Finite Group Databasebeta

← C3×#80137 #11872783

Subgroups — C3×#80137 #11872783

Order 1152.

882 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2C3×#5625C211yesmaximal, characteristic, complemented
3C32×#450C211yesmaximal, characteristic
4C3×#5218C211yesmaximal, characteristic
5C3×#5164C211yesmaximal, characteristic, complemented
6C3×#5162C211yesmaximal, characteristic, complemented
7C3×#5162C211yesmaximal, characteristic, complemented
8C3×Dic3×SD16C211yesmaximal, characteristic, complemented
9C3×#5045C211yesmaximal, characteristic, complemented
10C3×#4766C211yesmaximal, characteristic, complemented
11C3×#4763C211yesmaximal, characteristic, complemented
12C3×#4758C211yesmaximal, characteristic, complemented
13C3×#4757C211yesmaximal, characteristic, complemented
14C3×#4723C211yesmaximal, characteristic, complemented
15C3×#4720C211yesmaximal, characteristic, complemented
16C3×#3123—31nomaximal
17#80137C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×C3×#217—21no—
23C2×C3×#217—21no—
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C3×#944C2211yescharacteristic, complemented
26C3×D4×Dic3—21no—
27C3×D4×Dic3—21no—
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C3×D4×Dic3C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic
34C3×#926C2211yescharacteristic
35C3×#926C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C3×#890—21no—
38C3×#890C2211yescharacteristic, complemented
39C3×#889—21no—
40C3×#887C2211yescharacteristic, complemented
41C3×#879—21no—
42C3×#879—21no—
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C8×Dic3C2211yescharacteristic, complemented
59C3×#808C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#541—31no—
62C3×#518—31no—
63#5798C2×C311yescharacteristic
64#5625C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#485—31no—
67C3×#478—31no—
68C3×#478—31no—
69C3×#461—31no—
70C3×#461—31no—
71C3×#450—21no—
72C3×#450—31no—
73C3×#450D311yescharacteristic
74C3×#450C2×C311yescharacteristic
75C3×#440—31no—
76C3×#440—31no—
77C3×C4×SD16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5218C2×C311yescharacteristic
81#5164C2×C311yescharacteristic, complemented
82#5162C2×C311yescharacteristic, complemented
83#5162C2×C311yescharacteristic, complemented
84Dic3×SD16C2×C311yescharacteristic, complemented
85#5045C2×C311yescharacteristic, complemented
86#4766C2×C311yescharacteristic, complemented
87#4763C2×C311yescharacteristic, complemented
88#4758C2×C311yescharacteristic, complemented
89#4757C2×C311yescharacteristic, complemented
90#4723C2×C311yescharacteristic, complemented
91#4720C2×C311yescharacteristic, complemented
92C24×C32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4—22no—
95C2×C32×D4—22no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C2×C3×Dic6C2311yescharacteristic
105C32×SD16—22no—
106C32×SD16—22no—
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C3×#217—21no—
113C3×#217—21no—
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#217D411yescharacteristic
120C3×#214—22no—
121C3×#214—22no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3123—31noSylow
142C22×C3×D4—21no—
143C22×C3×D4C2×D311yescharacteristic
144C22×C3×D4C22×C311yescharacteristic
145C2×C3×SD16—21no—
146C2×C3×SD16—21no—
147C2×C3×SD16—31no—
148C2×C3×SD16—31no—
149C2×C3×SD16C2×D311yescharacteristic
150C2×C3×SD16C2×D311yescharacteristic
151C2×C3×SD16C22×C311yescharacteristic
152C2×C3×SD16C22×C311yescharacteristic
153C3×C4⋊Q8—31no—
154C3×#126—61no—
155C3×#126—61no—
156C3×#125—31no—
157C3×#125—61no—
158C3×#125—61no—
159C3×C22⋊Q8—21no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8C2×D311yescharacteristic
162C3×C22⋊Q8C22×C311yescharacteristic
