Finite Group Databasebeta

← C3×#80216 #11872389

Subgroups — C3×#80216 #11872389

Order 1152.

820 conjugacy classes of subgroups.

The subgroup lattice has 737 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5827C211yesmaximal, characteristic
2C3×#5625C211yesmaximal, characteristic, complemented
3C32×#452C211yesmaximal, characteristic
4C3×#5239C211yesmaximal, characteristic
5C3×#5184C211yesmaximal, characteristic, complemented
6C3×#5182C211yesmaximal, characteristic, complemented
7C3×#5162C211yesmaximal, characteristic, complemented
8C3×Dic3×SD16C211yesmaximal, characteristic, complemented
9C3×#5044C211yesmaximal, characteristic, complemented
10C3×#4799C211yesmaximal, characteristic, complemented
11C3×#4790C211yesmaximal, characteristic, complemented
12C3×#4763C211yesmaximal, characteristic, complemented
13C3×#4757C211yesmaximal, characteristic, complemented
14C3×#4721C211yesmaximal, characteristic, complemented
15C3×#4720C211yesmaximal, characteristic, complemented
16C3×#3120—31nomaximal
17#80216C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×D4×Dic3—21no—
28C3×D4×Dic3—21no—
29C3×D4×Dic3C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×#926—21no—
33C3×#926C2211yescharacteristic
34C2×C3×C4⋊Dic3—21no—
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C3×#890—21no—
38C3×#890C2211yescharacteristic
39C3×#889—21no—
40C3×#887C2211yescharacteristic
41C3×#879—21no—
42C3×#879—21no—
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#815C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic
58C3×C8×Dic3C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#541—31no—
62C3×#520—31no—
63#5827C2×C311yescharacteristic
64#5625C2×C311yescharacteristic, complemented
65C3×#484—31no—
66C3×#483—31no—
67C3×#479—31no—
68C3×#478—31no—
69C3×#462—31no—
70C3×#461—31no—
71C3×#452—21no—
72C3×#452—31no—
73C3×#452D311yescharacteristic
74C3×#452C2×C311yescharacteristic
75C3×#441—31no—
76C3×#440—31no—
77C3×C4×Q16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5239C2×C311yescharacteristic
81#5184C2×C311yescharacteristic, complemented
82#5182C2×C311yescharacteristic, complemented
83#5162C2×C311yescharacteristic, complemented
84Dic3×SD16C2×C311yescharacteristic, complemented
85#5044C2×C311yescharacteristic, complemented
86#4799C2×C311yescharacteristic, complemented
87#4790C2×C311yescharacteristic, complemented
88#4763C2×C311yescharacteristic, complemented
89#4757C2×C311yescharacteristic, complemented
90#4721C2×C311yescharacteristic, complemented
91#4720C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—22no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C32×Q16—22no—
105C32×SD16—22no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C3×#217—21no—
112C3×#217—21no—
113C3×#217—21no—
114C3×#217D411yescharacteristic
115C3×#217D411yescharacteristic
116C3×#216—22no—
117C3×#214—22no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—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#3120—31noSylow
142C2×C3×#41—21no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C22×C311yescharacteristic
145C2×C3×Q16—21no—
146C2×C3×Q16—31no—
147C2×C3×Q16C2×D311yescharacteristic
148C2×C3×Q16C22×C311yescharacteristic
149C2×C3×SD16—21no—
150C2×C3×SD16—31no—
151C2×C3×SD16C2×D311yescharacteristic
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×Q8—31no—
166C3×C4×Q8—31no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—61no—
170C3×C4×D4—61no—
171C3×#117—31no—
172C3×#117—61no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4—61no—
175Q8×Dic3C22×C311yescharacteristic
176Q8×Dic3C22×C311yescharacteristic
177Q8×Dic3C22×C311yescharacteristic
178#944C22×C311yescharacteristic
179C2×#216C22×C311yescharacteristic
180D4×Dic3—21no—
181D4×Dic3—21no—
182D4×Dic3C22×C311yescharacteristic
183D4×Dic3C22×C311yescharacteristic
184C2×#214C22×C311yescharacteristic
185#926—21no—
186#926C22×C311yescharacteristic
187C2×C4⋊Dic3—21no—
188C2×C4⋊Dic3C22×C311yescharacteristic
189#924C22×C311yescharacteristic
190#890—21no—
191#890C22×C311yescharacteristic
192#889—21no—
193#887C22×C311yescharacteristic
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—21no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic
209C3×#103C22×C311yescharacteristic
210C3×#102—21no—
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×#97—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic
221#835C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#830C22×C311yescharacteristic
225#817C22×C311yescharacteristic
