Finite Group Databasebeta

← C3×#83987 #11884050

Subgroups — C3×#83987 #11884050

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic, complemented
2C3×#5829C211yesmaximal, characteristic
3C3×Q8×#67C211yesmaximal, characteristic, complemented
4C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6C3×#5227C211yesmaximal, characteristic, complemented
7C3×#5190C211yesmaximal, characteristic, complemented
8C3×#5188C211yesmaximal, characteristic, complemented
9C3×#5186C211yesmaximal, characteristic, complemented
10C3×#5185C211yesmaximal, characteristic, complemented
11C3×#5169C211yesmaximal, characteristic, complemented
12C3×#5164C211yesmaximal, characteristic, complemented
13C3×#5162C211yesmaximal, characteristic, complemented
14C3×#5134C211yesmaximal, characteristic, complemented
15C3×#5127C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#83987C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic, complemented
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C32×#137—24no—
23C2×C32×Q16C2211yescharacteristic, complemented
24C2×C32×Q16C2211yescharacteristic, complemented
25C2×C32×SD16C2211yescharacteristic
26C2×C32×SD16C2211yescharacteristic
27C2×C32×M16C2211yescharacteristic, complemented
28C3×#947C2211yescharacteristic
29C3×#946—21no—
30C3×#946C2211yescharacteristic
31C3×#946C2211yescharacteristic
32C3×Q8×Dic3C2211yescharacteristic, complemented
33C3×#944—21no—
34C3×#944C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic
37C2×C3×#215C2211yescharacteristic
38C3×#939—21no—
39C3×#937—21no—
40C3×D4×Dic3C2211yescharacteristic
41C2×C3×#214C2211yescharacteristic
42C3×#930C2211yescharacteristic
43C3×#929—21no—
44C3×C4×#67—21no—
45C3×C4×#67C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4—21no—
47C3×#924—21no—
48C3×#924C2211yescharacteristic, complemented
49C3×D3×SD16—24no—
50C2×C3×#204C2211yescharacteristic
51C2×C3×D3×C8C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#830C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic
59C3×#818C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61C3×#815C2211yescharacteristic, complemented
62C3×Dic3⋊C8C2211yescharacteristic, complemented
63C2×C3×#137—21no—
64C2×C3×#137D311yescharacteristic, complemented
65C2×C3×#137C2×C311yescharacteristic, complemented
66C22×C3×SD16—31no—
67C3×D4×Q8—31no—
68C3×#546—31no—
69#5829C2×C311yescharacteristic
70Q8×#67C2×C311yescharacteristic, complemented
71C2×D3×SD16C2×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#5239C2×C311yescharacteristic, complemented
84#5227C2×C311yescharacteristic, complemented
85#5190C2×C311yescharacteristic, complemented
86#5188C2×C311yescharacteristic, complemented
87#5186C2×C311yescharacteristic, complemented
88#5185C2×C311yescharacteristic, complemented
89#5169C2×C311yescharacteristic, complemented
90#5164C2×C311yescharacteristic, complemented
91#5162C2×C311yescharacteristic, complemented
92#5134C2×C311yescharacteristic, complemented
93#5127C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8—21no—
98C2×C32×Q8—22no—
99C2×C32×Q8—41no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×Q8C2311yescharacteristic
102C2×C32×Q8C2311yescharacteristic
103C2×C32×D4—21no—
104C2×C32×D4C2311yescharacteristic
105C22×C32×C4—21no—
106C22×C32×C4—21no—
107C22×C32×C4C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C22×C3×Dic3—21no—
112C3×D3×Q8—22no—
113C3×D3×Q8—41no—
114C3×D3×D4—22no—
115C3×D3×D4—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6—21no—
120C2×C3×Dic6C2311yescharacteristic
121C32×Q16—22no—
122C32×Q16—22no—
123C32×SD16—22no—
124C32×SD16D414yescomplemented
125C32×M16—22no—
