Finite Group Databasebeta

← C3×#83866 #11884068

Subgroups — C3×#83866 #11884068

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×SD16C211yesmaximal, characteristic, complemented
2C3×Q8×#67C211yesmaximal, characteristic, complemented
3C3×#5806C211yesmaximal, characteristic
4C2×C3×#915C211yesmaximal, characteristic, complemented
5C3×#5228C211yesmaximal, characteristic, complemented
6C3×#5218C211yesmaximal, characteristic, complemented
7C3×#5174C211yesmaximal, characteristic, complemented
8C3×#5173C211yesmaximal, characteristic, complemented
9C3×#5170C211yesmaximal, characteristic, complemented
10C3×#5167C211yesmaximal, characteristic, complemented
11C3×#5166C211yesmaximal, characteristic, complemented
12C3×#5164C211yesmaximal, characteristic, complemented
13C3×#5162C211yesmaximal, characteristic, complemented
14C3×#5116C211yesmaximal, characteristic, complemented
15C3×#5111C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#83866C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C2×C3×#237C2211yescharacteristic
22C2×C32×SD16—24no—
23C2×C32×SD16C2211yescharacteristic
24C2×C32×SD16C2211yescharacteristic
25C2×C32×SD16C2211yescharacteristic
26C2×C32×SD16C2211yescharacteristic
27C22×C32×C8C2211yescharacteristic
28C3×#953—21no—
29C2×C3×#217—21no—
30C3×#946—21no—
31C3×#946C2211yescharacteristic, complemented
32C3×Q8×Dic3C2211yescharacteristic, complemented
33C3×#944—21no—
34C3×#944C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×#216C2211yescharacteristic, complemented
37C3×#939—21no—
38C3×#938C2211yescharacteristic
39C3×#936C2211yescharacteristic
40C3×#935—21no—
41C3×D4×Dic3C2211yescharacteristic
42C2×C3×#214C2211yescharacteristic
43C2×C3×#214C2211yescharacteristic
44C3×C4×#67—21no—
45C3×C4×#67C2211yescharacteristic
46C3×#924—21no—
47C3×#924C2211yescharacteristic
48C3×#924C2211yescharacteristic
49C3×#915—24no—
50C2×C3×Dic12C2211yescharacteristic, complemented
51C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic
55C3×#832C2211yescharacteristic
56C3×#830C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#818C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61C3×#815C2211yescharacteristic, complemented
62C3×Dic3⋊C8C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—21no—
65C22×C3×SD16D311yescharacteristic, complemented
66C22×C3×SD16C2×C311yescharacteristic, complemented
67C3×D4×Q8—31no—
68C3×#546—31no—
69Q8×#67C2×C311yescharacteristic, complemented
70#5806C2×C311yescharacteristic
71C2×#915C2×C311yescharacteristic, complemented
72C3×#497—31no—
73C3×#468—31no—
74C3×#467—31no—
75C3×#464—31no—
76C3×#461—31no—
77C3×#452—31no—
78C3×#451—31no—
79C3×#450—31no—
80C3×#448—31no—
81C3×#440—31no—
82C3×#435—31no—
83#5228C2×C311yescharacteristic, complemented
84#5218C2×C311yescharacteristic, complemented
85#5174C2×C311yescharacteristic, complemented
86#5173C2×C311yescharacteristic, complemented
87#5170C2×C311yescharacteristic, complemented
88#5167C2×C311yescharacteristic, complemented
89#5166C2×C311yescharacteristic, complemented
90#5164C2×C311yescharacteristic, complemented
91#5162C2×C311yescharacteristic, complemented
92#5116C2×C311yescharacteristic, complemented
93#5111C2×C311yescharacteristic, complemented
94C24×C32—21no—
95C2×C32×Q8—21no—
96C2×C32×Q8—22no—
97C2×C32×Q8—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4—22no—
101C2×C32×D4—21no—
102C2×C32×D4—41no—
