2×D411yescharacteristic
261C22×C3×D3—21no—
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—21no—
273C2×C32×C4—21no—
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276C3×#67—41no—
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—42no—
280C3×#67—42no—
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×Dic3—81no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—81no—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—42no—
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#459—31no—
315#452—31no—
316#449—31no—
317#449—31no—
318#447C3×D311yescharacteristic, complemented
319#440—31no—
320#435—31no—
321C24×C3—21no—
322C24×C3—21no—
323C24×C3—41no—
324C3×#41—62no—
325C3×#41—62no—
326C3×#41—62no—
327C3×#41—121no—
328C3×#41—121no—
329C3×#41—121no—
330C2×C3×Q8—31no—
331C2×C3×Q8—31no—
332C2×C3×D4—22no—
333C2×C3×D4—22no—
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—21no—
341C2×C3×D4—31no—
342C2×C3×D4—31no—
343C2×C3×D4—41no—
344C2×C3×D4—42no—
345C2×C3×D4—41no—
346C2×C3×D4—41no—
347C2×C3×D4—41no—
348C2×C3×D4—42no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C2×C3×D4—61no—
353C2×C3×D4—61no—
354C2×C3×D4—61no—
355C2×C3×D4—61no—
356C2×C3×D4C22×D311yescharacteristic
357C2×C3×D4C22×D311yescharacteristic
358C2×C3×D4C22×D311yescharacteristic
359C2×C3×D4C23×C311yescharacteristic
360C2×C3×D4C23×C311yescharacteristic
361C2×C3×D4C23×C311yescharacteristic
362C22×C3×C4—21no—
363C22×C3×C4—31no—
364C22×C3×C4—61no—
365C22×C3×C4—61no—
366C22×C3×C4—61no—
367C22×C3×C4—61no—
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C23×C311yescharacteristic
370C2×#67—21no—
371C2×#67—21no—
372C2×#67—21no—
373C2×#67—21no—
374C2×#67—21no—
375C2×#67—21no—
376C2×#67C3×D411yescharacteristic
377C22×Dic3—21no—
378C22×Dic3—21no—
379C22×Dic3—21no—
380#237—22no—
381#237—22no—
382#237—41no—
383#237—41no—
384#235—22no—
385#235—41no—
386C2×D12—21no—
387C2×D12C23×C311yescharacteristic
388C2×C4×D3—21no—
389C2×C4×D3C23×C311yescharacteristic
390C2×Dic6C23×C311yescharacteristic
391C2×Dic6C23×C311yescharacteristic
392C3×Q16—62no—
393C3×SD16—34no—
394C3×SD16—62no—
395C3×SD16—62no—
396C3×SD16—121no—
397C3×D8—22no—
398C3×D8—22no—
399C3×D8—42no—
400C3×D8—41no—
401C3×D8—41no—
402C3×D8—42no—
403C3×D8—62no—
404C3×D8—62no—
405C3×M16—62no—
406C2×C3×C8—21no—
407C2×C3×C8—21no—
408C2×C3×C8—31no—
409C2×C3×C8—31no—
410C2×C3×C8—62no—
411C2×C3×C8C22×D311yescharacteristic
412C2×C3×C8C22×D311yescharacteristic
413C2×C3×C8C23×C311yescharacteristic
414C2×C3×C8C23×C311yescharacteristic
415C3×C4⋊C4—21no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—61no—
419C3×C4⋊C4—61no—
420C3×C4⋊C4C22×D311yescharacteristic
421C3×C4⋊C4C23×C311yescharacteristic
422C3×C22⋊C4—21no—
423C3×C22⋊C4—21no—
424C3×C22⋊C4—31no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—41no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C22⋊C4—61no—
433C3×C42—31no—
434C3×C42—61no—
435#217—21no—
436#217—21no—
437#217—21no—
438#217—21no—
439#217—21no—
440#217C3×D411yescharacteristic
441#214—22no—
442#214—22no—
443#214C3×D414yescomplemented
444#213—22no—
445#213—22no—
446(C2×D3)⋊C4—21no—
