Finite Group Databasebeta

← C3×#79497 #11884393

Subgroups — C3×#79497 #11884393

Order 1152.

1082 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2C2×C3×#904C211yesmaximal, characteristic, complemented
3C3×#5553C211yesmaximal, characteristic, complemented
4C3×#5550C211yesmaximal, characteristic, complemented
5C32×#435C211yesmaximal, characteristic, complemented
6C3×#5134C211yesmaximal, characteristic, complemented
7C3×#5115C211yesmaximal, characteristic, complemented
8C3×#4845C211yesmaximal, characteristic, complemented
9C3×#4843C211yesmaximal, characteristic, complemented
10C3×#4734C211yesmaximal, characteristic, complemented
11C3×#4734C211yesmaximal, characteristic, complemented
12C3×#4733C211yesmaximal, characteristic, complemented
13C3×#4732C211yesmaximal, characteristic, complemented
14C3×#4712C211yesmaximal, characteristic, complemented
15C3×#4710C211yesmaximal, characteristic, complemented
16C3×#3268—31nomaximal
17#79497C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic
22C2×C32×M16C2211yescharacteristic
23C22×C32×C8C2211yescharacteristic, complemented
24C32×C4×D4C2211yescharacteristic
25C3×#940—21no—
26C3×#937—21no—
27C3×#930C2211yescharacteristic
28C3×#930C2211yescharacteristic
29C3×#930C2211yescharacteristic, complemented
30C3×#924C2211yescharacteristic
31C3×#908—24no—
32C2×C3×Dic12C2211yescharacteristic, complemented
33C3×#904—24no—
34C2×C3×D24C2211yescharacteristic
35C2×C3×D24C2211yescharacteristic
36C2×C3×D24C2211yescharacteristic
37C2×C3×D24C2211yescharacteristic
38C2×C3×#204C2211yescharacteristic
39C2×C3×#204C2211yescharacteristic
40C2×C3×#204C2211yescharacteristic, complemented
41C2×C3×#204C2211yescharacteristic, complemented
42C3×#894—21no—
43C3×#893—21no—
44C3×#884—21no—
45C3×#884—21no—
46C3×#884—21no—
47C3×D3×C22⋊C4—21no—
48C3×#875C2211yescharacteristic
49C3×#874C2211yescharacteristic, complemented
50C3×C4×D12C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic, complemented
52C32×C4⋊C8C2211yescharacteristic, complemented
53C32×C22⋊C8C2211yescharacteristic
54C32×C22⋊C8C2211yescharacteristic, complemented
55C32×#97C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic
58C3×#821C2211yescharacteristic, complemented
59C3×#821C2211yescharacteristic, complemented
60C3×#818C2211yescharacteristic, complemented
61C3×#816C2211yescharacteristic, complemented
62C3×#816C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65C3×#550—31no—
66C3×#546—31no—
67C2×#908C2×C311yescharacteristic, complemented
68C2×#904C2×C311yescharacteristic, complemented
69#5553C2×C311yescharacteristic, complemented
70#5550C2×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—31no—
80C3×#440—31no—
81C3×#435—21no—
82C3×#435D311yescharacteristic, complemented
83C3×#435C2×C311yescharacteristic, complemented
84#5134C2×C311yescharacteristic, complemented
85#5115C2×C311yescharacteristic, complemented
86#4845C2×C311yescharacteristic, complemented
87#4843C2×C311yescharacteristic, complemented
88#4734C2×C311yescharacteristic, complemented
89#4734C2×C311yescharacteristic, complemented
90#4733C2×C311yescharacteristic, complemented
91#4732C2×C311yescharacteristic, complemented
92#4712C2×C311yescharacteristic, complemented
93#4710C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×D4D411yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C3×#235—22no—
105C3×#235—22no—
106C3×#235—22no—
107C3×#235—41no—
108C3×#235—41no—
109C3×#235—41no—
110C2×C3×D12—22no—
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12—41no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—21no—
123C2×C3×Dic6C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic
125C32×M16—22no—
126C2×C32×C8—22no—
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129C2×C32×C8C2311yescharacteristic
