Finite Group Databasebeta

← C3×#83714 #11896115

Subgroups — C3×#83714 #11896115

Order 1152.

834 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#559C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×#5072C211yesmaximal, characteristic
4C3×#5071C211yesmaximal, characteristic, complemented
5C3×#5057C211yesmaximal, characteristic, complemented
6C3×#5057C211yesmaximal, characteristic, complemented
7C3×#5056C211yesmaximal, characteristic, complemented
8C3×#5055C211yesmaximal, characteristic, complemented
9C3×#5026C211yesmaximal, characteristic, complemented
10C3×#5024C211yesmaximal, characteristic, complemented
11C3×#5022C211yesmaximal, characteristic, complemented
12C3×#5014C211yesmaximal, characteristic, complemented
13C3×C4×#213C211yesmaximal, characteristic, complemented
14C3×#5009C211yesmaximal, characteristic, complemented
15C3×#5007C211yesmaximal, characteristic, complemented
16C3×#3370—31nomaximal
17#83714C311yesmaximal, characteristic, direct product factor
18C32×#127C2211yescharacteristic
19C32×#124—21no—
20C32×#124C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C32×#123—21no—
23C32×#123—21no—
24C32×C4×Q8C2211yescharacteristic
25C32×C4×Q8C2211yescharacteristic
26C32×C4×D4—21no—
27C32×C4×D4C2211yescharacteristic
28C32×C4×D4C2211yescharacteristic
29C3×#946—21no—
30C2×C3×#215C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#896—21no—
34C3×#896—21no—
35C3×D3×C4⋊C4—21no—
36C3×C4×D12C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39C3×#870C2211yescharacteristic
40C3×#870C2211yescharacteristic
41C3×#869C2211yescharacteristic
42C3×#835C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×#807C2211yescharacteristic
54C3×#807C2211yescharacteristic
55C3×C4⋊(C3⋊C8)C2211yescharacteristic
56C3×C4⋊(C3⋊C8)C2211yescharacteristic
57C3×C4⋊(C3⋊C8)C2211yescharacteristic
58C3×#803C2211yescharacteristic
59C3×#803C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#559—21no—
62C3×#559D311yescharacteristic, complemented
63C3×#559C2×C311yescharacteristic, complemented
64C3×#554—31no—
65#5579C2×C311yescharacteristic, complemented
66C3×#490—31no—
67C3×#489—31no—
68C3×#488—31no—
69C3×#479—31no—
70C3×#478—31no—
71C3×#474—31no—
72C3×#463—31no—
73C3×#463—31no—
74C3×#459—31no—
75C3×#446—31no—
76C3×#442—31no—
77C3×#440—31no—
78C3×C4×D8—31no—
79#5072C2×C311yescharacteristic
80#5071C2×C311yescharacteristic, complemented
81#5057C2×C311yescharacteristic, complemented
82#5057C2×C311yescharacteristic, complemented
83#5056C2×C311yescharacteristic, complemented
84#5055C2×C311yescharacteristic, complemented
85#5026C2×C311yescharacteristic, complemented
86#5024C2×C311yescharacteristic, complemented
87#5022C2×C311yescharacteristic, complemented
88#5014C2×C311yescharacteristic, complemented
89C4×#213C2×C311yescharacteristic, complemented
90#5009C2×C311yescharacteristic, complemented
91#5007C2×C311yescharacteristic, complemented
92C2×C32×Q8D411yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4—21no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×Dic6—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4D411yescharacteristic
107C32×C4⋊C4D411yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C22⋊C4—21no—
116C32×C42—21no—
117C32×C42C2311yescharacteristic
118C32×C42C2311yescharacteristic
119C32×C42C2311yescharacteristic
120C3×#215—22no—
121C3×#213—22no—
122C3×#213—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3370—31noSylow
139C2×C3×SD16—31no—
140C2×C3×D8—31no—
141C2×C3×D8—31no—
142C3×C4⋊Q8—31no—
143C3×#127—21no—
144C3×#127C2×D311yescharacteristic
145C3×#127C22×C311yescharacteristic
146C3×#125—31no—
147C3×#125—31no—
148C3×#124—22no—
149C3×#124—21no—
150C3×#124—21no—
151C3×#124—21no—
152C3×#124—21no—
153C3×#124C2×D311yescharacteristic
154C3×#124C2×D311yescharacteristic
155C3×#124C22×C311yescharacteristic
156C3×#124C22×C311yescharacteristic
157C3×#123—22no—
158C3×#123—22no—
159C3×#123—21no—
160C3×#123—21no—
161C3×#123—21no—
162C3×#123—21no—
163C3×C22⋊Q8—61no—
164C3×C22⋊Q8—61no—
165C3×C22⋊Q8—61no—
166C3×C4×Q8—21no—
167C3×C4×Q8—21no—
168C3×C4×Q8C2×D311yescharacteristic
169C3×C4×Q8C2×D311yescharacteristic
170C3×C4×Q8C22×C311yescharacteristic
171C3×C4×Q8C22×C311yescharacteristic
172C3×C4×D4—22no—
173C3×C4×D4—21no—
174C3×C4×D4—21no—
175C3×C4×D4—21no—
176C3×C4×D4—21no—
177C3×C4×D4—31no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C3×C4×D4C2×D311yescharacteristic
181C3×C4×D4C2×D311yescharacteristic