447(C2×D3)⋊C4C3×D411yescharacteristic
448C4⋊Dic3C23×C311yescharacteristic
449Dic3⋊C4—21no—
450Dic3⋊C4—21no—
451Dic3⋊C4C3×D411yescharacteristic
452C4×Dic3—21no—
453C4×Dic3C23×C311yescharacteristic
454#208—22no—
455C2×C3⋊C8C23×C311yescharacteristic
456C2×C3⋊C8C23×C311yescharacteristic
457Dic12—22no—
458#204—41no—
459D3×C8—22no—
460C22×C32—21no—
461C22×C32—22no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—84no—
473C22×C32C22×D411yescharacteristic
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C32×C4—21no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3×Dic3—22no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—31no—
492C2×#41—31no—
493C22×D4C2×C3×D311yescharacteristic
494AGL(1,ℤ/8)—64no—
495#135—64no—
496C2×Q16—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16—31no—
500C2×SD16—31no—
501C2×D8—31no—
502C2×D8—31no—
503C2×D8C2×C3×D311yescharacteristic
504C2×D8C2×C3×D311yescharacteristic
505C2×M16—31no—
506C22×C8—31no—
507#127—31no—
508#127—61no—
509#124—31no—
510#123—61no—
511C22⋊Q8—31no—
512#121—31no—
513#121—31no—
514#121—61no—
515#121—61no—
516#121—61no—
517#121C2×C3×D311yescharacteristic
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#102C2×C3×D311yescharacteristic
531#102C2×C3×D311yescharacteristic
532C22⋊C8—31no—
533C22⋊C8C2×C3×D311yescharacteristic
534#97—31no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—31no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—42no—
547C23×C3—42no—
548C23×C3—42no—
549C23×C3—42no—
550C23×C3—44no—
551C23×C3—61no—
552C23×C3—82no—
553C23×C3—81no—
554C23×C3—81no—
555C23×C3—82no—
556C23×C3D3×D411yescharacteristic
557C23×C3C2×C3×D411yescharacteristic
558C22×D3—21no—
559C22×D3C2×C3×D411yescharacteristic
560C3×Q8—32no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×Q8—61no—
564C3×D4—22no—
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—22no—
576C3×D4—41no—
577C3×D4—41no—
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—42no—
581C3×D4—42no—
582C3×D4—44no—
583C3×D4—61no—
584C3×D4—61no—
585C3×D4—81no—
586C3×D4—81no—
587C3×D4—82no—
588C3×D4—121no—
589C3×D4—122no—
590C3×D4—122no—
591C3×D4—122no—
592C3×D4—122no—
593C3×D4—241no—
594C3×D4—241no—
595C3×D4—241no—
596C3×D4D3×D412yes—
597C3×D4C2×C3×D412yes—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—31no—
607C2×C3×C4—31no—
608C2×C3×C4—31no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—122no—
618C2×C3×C4—122no—
619C2×C3×C4—122no—
620C2×C3×C4—241no—
621C2×C3×C4D3×D411yescharacteristic
622C2×C3×C4C2×C3×D411yescharacteristic
623C2×C3×C4C23×D311yescharacteristic
624C2×C3×C4C24×C311yescharacteristic
625#67—41no—
626#67—42no—
627#67—42no—
628#67—42no—
629#67—42no—
630#67—81no—
631#67—81no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—42no—
636C2×Dic3—42no—
637C2×Dic3—81no—
638C2×Dic3C2×C3×D411yescharacteristic
639C2×Dic3C2×C3×D411yescharacteristic
640C2×Dic3C2×C3×D411yescharacteristic
641D12—21no—
642D12—21no—
643D12—81no—
644C4×D3—21no—
645C4×D3—21no—
646C4×D3—42no—
647Dic6—21no—
648Dic6—21no—
649Dic6—21no—
650Dic6C2×C3×D412yes—
651C3×C8—21no—
652C3×C8—21no—
