Finite Group Databasebeta

← C3×#80322 #11896112

Subgroups — C3×#80322 #11896112

Order 1152.

786 conjugacy classes of subgroups.

The subgroup lattice has 745 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5713C211yesmaximal, characteristic, complemented
2C3×#5539C211yesmaximal, characteristic, complemented
3C32×#459C211yesmaximal, characteristic
4C3×#5153C211yesmaximal, characteristic, complemented
5C3×#5153C211yesmaximal, characteristic, complemented
6C3×#5152C211yesmaximal, characteristic, complemented
7C3×Dic3×D8C211yesmaximal, characteristic, complemented
8C3×#5071C211yesmaximal, characteristic, complemented
9C3×#5018C211yesmaximal, characteristic, complemented
10C3×#4829C211yesmaximal, characteristic, complemented
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4768C211yesmaximal, characteristic, complemented
13C3×#4765C211yesmaximal, characteristic, complemented
14C3×#4763C211yesmaximal, characteristic, complemented
15C3×#4759C211yesmaximal, characteristic, complemented
16C3×#3370—31nomaximal
17#80322C311yesmaximal, characteristic, direct product factor
18C2×C32×D8C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20C32×#127C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C3×#936—21no—
23C3×#936C2211yescharacteristic
24C3×#936C2211yescharacteristic
25C3×#935—21no—
26C3×#935—21no—
27C3×D4×Dic3—21no—
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C3×D4×Dic3C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C3×#924—21no—
34C2×C3×Dic3⋊C4—21no—
35C3×#890C2211yescharacteristic
36C3×#888C2211yescharacteristic
37C3×#878—21no—
38C3×#878—21no—
39C3×#870C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#815C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#559—31no—
62C3×#554—31no—
63#5713C2×C311yescharacteristic, complemented
64#5539C2×C311yescharacteristic, complemented
65C3×#490—31no—
66C3×#489—31no—
67C3×#488—31no—
68C3×#479—31no—
69C3×#478—31no—
70C3×#474—31no—
71C3×#463—31no—
72C3×#463—31no—
73C3×#459—21no—
74C3×#459D311yescharacteristic
75C3×#459C2×C311yescharacteristic
76C3×#446—31no—
77C3×#442—31no—
78C3×#440—31no—
79C3×C4×D8—31no—
80#5153C2×C311yescharacteristic, complemented
81#5153C2×C311yescharacteristic, complemented
82#5152C2×C311yescharacteristic, complemented
83Dic3×D8C2×C311yescharacteristic, complemented
84#5071C2×C311yescharacteristic, complemented
85#5018C2×C311yescharacteristic, complemented
86#4829C2×C311yescharacteristic, complemented
87#4828C2×C311yescharacteristic, complemented
88#4768C2×C311yescharacteristic, complemented
89#4765C2×C311yescharacteristic, complemented
90#4763C2×C311yescharacteristic, complemented
91#4759C2×C311yescharacteristic, complemented
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6D411yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C32×D8—22no—
106C32×D8—22no—
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C42C2311yescharacteristic
112C3×#217—21no—
113C3×#217—21no—
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#214—22no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3370—31noSylow
139C2×C3×SD16—31no—
140C2×C3×D8—21no—
141C2×C3×D8—21no—
142C2×C3×D8C2×D311yescharacteristic
143C2×C3×D8C2×D311yescharacteristic
144C2×C3×D8C22×C311yescharacteristic
145C2×C3×D8C22×C311yescharacteristic
146C3×C4⋊Q8—31no—
147C3×#127—21no—
148C3×#127C2×D311yescharacteristic
149C3×#127C22×C311yescharacteristic
150C3×#125—31no—
151C3×#125—31no—
152C3×#124—31no—
153C3×#124—31no—
154C3×#124—61no—
155C3×#123—61no—
