Finite Group Databasebeta

← C3×#80158 #11887076

Subgroups — C3×#80158 #11887076

Order 1152.

1018 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#67C211yesmaximal, characteristic
2C3×#5635C211yesmaximal, characteristic, complemented
3C32×#450C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5C3×#5171C211yesmaximal, characteristic, complemented
6C3×#5169C211yesmaximal, characteristic, complemented
7C3×#5163C211yesmaximal, characteristic, complemented
8C3×Dic3×SD16C211yesmaximal, characteristic, complemented
9C3×#5048C211yesmaximal, characteristic, complemented
10C3×#4777C211yesmaximal, characteristic, complemented
11C3×D3×#102C211yesmaximal, characteristic, complemented
12C3×#4761C211yesmaximal, characteristic, complemented
13C3×#4760C211yesmaximal, characteristic, complemented
14C3×#4735C211yesmaximal, characteristic, complemented
15C3×#67⋊C8C211yesmaximal, characteristic, complemented
16C3×#3295—31nomaximal
17#80158C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23C32×C22⋊Q8C2211yescharacteristic, complemented
24C3×#953—21no—
25C3×#946C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#940C2211yescharacteristic
29C3×#939—21no—
30C3×#938C2211yescharacteristic
31C3×#937—21no—
32C3×D4×Dic3C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C3×C4×#67C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
36C22×C3×C3⋊C8C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#897—21no—
39C3×D3×C4⋊C4C2211yescharacteristic, complemented
40C3×#889—21no—
41C3×#888C2211yescharacteristic, complemented
42C3×#67⋊C4—21no—
43C3×#878—21no—
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic, complemented
46C32×C22⋊C8C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic, complemented
51C3×#832C2211yescharacteristic, complemented
52C3×#821C2211yescharacteristic, complemented
53C3×#821C2211yescharacteristic, complemented
54C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C3×#817C2211yescharacteristic, complemented
56C3×#817C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C8×Dic3C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#808C2211yescharacteristic, complemented
61C3×#554—31no—
62C3×D42—31no—
63D4×#67C2×C311yescharacteristic
64#5635C2×C311yescharacteristic, complemented
65C3×#486—31no—
66C3×#481—31no—
67C3×#481—31no—
68C3×#476—31no—
69C3×#465—31no—
70C3×#465—31no—
71C3×#460—31no—
72C3×#450—21no—
73C3×#450—31no—
74C3×#450D311yescharacteristic, complemented
75C3×#450C2×C311yescharacteristic, complemented
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C2×C3×#102—31no—
79C2×C3×#102—31no—
80C2×#832C2×C311yescharacteristic, complemented
81#5171C2×C311yescharacteristic, complemented
82#5169C2×C311yescharacteristic, complemented
83#5163C2×C311yescharacteristic, complemented
84Dic3×SD16C2×C311yescharacteristic, complemented
85#5048C2×C311yescharacteristic, complemented
86#4777C2×C311yescharacteristic, complemented
87D3×#102C2×C311yescharacteristic, complemented
88#4761C2×C311yescharacteristic, complemented
89#4760C2×C311yescharacteristic, complemented
90#4735C2×C311yescharacteristic, complemented
91#67⋊C8C2×C311yescharacteristic, complemented
92C24×C32—21no—
93C23×C3×D3—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—22no—
96C2×C32×D4—21no—