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—32no—
656C3×C8—41no—
657C3×C8—41no—
658C3×C8—61no—
659C3⋊C8—21no—
660C3⋊C8C2×C3×D412yes—
661C2×C32—41no—
662C2×C32—42no—
663C2×C32—81no—
664C2×C32—81no—
665C2×C32D4211yescharacteristic
666C2×C32#57511yescharacteristic
667C2×C32#57611yescharacteristic
668C3×D3—41no—
669C3×D3—81no—
670C24—21no—
671#41—62no—
672#41—62no—
673#41—62no—
674#41—121no—
675#41—121no—
676#41—121no—
677C2×Q8—31no—
678C2×Q8—31no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—41no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4C22×C3×D311yescharacteristic
693C2×D4C22×C3×D311yescharacteristic
694C2×D4C22×C3×D311yescharacteristic
695C22×C4—31no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4C22×C3×D311yescharacteristic
701Q16—62no—
702SD16—34no—
703SD16—62no—
704SD16—62no—
705SD16—121no—
706D8—22no—
707D8—41no—
708D8—62no—
709D8—62no—
710M16—62no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—62no—
714C2×C8C22×C3×D311yescharacteristic
715C2×C8C22×C3×D311yescharacteristic
716C4⋊C4—31no—
717C4⋊C4—31no—
718C4⋊C4—61no—
719C4⋊C4—61no—
720C4⋊C4C22×C3×D311yescharacteristic
721C22⋊C4—21no—
722C22⋊C4—31no—
723C22⋊C4—31no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C42—31no—
731C42—61no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—42no—
745C22×C3—42no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—61no—
763C22×C3—61no—
764C22×C3—61no—
765C22×C3—81no—
766C22×C3—81no—
767C22×C3—81no—
768C22×C3—81no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—84no—
773C22×C3—84no—
774C22×C3—88no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3C2×D3×D411yescharacteristic
779C22×C3C22×C3×D411yescharacteristic
780C2×D3—21no—
781C2×D3—21no—
782C2×D3—21no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—61no—
794C3×C4—61no—
795C3×C4—61no—
796C3×C4—62no—
797C3×C4—81no—
798C3×C4—121no—
799C3×C4—121no—
800C3×C4C2×D3×D411yescharacteristic
801C3×C4#100411yescharacteristic
802C3×C4C22×C3×D411yescharacteristic
803C3×C4C3×H(5,𝔽2)11yescharacteristic
804Dic3—21no—
805Dic3—21no—
806Dic3—22no—
807Dic3—21no—
808Dic3—41no—
809Dic3—41no—
810C32#326811yescharacteristic, complemented, Sylow
811C23—21no—
812C23—21no—
813C23—21no—
814C23—31no—
815C23—42no—
816C23—42no—
817C23—61no—
818C23—81no—
819C23C3×D3×D411yescharacteristic
820Q8—32no—
821Q8—61no—
822Q8—61no—
823Q8—61no—
824D4—21no—
825D4—21no—
826D4—21no—
827D4—21no—
828D4—21no—
829D4—42no—
830D4—61no—
831D4—61no—
832D4—81no—
833D4—121no—
834D4—122no—
835D4—122no—
836D4—122no—
837D4—122no—
838D4—241no—
839D4—241no—
840D4—241no—
841D4C3×D3×D412yes—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—31no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—122no—
854C2×C4—122no—
855C2×C4—122no—
856C2×C4—241no—
857C2×C4C3×D3×D411yescharacteristic
858C2×C4C23×C3×D311yescharacteristic
859C8—21no—
860C8—21no—
861C8—32no—
862C8—61no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—42no—
867C2×C3—41no—
868C2×C3—42no—
869C2×C3—41no—
870C2×C3—42no—
871C2×C3—82no—
872C2×C3—82no—
873C2×C3—81no—
874C2×C3—81no—
875C2×C3—81no—
876C2×C3—81no—
877C2×C3—121no—