126C2×C32×C8C2311yescharacteristic
127C2×C32×C8C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#216—41no—
132C3×#215—22no—
133C3×#215—41no—
134C3×#214—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
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×#204—22no—
155C3×D3×C8—22no—
156#3266—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C22×C311yescharacteristic
160C22×C3×Q8—21no—
161C22×C3×Q8—31no—
162C22×C3×Q8C2×D311yescharacteristic, complemented
163C22×C3×Q8C22×C311yescharacteristic, complemented
164C22×C3×D4—31no—
165C2×D3×Q8C22×C311yescharacteristic
166C2×D3×D4C22×C311yescharacteristic
167C3×#137—28no—
168C3×#137—24no—
169C3×#137—24no—
170C2×C3×Q16—21no—
171C2×C3×Q16—21no—
172C2×C3×Q16—31no—
173C2×C3×Q16C2×D311yescharacteristic, complemented
174C2×C3×Q16C2×D311yescharacteristic, complemented
175C2×C3×Q16C22×C311yescharacteristic, complemented
176C2×C3×Q16C22×C311yescharacteristic, complemented
177C2×C3×SD16—21no—
178C2×C3×SD16—21no—
179C2×C3×SD16—31no—
180C2×C3×SD16—31no—
181C2×C3×SD16—31no—
182C2×C3×SD16—31no—
183C2×C3×SD16—64no—
184C2×C3×SD16C2×D311yescharacteristic
185C2×C3×SD16C2×D311yescharacteristic
186C2×C3×SD16C22×C311yescharacteristic
187C2×C3×SD16C22×C311yescharacteristic
188C2×C3×M16—21no—
189C2×C3×M16C2×D311yescharacteristic, complemented
190C2×C3×M16C22×C311yescharacteristic, complemented
191C22×C3×C8—31no—
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#947C22×C311yescharacteristic
210#946—21no—
211#946C22×C311yescharacteristic
212#946C22×C311yescharacteristic
213Q8×Dic3C22×C311yescharacteristic, complemented
214#944—21no—
215#944C22×C311yescharacteristic, complemented
216C2×#216C22×C311yescharacteristic, complemented
217C2×#215C22×C311yescharacteristic
218C2×#215C22×C311yescharacteristic
219#939—21no—
220#937—21no—
221D4×Dic3C22×C311yescharacteristic
222C2×#214C22×C311yescharacteristic
223#930C22×C311yescharacteristic
224#929—21no—
225C4×#67—21no—
226C4×#67C22×C311yescharacteristic
227C2×(C2×D3)⋊C4—21no—
228#924—21no—
229#924C22×C311yescharacteristic, complemented
230D3×SD16—24no—
231C2×#204C22×C311yescharacteristic
232C2×D3×C8C22×C311yescharacteristic
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#835C22×C311yescharacteristic, complemented
247#832C22×C311yescharacteristic
248#830C22×C311yescharacteristic, complemented
249#821C22×C311yescharacteristic
250(C2×D3)⋊C8C22×C311yescharacteristic
251#818C22×C311yescharacteristic, complemented
252#816C22×C311yescharacteristic, complemented
253#815C22×C311yescharacteristic, complemented
254Dic3⋊C8C22×C311yescharacteristic, complemented
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C32×Q8—21no—
267C32×Q8—42no—
268C32×Q8C2×D412yes—
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—21no—
277C2×C32×C4—42no—
278C2×C32×C4—42no—
279C2×C32×C4C2×D411yescharacteristic
280C2×C32×C4C2411yescharacteristic
281C3×#67—22no—
282C3×#67—42no—
283C3×#67—81no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—81no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×D12—21no—
292C3×D12—21no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—42no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—42no—
299C32×C8—21no—
300C32×C8C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×#137C3×D311yescharacteristic, complemented
304C22×SD16—31no—
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—61no—
319C23×D3—21no—
320C3×#41—24no—
321C3×#41—22no—
322C3×#41—22no—
323C3×#41—41no—
324C3×#41—41no—
325C3×#41—42no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×Q8—24no—
329C2×C3×Q8—22no—
330C2×C3×Q8—22no—
331C2×C3×Q8—21no—
