Finite Group Databasebeta

← C3×#80068 #11870542

Subgroups — C3×#80068 #11870542

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Dic3×#41C211yesmaximal, characteristic, complemented
2C3×#5600C211yesmaximal, characteristic, complemented
3C32×#449C211yesmaximal, characteristic
4C3×#5239C211yesmaximal, characteristic, complemented
5C3×#5166C211yesmaximal, characteristic, complemented
6C3×Dic3×SD16C211yesmaximal, characteristic, complemented
7C3×#5153C211yesmaximal, characteristic, complemented
8C3×Dic3×D8C211yesmaximal, characteristic, complemented
9C3×#5035C211yesmaximal, characteristic, complemented
10C3×#4796C211yesmaximal, characteristic, complemented
11C3×#4790C211yesmaximal, characteristic, complemented
12C3×#4763C211yesmaximal, characteristic, complemented
13C3×#4758C211yesmaximal, characteristic, complemented
14C3×#4723C211yesmaximal, characteristic, complemented
15C3×#4718C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#80068C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C32×#121C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#936C2211yescharacteristic
26C3×#935—21no—
27C3×D4×Dic3—21no—
28C3×D4×Dic3—21no—
29C3×D4×Dic3—21no—
30C3×D4×Dic3C2211yescharacteristic
31C3×D4×Dic3C2211yescharacteristic
32C3×D4×Dic3C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic
34C3×#926—21no—
35C3×#926C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C2×C3×C4×Dic3—21no—
38C2×C3×C4×Dic3C2211yescharacteristic
39C3×#890C2211yescharacteristic
40C3×#887C2211yescharacteristic
41C3×#879—21no—
42C3×#877—21no—
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×C8×Dic3C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63Dic3×#41C2×C311yescharacteristic, complemented
64#5600C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#479—31no—
68C3×#478—31no—
69C3×#464—31no—
70C3×#463—31no—
71C3×#452—31no—
72C3×#449—21no—
73C3×#449D311yescharacteristic
74C3×#449C2×C311yescharacteristic
75C3×C4×Q16—31no—
76C3×C4×SD16—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#431—31no—
80#5239C2×C311yescharacteristic, complemented
81#5166C2×C311yescharacteristic, complemented
82Dic3×SD16C2×C311yescharacteristic, complemented
83#5153C2×C311yescharacteristic, complemented
84Dic3×D8C2×C311yescharacteristic, complemented
85#5035C2×C311yescharacteristic, complemented
86#4796C2×C311yescharacteristic, complemented
87#4790C2×C311yescharacteristic, complemented
88#4763C2×C311yescharacteristic, complemented
89#4758C2×C311yescharacteristic, complemented
90#4723C2×C311yescharacteristic, complemented
91#4718C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—22no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C22×C32×C4C2311yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3D411yescharacteristic
105C22×C3×Dic3D411yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C32×SD16—22no—
108C32×D8—22no—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C3×#217—21no—
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#216—22no—
121C3×#214—22no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3D411yescharacteristic
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3102—31noSylow
142C2×C3×#41—21no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C22×C311yescharacteristic
145C2×C3×Q16—31no—
146C2×C3×SD16—21no—
147C2×C3×SD16—31no—
148C2×C3×SD16C2×D311yescharacteristic
149C2×C3×SD16C22×C311yescharacteristic
150C2×C3×D8—21no—
151C2×C3×D8C2×D311yescharacteristic
152C2×C3×D8C22×C311yescharacteristic
153C3×#126—61no—
154C3×#125—31no—
155C3×#124—31no—
156C3×#123—61no—
157C3×C22⋊Q8—31no—
158C3×#121—21no—
159C3×#121C2×D311yescharacteristic
160C3×#121C22×C311yescharacteristic
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—61no—
168C3×C4×D4—61no—
169C3×C4×D4—61no—
170C3×#117—31no—
171C3×#117—61no—
172C3×#117—61no—
173C2×C3×C42—31no—
174C2×C3×C42—61no—
175Q8×Dic3C22×C311yescharacteristic
176Q8×Dic3C22×C311yescharacteristic
177C2×#216C22×C311yescharacteristic
178#936C22×C311yescharacteristic
179#935—21no—
180D4×Dic3—21no—
181D4×Dic3—21no—
182D4×Dic3—21no—
183D4×Dic3C22×C311yescharacteristic
184D4×Dic3C22×C311yescharacteristic
185D4×Dic3C22×C311yescharacteristic
186C2×#214C22×C311yescharacteristic
187#926—21no—
188#926C22×C311yescharacteristic
189#924C22×C311yescharacteristic
190C2×C4×Dic3—21no—
191C2×C4×Dic3C22×C311yescharacteristic
192#890C22×C311yescharacteristic
193#887C22×C311yescharacteristic
194#879—21no—
195#877—21no—
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—31no—
201C3×C4⋊C8—31no—
202C3×#103—21no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic
207C3×#103C22×C311yescharacteristic
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×C22⋊C8—21no—