156C3×#123—61no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8—61no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×D4—21no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—61no—
168C3×C4×D4C2×D311yescharacteristic
169C3×C4×D4C22×C311yescharacteristic
170C2×C3×C4⋊C4—61no—
171#936—21no—
172#936C22×C311yescharacteristic
173#936C22×C311yescharacteristic
174#935—21no—
175#935—21no—
176D4×Dic3—21no—
177D4×Dic3C22×C311yescharacteristic
178D4×Dic3C22×C311yescharacteristic
179D4×Dic3C22×C311yescharacteristic
180D4×Dic3C22×C311yescharacteristic
181C2×#214C22×C311yescharacteristic
182#924—21no—
183C2×Dic3⋊C4—21no—
184#890C22×C311yescharacteristic
185#888C22×C311yescharacteristic
186#878—21no—
187#878—21no—
188#870C22×C311yescharacteristic
189C4×Dic6C22×C311yescharacteristic
190C4×Dic6C22×C311yescharacteristic
191C3×#107—31no—
192C3×#107—31no—
193C3×#106—31no—
194C3×C4⋊C8—21no—
195C3×C4⋊C8—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8C2×D311yescharacteristic
198C3×C4⋊C8C22×C311yescharacteristic
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#102—21no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102C2×D311yescharacteristic
210C3×#102C2×D311yescharacteristic
211C3×#102C22×C311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#97—31no—
214C3×#97—31no—
215C3×C4×C8—31no—
216#832C22×C311yescharacteristic
217#832C22×C311yescharacteristic
218#832C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#832C22×C311yescharacteristic
221#818C22×C311yescharacteristic
222#817C22×C311yescharacteristic
223#816C22×C311yescharacteristic
224#816C22×C311yescharacteristic
225#815C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227Dic3⋊C8C22×C311yescharacteristic
228C8×Dic3C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231#803C22×C311yescharacteristic
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C32×D4—21no—
236C32×D4—21no—
237C32×D4—21no—
238C32×D4—21no—
239C32×D4—21no—
240C32×D4—42no—
241C32×D4—81no—
242C32×D4#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—42no—
253C2×C3×Dic3—81no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3—81no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—41no—
263C3×Dic6—81no—
264C32×C8—21no—
265C32×C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#559—31no—
269#554—31no—
270#490—31no—
271#489—31no—
272#488—31no—
273#479—31no—
274#478—31no—
275#474—31no—
276#463—31no—
277#463—31no—
278#459C3×D311yescharacteristic
279#446—31no—
280#442—31no—
281#440—31no—
282C4×D8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—41no—
294C2×C3×D4—41no—
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C23×C311yescharacteristic
299C2×C3×D4C23×C311yescharacteristic
300C2×C3×D4C23×C311yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—41no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C2×Dic6—21no—
313C2×Dic6C3×D411yescharacteristic
314C2×Dic6C23×C311yescharacteristic
315C3×SD16—62no—
316C3×D8—22no—
317C3×D8—22no—
318C3×D8—22no—
319C3×D8—22no—
320C3×D8—42no—
321C3×D8—42no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8C22×D311yescharacteristic
327C2×C3×C8C22×D311yescharacteristic
328C2×C3×C8C23×C311yescharacteristic
329C2×C3×C8C23×C311yescharacteristic
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C23×C311yescharacteristic
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—21no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—61no—
360C3×C42C22×D311yescharacteristic
361C3×C42C23×C311yescharacteristic
362#217—21no—
363#217—21no—
364#217—21no—
365#217—21no—
366#217—21no—
367#217—21no—