97C2×C32×D4—41no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—44no—
107C2×C3×#67D411yescharacteristic
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6—21no—
116C32×SD16—22no—
117C32×SD16—41no—
118C2×C32×C8C2311yescharacteristic
119C2×C32×C8C2311yescharacteristic
120C32×C4⋊C4—21no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123C3×#217—21no—
124C3×#217—21no—
125C3×#217D411yescharacteristic
126C3×#215—41no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8—41no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×D3×C8—41no—
145#3295—31noSylow
146C22×C3×D4—21no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C22×C3×D4C2×D311yescharacteristic
150C22×C3×D4C22×C311yescharacteristic
151C22×#67—21no—
152C2×D3×D4C22×C311yescharacteristic
153C2×C3×SD16—21no—
154C2×C3×SD16—21no—
155C2×C3×SD16—31no—
156C2×C3×SD16C2×D311yescharacteristic
157C2×C3×SD16C2×D311yescharacteristic, complemented
158C2×C3×SD16C22×C311yescharacteristic
159C2×C3×SD16C22×C311yescharacteristic, complemented
160C22×C3×C8—31no—
161C22×C3×C8—31no—
162C3×C4⋊Q8—31no—
163C3×#127—31no—
164C3×#125—61no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—61no—
168C3×C22⋊Q8—61no—
169C3×C22⋊Q8C2×D311yescharacteristic, complemented
170C3×C22⋊Q8C22×C311yescharacteristic, complemented
171C3×#121—31no—
172C3×#121—31no—
173C3×#121—61no—
174C3×#120—61no—
175C3×#120—61no—
176C3×C4×Q8—31no—
177C3×C4×D4—31no—
178C3×C4×D4—31no—
179C3×C4×D4—61no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4—31no—
182#953—21no—
183#946C22×C311yescharacteristic, complemented
184Q8×Dic3C22×C311yescharacteristic, complemented
185C2×#215C22×C311yescharacteristic, complemented
186#940C22×C311yescharacteristic
187#939—21no—
188#938C22×C311yescharacteristic
189#937—21no—
190D4×Dic3C22×C311yescharacteristic
191#930C22×C311yescharacteristic
192C4×#67C22×C311yescharacteristic
193C2×C4⋊Dic3C22×C311yescharacteristic, complemented
194C22×C3⋊C8C22×C311yescharacteristic, complemented
195C2×D3×C8C22×C311yescharacteristic, complemented
196#897—21no—
197D3×C4⋊C4C22×C311yescharacteristic, complemented
198#889—21no—
199#888C22×C311yescharacteristic, complemented
200#67⋊C4—21no—
201#878—21no—
202C3×#106—31no—
203C3×#106—31no—
204C3×#106—31no—
205C3×C4⋊C8—31no—
206C3×#103—31no—
207C3×#102—21no—
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102C2×D311yescharacteristic
217C3×#102C2×D311yescharacteristic, complemented
218C3×#102C22×C311yescharacteristic
219C3×#102C22×C311yescharacteristic, complemented
220C3×C22⋊C8—21no—
221C3×C22⋊C8—31no—
222C3×C22⋊C8C2×D311yescharacteristic, complemented
223C3×C22⋊C8C22×C311yescharacteristic, complemented
224C3×C4×C8—31no—
225#835C22×C311yescharacteristic, complemented
226#832C22×C311yescharacteristic
227#832C22×C311yescharacteristic
228#832C22×C311yescharacteristic, complemented
229#832C22×C311yescharacteristic, complemented
230#821C22×C311yescharacteristic, complemented
231#821C22×C311yescharacteristic, complemented
232(C2×D3)⋊C8C22×C311yescharacteristic, complemented
233#817C22×C311yescharacteristic, complemented
234#817C22×C311yescharacteristic, complemented
235Dic3⋊C8C22×C311yescharacteristic, complemented
236C8×Dic3C22×C311yescharacteristic, complemented
237#809C22×C311yescharacteristic, complemented