332C2×C3×Q8—21no—
333C2×C3×Q8—21no—
334C2×C3×Q8—31no—
335C2×C3×Q8—41no—
336C2×C3×Q8—41no—
337C2×C3×Q8—41no—
338C2×C3×Q8—42no—
339C2×C3×Q8—61no—
340C2×C3×Q8—62no—
341C2×C3×Q8—121no—
342C2×C3×Q8C22×D311yescharacteristic
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×Q8C22×D311yescharacteristic
345C2×C3×Q8C23×C311yescharacteristic
346C2×C3×Q8C23×C311yescharacteristic
347C2×C3×Q8C23×C311yescharacteristic
348C2×C3×D4—21no—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—31no—
352C2×C3×D4—31no—
353C2×C3×D4—41no—
354C2×C3×D4—61no—
355C2×C3×D4—62no—
356C2×C3×D4—61no—
357C2×C3×D4—121no—
358C2×C3×D4C22×D311yescharacteristic
359C2×C3×D4C23×C311yescharacteristic
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—31no—
366C22×C3×C4—41no—
367C22×C3×C4—41no—
368C22×C3×C4—61no—
369C22×C3×C4—61no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C23×C311yescharacteristic
372C2×#67—21no—
373C2×#67—21no—
374C2×#67C3×D411yescharacteristic
375C22×Dic3—21no—
376D3×Q8—22no—
377D3×Q8—41no—
378D3×D4—22no—
379D3×D4—41no—
380C2×D12C23×C311yescharacteristic
381C2×C4×D3—21no—
382C2×C4×D3C23×C311yescharacteristic
383C2×Dic6—21no—
384C2×Dic6C23×C311yescharacteristic
385C3×Q16—24no—
386C3×Q16—24no—
387C3×Q16—22no—
388C3×Q16—22no—
389C3×Q16—22no—
390C3×Q16—22no—
391C3×Q16—121no—
392C3×SD16—24no—
393C3×SD16—22no—
394C3×SD16—22no—
395C3×SD16—24no—
396C3×SD16—62no—
397C3×SD16—62no—
398C3×SD16—62no—
399C3×SD16—121no—
400C3×SD16#6714yescomplemented
401C3×SD16C3×D414yescomplemented
402C3×M16—24no—
403C3×M16—22no—
404C3×M16—22no—
405C2×C3×C8—21no—
406C2×C3×C8—21no—
407C2×C3×C8—31no—
408C2×C3×C8—31no—
409C2×C3×C8—62no—
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#217C3×D411yescharacteristic
437#216—41no—
438#215—22no—
439#215—41no—
440#214—22no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4—21no—
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
460#204—22no—
461D3×C8—22no—
462C22×C32—21no—
463C22×C32—22no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—84no—
475C2×C3×D3#13712yescomplemented
476C32×C4—21no—
477C32×C4—22no—
478C32×C4—41no—
479C32×C4—41no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—21no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41C2×C3×D311yescharacteristic
489C22×Q8—31no—
490C22×Q8C2×C3×D311yescharacteristic, complemented
491C22×D4—31no—
492#137—24no—
493C2×Q16—31no—
494C2×Q16C2×C3×D311yescharacteristic, complemented
495C2×Q16C2×C3×D311yescharacteristic, complemented
496C2×SD16—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16—31no—
500C2×SD16—64no—
501C2×SD16C2×C3×D311yescharacteristic
502C2×SD16C2×C3×D311yescharacteristic
503C2×M16C2×C3×D311yescharacteristic, complemented
504C22×C8—31no—
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—31no—
537C23×C3—41no—
538C23×C3—61no—
539C23×C3—122no—
540C23×C3—122no—
541C23×C3—241no—
542C23×C3D3×D411yescharacteristic
543C23×C3C2×C3×D411yescharacteristic
544C22×D3—21no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3—81no—
548C22×D3C2×C3×D411yescharacteristic
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—22no—
552C3×Q8—22no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—21no—
561C3×Q8—22no—
562C3×Q8—41no—
563C3×Q8—41no—
564C3×Q8—41no—
565C3×Q8—42no—
566C3×Q8—42no—
567C3×Q8—44no—
568C3×Q8—61no—
569C3×Q8—61no—
570C3×Q8—122no—
571C3×Q8C2×#6712yes—
572C3×Q8C2×C3×D412yes—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—22no—
576C3×D4—41no—
577C3×D4—42no—
578C3×D4—42no—
579C3×D4—44no—
580C3×D4—62no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—122no—
584C3×D4—241no—
585C3×D4C2×#6712yes—