226#817C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229#815C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231Dic3⋊C8C22×C311yescharacteristic
232C8×Dic3C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C23×C32—21no—
236C23×C32C2×D411yescharacteristic
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8—21no—
240C32×Q8#4112yes—
241C32×D4—24no—
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—24no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3—81no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×Dic6—21no—
264C3×Dic6—21no—
265C32×C8—21no—
266C32×C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#541—31no—
270#520—31no—
271#484—31no—
272#483—31no—
273#479—31no—
274#478—31no—
275#462—31no—
276#461—31no—
277#452—31no—
278#452C3×D311yescharacteristic
279#441—31no—
280#440—31no—
281C4×Q16—31no—
282C4×SD16—31no—
283#433—31no—
284C3×#41—22no—
285C3×#41—22no—
286C3×#41—22no—
287C3×#41—22no—
288C3×#41—42no—
289C3×#41—42no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C23×C311yescharacteristic
296C2×C3×Q8C23×C311yescharacteristic
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—41no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C23×C311yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—41no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C2×Dic6C23×C311yescharacteristic
316C3×Q16—22no—
317C3×Q16—22no—
318C3×Q16—42no—
319C3×Q16—62no—
320C3×SD16—22no—
321C3×SD16—22no—
322C3×SD16—42no—
323C3×SD16—62no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C23×C311yescharacteristic
331C2×C3×C8C23×C311yescharacteristic
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—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C23×C311yescharacteristic
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—41no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—31no—
362C3×C42—31no—
363C3×C42—61no—
364C3×C42—61no—
365C3×C42—61no—
366C3×C42—61no—
367#217—21no—
368#217—21no—
369#217—21no—
370#217C3×D411yescharacteristic
371#217C3×D411yescharacteristic
372#216—22no—
373#214—22no—
374C4⋊Dic3—21no—
375C4⋊Dic3—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3C3×D411yescharacteristic
380C4⋊Dic3C3×D411yescharacteristic
381C4⋊Dic3C23×C311yescharacteristic
382C4⋊Dic3C23×C311yescharacteristic
383C4⋊Dic3C23×C311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3C23×C311yescharacteristic
394C4×Dic3C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397C22×C32—21no—
398C22×C32—22no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C32×C4—21no—
405C32×C4—22no—
406C32×C4—41no—
407C32×C4—41no—
408C32×C4C2×#4111yescharacteristic
409C32×C4C2×#4111yescharacteristic
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C2×#41C2×C3×D311yescharacteristic
419C2×Q16—31no—
420C2×Q16C2×C3×D311yescharacteristic
421C2×SD16—31no—
422C2×SD16C2×C3×D311yescharacteristic
423C4⋊Q8—31no—
424#126—61no—
425#126—61no—
426#125—31no—
427#125—61no—
428#125—61no—
429C22⋊Q8—31no—
430C22⋊Q8C2×C3×D311yescharacteristic
431C4×Q8—31no—
432C4×Q8—31no—
433C4×Q8—31no—
434C4×Q8—31no—
435C4×D4—31no—
436C4×D4—31no—
437C4×D4—61no—
438C4×D4—61no—
439#117—31no—
440#117—61no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—61no—
443#107—31no—
444#107—31no—
445#106—31no—
446#106—31no—
447C4⋊C8—31no—
448C4⋊C8—31no—
449#103—31no—
450#103—31no—
451#103—31no—
452#103—31no—
453#103—31no—
454#103C2×C3×D311yescharacteristic
455#102—31no—
456#102C2×C3×D311yescharacteristic
457C22⋊C8—31no—
458C22⋊C8C2×C3×D311yescharacteristic
459#97—31no—
460C4×C8—31no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—41no—
465C23×C3D3×D411yescharacteristic
466C23×C3C2×C3×D411yescharacteristic
467C3×Q8—21no—
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—21no—
471C3×Q8—21no—
472C3×Q8—21no—
473C3×Q8—22no—
474C3×Q8—41no—
475C3×Q8—41no—
476C3×Q8—41no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8#23712yes—
480C3×Q8C3×#4112yes—
481C3×D4—24no—
482C3×D4—24no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—22no—
486C3×D4—41no—
487C3×D4—44no—
488C3×D4#23712yes—
489C3×D4C3×#4112yes—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—44no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—241no—
519C2×C3×C4—241no—
520C2×C3×C4—241no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×C3×D411yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C24×C311yescharacteristic
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—81no—
530C2×Dic3—81no—
531C2×Dic3—81no—
532C2×Dic3C2×C3×D411yescharacteristic
533C2×Dic3C2×C3×D411yescharacteristic
