Finite Group Databasebeta

← C3×#80169 #11884080

Subgroups — C3×#80169 #11884080

Order 1152.

1082 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×C3×#915C211yesmaximal, characteristic, complemented
4C3×#5632C211yesmaximal, characteristic, complemented
5C32×#450C211yesmaximal, characteristic, complemented
6C3×#5170C211yesmaximal, characteristic, complemented
7C3×#5167C211yesmaximal, characteristic, complemented
8C3×#5162C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×#4783C211yesmaximal, characteristic, complemented
11C3×#4780C211yesmaximal, characteristic, complemented
12C3×#4767C211yesmaximal, characteristic, complemented
13C3×#4757C211yesmaximal, characteristic, complemented
14C3×#4739C211yesmaximal, characteristic, complemented
15C3×#4730C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#80169C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25C3×#953—21no—
26C2×C3×#217—21no—
27C3×#944C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C3×#939—21no—
30C3×#938C2211yescharacteristic
31C3×#936C2211yescharacteristic
32C3×#935—21no—
33C3×D4×Dic3C2211yescharacteristic
34C2×C3×#214—24no—
35C2×C3×#214C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C2×C3×#214C2211yescharacteristic
38C2×C3×#214C2211yescharacteristic
39C3×C4×#67C2211yescharacteristic
40C3×#924C2211yescharacteristic
41C22×C3×C3⋊C8C2211yescharacteristic
42C3×#915—24no—
43C2×C3×Dic12C2211yescharacteristic, complemented
44C2×C3×Dic12C2211yescharacteristic, complemented
45C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
46C3×#897C2211yescharacteristic, complemented
47C3×#896—21no—
48C3×#888—21no—
49C3×#887C2211yescharacteristic, complemented
50C3×#67⋊C4—21no—
51C3×#878—21no—
52C32×#102C2211yescharacteristic
53C32×#102C2211yescharacteristic
54C32×C22⋊C8C2211yescharacteristic
55C3×#835C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#815C2211yescharacteristic, complemented
60C3×Dic3⋊C8C2211yescharacteristic, complemented
61C3×#810C2211yescharacteristic, complemented
62C3×#807C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×D4×Q8—31no—
66C3×#546—31no—
67#5806C2×C311yescharacteristic
68C22×#214C2×C311yescharacteristic, complemented
69C2×#915C2×C311yescharacteristic, complemented
70#5632C2×C311yescharacteristic, complemented
71C3×#497—31no—
72C3×#468—31no—
73C3×#467—31no—
74C3×#464—31no—
75C3×#461—31no—
76C3×#452—31no—
77C3×#451—31no—
78C3×#450—21no—
79C3×#450D311yescharacteristic, complemented
80C3×#450C2×C311yescharacteristic, complemented
81C3×#448—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5170C2×C311yescharacteristic, complemented
85#5167C2×C311yescharacteristic, complemented
86#5162C2×C311yescharacteristic, complemented
87#5051C2×C311yescharacteristic, complemented
88#4783C2×C311yescharacteristic, complemented
89#4780C2×C311yescharacteristic, complemented
90#4767C2×C311yescharacteristic, complemented
91#4757C2×C311yescharacteristic, complemented
92#4739C2×C311yescharacteristic, complemented
93#4730C2×C311yescharacteristic, complemented
94C24×C32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—22no—
97C2×C32×D4—21no—
98C2×C32×D4—41no—
99C2×C32×D4C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C3×D3×Q8—22no—
109C3×D3×Q8—41no—
110C3×#237—22no—
111C3×#237—41no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6—22no—
115C2×C3×Dic6—21no—
116C2×C3×Dic6—21no—
117C2×C3×Dic6—41no—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×SD16—22no—
122C32×SD16—41no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C32×C4⋊C4—21no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#217D411yescharacteristic