130C2×C32×C8C2311yescharacteristic
131C32×C4⋊C4D411yescharacteristic
132C32×C22⋊C4D411yescharacteristic
133C32×C22⋊C4D411yescharacteristic
134C32×C42C2311yescharacteristic
135C3×#217—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×C4×Dic3—21no—
147C3×Dic12—22no—
148C3×D24—22no—
149C3×D24—22no—
150C3×D24—22no—
151C3×D24—41no—
152C3×#204—22no—
153C3×#204—22no—
154C3×#204—41no—
155C3×#204D414yescomplemented
156#3268—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×D4—31no—
161C2×#235C22×C311yescharacteristic
162C2×#235C22×C311yescharacteristic
163C2×#235C22×C311yescharacteristic, complemented
164C22×D12C22×C311yescharacteristic
165C3×AGL(1,ℤ/8)—64no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×M16—21no—
177C2×C3×M16C2×D311yescharacteristic
178C2×C3×M16C22×C311yescharacteristic
179C22×C3×C8—21no—
180C22×C3×C8C2×D311yescharacteristic, complemented
181C22×C3×C8C22×C311yescharacteristic, complemented
182C3×#127—31no—
183C3×#127—61no—
184C3×#124—31no—
185C3×#123—61no—
186C3×C22⋊Q8—31no—
187C3×#121—31no—
188C3×#121—31no—
189C3×#121—31no—
190C3×#121—61no—
191C3×#121—61no—
192C3×#121—61no—
193C3×#120—61no—
194C3×C4×Q8—31no—
195C3×C4×D4—21no—
196C3×C4×D4—31no—
197C3×C4×D4—61no—
198C3×C4×D4C2×D311yescharacteristic
199C3×C4×D4C22×C311yescharacteristic
200C2×C3×C22⋊C4—61no—
201#940—21no—
202#937—21no—
203#930C22×C311yescharacteristic
204#930C22×C311yescharacteristic
205#930C22×C311yescharacteristic, complemented
206#924C22×C311yescharacteristic
207#908—24no—
208C2×Dic12C22×C311yescharacteristic, complemented
209#904—24no—
210C2×D24C22×C311yescharacteristic
211C2×D24C22×C311yescharacteristic
212C2×D24C22×C311yescharacteristic
213C2×D24C22×C311yescharacteristic
214C2×#204C22×C311yescharacteristic
215C2×#204C22×C311yescharacteristic
216C2×#204C22×C311yescharacteristic, complemented
217C2×#204C22×C311yescharacteristic, complemented
218#894—21no—
219#893—21no—
220#884—21no—
221#884—21no—
222#884—21no—
223D3×C22⋊C4—21no—
224#875C22×C311yescharacteristic
225#874C22×C311yescharacteristic, complemented
226C4×D12C22×C311yescharacteristic
227C4×Dic6C22×C311yescharacteristic, complemented
228C3×#107—31no—
229C3×C4⋊C8—21no—
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×C4⋊C8C22×C311yescharacteristic, complemented
232C3×#103—31no—
233C3×#103—31no—
234C3×#102—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×C22⋊C8—21no—
239C3×C22⋊C8—21no—
240C3×C22⋊C8C2×D311yescharacteristic
241C3×C22⋊C8C2×D311yescharacteristic, complemented
242C3×C22⋊C8C22×C311yescharacteristic
243C3×C22⋊C8C22×C311yescharacteristic, complemented
244C3×#97—21no—
245C3×#97C2×D311yescharacteristic, complemented
246C3×#97C22×C311yescharacteristic, complemented
247#821C22×C311yescharacteristic
248#821C22×C311yescharacteristic
249#821C22×C311yescharacteristic, complemented
250#821C22×C311yescharacteristic, complemented
251#818C22×C311yescharacteristic, complemented
252#816C22×C311yescharacteristic, complemented
253#816C22×C311yescharacteristic, complemented
254C23×C32C2×D411yescharacteristic
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C32×D4—41no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—42no—
276C3×#67—81no—
277C3×#67—81no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12—42no—
292C3×D12—81no—
293C3×D12C2×D412yes—
294C3×C4×D3—42no—
295C3×C4×D3—42no—
296C3×C4×D3—42no—
297C3×C4×D3—81no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300C3×Dic6—21no—
301C3×Dic6C2×D412yes—
302C32×C8—21no—
303C32×C8—21no—
304C32×C8—21no—
305C32×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#447—31no—
319#440—31no—
320#435C3×D311yescharacteristic, complemented
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—62no—
326C3×#41—121no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—31no—