368#217—21no—
369#217—21no—
370#214—22no—
371C4⋊Dic3—21no—
372C4⋊Dic3C3×D411yescharacteristic
373C4⋊Dic3C23×C311yescharacteristic
374C4⋊Dic3C23×C311yescharacteristic
375C4⋊Dic3C23×C311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4C3×D411yescharacteristic
382Dic3⋊C4C3×D411yescharacteristic
383C4×Dic3—21no—
384C4×Dic3C23×C311yescharacteristic
385C4×Dic3C23×C311yescharacteristic
386C2×C3⋊C8C23×C311yescharacteristic
387C2×C3⋊C8C23×C311yescharacteristic
388C22×C32—22no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
398C32×C4—21no—
399C32×C4—21no—
400C32×C4—41no—
401C32×C4C2×#4111yescharacteristic
402C32×C42−1+411yescharacteristic
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C2×SD16—31no—
412C2×D8C2×C3×D311yescharacteristic
413C2×D8C2×C3×D311yescharacteristic
414C4⋊Q8—31no—
415#127C2×C3×D311yescharacteristic
416#125—31no—
417#125—31no—
418#124—31no—
419#124—31no—
420#124—61no—
421#123—61no—
422#123—61no—
423C22⋊Q8—61no—
424C22⋊Q8—61no—
425C22⋊Q8—61no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×D4—31no—
429C4×D4—31no—
430C4×D4—31no—
431C4×D4—31no—
432C4×D4—61no—
433C4×D4C2×C3×D311yescharacteristic
434C2×C4⋊C4—61no—
435#107—31no—
436#107—31no—
437#106—31no—
438C4⋊C8—31no—
439C4⋊C8—31no—
440C4⋊C8C2×C3×D311yescharacteristic
441#103—31no—
442#103—31no—
443#103—31no—
444#102—31no—
445#102—31no—
446#102—31no—
447#102—31no—
448#102—31no—
449#102C2×C3×D311yescharacteristic
450#102C2×C3×D311yescharacteristic
451#97—31no—
452#97—31no—
453C4×C8—31no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C3×Q8—61no—
464C3×Q8—61no—
465C3×Q8—121no—
466C3×Q8—241no—
467C3×D4—21no—
468C3×D4—21no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—21no—
473C3×D4—21no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—22no—
478C3×D4—41no—
479C3×D4—41no—
480C3×D4—41no—
481C3×D4—41no—
482C3×D4—41no—
483C3×D4—42no—
484C3×D4—42no—
485C3×D4—82no—
486C3×D4—81no—
487C3×D4—81no—
488C3×D4—82no—
489C3×D4#23712yes—
490C3×D4C3×#4112yes—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—81no—
506C2×C3×C4—81no—
507C2×C3×C4—82no—
508C2×C3×C4—122no—
509C2×C3×C4—241no—
510C2×C3×C4—241no—
511C2×C3×C4—241no—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C2×C3×D411yescharacteristic
515C2×C3×C4C2×C3×D411yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C24×C311yescharacteristic
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—42no—
523C2×Dic3—81no—
524C2×Dic3—81no—
525C2×Dic3—81no—
526C2×Dic3C2×C3×D411yescharacteristic
527C2×Dic3C2×C3×D411yescharacteristic
528C2×Dic3C2×C3×D411yescharacteristic
529C2×Dic3C2×C3×D411yescharacteristic
530Dic6—21no—
531Dic6—21no—
532Dic6—41no—
533Dic6—81no—
534C3×C8—21no—
535C3×C8—21no—
536C3×C8—21no—
537C3×C8—21no—
538C3×C8—41no—
539C3×C8—41no—
540C3×C8—61no—
541C3×C8—61no—
542C3⋊C8—21no—
543C3⋊C8—21no—
544C2×C32—42no—
545C2×C32—81no—
546C2×C32—81no—
547C2×C32#54811yescharacteristic
548C2×C32#57511yescharacteristic
549C2×C32#57611yescharacteristic
550C2×Q8—31no—
551C2×Q8—31no—
552C2×Q8—61no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4C22×C3×D311yescharacteristic
556C2×D4C22×C3×D311yescharacteristic
557C2×D4C22×C3×D311yescharacteristic
558C22×C4—21no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563SD16—62no—
564D8—22no—
565D8—22no—
566C2×C8—31no—
567C2×C8—31no—
568C2×C8C22×C3×D311yescharacteristic
569C2×C8C22×C3×D311yescharacteristic
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—31no—
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4C22×C3×D311yescharacteristic
583C22⋊C4—21no—