103C2×C32×D4C2311yescharacteristic
104C2×C32×D4C2311yescharacteristic
105C22×C32×C4—21no—
106C22×C32×C4C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C3×D3×Q8—22no—
113C3×D3×Q8—41no—
114C3×#237—22no—
115C3×#237—41no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×SD16—22no—
122C32×SD16—22no—
123C32×SD16—22no—
124C32×SD16D414yescomplemented
125C2×C32×C8—22no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×#217D411yescharacteristic
135C3×#216—22no—
136C3×#216—41no—
137C3×#214—22no—
138C3×#214—41no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4—21no—
149C3×Dic3⋊C4D411yescharacteristic
150C3×C4×Dic3—21no—
151C3×C4×Dic3C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C3×Dic12—22no—
155C3×ΓL(1,𝔽25)—22no—
156#3266—31noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—21no—
159C22×C3×Q8—31no—
160C22×C3×Q8C2×D311yescharacteristic
161C22×C3×Q8C22×C311yescharacteristic
162C22×C3×D4—21no—
163C22×C3×D4C2×D311yescharacteristic
164C22×C3×D4C22×C311yescharacteristic
165C2×D3×Q8C22×C311yescharacteristic, complemented
166C2×#237C22×C311yescharacteristic
167C3×#137—64no—
168C2×C3×Q16—31no—
169C2×C3×Q16—31no—
170C2×C3×Q16—31no—
171C2×C3×SD16—28no—
172C2×C3×SD16—24no—
173C2×C3×SD16—24no—
174C2×C3×SD16—21no—
175C2×C3×SD16—21no—
176C2×C3×SD16—21no—
177C2×C3×SD16—21no—
178C2×C3×SD16—31no—
179C2×C3×SD16—31no—
180C2×C3×SD16C2×D311yescharacteristic
181C2×C3×SD16C2×D311yescharacteristic
182C2×C3×SD16C2×D311yescharacteristic
183C2×C3×SD16C2×D311yescharacteristic
184C2×C3×SD16C22×C311yescharacteristic
185C2×C3×SD16C22×C311yescharacteristic
186C2×C3×SD16C22×C311yescharacteristic
187C2×C3×SD16C22×C311yescharacteristic
188C2×C3×M16—31no—
189C22×C3×C8—21no—
190C22×C3×C8C2×D311yescharacteristic
191C22×C3×C8C22×C311yescharacteristic
192C3×C4⋊Q8—31no—
193C3×C4⋊Q8—61no—
194C3×#124—31no—
195C3×#123—61no—
196C3×C22⋊Q8—31no—
197C3×C22⋊Q8—31no—
198C3×C22⋊Q8—31no—
199C3×C22⋊Q8—61no—
200C3×C22⋊Q8—61no—
201C3×#121—31no—
202C3×#121—61no—
203C3×#120—61no—
204C3×C4×Q8—31no—
205C3×C4×D4—31no—
206C3×C4×D4—31no—
207C3×C4×D4—61no—
208C2×C3×C22⋊C4—61no—
209#953—21no—
210C2×#217—21no—
211#946—21no—
212#946C22×C311yescharacteristic, complemented
213Q8×Dic3C22×C311yescharacteristic, complemented
214#944—21no—
215#944C22×C311yescharacteristic, complemented
216C2×#216C22×C311yescharacteristic, complemented
217C2×#216C22×C311yescharacteristic, complemented
218#939—21no—
219#938C22×C311yescharacteristic
220#936C22×C311yescharacteristic
221#935—21no—
222D4×Dic3C22×C311yescharacteristic
223C2×#214C22×C311yescharacteristic
224C2×#214C22×C311yescharacteristic
225C4×#67—21no—
226C4×#67C22×C311yescharacteristic
227#924—21no—
228#924C22×C311yescharacteristic
229#924C22×C311yescharacteristic
230#915—24no—
231C2×Dic12C22×C311yescharacteristic, complemented
232C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
233C3×#107—31no—
234C3×C4⋊C8—31no—
235C3×#103—31no—
236C3×#103—31no—
237C3×#103—31no—
238C3×#103—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×C22⋊C8—31no—
242C3×C22⋊C8—31no—
243C3×#97—31no—
244#835C22×C311yescharacteristic, complemented
245#835C22×C311yescharacteristic, complemented
246#832C22×C311yescharacteristic
247#832C22×C311yescharacteristic
248#830C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic, complemented
250#818C22×C311yescharacteristic, complemented
251#816C22×C311yescharacteristic, complemented