215C3×C22⋊C8—31no—
216C3×C22⋊C8C2×D311yescharacteristic
217C3×C22⋊C8C22×C311yescharacteristic
218C3×C4×C8—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic
221#832C22×C311yescharacteristic
222#832C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#830C22×C311yescharacteristic
225#818C22×C311yescharacteristic
226#817C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231C8×Dic3C22×C311yescharacteristic
232C8×Dic3C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C23×C32—21no—
236C23×C32—21no—
237C23×C32C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8#4112yes—
240C32×D4—24no—
241C32×D4—21no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—42no—
245C32×D4#4112yes—
246C2×C32×C4—24no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3×Dic3—22no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—41no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—42no—
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#529—31no—
273C4×#41—31no—
274#485—31no—
275#482—31no—
276#479—31no—
277#478—31no—
278#464—31no—
279#463—31no—
280#452—31no—
281#449C3×D311yescharacteristic
282C4×Q16—31no—
283C4×SD16—31no—
284C4×SD16—31no—
285C4×D8—31no—
286#431—31no—
287C3×#41—22no—
288C3×#41—22no—
289C3×#41—22no—
290C3×#41—22no—
291C3×#41—42no—
292C3×#41—42no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C23×C311yescharacteristic
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—41no—
304C2×C3×D4—41no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C23×C311yescharacteristic
308C2×C3×D4C23×C311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—41no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3C3×D411yescharacteristic
324C22×Dic3C3×D411yescharacteristic
325C2×Dic6C23×C311yescharacteristic
326C3×Q16—62no—
327C3×SD16—22no—
328C3×SD16—22no—
329C3×SD16—42no—
330C3×SD16—62no—
331C3×D8—22no—
332C3×D8—22no—
333C3×D8—42no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C23×C311yescharacteristic
341C2×C3×C8C23×C311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
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⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C23×C311yescharacteristic
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—41no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—31no—
368C3×C42—61no—
369C3×C42—61no—
370C3×C42—61no—
371C3×C42—61no—
372#217—21no—
373#217—21no—
374#217—21no—
375#217—21no—
376#217—21no—
377#217—21no—
378#217—21no—
379#216—22no—
380#214—22no—
381C4⋊Dic3—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3C23×C311yescharacteristic
385C4⋊Dic3C23×C311yescharacteristic
386C4⋊Dic3C23×C311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3C3×D411yescharacteristic
395C4×Dic3C3×D411yescharacteristic
396C4×Dic3C23×C311yescharacteristic
397C4×Dic3C23×C311yescharacteristic
398C2×C3⋊C8C23×C311yescharacteristic
399C2×C3⋊C8C23×C311yescharacteristic
400C22×C32—21no—
401C22×C32—22no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32C22×D411yescharacteristic
410C32×C4—21no—
411C32×C4—22no—
412C32×C4—41no—
413C32×C4C2×#4111yescharacteristic
414C32×C4C2×#4111yescharacteristic
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3#13512yes—
423C2×#41C2×C3×D311yescharacteristic
424C2×Q16—31no—
425C2×SD16—31no—
426C2×SD16C2×C3×D311yescharacteristic
427C2×D8C2×C3×D311yescharacteristic
428#126—61no—
429#125—31no—
430#124—31no—
431#123—61no—
432C22⋊Q8—31no—
433#121C2×C3×D311yescharacteristic
434C4×Q8—31no—
435C4×Q8—31no—
436C4×Q8—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—61no—
441C4×D4—61no—
442C4×D4—61no—
443#117—31no—
444#117—61no—
445#117—61no—
446C2×C42—31no—
447C2×C42—61no—
448#107—31no—
449#107—31no—
450#106—31no—
451#106—31no—
452C4⋊C8—31no—
453C4⋊C8—31no—
454#103—31no—
455#103—31no—
456#103—31no—
457#103C2×C3×D311yescharacteristic
458#102—31no—
459#102—31no—
460#102—31no—
461#102C2×C3×D311yescharacteristic
462C22⋊C8—31no—
463C22⋊C8C2×C3×D311yescharacteristic
464C4×C8—31no—
465C4×C8—31no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3D3×D411yescharacteristic
474C23×C3C2×C3×D411yescharacteristic
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—22no—
478C3×Q8—41no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8#23712yes—
482C3×Q8C3×#4112yes—
483C3×D4—24no—
484C3×D4—24no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—22no—
492C3×D4—41no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—44no—
496C3×D4—42no—
497C3×D4—42no—
498C3×D4—82no—
499C3×D4#23712yes—
500C3×D4C3×#4112yes—
501C2×C3×C4—24no—
502C2×C3×C4—24no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—44no—
521C2×C3×C4—41no—
522C2×C3×C4—62no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—121no—