182C3×C4×D4C22×C311yescharacteristic
183C3×C4×D4C22×C311yescharacteristic
184C2×C3×C4⋊C4—61no—
185#946—21no—
186C2×#215C22×C311yescharacteristic
187C2×#213C22×C311yescharacteristic
188C2×#213C22×C311yescharacteristic
189#896—21no—
190#896—21no—
191D3×C4⋊C4—21no—
192C4×D12C22×C311yescharacteristic
193C4×D12C22×C311yescharacteristic
194C4×D12C22×C311yescharacteristic
195#870C22×C311yescharacteristic
196#870C22×C311yescharacteristic
197#869C22×C311yescharacteristic
198C3×#107—31no—
199C3×#107—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#97—31no—
215C3×#97—31no—
216C3×C4×C8—31no—
217#835C22×C311yescharacteristic
218#835C22×C311yescharacteristic
219#835C22×C311yescharacteristic
220#832C22×C311yescharacteristic
221#832C22×C311yescharacteristic
222#832C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#832C22×C311yescharacteristic
225#832C22×C311yescharacteristic
226#809C22×C311yescharacteristic
227#808C22×C311yescharacteristic
228#807C22×C311yescharacteristic
229#807C22×C311yescharacteristic
230C4⋊(C3⋊C8)C22×C311yescharacteristic
231C4⋊(C3⋊C8)C22×C311yescharacteristic
232C4⋊(C3⋊C8)C22×C311yescharacteristic
233#803C22×C311yescharacteristic
234#803C22×C311yescharacteristic
235C4×C3⋊C8C22×C311yescharacteristic
236C23×C32—21no—
237C23×C32—21no—
238C22×C3×D3—21no—
239C32×Q8—21no—
240C32×Q8—21no—
241C32×Q8—41no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4—42no—
247C32×D4—81no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—81no—
251C2×C32×C4—81no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—42no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267C3×Dic6—81no—
268C3×C3⋊C8—21no—
269C3×C3⋊C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#559C3×D311yescharacteristic, complemented
273#554—31no—
274#490—31no—
275#489—31no—
276#488—31no—
277#479—31no—
278#478—31no—
279#474—31no—
280#463—31no—
281#463—31no—
282#459—31no—
283#446—31no—
284#442—31no—
285#440—31no—
286C4×D8—31no—
287C2×C3×Q8—21no—
288C2×C3×Q8—21no—
289C2×C3×Q8—61no—
290C2×C3×Q8#6711yescharacteristic
291C2×C3×Q8C3×D411yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C2×C3×D4—22no—
295C2×C3×D4—22no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C23×C311yescharacteristic
306C2×C3×D4C23×C311yescharacteristic
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×D12C23×C311yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×Dic6—21no—
321C3×SD16—62no—
322C3×D8—62no—
323C3×D8—62no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4#6711yescharacteristic
344C3×C4⋊C4#6711yescharacteristic
345C3×C4⋊C4#6711yescharacteristic
346C3×C4⋊C4C3×D411yescharacteristic
347C3×C4⋊C4C3×D411yescharacteristic
348C3×C4⋊C4C3×D411yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C23×C311yescharacteristic
351C3×C22⋊C4—22no—
352C3×C22⋊C4—22no—
353C3×C22⋊C4—22no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C42—22no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42C22×D311yescharacteristic
379C3×C42C22×D311yescharacteristic
380C3×C42C22×D311yescharacteristic
381C3×C42C23×C311yescharacteristic
382C3×C42C23×C311yescharacteristic
383C3×C42C23×C311yescharacteristic
384#215—22no—
385#213—22no—
386#213—22no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3C23×C311yescharacteristic
392C4⋊Dic3C23×C311yescharacteristic
393C4⋊Dic3C23×C311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398C2×C3⋊C8C23×C311yescharacteristic
399C2×C3⋊C8C23×C311yescharacteristic
400C2×C3⋊C8C23×C311yescharacteristic
401C2×C3⋊C8C23×C311yescharacteristic
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32C22×D411yescharacteristic
409C2×C3×D3—22no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C42−1+411yescharacteristic
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C2×SD16—31no—
426C2×D8—31no—
427C2×D8—31no—
428C4⋊Q8—31no—
429#127C2×C3×D311yescharacteristic
430#125—31no—
431#125—31no—
432#124—21no—
433#124C2×C3×D311yescharacteristic
434#124C2×C3×D311yescharacteristic
435#123—21no—
436#123—21no—
437C22⋊Q8—61no—
438C22⋊Q8—61no—
439C22⋊Q8—61no—
440C4×Q8C2×C3×D311yescharacteristic
441C4×Q8C2×C3×D311yescharacteristic
442C4×D4—21no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4C2×C3×D311yescharacteristic
447C4×D4C2×C3×D311yescharacteristic
448C2×C4⋊C4—61no—
449#107—31no—
450#107—31no—
451#106—31no—
452C4⋊C8—31no—
453C4⋊C8—31no—
454C4⋊C8—31no—
455#103—31no—
456#103—31no—
457#103—31no—
458#102—31no—
459#102—31no—
460#102—31no—