238#808C22×C311yescharacteristic, complemented
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—42no—
242C23×C32—42no—
243C23×C32—81no—
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C22×C3×D3C2×D411yescharacteristic
250C32×Q8—21no—
251C32×Q8—21no—
252C32×D4—21no—
253C32×D4—21no—
254C32×D4—21no—
255C32×D4—42no—
256C32×D4#4112yes—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263C3×#67—42no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—42no—
267C3×#67—81no—
268C3×#67SD1614yescomplemented
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—42no—
273C2×C3×Dic3—81no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
281C3×C4×D3—81no—
282C3×Dic6—81no—
283C32×C8—21no—
284C32×C8—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—31no—
288D42—31no—
289#486—31no—
290#481—31no—
291#481—31no—
292#476—31no—
293#465—31no—
294#465—31no—
295#460—31no—
296#450—31no—
297#450C3×D311yescharacteristic, complemented
298C4×SD16—31no—
299C8×D4—31no—
300C2×#102—31no—
301C2×#102—31no—
302C24×C3—21no—
303C24×C3—21no—
304C24×C3—41no—
305C24×C3—61no—
306C23×D3—21no—
307C2×C3×Q8—21no—
308C2×C3×Q8—61no—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C23×C311yescharacteristic
311C2×C3×D4—22no—
312C2×C3×D4—22no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—41no—
320C2×C3×D4—42no—
321C2×C3×D4—41no—
322C2×C3×D4—41no—
323C2×C3×D4—42no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—121no—
331C2×C3×D4—124no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C23×C311yescharacteristic
335C2×C3×D4C23×C311yescharacteristic
336C22×C3×C4—21no—
337C22×C3×C4—31no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C23×C311yescharacteristic
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—21no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—44no—
349C2×#67C3×D411yescharacteristic
350C22×Dic3—21no—
351C22×Dic3—21no—
352D3×D4—22no—
353D3×D4—41no—
354C2×D12C23×C311yescharacteristic
355C2×C4×D3—21no—
356C2×C4×D3C23×C311yescharacteristic
357C2×Dic6—21no—
358C3×SD16—22no—
359C3×SD16—22no—
360C3×SD16—42no—
361C3×SD16—41no—
362C3×SD16—41no—
363C3×SD16—42no—
364C3×SD16—121no—
365C2×C3×C8—21no—
366C2×C3×C8—21no—
367C2×C3×C8—31no—
368C2×C3×C8—31no—
369C2×C3×C8—121no—
370C2×C3×C8—121no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C23×C311yescharacteristic
374C2×C3×C8C23×C311yescharacteristic
375C3×C4⋊C4—21no—
376C3×C4⋊C4—21no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—41no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C23×C311yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—41no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C42—31no—
400C3×C42—61no—
401#217—21no—
402#217—21no—
403#217C3×D411yescharacteristic
404#215—41no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4C3×D411yescharacteristic
408C4⋊Dic3—21no—
409C4⋊Dic3—21no—
410C4⋊Dic3C23×C311yescharacteristic
411C4⋊Dic3C23×C311yescharacteristic
412C4⋊Dic3C23×C311yescharacteristic
413Dic3⋊C4—21no—
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416Dic3⋊C4C3×D411yescharacteristic
417C4×Dic3—21no—
418C4×Dic3C23×C311yescharacteristic
419C2×C3⋊C8—41no—
420C2×C3⋊C8C23×C311yescharacteristic
421C2×C3⋊C8C23×C311yescharacteristic