330C2×C3×Q8—31no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—121no—
347C2×C3×D4D1211yescharacteristic
348C2×C3×D4C3×D411yescharacteristic
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4—61no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C23×C311yescharacteristic
358C22×C3×C4C23×C311yescharacteristic
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—21no—
365#235—22no—
366#235—22no—
367#235—22no—
368#235—41no—
369#235—41no—
370#235—41no—
371C2×D12—22no—
372C2×D12—21no—
373C2×D12—21no—
374C2×D12—21no—
375C2×D12—41no—
376C2×D12C23×C311yescharacteristic
377C2×D12C23×C311yescharacteristic
378C2×D12C23×C311yescharacteristic
379C2×D12C23×C311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3—21no—
384C2×Dic6C23×C311yescharacteristic
385C2×Dic6C23×C311yescharacteristic
386C3×Q16—62no—
387C3×SD16—34no—
388C3×SD16—62no—
389C3×SD16—62no—
390C3×SD16—121no—
391C3×D8—62no—
392C3×D8—62no—
393C3×D8—62no—
394C3×D8—121no—
395C3×M16—22no—
396C3×M16—22no—
397C3×M16—42no—
398C2×C3×C8—22no—
399C2×C3×C8—22no—
400C2×C3×C8—21no—
401C2×C3×C8—21no—
402C2×C3×C8—21no—
403C2×C3×C8—21no—
404C2×C3×C8—42no—
405C2×C3×C8C22×D311yescharacteristic
406C2×C3×C8C22×D311yescharacteristic
407C2×C3×C8C22×D311yescharacteristic
408C2×C3×C8C22×D311yescharacteristic
409C2×C3×C8C23×C311yescharacteristic
410C2×C3×C8C23×C311yescharacteristic
411C2×C3×C8C23×C311yescharacteristic
412C2×C3×C8C23×C311yescharacteristic
413C3×C4⋊C4—21no—
414C3×C4⋊C4—31no—
415C3×C4⋊C4—31no—
416C3×C4⋊C4—61no—
417C3×C4⋊C4—61no—
418C3×C4⋊C4D1211yescharacteristic
419C3×C4⋊C4C3×D411yescharacteristic
420C3×C22⋊C4—21no—
421C3×C22⋊C4—21no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4D1211yescharacteristic
430C3×C22⋊C4D1211yescharacteristic
431C3×C22⋊C4C3×D411yescharacteristic
432C3×C22⋊C4C3×D411yescharacteristic
433C3×C42—21no—
434C3×C42—61no—
435C3×C42C22×D311yescharacteristic
436C3×C42C23×C311yescharacteristic
437#217—21no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4—21no—
444C4⋊Dic3C23×C311yescharacteristic
445C4⋊Dic3C23×C311yescharacteristic
446Dic3⋊C4—21no—
447Dic3⋊C4—21no—
448C4×Dic3—21no—
449Dic12—22no—
450D24—22no—
451D24—22no—
452D24—22no—
453D24—41no—
454#204—22no—
455#204—22no—
456#204—41no—
457#204C3×D414yescomplemented
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32C22×D411yescharacteristic
465C2×C3×D3—22no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—84no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3×Dic3—22no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—31no—
491C22×D4—31no—
492AGL(1,ℤ/8)—64no—
493#135—64no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—31no—
502C2×D8—31no—
503C2×M16C2×C3×D311yescharacteristic
504C22×C8C2×C3×D311yescharacteristic, complemented
505#127—31no—
506#127—61no—
507#124—31no—
508#123—61no—
509C22⋊Q8—31no—
510#121—31no—
511#121—31no—
512#121—31no—
513#121—61no—
514#121—61no—
515#121—61no—
516#120—61no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—61no—
520C4×D4C2×C3×D311yescharacteristic
521C2×C22⋊C4—61no—
522#107—31no—
523C4⋊C8C2×C3×D311yescharacteristic, complemented
524#103—31no—
525#103—31no—
526#102—31no—
527#102—31no—
528#102—31no—
529#102—31no—
530C22⋊C8C2×C3×D311yescharacteristic
531C22⋊C8C2×C3×D311yescharacteristic, complemented
532#97C2×C3×D311yescharacteristic, complemented
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—122no—
540C23×C3—122no—
541C23×C3—241no—
542C23×C3C2×D1211yescharacteristic
543C23×C3C2×D1211yescharacteristic
544C23×C3C2×C3×D411yescharacteristic
545C23×C3C2×C3×D411yescharacteristic
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—81no—
553C3×Q8—32no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—32no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—42no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—122no—