461#102—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465#97—31no—
466#97—31no—
467C4×C8—31no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—61no—
475C22×D3—21no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×Q8—42no—
485C3×Q8—241no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—32no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—44no—
500C3×D4—42no—
501C3×D4—42no—
502C3×D4—61no—
503C3×D4—81no—
504C3×D4—81no—
505C3×D4—82no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—81no—
523C2×C3×C4—81no—
524C2×C3×C4—81no—
525C2×C3×C4—81no—
526C2×C3×C4—82no—
527C2×C3×C4—82no—
528C2×C3×C4—122no—
529C2×C3×C4—241no—
530C2×C3×C4—241no—
531C2×C3×C4C2×#6711yescharacteristic
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C2×#6711yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C2×C3×D411yescharacteristic
538C2×C3×C4C2×C3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C2×C3×D411yescharacteristic
541C2×C3×C4C2×C3×D411yescharacteristic
542C2×C3×C4C2×C3×D411yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C24×C311yescharacteristic
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548D12—21no—
549D12C3×#4112yes—
550C4×D3—42no—
551C4×D3—81no—
552C4×D3—81no—
553Dic6—81no—
554C3×C8—61no—
555C3×C8—61no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C2×C32—81no—
563C2×C32—81no—
564C2×C32#54811yescharacteristic
565C2×C32#57511yescharacteristic
566C2×C32#57611yescharacteristic
567C3×D3—42no—
568C2×Q8—61no—
569C2×Q8C3×#6711yescharacteristic
570C2×Q8C22×C3×D311yescharacteristic
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—31no—
574C2×D4C22×C3×D311yescharacteristic
575C2×D4C22×C3×D311yescharacteristic
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581SD16—62no—
582D8—62no—
583D8—62no—
584C2×C8—31no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—31no—
588C4⋊C4—21no—
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4C3×#6711yescharacteristic
598C4⋊C4C3×#6711yescharacteristic
599C4⋊C4C3×#6711yescharacteristic
600C4⋊C4C22×C3×D311yescharacteristic
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C42—21no—
611C42C22×C3×D311yescharacteristic
612C42C22×C3×D311yescharacteristic
613C42C22×C3×D311yescharacteristic
614C22×C3—21no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—62no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3C22×#6711yescharacteristic
637C22×C3C22×C3×D411yescharacteristic
638C2×D3—22no—
639C2×D3—41no—
640C2×D3—41no—
641C3×C4—22no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4D3×#4111yescharacteristic
671C3×C4#101011yescharacteristic
672C3×C4C2×C3×#4111yescharacteristic
673C3×C4C3×2−1+411yescharacteristic
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677C32#337011yescharacteristic, complemented, Sylow
678C23—21no—
679C23—21no—
680C23—61no—
681Q8—21no—
682Q8—21no—
683Q8—41no—
684Q8—241no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—32no—
690D4—42no—
691D4—61no—
692D4—81no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—122no—
701C2×C4—241no—
702C2×C4—241no—
703C2×C4C2×C3×#6711yescharacteristic
704C2×C4C2×C3×#6711yescharacteristic
705C2×C4C2×C3×#6711yescharacteristic
706C2×C4C2×C3×#6711yescharacteristic
707C2×C4C2×C3×#6711yescharacteristic
708C2×C4C2×C3×#6711yescharacteristic
709C2×C4C23×C3×D311yescharacteristic
710C8—61no—
711C8—61no—
712C8—61no—
713C8—61no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—82no—
718C2×C3—82no—
719C2×C3—81no—
720C2×C3—81no—
721C2×C3—81no—
722C2×C3—81no—
723C2×C3—122no—
724C2×C3#582211yescharacteristic
725C2×C3#583111yescharacteristic
726C2×C3#583511yescharacteristic
727C2×C3C3×#54811yescharacteristic
728C2×C3C3×#57511yescharacteristic
729C2×C3C3×#57611yescharacteristic
730D3—42no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—62no—
738C22—121no—
739C22—121no—
740C22C22×C3×#6711yescharacteristic
741C4—21no—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—41no—
748C4—41no—
749C4—121no—
750C4—121no—
751C4—121no—
752C4C3×D3×#4111yescharacteristic
753C4C3×#101011yescharacteristic
754C3—21no—
755C3#8371411yescharacteristic, direct product factor
756C3C3×#337011yescharacteristic, complemented
757C2—81no—
758C2—81no—
759C2—122no—
760C2C3×#582211yescharacteristic
761C2C3×#583111yescharacteristic
762C2C3×#583511yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#559C2
socleC22×C32C22×D4
prime radicalC3×#5072C2
hypercenterC3×#559D3
hypocenterC3C3×#3370
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#559