878C2×C3—161no—
879C2×C3—241no—
880C2×C3#559011yescharacteristic
881C2×C3#575711yescharacteristic
882C2×C3#577311yescharacteristic
883C2×C3C3×D4211yescharacteristic
884C2×C3C3×#57511yescharacteristic
885C2×C3C3×#57611yescharacteristic
886D3—41no—
887D3—81no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—61no—
901C22—61no—
902C22—61no—
903C22—84no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22C2×C3×D3×D411yescharacteristic
908C4—21no—
909C4—41no—
910C4—61no—
911C4—61no—
912C4—61no—
913C4—62no—
914C4—121no—
915C4—121no—
916C4C2×C3×D3×D411yescharacteristic
917C4C3×#100411yescharacteristic
918C3—21no—
919C3#8001311yescharacteristic, direct product factor
920C3C3×#326811yescharacteristic, complemented
921C2—41no—
922C2—42no—
923C2—81no—
924C2—81no—
925C2—121no—
926C2—241no—
927C2C3×#559011yescharacteristic
928C2C3×#575711yescharacteristic
929C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#447C2
socleC22×C32C22×D4
hypercenterC3×#447D3
hypocenterC3C3×#3268
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#447

Complements

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

NH ≅ G/Ntype
1. C3×#5806C2semidirect
2. C2×C3×#932C2semidirect
3. C2×C3×#912C2semidirect
4. C3×#5599C2semidirect
5. C32×#447C2semidirect
6. C3×#5158C2semidirect
7. C3×#5154C2semidirect
8. C3×#5150C2semidirect
9. C3×#5042C2semidirect
10. C3×#4781C2semidirect
11. C3×#4775C2semidirect
12. C3×#4767C2semidirect
13. C3×#4757C2semidirect
14. C3×#4733C2semidirect
15. C3×#4728C2semidirect
17. #80013C3direct (N × H)
20. C2×C3×#237C22semidirect
28. C3×#940C22semidirect
37. C2×C3×#214C22semidirect
45. C2×C3×Dic12C22semidirect
46. C2×C3×#204C22semidirect
47. C2×C3×D3×C8C22semidirect
48. C3×#895C22semidirect
49. C3×#887C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#815C22semidirect
60. C3×Dic3⋊C8C22semidirect
61. C3×#810C22semidirect
62. C3×#807C22semidirect
67. #5806C2×C3semidirect
68. C2×#932C2×C3semidirect
69. C2×#912C2×C3semidirect
70. #5599C2×C3semidirect
80. C3×#447D3semidirect
81. C3×#447C2×C3semidirect
84. #5158C2×C3semidirect
85. #5154C2×C3semidirect
86. #5150C2×C3semidirect
87. #5042C2×C3semidirect
88. #4781C2×C3semidirect
89. #4775C2×C3semidirect
90. #4767C2×C3semidirect
91. #4757C2×C3semidirect
92. #4733C2×C3semidirect
93. #4728C2×C3semidirect
139. C3×#214D4semidirect
164. C2×#237C22×C3semidirect
205. #940C22×C3semidirect
214. C2×#214C22×C3semidirect
222. C2×Dic12C22×C3semidirect
223. C2×#204C22×C3semidirect
224. C2×D3×C8C22×C3semidirect
225. #895C22×C3semidirect
226. #887C22×C3semidirect
246. #832C22×C3semidirect
247. #821C22×C3semidirect
248. (C2×D3)⋊C8C22×C3semidirect
249. #816C22×C3semidirect
250. #815C22×C3semidirect
251. Dic3⋊C8C22×C3semidirect
252. #810C22×C3semidirect
253. #807C22×C3semidirect
318. #447C3×D3semidirect
443. #214C3×D4semidirect
810. C32#3268semidirect
919. C3#80013direct (N × H)
920. C3C3×#3268semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
C2×C3×#9322
C2×C3×#9122
C3×#55992
C32×#4472
C3×#51582
C3×#51542
C3×#51502
C3×#50422
C3×#47812
C3×#47752
C3×#47672
C3×#47572
C3×#47332
C3×#47282
C3×#32683
#800133