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—61no—
170C3×C4×D4—61no—
171C3×#117—31no—
172C3×#117—31no—
173C2×C3×C22⋊C4—61no—
174C2×C3×C22⋊C4—61no—
175C2×#217—21no—
176C2×#217—21no—
177Q8×Dic3C22×C311yescharacteristic, complemented
178#944C22×C311yescharacteristic, complemented
179D4×Dic3—21no—
180D4×Dic3—21no—
181D4×Dic3C22×C311yescharacteristic
182D4×Dic3C22×C311yescharacteristic
183D4×Dic3C22×C311yescharacteristic
184D4×Dic3C22×C311yescharacteristic
185C2×#214C22×C311yescharacteristic
186C2×#214C22×C311yescharacteristic
187#926C22×C311yescharacteristic
188#926C22×C311yescharacteristic
189#924C22×C311yescharacteristic
190#890—21no—
191#890C22×C311yescharacteristic, complemented
192#889—21no—
193#887C22×C311yescharacteristic, complemented
194#879—21no—
195#879—21no—
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—21no—
207C3×#102—21no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102C2×D311yescharacteristic
211C3×#102C2×D311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×C22⋊C8—21no—
215C3×C22⋊C8—31no—
216C3×C22⋊C8C2×D311yescharacteristic
217C3×C22⋊C8C22×C311yescharacteristic
218C3×#97—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic, complemented
221#835C22×C311yescharacteristic, complemented
222#832C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#830C22×C311yescharacteristic
225#818C22×C311yescharacteristic, complemented
226#817C22×C311yescharacteristic, complemented
227#816C22×C311yescharacteristic, complemented
228#816C22×C311yescharacteristic, complemented
229#815C22×C311yescharacteristic, complemented
230Dic3⋊C8C22×C311yescharacteristic, complemented
231Dic3⋊C8C22×C311yescharacteristic, complemented
232C8×Dic3C22×C311yescharacteristic, complemented
233#808C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235C23×C32—24no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—81no—
239C23×C32—81no—
240C23×C32C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×D4—24no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C32×D4#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×Dic6—21no—
267C3×Dic6—21no—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—31no—
273#518—31no—
274#485—31no—
275#485—31no—
276#478—31no—
277#478—31no—
278#461—31no—
279#461—31no—
280#450—31no—
281#450C3×D311yescharacteristic
282#440—31no—
283#440—31no—
284C4×SD16—31no—
285C4×SD16—31no—
286#433—31no—
287C24×C3—21no—
288C24×C3—21no—
289C24×C3—41no—
290C2×C3×Q8—21no—
291C2×C3×Q8—31no—
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C2×C3×D4—22no—
295C2×C3×D4—22no—
296C2×C3×D4—22no—
297C2×C3×D4—22no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—41no—
303C2×C3×D4—42no—
304C2×C3×D4—42no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C23×C311yescharacteristic
308C2×C3×D4C23×C311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C23×C311yescharacteristic
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C2×Dic6C23×C311yescharacteristic
321C3×SD16—22no—
322C3×SD16—22no—
323C3×SD16—22no—
324C3×SD16—22no—
325C3×SD16—42no—
326C3×SD16—42no—
327C3×SD16—62no—
328C3×SD16—62no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C23×C311yescharacteristic
336C2×C3×C8C23×C311yescharacteristic
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—41no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C23×C311yescharacteristic
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—41no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367C3×C42—31no—
368C3×C42—61no—
369C3×C42—61no—
370C3×C42—61no—
371#217—21no—
372#217—21no—
373#217—21no—
374#217—21no—
375#217—21no—
376#217—21no—
377#217C3×D411yescharacteristic
378#217C3×D411yescharacteristic