134C3×#216—22no—
135C3×#214—22no—
136C3×#214—22no—
137C3×#214—22no—
138C3×#214D414yescomplemented
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4D411yescharacteristic
148C3×C4×Dic3—21no—
149C3×C4×Dic3C2311yescharacteristic
150C2×C3×C3⋊C8—22no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×Dic12—22no—
154C3×Dic12—41no—
155C3×ΓL(1,𝔽25)—22no—
156#3266—31noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—21no—
161C22×C3×D4C2×D311yescharacteristic
162C22×C3×D4C22×C311yescharacteristic
163C2×D3×Q8C22×C311yescharacteristic, complemented
164C2×#237C22×C311yescharacteristic
165C22×Dic6C22×C311yescharacteristic
166C3×#137—64no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×Q16—31no—
170C2×C3×SD16—21no—
171C2×C3×SD16—21no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—31no—
176C2×C3×SD16—64no—
177C2×C3×SD16C2×D311yescharacteristic
178C2×C3×SD16C2×D311yescharacteristic
179C2×C3×SD16C22×C311yescharacteristic
180C2×C3×SD16C22×C311yescharacteristic
181C2×C3×M16—31no—
182C22×C3×C8—31no—
183C3×C4⋊Q8—31no—
184C3×C4⋊Q8—61no—
185C3×#124—31no—
186C3×#123—61no—
187C3×C22⋊Q8—21no—
188C3×C22⋊Q8—31no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8—61no—
191C3×C22⋊Q8—61no—
192C3×C22⋊Q8C2×D311yescharacteristic
193C3×C22⋊Q8C22×C311yescharacteristic
194C3×#121—31no—
195C3×#121—61no—
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#944C22×C311yescharacteristic, complemented
205C2×#216C22×C311yescharacteristic, complemented
206#939—21no—
207#938C22×C311yescharacteristic
208#936C22×C311yescharacteristic
209#935—21no—
210D4×Dic3C22×C311yescharacteristic
211C2×#214—24no—
212C2×#214C22×C311yescharacteristic
213C2×#214C22×C311yescharacteristic
214C2×#214C22×C311yescharacteristic
215C2×#214C22×C311yescharacteristic
216C4×#67C22×C311yescharacteristic
217#924C22×C311yescharacteristic
218C22×C3⋊C8C22×C311yescharacteristic
219#915—24no—
220C2×Dic12C22×C311yescharacteristic, complemented
221C2×Dic12C22×C311yescharacteristic, complemented
222C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
223#897C22×C311yescharacteristic, complemented
224#896—21no—
225#888—21no—
226#887C22×C311yescharacteristic, complemented
227#67⋊C4—21no—
228#878—21no—
229C3×#107—31no—
230C3×C4⋊C8—31no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#102—21no—
236C3×#102—21no—
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#835C22×C311yescharacteristic, complemented
247(C2×D3)⋊C8C22×C311yescharacteristic, complemented
248#816C22×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—42no—
257C23×C32—42no—
258C23×C32—81no—
259C23×C32C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8—21no—
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—21no—
266C32×D4—42no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C3×#67—22no—
275C3×#67—42no—
276C3×#67—81no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yes—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—31no—
303C22×SD16—31no—
304D4×Q8—31no—
305#546—31no—
306#497—31no—
307#468—31no—
308#467—31no—
309#464—31no—
310#461—31no—
311#452—31no—
312#451—31no—
313#450C3×D311yescharacteristic, complemented
314#448—31no—
315#440—31no—
316#435—31no—
317C24×C3—21no—
318C24×C3—21no—
319C24×C3—41no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—31no—
326C2×C3×Q8—61no—
327C2×C3×Q8—62no—
328C2×C3×Q8—61no—
329C2×C3×Q8—62no—
330C2×C3×Q8—121no—
331C2×C3×Q8—121no—
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C23×C311yescharacteristic
334C2×C3×D4—22no—
335C2×C3×D4—22no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—31no—
341C2×C3×D4—41no—
342C2×C3×D4—42no—