252#816C22×C311yescharacteristic, complemented
253#815C22×C311yescharacteristic, complemented
254Dic3⋊C8C22×C311yescharacteristic, complemented
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—42no—
258C23×C32—42no—
259C23×C32—81no—
260C23×C32C2×D411yescharacteristic
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—42no—
266C32×Q8C2×D412yes—
267C32×D4—21no—
268C32×D4—21no—
269C32×D4—21no—
270C32×D4—42no—
271C32×D4C2×D412yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—42no—
277C2×C32×C4C2×D411yescharacteristic
278C2×C32×C4C2411yescharacteristic
279C3×#67—22no—
280C3×#67—42no—
281C3×#67—81no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—42no—
287C2×C3×Dic3—81no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—42no—
299C32×C8—21no—
300C32×C8C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×#137—31no—
304C22×SD16C3×D311yescharacteristic, complemented
305D4×Q8—31no—
306#546—31no—
307#497—31no—
308#468—31no—
309#467—31no—
310#464—31no—
311#461—31no—
312#452—31no—
313#451—31no—
314#450—31no—
315#448—31no—
316#440—31no—
317#435—31no—
318C24×C3—21no—
319C24×C3—21no—
320C24×C3—41no—
321C3×#41—62no—
322C3×#41—121no—
323C2×C3×Q8—21no—
324C2×C3×Q8—21no—
325C2×C3×Q8—24no—
326C2×C3×Q8—22no—
327C2×C3×Q8—22no—
328C2×C3×Q8—21no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8—31no—
332C2×C3×Q8—41no—
333C2×C3×Q8—41no—
334C2×C3×Q8—41no—
335C2×C3×Q8—42no—
336C2×C3×Q8—61no—
337C2×C3×Q8—62no—
338C2×C3×Q8—121no—
339C2×C3×Q8C22×D311yescharacteristic
340C2×C3×Q8C22×D311yescharacteristic
341C2×C3×Q8C23×C311yescharacteristic
342C2×C3×Q8C23×C311yescharacteristic
343C2×C3×D4—24no—
344C2×C3×D4—22no—
345C2×C3×D4—22no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—21no—
349C2×C3×D4—21no—
350C2×C3×D4—31no—
351C2×C3×D4—41no—
352C2×C3×D4—41no—
353C2×C3×D4—41no—
354C2×C3×D4—42no—
355C2×C3×D4—61no—
356C2×C3×D4—61no—
357C2×C3×D4C22×D311yescharacteristic
358C2×C3×D4C22×D311yescharacteristic
359C2×C3×D4C23×C311yescharacteristic
360C2×C3×D4C23×C311yescharacteristic
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—31no—
365C22×C3×C4—41no—
366C22×C3×C4—61no—
367C22×C3×C4—61no—
368C22×C3×C4—61no—
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C23×C311yescharacteristic
371C2×#67—21no—
372C2×#67—21no—
373C2×#67C3×D411yescharacteristic
374C22×Dic3—21no—
375C22×Dic3—21no—
376D3×Q8—22no—
377D3×Q8—41no—
378#237—22no—
379#237—41no—
380C2×C4×D3—21no—
381C2×C4×D3C23×C311yescharacteristic
382C2×Dic6—21no—
383C2×Dic6C23×C311yescharacteristic
384C2×Dic6C23×C311yescharacteristic
385C3×Q16—62no—
386C3×Q16—62no—
387C3×Q16—121no—
388C3×SD16—24no—
389C3×SD16—24no—
390C3×SD16—24no—
391C3×SD16—22no—
392C3×SD16—22no—
393C3×SD16—22no—
394C3×SD16—22no—
395C3×SD16—22no—
396C3×SD16—22no—
397C3×SD16—24no—
398C3×SD16—62no—
399C3×SD16—121no—
400C3×SD16#6714yescomplemented
401C3×SD16C3×D414yescomplemented
402C3×M16—62no—
403C2×C3×C8—24no—
404C2×C3×C8—22no—
405C2×C3×C8—22no—
406C2×C3×C8—21no—
407C2×C3×C8—21no—
408C2×C3×C8—31no—
409C2×C3×C8—31no—
410C2×C3×C8C22×D311yescharacteristic
411C2×C3×C8C22×D311yescharacteristic
412C2×C3×C8C23×C311yescharacteristic
413C2×C3×C8C23×C311yescharacteristic
414C3×C4⋊C4—31no—
415C3×C4⋊C4—31no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—61no—
418C3×C4⋊C4—61no—
419C3×C4⋊C4—61no—
420C3×C4⋊C4—61no—
421C3×C4⋊C4—61no—
422C3×C4⋊C4—61no—
423C3×C22⋊C4—31no—