586C3×D4C2×C3×D412yes—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
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—31no—
602C2×C3×C4—31no—
603C2×C3×C4—31no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—42no—
608C2×C3×C4—42no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—44no—
612C2×C3×C4—44no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
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—81no—
631C2×Dic3C2×C3×D411yescharacteristic
632C2×Dic3C2×C3×D411yescharacteristic
633C2×Dic3C2×C3×D411yescharacteristic
634D12—21no—
635D12—21no—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—42no—
639Dic6—21no—
640Dic6—21no—
641Dic6—42no—
642C3×C8—22no—
643C3×C8—21no—
644C3×C8—21no—
645C3×C8—22no—
646C3×C8—61no—
647C3×C8—61no—
648C3×C8C2×#6712yes—
649C3×C8C2×C3×D412yes—
650C3⋊C8—21no—
651C3⋊C8—21no—
652C2×C32—41no—
653C2×C32—42no—
654C2×C32D4211yescharacteristic
655C2×C32C2×#13711yescharacteristic
656C2×C32#57711yescharacteristic
657C3×D3—22no—
658C3×D3—81no—
659C24—61no—
660#41—22no—
661#41—41no—
662C2×Q8—21no—
663C2×Q8—22no—
664C2×Q8—31no—
665C2×Q8—41no—
666C2×Q8—61no—
667C2×Q8—62no—
668C2×Q8—121no—
669C2×Q8C22×C3×D311yescharacteristic
670C2×Q8C22×C3×D311yescharacteristic
671C2×Q8C22×C3×D311yescharacteristic
672C2×D4—21no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—61no—
676C2×D4—62no—
677C2×D4—61no—
678C2×D4—121no—
679C2×D4C22×C3×D311yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—31no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4C22×C3×D311yescharacteristic
686Q16—22no—
687Q16—22no—
688Q16—121no—
689SD16—22no—
690SD16—62no—
691SD16—62no—
692SD16—62no—
693SD16—121no—
694SD16C3×#6714yescomplemented
695M16—22no—
696C2×C8—31no—
697C2×C8—31no—
698C2×C8—62no—
699C2×C8C22×C3×D311yescharacteristic
700C2×C8C22×C3×D311yescharacteristic
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—31no—
704C4⋊C4—61no—
705C4⋊C4—61no—
706C4⋊C4—61no—
707C4⋊C4—61no—
708C4⋊C4—61no—
709C4⋊C4—61no—
710C22⋊C4—31no—
711C22⋊C4—31no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C42—31no—
720C42—61no—
721C22×C3—22no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—32no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—42no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—244no—
747C22×C3C2×D3×D411yescharacteristic
748C22×C3C22×C3×D411yescharacteristic
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—84no—
755C2×D3C3×#13712yescomplemented
756C3×C4—22no—
757C3×C4—21no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—42no—
764C3×C4—42no—
765C3×C4—42no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—41no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—61no—
773C3×C4—121no—
774C3×C4—121no—
775C3×C4—121no—
776C3×C4#100411yescharacteristic
777C3×C4C22×#6711yescharacteristic
778C3×C4C22×C3×D411yescharacteristic
779C3×C4C3×H(5,𝔽2)11yescharacteristic
780Dic3—21no—
781Dic3—21no—
782Dic3—21no—
783Dic3—41no—
784Dic3—41no—
785Dic3—41no—
786C32#326611yescharacteristic, complemented, Sylow
787C23—21no—
788C23—31no—
789C23—61no—
790C23—122no—
791C23—122no—
792C23—241no—
793C23C3×D3×D411yescharacteristic
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—21no—
798Q8—21no—
799Q8—42no—
800Q8—61no—
801Q8—61no—
802Q8—122no—
803Q8C2×C3×#6712yes—
804D4—21no—
805D4—42no—
806D4—62no—
807D4—61no—
808D4—61no—
809D4—122no—
810D4—241no—
811D4C2×C3×#6712yes—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—31no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—122no—
828C2×C4—241no—
829C2×C4C3×D3×D411yescharacteristic
830C2×C4C23×C3×D311yescharacteristic
831C8—21no—
832C8—61no—