343C2×C3×D4—41no—
344C2×C3×D4—41no—
345C2×C3×D4—42no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4C22×D311yescharacteristic
349C2×C3×D4C22×D311yescharacteristic
350C2×C3×D4C23×C311yescharacteristic
351C2×C3×D4C23×C311yescharacteristic
352C22×C3×C4—21no—
353C22×C3×C4—31no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C23×C311yescharacteristic
360C2×#67—21no—
361C2×#67—21no—
362C2×#67C3×D411yescharacteristic
363C22×Dic3—21no—
364C22×Dic3—21no—
365C22×Dic3—21no—
366D3×Q8—22no—
367D3×Q8—41no—
368#237—22no—
369#237—41no—
370C2×C4×D3—21no—
371C2×C4×D3C23×C311yescharacteristic
372C2×Dic6—22no—
373C2×Dic6—21no—
374C2×Dic6—21no—
375C2×Dic6—41no—
376C2×Dic6C23×C311yescharacteristic
377C2×Dic6C23×C311yescharacteristic
378C2×Dic6C23×C311yescharacteristic
379C3×Q16—62no—
380C3×Q16—62no—
381C3×Q16—121no—
382C3×SD16—22no—
383C3×SD16—22no—
384C3×SD16—34no—
385C3×SD16—42no—
386C3×SD16—41no—
387C3×SD16—41no—
388C3×SD16—42no—
389C3×SD16—62no—
390C3×SD16—62no—
391C3×SD16—62no—
392C3×M16—62no—
393C2×C3×C8—21no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—62no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C23×C311yescharacteristic
401C2×C3×C8C23×C311yescharacteristic
402C3×C4⋊C4—21no—
403C3×C4⋊C4—21no—
404C3×C4⋊C4—21no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—41no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4C22×D311yescharacteristic
414C3×C4⋊C4C23×C311yescharacteristic
415C3×C22⋊C4—21no—
416C3×C22⋊C4—21no—
417C3×C22⋊C4—31no—
418C3×C22⋊C4—31no—
419C3×C22⋊C4—41no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C42—31no—
427C3×C42—61no—
428#217—21no—
429#217—21no—
430#217—21no—
431#217—21no—
432#217—21no—
433#217C3×D411yescharacteristic
434#216—22no—
435#214—22no—
436#214—22no—
437#214—22no—
438#214C3×D414yescomplemented
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4C3×D411yescharacteristic
441C4⋊Dic3—21no—
442C4⋊Dic3C23×C311yescharacteristic
443Dic3⋊C4—21no—
444Dic3⋊C4—21no—
445Dic3⋊C4—21no—
446Dic3⋊C4—21no—
447Dic3⋊C4C3×D411yescharacteristic
448C4×Dic3—21no—
449C4×Dic3C23×C311yescharacteristic
450C2×C3⋊C8—22no—
451C2×C3⋊C8C23×C311yescharacteristic
452C2×C3⋊C8C23×C311yescharacteristic
453Dic12—22no—
454Dic12—41no—
455ΓL(1,𝔽25)—22no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—22no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—84no—
465C22×C32#13712yescomplemented
466C22×C32C22×D411yescharacteristic
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C32×C4—21no—
471C32×C4—41no—
472C32×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3×Dic3—22no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—31no—
483C22×Q8—31no—
484C22×Q8—31no—
485C22×D4C2×C3×D311yescharacteristic
486#137—64no—
487C2×Q16—31no—
488C2×Q16—31no—
489C2×Q16—31no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—64no—
495C2×SD16C2×C3×D311yescharacteristic
496C2×SD16C2×C3×D311yescharacteristic
497C2×M16—31no—
498C22×C8—31no—
499C4⋊Q8—31no—
500C4⋊Q8—61no—
501#124—31no—
502#123—61no—
503C22⋊Q8—31no—
504C22⋊Q8—31no—
505C22⋊Q8—61no—
506C22⋊Q8—61no—
507C22⋊Q8C2×C3×D311yescharacteristic
508#121—31no—
509#121—61no—
510#120—61no—
511C4×Q8—31no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—61no—
515C2×C22⋊C4—61no—
516#107—31no—
517C4⋊C8—31no—
518#103—31no—
519#103—31no—
520#103—31no—
521#103—31no—
522#102C2×C3×D311yescharacteristic
523#102C2×C3×D311yescharacteristic
524C22⋊C8—31no—
525C22⋊C8C2×C3×D311yescharacteristic
526#97—31no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—31no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—42no—
536C23×C3—42no—
537C23×C3—44no—
538C23×C3—42no—