424C3×C22⋊C4—31no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C42—31no—
433C3×C42—61no—
434#217—21no—
435#217—21no—
436#217—21no—
437#217—21no—
438#217—21no—
439#217—21no—
440#217C3×D411yescharacteristic
441#216—22no—
442#216—41no—
443#214—22no—
444#214—41no—
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4C3×D411yescharacteristic
447C4⋊Dic3—21no—
448C4⋊Dic3C23×C311yescharacteristic
449C4⋊Dic3C23×C311yescharacteristic
450Dic3⋊C4—21no—
451Dic3⋊C4—21no—
452Dic3⋊C4—21no—
453Dic3⋊C4—21no—
454Dic3⋊C4—21no—
455Dic3⋊C4C3×D411yescharacteristic
456C4×Dic3—21no—
457C4×Dic3C23×C311yescharacteristic
458C2×C3⋊C8C23×C311yescharacteristic
459C2×C3⋊C8C23×C311yescharacteristic
460Dic12—22no—
461ΓL(1,𝔽25)—22no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—84no—
471C22×C32#13712yescomplemented
472C22×C32C22×D411yescharacteristic
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C32×C4—21no—
477C32×C4—22no—
478C32×C4—41no—
479C32×C4C22×D411yescharacteristic
480C32×C4H(5,𝔽2)11yescharacteristic
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—41no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—31no—
489C22×Q8—31no—
490C22×Q8C2×C3×D311yescharacteristic
491C22×D4C2×C3×D311yescharacteristic
492#137—64no—
493C2×Q16—31no—
494C2×Q16—31no—
495C2×Q16—31no—
496C2×SD16—24no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16C2×C3×D311yescharacteristic
500C2×SD16C2×C3×D311yescharacteristic
501C2×SD16C2×C3×D311yescharacteristic
502C2×SD16C2×C3×D311yescharacteristic
503C2×M16—31no—
504C22×C8C2×C3×D311yescharacteristic
505C4⋊Q8—31no—
506C4⋊Q8—61no—
507#124—31no—
508#123—61no—
509C22⋊Q8—31no—
510C22⋊Q8—31no—
511C22⋊Q8—31no—
512C22⋊Q8—61no—
513C22⋊Q8—61no—
514#121—31no—
515#121—61no—
516#120—61no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—31no—
520C4×D4—61no—
521C2×C22⋊C4—61no—
522#107—31no—
523C4⋊C8—31no—
524#103—31no—
525#103—31no—
526#103—31no—
527#103—31no—
528#102—31no—
529#102—31no—
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—31no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—42no—
542C23×C3—42no—
543C23×C3—44no—
544C23×C3—42no—
545C23×C3—42no—
546C23×C3—82no—
547C23×C3—81no—
548C23×C3—81no—
549C23×C3—82no—
550C23×C3D3×D411yescharacteristic
551C23×C3C2×C3×D411yescharacteristic
552C22×D3C2×C3×D411yescharacteristic
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—22no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—22no—
561C3×Q8—41no—
562C3×Q8—41no—
563C3×Q8—42no—
564C3×Q8—42no—
565C3×Q8—44no—
566C3×Q8—61no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—61no—
570C3×Q8—122no—
571C3×Q8C2×#6712yes—
572C3×Q8C2×C3×D412yes—
573C3×D4—22no—
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—22no—
581C3×D4—41no—
582C3×D4—41no—
583C3×D4—42no—
584C3×D4—42no—
585C3×D4—44no—
586C3×D4—62no—
587C3×D4—122no—
588C3×D4—241no—
589C3×D4C2×#6712yes—
590C3×D4C2×C3×D412yes—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—31no—
604C2×C3×C4—31no—
605C2×C3×C4—31no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—42no—
609C2×C3×C4—42no—
610C2×C3×C4—44no—
611C2×C3×C4—61no—
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—241no—
620C2×C3×C4D3×D411yescharacteristic
621C2×C3×C4C2×C3×D411yescharacteristic
622C2×C3×C4C23×D311yescharacteristic
623C2×C3×C4C24×C311yescharacteristic
624#67—22no—
625#67—42no—
626#67—81no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—42no—