422D3×C8—41no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—22no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—84no—
432C22×C32C2×SD1612yes—
433C22×C32C22×D411yescharacteristic
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—84no—
440C2×C3×D3C2×SD1612yes—
441C32×C4—21no—
442C32×C4—41no—
443C32×C4—41no—
444C32×C4C2×#4111yescharacteristic
445C32×C4H(5,𝔽2)11yescharacteristic
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C3×Dic3C2×SD1612yes—
452C22×D4—31no—
453C22×D4—61no—
454C22×D4C2×C3×D311yescharacteristic
455C2×SD16—31no—
456C2×SD16C2×C3×D311yescharacteristic
457C2×SD16C2×C3×D311yescharacteristic, complemented
458C22×C8—31no—
459C22×C8—31no—
460C4⋊Q8—31no—
461#127—31no—
462#125—61no—
463C22⋊Q8—31no—
464C22⋊Q8—61no—
465C22⋊Q8—61no—
466C22⋊Q8C2×C3×D311yescharacteristic, complemented
467#121—31no—
468#121—31no—
469#121—61no—
470#120—61no—
471#120—61no—
472C4×Q8—31no—
473C4×D4—31no—
474C4×D4—31no—
475C4×D4—61no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—31no—
478#106—31no—
479#106—31no—
480#106—31no—
481C4⋊C8—31no—
482#103—31no—
483#102—31no—
484#102—31no—
485#102—31no—
486#102—31no—
487#102—31no—
488#102—31no—
489#102—31no—
490#102C2×C3×D311yescharacteristic
491#102C2×C3×D311yescharacteristic, complemented
492C22⋊C8—31no—
493C22⋊C8C2×C3×D311yescharacteristic, complemented
494C4×C8—31no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—31no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—42no—
504C23×C3—42no—
505C23×C3—44no—
506C23×C3—42no—
507C23×C3—42no—
508C23×C3—61no—
509C23×C3—82no—
510C23×C3—81no—
511C23×C3—81no—
512C23×C3—82no—
513C23×C3—122no—
514C23×C3—122no—
515C23×C3—241no—
516C23×C3D3×D411yescharacteristic
517C23×C3C2×C3×D411yescharacteristic
518C22×D3—21no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—81no—
522C22×D3C2×C3×D411yescharacteristic
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—41no—
528C3×Q8—41no—
529C3×Q8—241no—
530C3×D4—22no—
531C3×D4—21no—
532C3×D4—21no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—22no—
538C3×D4—34no—
539C3×D4—41no—
540C3×D4—41no—
541C3×D4—42no—
542C3×D4—42no—
543C3×D4—44no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—122no—
547C3×D4—122no—
548C3×D4—122no—
549C3×D4—122no—
550C3×D4—241no—
551C3×D4#23712yes—
552C3×D4C3×#4112yes—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—122no—
576C2×C3×C4—241no—
577C2×C3×C4—241no—
578C2×C3×C4D3×D411yescharacteristic
579C2×C3×C4C2×C3×D411yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581C2×C3×C4C24×C311yescharacteristic
582#67—42no—
583#67—42no—
584#67—42no—
585#67—42no—
586#67—81no—
587#67C3×SD1614yescomplemented
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—42no—
592C2×Dic3—81no—
593C2×Dic3C2×C3×D411yescharacteristic
594C2×Dic3C2×C3×D411yescharacteristic
595C2×Dic3C2×C3×D411yescharacteristic
596D12—21no—
597D12—21no—
598C4×D3—21no—
599C4×D3—21no—
600C4×D3—81no—
601Dic6—81no—
602C3×C8—21no—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—41no—
607C3×C8—41no—
608C3×C8—61no—
609C3×C8—61no—
610C3⋊C8—21no—
611C3⋊C8—21no—
612C2×C32—22no—
613C2×C32—42no—
614C2×C32—81no—
615C2×C32#54611yescharacteristic
616C2×C32C22×SD1611yescharacteristic
617C2×C32#57611yescharacteristic
618C3×D3—22no—
619C3×D3—81no—
620C24—21no—
621C24—61no—
622C2×Q8—61no—