539C23×C3—42no—
540C23×C3—82no—
541C23×C3—81no—
542C23×C3—81no—
543C23×C3—82no—
544C23×C3D3×D411yescharacteristic
545C23×C3C2×C3×D411yescharacteristic
546C22×D3C2×C3×D411yescharacteristic
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—32no—
552C3×Q8—41no—
553C3×Q8—41no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×Q8—122no—
560C3×Q8—122no—
561C3×D4—22no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—22no—
569C3×D4—41no—
570C3×D4—41no—
571C3×D4—42no—
572C3×D4—42no—
573C3×D4—44no—
574C3×D4—62no—
575C3×D4—122no—
576C3×D4—241no—
577C3×D4D3×D412yes—
578C3×D4C2×C3×D412yes—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—122no—
603C2×C3×C4—122no—
604C2×C3×C4—122no—
605C2×C3×C4—241no—
606C2×C3×C4D3×D411yescharacteristic
607C2×C3×C4C2×C3×D411yescharacteristic
608C2×C3×C4C23×D311yescharacteristic
609C2×C3×C4C24×C311yescharacteristic
610#67—22no—
611#67—42no—
612#67—81no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—42no—
618C2×Dic3—42no—
619C2×Dic3—81no—
620C2×Dic3C2×C3×D411yescharacteristic
621C2×Dic3C2×C3×D411yescharacteristic
622C2×Dic3C2×C3×D411yescharacteristic
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—42no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630Dic6—21no—
631Dic6—42no—
632Dic6—42no—
633Dic6C2×C3×D412yes—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—21no—
637C3×C8—21no—
638C3×C8—32no—
639C3×C8—41no—
640C3×C8—41no—
641C3×C8—61no—
642C3⋊C8—21no—
643C3⋊C8C2×C3×D412yes—
644C2×C32—22no—
645C2×C32—42no—
646C2×C32—81no—
647C2×C32D4211yescharacteristic
648C2×C32C2×#13711yescharacteristic
649C2×C32#57711yescharacteristic
650C3×D3—41no—
651C24—21no—
652#41—62no—
653#41—121no—
654C2×Q8—31no—
655C2×Q8—31no—
656C2×Q8—31no—
657C2×Q8—61no—
658C2×Q8—62no—
659C2×Q8—61no—
660C2×Q8—62no—
661C2×Q8—121no—
662C2×Q8—121no—
663C2×Q8C22×C3×D311yescharacteristic
664C2×D4—22no—
665C2×D4—21no—
666C2×D4—31no—
667C2×D4—41no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4C22×C3×D311yescharacteristic
671C2×D4C22×C3×D311yescharacteristic
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4C22×C3×D311yescharacteristic
678Q16—62no—
679Q16—62no—
680Q16—121no—
681SD16—22no—
682SD16—34no—
683SD16—41no—
684SD16—62no—
685SD16—62no—
686SD16—62no—
687M16—62no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—62no—
691C2×C8C22×C3×D311yescharacteristic
692C2×C8C22×C3×D311yescharacteristic
693C4⋊C4—21no—
694C4⋊C4—31no—
695C4⋊C4—31no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4—61no—
701C4⋊C4C22×C3×D311yescharacteristic
702C22⋊C4—21no—
703C22⋊C4—31no—
704C22⋊C4—31no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C42—31no—
712C42—61no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3—84no—
743C22×C3—84no—
744C22×C3—88no—
745C22×C3#91512yescomplemented
746C22×C3C3×#13712yescomplemented
747C22×C3C2×D3×D411yescharacteristic
748C22×C3C22×C3×D411yescharacteristic
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—62no—
765C3×C4—81no—
766C3×C4—81no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4C2×D3×D411yescharacteristic
771C3×C4#100411yescharacteristic
772C3×C4C22×C3×D411yescharacteristic
773C3×C4C3×H(5,𝔽2)11yescharacteristic
774Dic3—21no—
775Dic3—21no—
776Dic3—22no—
777Dic3—21no—
778Dic3—41no—
779Dic3—41no—
780Dic3—41no—
781C32#326611yescharacteristic, complemented, Sylow
782C23—21no—
783C23—21no—
784C23—31no—
785C23—42no—
786C23—42no—
787C23—81no—
788C23C3×D3×D411yescharacteristic
789Q8—21no—
790Q8—21no—
791Q8—32no—
792Q8—61no—
793Q8—61no—
794Q8—61no—
795Q8—61no—
796Q8—61no—
797Q8—122no—
798Q8—122no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—42no—