534C2×Dic3C2×C3×D411yescharacteristic
535C2×Dic3C2×C3×D411yescharacteristic
536Dic6—21no—
537Dic6—21no—
538C3×C8—21no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—41no—
543C3×C8—41no—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C2×C32—41no—
549C2×C32—42no—
550C2×C32#52511yescharacteristic
551C2×C32#57711yescharacteristic
552C2×C32#57811yescharacteristic
553#41—22no—
554#41—22no—
555C2×Q8—31no—
556C2×Q8C22×C3×D311yescharacteristic
557C2×Q8C22×C3×D311yescharacteristic
558C2×D4—21no—
559C2×D4C22×C3×D311yescharacteristic
560C22×C4—21no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4C22×C3×D311yescharacteristic
565Q16—22no—
566Q16—62no—
567SD16—22no—
568SD16—62no—
569C2×C8—31no—
570C2×C8—31no—
571C2×C8C22×C3×D311yescharacteristic
572C2×C8C22×C3×D311yescharacteristic
573C4⋊C4—21no—
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—31no—
577C4⋊C4—31no—
578C4⋊C4—31no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4C22×C3×D311yescharacteristic
590C22⋊C4—21no—
591C22⋊C4—31no—
592C22⋊C4—31no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C42—31no—
597C42—31no—
598C42—61no—
599C42—61no—
600C42—61no—
601C42—61no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—22no—
608C22×C3—21no—
609C22×C3—22no—
610C22×C3—21no—
611C22×C3—42no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C22×C3×D411yescharacteristic
623C3×C4—21no—
624C3×C4—22no—
625C3×C4—21no—
626C3×C4—22no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—41no—
630C3×C4—42no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—61no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—61no—
639C3×C4—81no—
640C3×C4—81no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4—121no—
645C3×C4C2×#23711yescharacteristic
646C3×C4C2×#23711yescharacteristic
647C3×C4C2×C3×#4111yescharacteristic
648C3×C4C2×C3×#4111yescharacteristic
649Dic3—21no—
650Dic3—21no—
651Dic3—21no—
652Dic3—21no—
653Dic3—41no—
654Dic3—41no—
655Dic3—41no—
656Dic3—41no—
657C32#312011yescharacteristic, complemented, Sylow
658C23—21no—
659C23C3×D3×D411yescharacteristic
660Q8—21no—
661Q8—21no—
662Q8—21no—
663Q8—61no—
664Q8—61no—
665Q8C3×#23712yes—
666D4—24no—
667D4—21no—
668D4C3×#23712yes—
669C2×C4—24no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—241no—
684C2×C4—241no—
685C2×C4—241no—
686C2×C4C3×D3×D411yescharacteristic
687C2×C4C23×C3×D311yescharacteristic
688C8—21no—
689C8—21no—
690C8—61no—
691C8—61no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—41no—
696C2×C3—42no—
697C2×C3—41no—
698C2×C3—42no—
699C2×C3—81no—
700C2×C3—82no—
701C2×C3#558611yescharacteristic
702C2×C3#577011yescharacteristic
703C2×C3#577911yescharacteristic
704C2×C3C3×#52511yescharacteristic
705C2×C3C3×#57711yescharacteristic
706C2×C3C3×#57811yescharacteristic
707C22—21no—
708C22—21no—
709C22—21no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22C2×C3×D3×D411yescharacteristic
714C4—21no—
715C4—22no—
716C4—41no—
717C4—41no—
718C4—61no—
719C4—61no—
720C4—61no—
721C4—61no—
722C4—121no—
723C4—121no—
724C4—121no—
725C4—121no—
726C4C2×C3×#23711yescharacteristic
727C4C2×C3×#23711yescharacteristic
728C3—21no—
729C3#8021611yescharacteristic, direct product factor
730C3C3×#312011yescharacteristic, complemented
731C2—41no—
732C2—42no—
733C2C3×#558611yescharacteristic
734C2C3×#577011yescharacteristic
735C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#452C2
socleC22×C32C22×D4
prime radicalC2×C32×#41C22
hypercenterC3×#452D3
hypocenterC3C3×#3120
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
2. C3×#5625C2semidirect
5. C3×#5184C2semidirect
6. C3×#5182C2semidirect
7. C3×#5162C2semidirect
8. C3×Dic3×SD16C2semidirect
9. C3×#5044C2semidirect
10. C3×#4799C2semidirect
11. C3×#4790C2semidirect
12. C3×#4763C2semidirect
13. C3×#4757C2semidirect
14. C3×#4721C2semidirect
15. C3×#4720C2semidirect
17. #80216C3direct (N × H)
64. #5625C2×C3semidirect
81. #5184C2×C3semidirect
82. #5182C2×C3semidirect
83. #5162C2×C3semidirect
84. Dic3×SD16C2×C3semidirect
85. #5044C2×C3semidirect
86. #4799C2×C3semidirect
87. #4790C2×C3semidirect
88. #4763C2×C3semidirect
89. #4757C2×C3semidirect
90. #4721C2×C3semidirect
91. #4720C2×C3semidirect
657. C32#3120semidirect
729. C3#80216direct (N × H)
730. C3C3×#3120semidirect

Maximal subgroups

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

subgroupindex
C3×#58272
C3×#56252
C32×#4522
C3×#52392
C3×#51842
C3×#51822
C3×#51622
C3×Dic3×SD162
C3×#50442
C3×#47992
C3×#47902
C3×#47632
C3×#47572
C3×#47212
C3×#47202
C3×#31203
#802163