632C2×Dic3—81no—
633C2×Dic3C2×C3×D411yescharacteristic
634C2×Dic3C2×C3×D411yescharacteristic
635C2×Dic3C2×C3×D411yescharacteristic
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—42no—
639Dic6—21no—
640Dic6—21no—
641Dic6—21no—
642Dic6—21no—
643Dic6—42no—
644C3×C8—22no—
645C3×C8—21no—
646C3×C8—21no—
647C3×C8—22no—
648C3×C8—61no—
649C3×C8—61no—
650C3×C8C2×#6712yes—
651C3×C8C2×C3×D412yes—
652C3⋊C8—21no—
653C3⋊C8—21no—
654C2×C32—22no—
655C2×C32—42no—
656C2×C32—81no—
657C2×C32D4211yescharacteristic
658C2×C32C2×#13711yescharacteristic
659C2×C32#57711yescharacteristic
660C3×D3—41no—
661C24—21no—
662#41—62no—
663#41—121no—
664C2×Q8—21no—
665C2×Q8—22no—
666C2×Q8—31no—
667C2×Q8—31no—
668C2×Q8—41no—
669C2×Q8—61no—
670C2×Q8—62no—
671C2×Q8—121no—
672C2×Q8C22×C3×D311yescharacteristic
673C2×Q8C22×C3×D311yescharacteristic
674C2×D4—22no—
675C2×D4—21no—
676C2×D4—31no—
677C2×D4—41no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4C22×C3×D311yescharacteristic
681C2×D4C22×C3×D311yescharacteristic
682C22×C4—21no—
683C22×C4—31no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4C22×C3×D311yescharacteristic
688Q16—62no—
689Q16—62no—
690Q16—121no—
691SD16—22no—
692SD16—22no—
693SD16—22no—
694SD16—62no—
695SD16—121no—
696SD16C3×#6714yescomplemented
697M16—62no—
698C2×C8—22no—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8C22×C3×D311yescharacteristic
702C2×C8C22×C3×D311yescharacteristic
703C4⋊C4—31no—
704C4⋊C4—31no—
705C4⋊C4—31no—
706C4⋊C4—61no—
707C4⋊C4—61no—
708C4⋊C4—61no—
709C4⋊C4—61no—
710C4⋊C4—61no—
711C4⋊C4—61no—
712C22⋊C4—31no—
713C22⋊C4—31no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C42—31no—
722C42—61no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—21no—
733C22×C3—42no—
734C22×C3—42no—
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—61no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3—84no—
753C22×C3—84no—
754C22×C3—88no—
755C22×C3#91512yescomplemented
756C22×C3C3×#13712yescomplemented
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C22×C3×D411yescharacteristic
759C2×D3—21no—
760C2×D3—21no—
761C2×D3—21no—
762C3×C4—22no—
763C3×C4—21no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—42no—
770C3×C4—42no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—61no—
776C3×C4—121no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4#100411yescharacteristic
781C3×C4C22×#6711yescharacteristic
782C3×C4C22×C3×D411yescharacteristic
783C3×C4C3×H(5,𝔽2)11yescharacteristic
784Dic3—21no—
785Dic3—21no—
786Dic3—21no—
787Dic3—41no—
788Dic3—41no—
789Dic3—41no—
790Dic3—41no—
791C32#326611yescharacteristic, complemented, Sylow
792C23—21no—
793C23—21no—
794C23—31no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23C3×D3×D411yescharacteristic
799Q8—21no—
800Q8—21no—
801Q8—21no—
802Q8—42no—
803Q8—61no—
804Q8—61no—
805Q8—61no—
806Q8—61no—
807Q8—122no—
808Q8C2×C3×#6712yes—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—42no—
813D4—62no—
814D4—122no—
815D4—241no—
816D4C2×C3×#6712yes—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—31no—
822C2×C4—31no—
823C2×C4—31no—
824C2×C4—42no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—122no—
832C2×C4—122no—
833C2×C4—241no—
834C2×C4C3×D3×D411yescharacteristic
835C2×C4C23×C3×D311yescharacteristic
836C8—21no—
837C8—61no—
838C8—61no—
839C8C2×C3×#6712yes—
840C2×C3—24no—
841C2×C3—22no—