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C22⋊C4—61no—
588C22⋊C4—61no—
589C22⋊C4—61no—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C42—31no—
593C42—31no—
594C42—61no—
595C42C22×C3×D311yescharacteristic
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—21no—
599C22×C3—42no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C22×C3×D411yescharacteristic
626C3×C4—22no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—81no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4—121no—
645C3×C4C2×#23711yescharacteristic
646C3×C4#101011yescharacteristic
647C3×C4C2×C3×#4111yescharacteristic
648C3×C4C3×2−1+411yescharacteristic
649Dic3—21no—
650Dic3—21no—
651Dic3—21no—
652Dic3—21no—
653Dic3—41no—
654Dic3—41no—
655Dic3—41no—
656Dic3—41no—
657C32#337011yescharacteristic, complemented, Sylow
658C23—21no—
659C23—21no—
660C23—21no—
661Q8—61no—
662Q8—61no—
663Q8—121no—
664Q8—241no—
665D4—21no—
666D4—21no—
667D4—21no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—81no—
672D4C3×#23712yes—
673C2×C4—21no—
674C2×C4—31no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—31no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—81no—
683C2×C4—122no—
684C2×C4—241no—
685C2×C4—241no—
686C2×C4—241no—
687C2×C4C3×D3×D411yescharacteristic
688C2×C4C3×D3×D411yescharacteristic
689C2×C4C23×C3×D311yescharacteristic
690C8—21no—
691C8—21no—
692C8—61no—
693C8—61no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—42no—
698C2×C3—42no—
699C2×C3—82no—
700C2×C3—81no—
701C2×C3—81no—
702C2×C3—81no—
703C2×C3—81no—
704C2×C3—161no—
705C2×C3—161no—
706C2×C3#559811yescharacteristic
707C2×C3#575711yescharacteristic
708C2×C3#577311yescharacteristic
709C2×C3C3×#54811yescharacteristic
710C2×C3C3×#57511yescharacteristic
711C2×C3C3×#57611yescharacteristic
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22C2×C3×D3×D411yescharacteristic
722C4—21no—
723C4—21no—
724C4—41no—
725C4—61no—
726C4—61no—
727C4—61no—
728C4—61no—
729C4—121no—
730C4—121no—
731C4—121no—
732C4—121no—
733C4C2×C3×#23711yescharacteristic
734C4C3×#101011yescharacteristic
735C3—21no—
736C3#8032211yescharacteristic, direct product factor
737C3C3×#337011yescharacteristic, complemented
738C2—42no—
739C2—81no—
740C2—81no—
741C2C3×#559811yescharacteristic
742C2C3×#575711yescharacteristic
743C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC32×#459C2
socleC22×C32C22×D4
hypercenterC3×#459D3
hypocenterC3C3×#3370
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C3×#5713C2semidirect
2. C3×#5539C2semidirect
4. C3×#5153C2semidirect
5. C3×#5153C2semidirect
6. C3×#5152C2semidirect
7. C3×Dic3×D8C2semidirect
8. C3×#5071C2semidirect
9. C3×#5018C2semidirect
10. C3×#4829C2semidirect
11. C3×#4828C2semidirect
12. C3×#4768C2semidirect
13. C3×#4765C2semidirect
14. C3×#4763C2semidirect
15. C3×#4759C2semidirect
17. #80322C3direct (N × H)
63. #5713C2×C3semidirect
64. #5539C2×C3semidirect
80. #5153C2×C3semidirect
81. #5153C2×C3semidirect
82. #5152C2×C3semidirect
83. Dic3×D8C2×C3semidirect
84. #5071C2×C3semidirect
85. #5018C2×C3semidirect
86. #4829C2×C3semidirect
87. #4828C2×C3semidirect
88. #4768C2×C3semidirect
89. #4765C2×C3semidirect
90. #4763C2×C3semidirect
91. #4759C2×C3semidirect
657. C32#3370semidirect
736. C3#80322direct (N × H)
737. C3C3×#3370semidirect

Maximal subgroups

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

subgroupindex
C3×#57132
C3×#55392
C32×#4592
C3×#51532
C3×#51522
C3×Dic3×D82
C3×#50712
C3×#50182
C3×#48292
C3×#48282
C3×#47682
C3×#47652
C3×#47632
C3×#47592
C3×#33703
#803223