623C2×Q8C22×C3×D311yescharacteristic
624C2×D4—22no—
625C2×D4—21no—
626C2×D4—31no—
627C2×D4—31no—
628C2×D4—41no—
629C2×D4—61no—
630C2×D4—61no—
631C2×D4—61no—
632C2×D4—62no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—121no—
636C2×D4—124no—
637C2×D4C22×C3×D311yescharacteristic
638C2×D4C22×C3×D311yescharacteristic
639C22×C4—31no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4C22×C3×D311yescharacteristic
644SD16—22no—
645SD16—41no—
646SD16—121no—
647C2×C8—31no—
648C2×C8—31no—
649C2×C8—121no—
650C2×C8—121no—
651C2×C8C22×C3×D311yescharacteristic
652C2×C8C22×C3×D311yescharacteristic
653C4⋊C4—21no—
654C4⋊C4—31no—
655C4⋊C4—31no—
656C4⋊C4—31no—
657C4⋊C4—31no—
658C4⋊C4—61no—
659C4⋊C4—61no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4C22×C3×D311yescharacteristic
664C22⋊C4—21no—
665C22⋊C4—31no—
666C22⋊C4—31no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C42—31no—
672C42—61no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—21no—
681C22×C3—32no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—81no—
701C22×C3—81no—
702C22×C3—84no—
703C22×C3—84no—
704C22×C3—88no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—244no—
709C22×C3D3×SD1612yes—
710C22×C3C2×C3×SD1612yes—
711C22×C3C2×D3×D411yescharacteristic
712C22×C3C22×C3×D411yescharacteristic
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—84no—
719C2×D3C2×C3×SD1612yes—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—61no—
731C3×C4—61no—
732C3×C4—81no—
733C3×C4—81no—
734C3×C4—121no—
735C3×C4—121no—
736C3×C4—121no—
737C3×C4C2×#23711yescharacteristic
738C3×C4#100411yescharacteristic
739C3×C4C2×C3×#4111yescharacteristic
740C3×C4C3×H(5,𝔽2)11yescharacteristic
741Dic3—21no—
742Dic3—21no—
743Dic3—41no—
744Dic3—41no—
745Dic3—41no—
746Dic3C2×C3×SD1612yes—
747C32#329511yescharacteristic, complemented, Sylow
748C23—21no—
749C23—21no—
750C23—31no—
751C23—42no—
752C23—42no—
753C23—61no—
754C23—81no—
755C23—122no—
756C23—122no—
757C23—241no—
758C23C3×D3×D411yescharacteristic
759Q8—21no—
760Q8—21no—
761Q8—241no—
762D4—21no—
763D4—21no—
764D4—21no—
765D4—34no—
766D4—42no—
767D4—61no—
768D4—61no—
769D4—122no—
770D4—122no—
771D4—122no—
772D4—122no—
773D4—241no—
774D4C3×#23712yes—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—31no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—122no—
788C2×C4—241no—
789C2×C4—241no—
790C2×C4C3×D3×D411yescharacteristic
791C2×C4C23×C3×D311yescharacteristic
792C8—21no—
793C8—21no—
794C8—61no—
795C8—61no—
796C2×C3—22no—
797C2×C3—22no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—42no—
802C2×C3—42no—
803C2×C3—42no—
804C2×C3—62no—
805C2×C3—82no—
806C2×C3—82no—
807C2×C3—81no—
808C2×C3—81no—
809C2×C3—241no—
810C2×C3#559111yescharacteristic
811C2×C3C2×D3×SD1611yescharacteristic
812C2×C3#577411yescharacteristic
813C2×C3C3×#54611yescharacteristic
814C2×C3C22×C3×SD1611yescharacteristic
815C2×C3C3×#57611yescharacteristic
816D3—22no—
817D3—81no—
818C22—21no—
819C22—21no—
820C22—22no—
821C22—32no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—61no—
828C22—61no—
829C22—84no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—244no—
834C22C3×D3×SD1612yes—
835C22C2×C3×D3×D411yescharacteristic
836C4—21no—
837C4—32no—
838C4—41no—
839C4—41no—
840C4—61no—
841C4—61no—