569C3×D4—122no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—241no—
574C3×D4—241no—
575C3×D4—241no—
576C3×D4—241no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
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—21no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—122no—
599C2×C3×C4—122no—
600C2×C3×C4—122no—
601C2×C3×C4—241no—
602C2×C3×C4C2×D1211yescharacteristic
603C2×C3×C4C2×D1211yescharacteristic
604C2×C3×C4C2×D1211yescharacteristic
605C2×C3×C4C2×D1211yescharacteristic
606C2×C3×C4C2×C3×D411yescharacteristic
607C2×C3×C4C2×C3×D411yescharacteristic
608C2×C3×C4C2×C3×D411yescharacteristic
609C2×C3×C4C2×C3×D411yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611C2×C3×C4C24×C311yescharacteristic
612#67—42no—
613#67—42no—
614#67—42no—
615#67—81no—
616#67—81no—
617#67—81no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622D12—21no—
623D12—21no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—21no—
628D12—21no—
629D12—42no—
630D12—42no—
631D12—81no—
632D12C2×C3×D412yes—
633C4×D3—42no—
634C4×D3—42no—
635C4×D3—42no—
636C4×D3—81no—
637Dic6—21no—
638Dic6—21no—
639Dic6—21no—
640Dic6C2×C3×D412yes—
641C3×C8—21no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—21no—
645C3×C8—21no—
646C3×C8—21no—
647C3×C8—22no—
648C3×C8—41no—
649C3×C8—41no—
650C3×C8—41no—
651C3×C8D3×D412yes—
652C3×C8C2×C3×D412yes—
653C2×C32—41no—
654C2×C32—41no—
655C2×C32D4211yescharacteristic
656C2×C32#57511yescharacteristic
657C2×C32#57611yescharacteristic
658C3×D3—42no—
659C3×D3—81no—
660C3×D3—81no—
661C3×D3—81no—
662C24—61no—
663#41—62no—
664#41—62no—
665#41—62no—
666#41—121no—
667#41—121no—
668#41—121no—
669C2×Q8—31no—
670C2×Q8—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—62no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—121no—
686C2×D4C3×D1211yescharacteristic
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4C22×C3×D311yescharacteristic
692C22×C4C22×C3×D311yescharacteristic
693Q16—62no—
694SD16—34no—
695SD16—62no—
696SD16—62no—
697SD16—121no—
698D8—62no—
699D8—62no—
700D8—62no—
701D8—121no—
702M16—22no—
703C2×C8—22no—
704C2×C8C22×C3×D311yescharacteristic
705C2×C8C22×C3×D311yescharacteristic
706C2×C8C22×C3×D311yescharacteristic
707C2×C8C22×C3×D311yescharacteristic
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—61no—
711C4⋊C4—61no—
712C4⋊C4C3×D1211yescharacteristic
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4C3×D1211yescharacteristic
721C22⋊C4C3×D1211yescharacteristic
722C42—61no—
723C42C22×C3×D311yescharacteristic
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—62no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—244no—
756C22×C3C22×D1211yescharacteristic
757C22×C3C22×C3×D411yescharacteristic
758C2×D3—22no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—84no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—62no—
786C3×C4—121no—
787C3×C4—121no—
788C3×C4—121no—
789C3×C4C2×D3×D411yescharacteristic
790C3×C4#100911yescharacteristic
791C3×C4C22×C3×D411yescharacteristic
792C3×C4C3×H(5,𝔽2)11yescharacteristic
793Dic3—22no—
794Dic3—41no—
795Dic3—41no—
796Dic3—41no—
797C32#326811yescharacteristic, complemented, Sylow
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—122no—
803C23—122no—
804C23—241no—
805C23C2×C3×D1211yescharacteristic
806C23C2×C3×D1211yescharacteristic
807Q8—32no—
808Q8—61no—
809Q8—61no—
810Q8—61no—
811D4—32no—
812D4—41no—
813D4—61no—
814D4—61no—
815D4—61no—
816D4—61no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—122no—
821D4—122no—
822D4—122no—
823D4—122no—
824D4—122no—
825D4—241no—
826D4—241no—
827D4—241no—
828D4—241no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C4—122no—
840C2×C4—241no—
841C2×C4C2×C3×D1211yescharacteristic
842C2×C4C2×C3×D1211yescharacteristic