Complements

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

NH ≅ G/Ntype
1. C32×#559C2semidirect
2. C3×#5579C2semidirect
4. C3×#5071C2semidirect
5. C3×#5057C2semidirect
6. C3×#5057C2semidirect
7. C3×#5056C2semidirect
8. C3×#5055C2semidirect
9. C3×#5026C2semidirect
10. C3×#5024C2semidirect
11. C3×#5022C2semidirect
12. C3×#5014C2semidirect
13. C3×C4×#213C2semidirect
14. C3×#5009C2semidirect
15. C3×#5007C2semidirect
17. #83714C3direct (N × H)
62. C3×#559D3semidirect
63. C3×#559C2×C3semidirect
65. #5579C2×C3semidirect
80. #5071C2×C3semidirect
81. #5057C2×C3semidirect
82. #5057C2×C3semidirect
83. #5056C2×C3semidirect
84. #5055C2×C3semidirect
85. #5026C2×C3semidirect
86. #5024C2×C3semidirect
87. #5022C2×C3semidirect
88. #5014C2×C3semidirect
89. C4×#213C2×C3semidirect
90. #5009C2×C3semidirect
91. #5007C2×C3semidirect
272. #559C3×D3semidirect
677. C32#3370semidirect
755. C3#83714direct (N × H)
756. C3C3×#3370semidirect

Maximal subgroups

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

subgroupindex
C32×#5592
C3×#55792
C3×#50722
C3×#50712
C3×#50572
C3×#50562
C3×#50552
C3×#50262
C3×#50242
C3×#50222
C3×#50142
C3×C4×#2132
C3×#50092
C3×#50072
C3×#33703
#837143