379#214—22no—
380#214—22no—
381C4⋊Dic3—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3C3×D411yescharacteristic
384C4⋊Dic3C3×D411yescharacteristic
385C4⋊Dic3C23×C311yescharacteristic
386C4⋊Dic3C23×C311yescharacteristic
387C4⋊Dic3C23×C311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3C23×C311yescharacteristic
397C4×Dic3C23×C311yescharacteristic
398C2×C3⋊C8C23×C311yescharacteristic
399C2×C3⋊C8C23×C311yescharacteristic
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—22no—
403C22×C32—22no—
404C22×C32—21no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32—84no—
410C22×C32C22×D411yescharacteristic
411C32×C4—21no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—21no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C22×D4C2×C3×D311yescharacteristic
425C2×SD16—31no—
426C2×SD16—31no—
427C2×SD16C2×C3×D311yescharacteristic
428C2×SD16C2×C3×D311yescharacteristic
429C4⋊Q8—31no—
430#126—61no—
431#126—61no—
432#125—31no—
433#125—61no—
434#125—61no—
435C22⋊Q8—31no—
436C22⋊Q8C2×C3×D311yescharacteristic
437C4×Q8—31no—
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—61no—
444C4×D4—61no—
445#117—31no—
446#117—31no—
447C2×C22⋊C4—61no—
448C2×C22⋊C4—61no—
449#107—31no—
450#107—31no—
451#106—31no—
452#106—31no—
453C4⋊C8—31no—
454C4⋊C8—31no—
455#103—31no—
456#103—31no—
457#103—31no—
458#103—31no—
459#102—31no—
460#102—31no—
461#102C2×C3×D311yescharacteristic
462#102C2×C3×D311yescharacteristic
463C22⋊C8—31no—
464C22⋊C8C2×C3×D311yescharacteristic
465#97—31no—
466C4×C8—31no—
467C23×C3—24no—
468C23×C3—24no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—44no—
477C23×C3—81no—
478C23×C3—81no—
479C23×C3—81no—
480C23×C3—81no—
481C23×C3—82no—
482C23×C3—82no—
483C23×C3D3×D411yescharacteristic
484C23×C3C2×C3×D411yescharacteristic
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×D4—24no—
494C3×D4—24no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—22no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—44no—
504C3×D4#23712yes—
505C3×D4#23712yes—
506C3×D4C3×#4112yes—
507C3×D4C3×#4112yes—
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—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—241no—
531C2×C3×C4—241no—
532C2×C3×C4—241no—
533C2×C3×C4—241no—
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C2×C3×D411yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C24×C311yescharacteristic
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—81no—
543C2×Dic3—81no—
544C2×Dic3—81no—
545C2×Dic3—81no—
546C2×Dic3C2×C3×D411yescharacteristic
547C2×Dic3C2×C3×D411yescharacteristic
548C2×Dic3C2×C3×D411yescharacteristic
549C2×Dic3C2×C3×D411yescharacteristic
550Dic6—21no—
551Dic6—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—41no—
557C3×C8—41no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C2×C32—41no—
563C2×C32—42no—
564C2×C32—42no—
565C2×C32#52511yescharacteristic
566C2×C32#57711yescharacteristic
567C2×C32#57711yescharacteristic
568C24—21no—
569C2×Q8—31no—
570C2×Q8C22×C3×D311yescharacteristic
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4C22×C3×D311yescharacteristic
575C2×D4C22×C3×D311yescharacteristic
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4C22×C3×D311yescharacteristic
581SD16—22no—
582SD16—22no—
583SD16—62no—
584SD16—62no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8C22×C3×D311yescharacteristic
588C2×C8C22×C3×D311yescharacteristic
589C4⋊C4—21no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4C22×C3×D311yescharacteristic
603C22⋊C4—21no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C42—31no—
613C42—31no—
614C42—61no—
615C42—61no—
616C42—61no—
617C22×C3—22no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—84no—