803D4—62no—
804D4—122no—
805D4—241no—
806D4C3×D3×D412yes—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—31no—
812C2×C4—31no—
813C2×C4—31no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4—122no—
823C2×C4—241no—
824C2×C4C3×D3×D411yescharacteristic
825C2×C4C23×C3×D311yescharacteristic
826C8—21no—
827C8—21no—
828C8—32no—
829C8—61no—
830C2×C3—22no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—42no—
836C2×C3—42no—
837C2×C3—42no—
838C2×C3—82no—
839C2×C3—82no—
840C2×C3—81no—
841C2×C3—81no—
842C2×C3—121no—
843C2×C3#559011yescharacteristic
844C2×C3C2×#91511yescharacteristic
845C2×C3#577511yescharacteristic
846C2×C3C3×D4211yescharacteristic
847C2×C3C2×C3×#13711yescharacteristic
848C2×C3C3×#57711yescharacteristic
849D3—41no—
850C22—21no—
851C22—21no—
852C22—22no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—84no—
862C22C3×#91512yescomplemented
863C22C2×C3×D3×D411yescharacteristic
864C4—21no—
865C4—41no—
866C4—41no—
867C4—61no—
868C4—61no—
869C4—61no—
870C4—62no—
871C4—121no—
872C4—121no—
873C4—121no—
874C4C2×C3×D3×D411yescharacteristic
875C4C3×#100411yescharacteristic
876C3—21no—
877C3#8016911yescharacteristic, direct product factor
878C3C3×#326611yescharacteristic, complemented
879C2—22no—
880C2—42no—
881C2—81no—
882C2—121no—
883C2C3×#559011yescharacteristic
884C2C2×C3×#91511yescharacteristic
885C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC3×#450D3
hypocenterC3C3×#3266
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. C22×C3×#214C2semidirect
3. C2×C3×#915C2semidirect
4. C3×#5632C2semidirect
5. C32×#450C2semidirect
6. C3×#5170C2semidirect
7. C3×#5167C2semidirect
8. C3×#5162C2semidirect
9. C3×#5051C2semidirect
10. C3×#4783C2semidirect
11. C3×#4780C2semidirect
12. C3×#4767C2semidirect
13. C3×#4757C2semidirect
14. C3×#4739C2semidirect
15. C3×#4730C2semidirect
17. #80169C3direct (N × H)
19. C2×C3×D3×Q8C22semidirect
27. C3×#944C22semidirect
28. C2×C3×#216C22semidirect
43. C2×C3×Dic12C22semidirect
44. C2×C3×Dic12C22semidirect
45. C2×C3×ΓL(1,𝔽25)C22semidirect
46. C3×#897C22semidirect
49. C3×#887C22semidirect
55. C3×#835C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#816C22semidirect
58. C3×#816C22semidirect
59. C3×#815C22semidirect
60. C3×Dic3⋊C8C22semidirect
61. C3×#810C22semidirect
62. C3×#807C22semidirect
68. C22×#214C2×C3semidirect
69. C2×#915C2×C3semidirect
70. #5632C2×C3semidirect
79. C3×#450D3semidirect
80. C3×#450C2×C3semidirect
84. #5170C2×C3semidirect
85. #5167C2×C3semidirect
86. #5162C2×C3semidirect
87. #5051C2×C3semidirect
88. #4783C2×C3semidirect
89. #4780C2×C3semidirect
90. #4767C2×C3semidirect
91. #4757C2×C3semidirect
92. #4739C2×C3semidirect
93. #4730C2×C3semidirect
138. C3×#214D4semidirect
163. C2×D3×Q8C22×C3semidirect
204. #944C22×C3semidirect
205. C2×#216C22×C3semidirect
220. C2×Dic12C22×C3semidirect
221. C2×Dic12C22×C3semidirect
222. C2×ΓL(1,𝔽25)C22×C3semidirect
223. #897C22×C3semidirect
226. #887C22×C3semidirect
246. #835C22×C3semidirect
247. (C2×D3)⋊C8C22×C3semidirect
248. #816C22×C3semidirect
249. #816C22×C3semidirect
250. #815C22×C3semidirect
251. Dic3⋊C8C22×C3semidirect
252. #810C22×C3semidirect
253. #807C22×C3semidirect
313. #450C3×D3semidirect
438. #214C3×D4semidirect
465. C22×C32#137semidirect
745. C22×C3#915semidirect
746. C22×C3C3×#137semidirect
781. C32#3266semidirect
862. C22C3×#915semidirect
877. C3#80169direct (N × H)
878. C3C3×#3266semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
C22×C3×#2142
C2×C3×#9152
C3×#56322
C32×#4502
C3×#51702
C3×#51672
C3×#51622
C3×#50512
C3×#47832
C3×#47802
C3×#47672
C3×#47572
C3×#47392
C3×#47302
C3×#32663
#801693