842C4—121no—
843C4—121no—
844C4—121no—
845C4C2×C3×#23711yescharacteristic
846C4C3×#100411yescharacteristic
847C3—21no—
848C3#8015811yescharacteristic, direct product factor
849C3C3×#329511yescharacteristic, complemented
850C2—22no—
851C2—42no—
852C2—62no—
853C2—81no—
854C2—241no—
855C2C3×#559111yescharacteristic
856C2C2×C3×D3×SD1611yescharacteristic
857C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radicalC3×D4×#67C2
hypercenterC3×#450D3
hypocenterC3C3×#3295
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
2. C3×#5635C2semidirect
3. C32×#450C2semidirect
4. C2×C3×#832C2semidirect
5. C3×#5171C2semidirect
6. C3×#5169C2semidirect
7. C3×#5163C2semidirect
8. C3×Dic3×SD16C2semidirect
9. C3×#5048C2semidirect
10. C3×#4777C2semidirect
11. C3×D3×#102C2semidirect
12. C3×#4761C2semidirect
13. C3×#4760C2semidirect
14. C3×#4735C2semidirect
15. C3×#67⋊C8C2semidirect
17. #80158C3direct (N × H)
22. C2×C32×SD16C22semidirect
23. C32×C22⋊Q8C22semidirect
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
27. C2×C3×#215C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C22×C3×C3⋊C8C22semidirect
37. C2×C3×D3×C8C22semidirect
39. C3×D3×C4⋊C4C22semidirect
41. C3×#888C22semidirect
45. C32×#102C22semidirect
46. C32×C22⋊C8C22semidirect
47. C3×#835C22semidirect
50. C3×#832C22semidirect
51. C3×#832C22semidirect
52. C3×#821C22semidirect
53. C3×#821C22semidirect
54. C3×(C2×D3)⋊C8C22semidirect
55. C3×#817C22semidirect
56. C3×#817C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C8×Dic3C22semidirect
59. C3×#809C22semidirect
60. C3×#808C22semidirect
64. #5635C2×C3semidirect
74. C3×#450D3semidirect
75. C3×#450C2×C3semidirect
80. C2×#832C2×C3semidirect
81. #5171C2×C3semidirect
82. #5169C2×C3semidirect
83. #5163C2×C3semidirect
84. Dic3×SD16C2×C3semidirect
85. #5048C2×C3semidirect
86. #4777C2×C3semidirect
87. D3×#102C2×C3semidirect
88. #4761C2×C3semidirect
89. #4760C2×C3semidirect
90. #4735C2×C3semidirect
91. #67⋊C8C2×C3semidirect
157. C2×C3×SD16C2×D3semidirect
159. C2×C3×SD16C22×C3semidirect
169. C3×C22⋊Q8C2×D3semidirect
170. C3×C22⋊Q8C22×C3semidirect
183. #946C22×C3semidirect
184. Q8×Dic3C22×C3semidirect
185. C2×#215C22×C3semidirect
193. C2×C4⋊Dic3C22×C3semidirect
194. C22×C3⋊C8C22×C3semidirect
195. C2×D3×C8C22×C3semidirect
197. D3×C4⋊C4C22×C3semidirect
199. #888C22×C3semidirect
217. C3×#102C2×D3semidirect
219. C3×#102C22×C3semidirect
222. C3×C22⋊C8C2×D3semidirect
223. C3×C22⋊C8C22×C3semidirect
225. #835C22×C3semidirect
228. #832C22×C3semidirect
229. #832C22×C3semidirect
230. #821C22×C3semidirect
231. #821C22×C3semidirect
232. (C2×D3)⋊C8C22×C3semidirect
233. #817C22×C3semidirect
234. #817C22×C3semidirect
235. Dic3⋊C8C22×C3semidirect
236. C8×Dic3C22×C3semidirect
237. #809C22×C3semidirect
238. #808C22×C3semidirect
268. C3×#67SD16semidirect
297. #450C3×D3semidirect
457. C2×SD16C2×C3×D3semidirect
466. C22⋊Q8C2×C3×D3semidirect
491. #102C2×C3×D3semidirect
493. C22⋊C8C2×C3×D3semidirect
587. #67C3×SD16semidirect
747. C32#3295semidirect
848. C3#80158direct (N × H)
849. C3C3×#3295semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
C3×#56352
C32×#4502
C2×C3×#8322
C3×#51712
C3×#51692
C3×#51632
C3×Dic3×SD162
C3×#50482
C3×#47772
C3×D3×#1022
C3×#47612
C3×#47602
C3×#47352
C3×#67⋊C82
C3×#32953
#801583