646C22×C3—84no—
647C22×C3—88no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C22×C3×D411yescharacteristic
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4C2×#23711yescharacteristic
670C3×C4C2×#23711yescharacteristic
671C3×C4C2×C3×#4111yescharacteristic
672C3×C4C2×C3×#4111yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681C32#312311yescharacteristic, complemented, Sylow
682C23—24no—
683C23—21no—
684C23—21no—
685C23—81no—
686C23—81no—
687C23C3×D3×D411yescharacteristic
688Q8—21no—
689Q8—21no—
690Q8—61no—
691Q8—61no—
692D4—24no—
693D4—21no—
694D4—21no—
695D4C3×#23712yes—
696D4C3×#23712yes—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—241no—
710C2×C4—241no—
711C2×C4—241no—
712C2×C4—241no—
713C2×C4C3×D3×D411yescharacteristic
714C2×C4C23×C3×D311yescharacteristic
715C8—21no—
716C8—21no—
717C8—61no—
718C8—61no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—42no—
723C2×C3—41no—
724C2×C3—42no—
725C2×C3—42no—
726C2×C3—41no—
727C2×C3—42no—
728C2×C3—42no—
729C2×C3—82no—
730C2×C3—82no—
731C2×C3#558611yescharacteristic
732C2×C3#576211yescharacteristic
733C2×C3#577511yescharacteristic
734C2×C3C3×#52511yescharacteristic
735C2×C3C3×#57711yescharacteristic
736C2×C3C3×#57711yescharacteristic
737C22—21no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—84no—
747C22C2×C3×D3×D411yescharacteristic
748C4—21no—
749C4—41no—
750C4—41no—
751C4—61no—
752C4—61no—
753C4—61no—
754C4—61no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4C2×C3×#23711yescharacteristic
760C4C2×C3×#23711yescharacteristic
761C3—21no—
762C3#8013711yescharacteristic, direct product factor
763C3C3×#312311yescharacteristic, complemented
764C2—41no—
765C2—42no—
766C2—42no—
767C2C3×#558611yescharacteristic
768C2C3×#576211yescharacteristic
769C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radicalC22×C32×D4C22
hypercenterC3×#450D3
hypocenterC3C3×#3123
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×#5625C2semidirect
5. C3×#5164C2semidirect
6. C3×#5162C2semidirect
7. C3×#5162C2semidirect
8. C3×Dic3×SD16C2semidirect
9. C3×#5045C2semidirect
10. C3×#4766C2semidirect
11. C3×#4763C2semidirect
12. C3×#4758C2semidirect
13. C3×#4757C2semidirect
14. C3×#4723C2semidirect
15. C3×#4720C2semidirect
17. #80137C3direct (N × H)
24. C3×Q8×Dic3C22semidirect
25. C3×#944C22semidirect
38. C3×#890C22semidirect
40. C3×#887C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
51. C3×#818C22semidirect
52. C3×#817C22semidirect
53. C3×#816C22semidirect
54. C3×#816C22semidirect
55. C3×#815C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C8×Dic3C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
64. #5625C2×C3semidirect
81. #5164C2×C3semidirect
82. #5162C2×C3semidirect
83. #5162C2×C3semidirect
84. Dic3×SD16C2×C3semidirect
85. #5045C2×C3semidirect
86. #4766C2×C3semidirect
87. #4763C2×C3semidirect
88. #4758C2×C3semidirect
89. #4757C2×C3semidirect
90. #4723C2×C3semidirect
91. #4720C2×C3semidirect
177. Q8×Dic3C22×C3semidirect
178. #944C22×C3semidirect
191. #890C22×C3semidirect
193. #887C22×C3semidirect
220. #835C22×C3semidirect
221. #835C22×C3semidirect
225. #818C22×C3semidirect
226. #817C22×C3semidirect
227. #816C22×C3semidirect
228. #816C22×C3semidirect
229. #815C22×C3semidirect
230. Dic3⋊C8C22×C3semidirect
231. Dic3⋊C8C22×C3semidirect
232. C8×Dic3C22×C3semidirect
233. #808C22×C3semidirect
234. #807C22×C3semidirect
681. C32#3123semidirect
762. C3#80137direct (N × H)
763. C3C3×#3123semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C3×#56252
C32×#4502
C3×#52182
C3×#51642
C3×#51622
C3×Dic3×SD162
C3×#50452
C3×#47662
C3×#47632
C3×#47582
C3×#47572
C3×#47232
C3×#47202
C3×#31233
#801373