843C2×C4C2×C3×D1211yescharacteristic
844C2×C4C2×C3×D1211yescharacteristic
845C2×C4C23×C3×D311yescharacteristic
846C8—21no—
847C8—21no—
848C8—21no—
849C8C3×D3×D412yes—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—42no—
854C2×C3—41no—
855C2×C3—41no—
856C2×C3—41no—
857C2×C3—41no—
858C2×C3—81no—
859C2×C3—122no—
860C2×C3—241no—
861C2×C3—241no—
862C2×C3—241no—
863C2×C3D4×D1211yescharacteristic
864C2×C3#574811yescharacteristic
865C2×C3#575211yescharacteristic
866C2×C3C3×D4211yescharacteristic
867C2×C3C3×#57511yescharacteristic
868C2×C3C3×#57611yescharacteristic
869D3—42no—
870D3—81no—
871D3—81no—
872D3—81no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—62no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—244no—
892C22C22×C3×D1211yescharacteristic
893C4—21no—
894C4—21no—
895C4—21no—
896C4—21no—
897C4—62no—
898C4—121no—
899C4—121no—
900C4—121no—
901C4C2×C3×D3×D411yescharacteristic
902C4C3×#100911yescharacteristic
903C3—21no—
904C3#7949711yescharacteristic, direct product factor
905C3C3×#326811yescharacteristic, complemented
906C2—41no—
907C2—41no—
908C2—122no—
909C2—241no—
910C2—241no—
911C2—241no—
912C2C3×D4×D1211yescharacteristic
913C2C3×#574811yescharacteristic
914C2C3×#575211yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#435C2
socleC22×C32C22×D4
hypercenterC3×#435D3
hypocenterC3C3×#3268
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#435

Complements

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

NH ≅ G/Ntype
1. C2×C3×#908C2semidirect
2. C2×C3×#904C2semidirect
3. C3×#5553C2semidirect
4. C3×#5550C2semidirect
5. C32×#435C2semidirect
6. C3×#5134C2semidirect
7. C3×#5115C2semidirect
8. C3×#4845C2semidirect
9. C3×#4843C2semidirect
10. C3×#4734C2semidirect
11. C3×#4734C2semidirect
12. C3×#4733C2semidirect
13. C3×#4732C2semidirect
14. C3×#4712C2semidirect
15. C3×#4710C2semidirect
17. #79497C3direct (N × H)
20. C2×C3×#235C22semidirect
23. C22×C32×C8C22semidirect
29. C3×#930C22semidirect
32. C2×C3×Dic12C22semidirect
40. C2×C3×#204C22semidirect
41. C2×C3×#204C22semidirect
49. C3×#874C22semidirect
51. C3×C4×Dic6C22semidirect
52. C32×C4⋊C8C22semidirect
54. C32×C22⋊C8C22semidirect
55. C32×#97C22semidirect
58. C3×#821C22semidirect
59. C3×#821C22semidirect
60. C3×#818C22semidirect
61. C3×#816C22semidirect
62. C3×#816C22semidirect
67. C2×#908C2×C3semidirect
68. C2×#904C2×C3semidirect
69. #5553C2×C3semidirect
70. #5550C2×C3semidirect
82. C3×#435D3semidirect
83. C3×#435C2×C3semidirect
84. #5134C2×C3semidirect
85. #5115C2×C3semidirect
86. #4845C2×C3semidirect
87. #4843C2×C3semidirect
88. #4734C2×C3semidirect
89. #4734C2×C3semidirect
90. #4733C2×C3semidirect
91. #4732C2×C3semidirect
92. #4712C2×C3semidirect
93. #4710C2×C3semidirect
155. C3×#204D4semidirect
163. C2×#235C22×C3semidirect
180. C22×C3×C8C2×D3semidirect
181. C22×C3×C8C22×C3semidirect
205. #930C22×C3semidirect
208. C2×Dic12C22×C3semidirect
216. C2×#204C22×C3semidirect
217. C2×#204C22×C3semidirect
225. #874C22×C3semidirect
227. C4×Dic6C22×C3semidirect
230. C3×C4⋊C8C2×D3semidirect
231. C3×C4⋊C8C22×C3semidirect
241. C3×C22⋊C8C2×D3semidirect
243. C3×C22⋊C8C22×C3semidirect
245. C3×#97C2×D3semidirect
246. C3×#97C22×C3semidirect
249. #821C22×C3semidirect
250. #821C22×C3semidirect
251. #818C22×C3semidirect
252. #816C22×C3semidirect
253. #816C22×C3semidirect
320. #435C3×D3semidirect
457. #204C3×D4semidirect
504. C22×C8C2×C3×D3semidirect
523. C4⋊C8C2×C3×D3semidirect
531. C22⋊C8C2×C3×D3semidirect
532. #97C2×C3×D3semidirect
797. C32#3268semidirect
904. C3#79497direct (N × H)
905. C3C3×#3268semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C2×C3×#9042
C3×#55532
C3×#55502
C32×#4352
C3×#51342
C3×#51152
C3×#48452
C3×#48432
C3×#47342
C3×#47332
C3×#47322
C3×#47122
C3×#47102
C3×#32683
#794973