833C8—61no—
834C8C2×C3×#6712yes—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—42no—
839C2×C3—41no—
840C2×C3—42no—
841C2×C3—42no—
842C2×C3—41no—
843C2×C3—62no—
844C2×C3—82no—
845C2×C3—241no—
846C2×C3D3×#13711yescharacteristic
847C2×C3#577811yescharacteristic
848C2×C3D4×#6711yescharacteristic
849C2×C3C3×D4211yescharacteristic
850C2×C3C2×C3×#13711yescharacteristic
851C2×C3C3×#57711yescharacteristic
852D3—22no—
853D3—81no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—22no—
858C22—32no—
859C22—41no—
860C22—41no—
861C22—61no—
862C22—61no—
863C22—121no—
864C22—121no—
865C22—121no—
866C22—244no—
867C22C2×C3×D3×D411yescharacteristic
868C4—21no—
869C4—22no—
870C4—41no—
871C4—41no—
872C4—61no—
873C4—61no—
874C4—61no—
875C4—121no—
876C4—121no—
877C4—121no—
878C4C3×#100411yescharacteristic
879C4C22×C3×#6711yescharacteristic
880C3—21no—
881C3#8398711yescharacteristic, direct product factor
882C3C3×#326611yescharacteristic, complemented
883C2—41no—
884C2—42no—
885C2—62no—
886C2—241no—
887C2C3×D3×#13711yescharacteristic
888C2C3×#577811yescharacteristic
889C2C3×D4×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
prime radicalC3×#5829C2
hypercenterC2×C3×#137D3
hypocenterC3C3×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
1. C2×C32×#137C2semidirect
3. C3×Q8×#67C2semidirect
4. C2×C3×D3×SD16C2semidirect
5. C3×#5239C2semidirect
6. C3×#5227C2semidirect
7. C3×#5190C2semidirect
8. C3×#5188C2semidirect
9. C3×#5186C2semidirect
10. C3×#5185C2semidirect
11. C3×#5169C2semidirect
12. C3×#5164C2semidirect
13. C3×#5162C2semidirect
14. C3×#5134C2semidirect
15. C3×#5127C2semidirect
17. #83987C3direct (N × H)
19. C22×C32×Q8C22semidirect
23. C2×C32×Q16C22semidirect
24. C2×C32×Q16C22semidirect
27. C2×C32×M16C22semidirect
32. C3×Q8×Dic3C22semidirect
34. C3×#944C22semidirect
35. C2×C3×#216C22semidirect
48. C3×#924C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#835C22semidirect
56. C3×#830C22semidirect
59. C3×#818C22semidirect
60. C3×#816C22semidirect
61. C3×#815C22semidirect
62. C3×Dic3⋊C8C22semidirect
64. C2×C3×#137D3semidirect
65. C2×C3×#137C2×C3semidirect
70. Q8×#67C2×C3semidirect
71. C2×D3×SD16C2×C3semidirect
83. #5239C2×C3semidirect
84. #5227C2×C3semidirect
85. #5190C2×C3semidirect
86. #5188C2×C3semidirect
87. #5186C2×C3semidirect
88. #5185C2×C3semidirect
89. #5169C2×C3semidirect
90. #5164C2×C3semidirect
91. #5162C2×C3semidirect
92. #5134C2×C3semidirect
93. #5127C2×C3semidirect
124. C32×SD16D4semidirect
162. C22×C3×Q8C2×D3semidirect
163. C22×C3×Q8C22×C3semidirect
173. C2×C3×Q16C2×D3semidirect
174. C2×C3×Q16C2×D3semidirect
175. C2×C3×Q16C22×C3semidirect
176. C2×C3×Q16C22×C3semidirect
189. C2×C3×M16C2×D3semidirect
190. C2×C3×M16C22×C3semidirect
213. Q8×Dic3C22×C3semidirect
215. #944C22×C3semidirect
216. C2×#216C22×C3semidirect
229. #924C22×C3semidirect
244. #835C22×C3semidirect
245. #835C22×C3semidirect
246. #835C22×C3semidirect
248. #830C22×C3semidirect
251. #818C22×C3semidirect
252. #816C22×C3semidirect
253. #815C22×C3semidirect
254. Dic3⋊C8C22×C3semidirect
303. C2×#137C3×D3semidirect
400. C3×SD16#67semidirect
401. C3×SD16C3×D4semidirect
475. C2×C3×D3#137semidirect
490. C22×Q8C2×C3×D3semidirect
494. C2×Q16C2×C3×D3semidirect
495. C2×Q16C2×C3×D3semidirect
503. C2×M16C2×C3×D3semidirect
694. SD16C3×#67semidirect
755. C2×D3C3×#137semidirect
786. C32#3266semidirect
881. C3#83987direct (N × H)
882. C3C3×#3266semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
C3×#58292
C3×Q8×#672
C2×C3×D3×SD162
C3×#52392
C3×#52272
C3×#51902
C3×#51882
C3×#51862
C3×#51852
C3×#51692
C3×#51642
C3×#51622
C3×#51342
C3×#51272
C3×#32663
#839873