842C2×C3—22no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—42no—
847C2×C3—42no—
848C2×C3—82no—
849C2×C3—82no—
850C2×C3—81no—
851C2×C3—81no—
852C2×C3—121no—
853C2×C3C2×#91511yescharacteristic
854C2×C3#576211yescharacteristic
855C2×C3D4×#6711yescharacteristic
856C2×C3C3×D4211yescharacteristic
857C2×C3C2×C3×#13711yescharacteristic
858C2×C3C3×#57711yescharacteristic
859D3—41no—
860C22—21no—
861C22—21no—
862C22—22no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—84no—
872C22C3×#91512yescomplemented
873C22C2×C3×D3×D411yescharacteristic
874C4—21no—
875C4—22no—
876C4—41no—
877C4—61no—
878C4—61no—
879C4—61no—
880C4—121no—
881C4—121no—
882C4—121no—
883C4—121no—
884C4C3×#100411yescharacteristic
885C4C22×C3×#6711yescharacteristic
886C3—21no—
887C3#8386611yescharacteristic, direct product factor
888C3C3×#326611yescharacteristic, complemented
889C2—22no—
890C2—42no—
891C2—81no—
892C2—121no—
893C2C2×C3×#91511yescharacteristic
894C2C3×#576211yescharacteristic
895C2C3×D4×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC22×C32×SD16C2
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC22×C3×SD16D3
hypocenterC3C3×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C32×SD16C2semidirect
2. C3×Q8×#67C2semidirect
4. C2×C3×#915C2semidirect
5. C3×#5228C2semidirect
6. C3×#5218C2semidirect
7. C3×#5174C2semidirect
8. C3×#5173C2semidirect
9. C3×#5170C2semidirect
10. C3×#5167C2semidirect
11. C3×#5166C2semidirect
12. C3×#5164C2semidirect
13. C3×#5162C2semidirect
14. C3×#5116C2semidirect
15. C3×#5111C2semidirect
17. #83866C3direct (N × H)
20. C2×C3×D3×Q8C22semidirect
31. C3×#946C22semidirect
32. C3×Q8×Dic3C22semidirect
34. C3×#944C22semidirect
35. C2×C3×#216C22semidirect
36. C2×C3×#216C22semidirect
50. C2×C3×Dic12C22semidirect
51. C2×C3×ΓL(1,𝔽25)C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#818C22semidirect
59. C3×#816C22semidirect
60. C3×#816C22semidirect
61. C3×#815C22semidirect
62. C3×Dic3⋊C8C22semidirect
65. C22×C3×SD16D3semidirect
66. C22×C3×SD16C2×C3semidirect
69. Q8×#67C2×C3semidirect
71. C2×#915C2×C3semidirect
83. #5228C2×C3semidirect
84. #5218C2×C3semidirect
85. #5174C2×C3semidirect
86. #5173C2×C3semidirect
87. #5170C2×C3semidirect
88. #5167C2×C3semidirect
89. #5166C2×C3semidirect
90. #5164C2×C3semidirect
91. #5162C2×C3semidirect
92. #5116C2×C3semidirect
93. #5111C2×C3semidirect
124. C32×SD16D4semidirect
165. C2×D3×Q8C22×C3semidirect
212. #946C22×C3semidirect
213. Q8×Dic3C22×C3semidirect
215. #944C22×C3semidirect
216. C2×#216C22×C3semidirect
217. C2×#216C22×C3semidirect
231. C2×Dic12C22×C3semidirect
232. C2×ΓL(1,𝔽25)C22×C3semidirect
244. #835C22×C3semidirect
245. #835C22×C3semidirect
249. (C2×D3)⋊C8C22×C3semidirect
250. #818C22×C3semidirect
251. #816C22×C3semidirect
252. #816C22×C3semidirect
253. #815C22×C3semidirect
254. Dic3⋊C8C22×C3semidirect
304. C22×SD16C3×D3semidirect
400. C3×SD16#67semidirect
401. C3×SD16C3×D4semidirect
471. C22×C32#137semidirect
696. SD16C3×#67semidirect
755. C22×C3#915semidirect
756. C22×C3C3×#137semidirect
791. C32#3266semidirect
872. C22C3×#915semidirect
887. C3#83866direct (N × H)
888. C3C3×#3266semidirect

Maximal subgroups

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

subgroupindex
C22×C32×SD162
C3×Q8×#672
C3×#58062
C2×C3×#9152
C3×#52282
C3×#52182
C3×#51742
C3×#51732
C3×#51702
C3×#51672
C3×#51662
C3×#51642
C3×#51622
C3×#51162
C3×#51112
C3×#32663
#838663