530C2×C3×C4—122no—
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4C2×C3×D411yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C24×C311yescharacteristic
535C2×Dic3—22no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—41no—
541C2×Dic3—42no—
542C2×Dic3—42no—
543C2×Dic3—42no—
544C2×Dic3C2×C3×D411yescharacteristic
545C2×Dic3C2×C3×D411yescharacteristic
546C2×Dic3C2×C3×D411yescharacteristic
547C2×Dic3C2×C3×D411yescharacteristic
548Dic6—21no—
549Dic6—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—41no—
555C3×C8—41no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C2×C32—41no—
561C2×C32—42no—
562C2×C32—81no—
563C2×C32#52511yescharacteristic
564C2×C32C2×#13511yescharacteristic
565C2×C32#57511yescharacteristic
566#41—22no—
567#41—22no—
568C2×Q8—31no—
569C2×Q8C22×C3×D311yescharacteristic
570C2×D4—21no—
571C2×D4—21no—
572C2×D4C22×C3×D311yescharacteristic
573C2×D4C22×C3×D311yescharacteristic
574C22×C4—21no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4C22×C3×D311yescharacteristic
581Q16—62no—
582SD16—22no—
583SD16—62no—
584D8—22no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8C22×C3×D311yescharacteristic
588C2×C8C22×C3×D311yescharacteristic
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⋊C4—61no—
598C4⋊C4C22×C3×D311yescharacteristic
599C22⋊C4—21no—
600C22⋊C4—61no—
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C42—31no—
608C42—31no—
609C42—31no—
610C42—31no—
611C42—61no—
612C42—61no—
613C42—61no—
614C42—61no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—42no—
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—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C22×C3×D411yescharacteristic
645C3×C4—21no—
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—22no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—42no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—81no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4C2×#23711yescharacteristic
665C3×C4C2×#23711yescharacteristic
666C3×C4C2×C3×#4111yescharacteristic
667C3×C4C2×C3×#4111yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3C3×#13512yes—
676C32#310211yescharacteristic, complemented, Sylow
677C23—21no—
678C23—21no—
679C23C3×D3×D411yescharacteristic
680Q8—21no—
681Q8—61no—
682Q8—61no—
683Q8C3×#23712yes—
684D4—24no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4C3×#23712yes—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—121no—
707C2×C4—122no—
708C2×C4C3×D3×D411yescharacteristic
709C2×C4C23×C3×D311yescharacteristic
710C8—21no—
711C8—21no—
712C8—61no—
713C8—61no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—41no—
718C2×C3—42no—
719C2×C3—41no—
720C2×C3—42no—
721C2×C3—81no—
722C2×C3—82no—
723C2×C3—81no—
724C2×C3—81no—
725C2×C3—161no—
726C2×C3#558611yescharacteristic
727C2×C3D3×#13511yescharacteristic
728C2×C3#577311yescharacteristic
729C2×C3C3×#52511yescharacteristic
730C2×C3C2×C3×#13511yescharacteristic
731C2×C3C3×#57511yescharacteristic
732C22—21no—
733C22—21no—
734C22—21no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22C2×C3×D3×D411yescharacteristic
742C4—21no—
743C4—22no—
744C4—32no—
745C4—41no—
746C4—61no—
747C4—61no—
748C4—61no—
749C4—121no—
750C4—121no—
751C4—121no—
752C4—121no—
753C4C2×C3×#23711yescharacteristic
754C4C2×C3×#23711yescharacteristic
755C3—21no—
756C3#8006811yescharacteristic, direct product factor
757C3C3×#310211yescharacteristic, complemented
758C2—41no—
759C2—42no—
760C2—81no—
761C2C3×#558611yescharacteristic
762C2C3×D3×#13511yescharacteristic
763C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC32×#449C2
socleC22×C32C22×D4
hypercenterC3×#449D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C3×Dic3×#41C2semidirect
2. C3×#5600C2semidirect
4. C3×#5239C2semidirect
5. C3×#5166C2semidirect
6. C3×Dic3×SD16C2semidirect
7. C3×#5153C2semidirect
8. C3×Dic3×D8C2semidirect
9. C3×#5035C2semidirect
10. C3×#4796C2semidirect
11. C3×#4790C2semidirect
12. C3×#4763C2semidirect
13. C3×#4758C2semidirect
14. C3×#4723C2semidirect
15. C3×#4718C2semidirect
17. #80068C3direct (N × H)
63. Dic3×#41C2×C3semidirect
64. #5600C2×C3semidirect
80. #5239C2×C3semidirect
81. #5166C2×C3semidirect
82. Dic3×SD16C2×C3semidirect
83. #5153C2×C3semidirect
84. Dic3×D8C2×C3semidirect
85. #5035C2×C3semidirect
86. #4796C2×C3semidirect
87. #4790C2×C3semidirect
88. #4763C2×C3semidirect
89. #4758C2×C3semidirect
90. #4723C2×C3semidirect
91. #4718C2×C3semidirect
676. C32#3102semidirect
756. C3#80068direct (N × H)
757. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
C3×#56002
C32×#4492
C3×#52392
C3×#51662
C3×Dic3×SD162
C3×#51532
C3×Dic3×D82
C3×#50352
C3×#47962
C3×#47902
C3×#47632
C3×#47582
C3×#47232
C3×#47182
C3×#31023
#800683