Finite Group Databasebeta

← C3×#83718 #11896269

Subgroups — C3×#83718 #11896269

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#559C211yesmaximal, characteristic
2C3×#5567C211yesmaximal, characteristic, complemented
3C3×#5075C211yesmaximal, characteristic
4C3×#5071C211yesmaximal, characteristic
5C3×#5056C211yesmaximal, characteristic, complemented
6C3×#5055C211yesmaximal, characteristic, complemented
7C3×#5054C211yesmaximal, characteristic, complemented
8C3×#5054C211yesmaximal, characteristic, complemented
9C3×#5030C211yesmaximal, characteristic, complemented
10C3×#5024C211yesmaximal, characteristic, complemented
11C3×#5022C211yesmaximal, characteristic, complemented
12C3×#5018C211yesmaximal, characteristic, complemented
13C3×C4×#214C211yesmaximal, characteristic, complemented
14C3×#5009C211yesmaximal, characteristic, complemented
15C3×#5008C211yesmaximal, characteristic, complemented
16C3×#3371—31nomaximal
17#83718C311yesmaximal, 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×#944—21no—
30C2×C3×#216C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C3×#889—21no—
34C3×#889—21no—
35C3×#887—21no—
36C3×#870C2211yescharacteristic
37C3×#870C2211yescharacteristic
38C3×#869C2211yescharacteristic
39C3×C4×Dic6C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C3×#835C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×#808C2211yescharacteristic
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
63C3×#559C2×C311yescharacteristic
64C3×#557—31no—
65#5567C2×C311yescharacteristic, complemented
66C3×#490—31no—
67C3×#489—31no—
68C3×#488—31no—
69C3×#479—31no—
70C3×#478—31no—
71C3×#476—31no—
72C3×#464—31no—
73C3×#464—31no—
74C3×#460—31no—
75C3×#446—31no—
76C3×#441—31no—
77C3×#440—31no—
78C3×C4×SD16—31no—
79#5075C2×C311yescharacteristic
80#5071C2×C311yescharacteristic
81#5056C2×C311yescharacteristic, complemented
82#5055C2×C311yescharacteristic, complemented
83#5054C2×C311yescharacteristic, complemented
84#5054C2×C311yescharacteristic, complemented
85#5030C2×C311yescharacteristic, complemented
86#5024C2×C311yescharacteristic, complemented
87#5022C2×C311yescharacteristic, complemented
88#5018C2×C311yescharacteristic, complemented
89C4×#214C2×C311yescharacteristic, complemented
90#5009C2×C311yescharacteristic, complemented
91#5008C2×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×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C32×C4⋊C4—21no—
103C32×C4⋊C4D411yescharacteristic
104C32×C4⋊C4D411yescharacteristic
105C32×C4⋊C4D411yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108C32×C22⋊C4—21no—
109C32×C22⋊C4—21no—
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C42—21no—
114C32×C42C2311yescharacteristic
115C32×C42C2311yescharacteristic
116C32×C42C2311yescharacteristic
117C3×#216—22no—
118C3×#214—22no—
119C3×#214—22no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3371—31noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C2×C3×SD16—31no—
142C3×C4⋊Q8—31no—
143C3×C4⋊Q8—61no—
144C3×#127—21no—
145C3×#127C2×D311yescharacteristic
146C3×#127C22×C311yescharacteristic
147C3×#125—31no—
148C3×#125—31no—
149C3×#125—61no—
150C3×#125—61no—
151C3×#124—22no—
152C3×#124—21no—
153C3×#124—21no—
154C3×#124—21no—
155C3×#124—21no—
156C3×#124C2×D311yescharacteristic
157C3×#124C2×D311yescharacteristic
158C3×#124C22×C311yescharacteristic
159C3×#124C22×C311yescharacteristic
160C3×#123—22no—
161C3×#123—22no—
162C3×#123—21no—
163C3×#123—21no—
164C3×#123—21no—
165C3×#123—21no—
166C3×C4×Q8—21no—
167C3×C4×Q8—21no—
168C3×C4×Q8—31no—
169C3×C4×Q8—31no—
170C3×C4×Q8—31no—
171C3×C4×Q8—61no—
172C3×C4×Q8C2×D311yescharacteristic
173C3×C4×Q8C2×D311yescharacteristic
174C3×C4×Q8C22×C311yescharacteristic
175C3×C4×Q8C22×C311yescharacteristic
176C3×C4×D4—22no—
177C3×C4×D4—21no—
178C3×C4×D4—21no—
179C3×C4×D4—21no—
180C3×C4×D4—21no—
181C3×C4×D4C2×D311yescharacteristic
182C3×C4×D4C2×D311yescharacteristic
183C3×C4×D4C22×C311yescharacteristic
184C3×C4×D4C22×C311yescharacteristic
185#944—21no—
186C2×#216C22×C311yescharacteristic
187C2×#214C22×C311yescharacteristic
188C2×#214C22×C311yescharacteristic
189#889—21no—
190#889—21no—
191#887—21no—
192#870C22×C311yescharacteristic
193#870C22×C311yescharacteristic
194#869C22×C311yescharacteristic
195C4×Dic6C22×C311yescharacteristic
196C4×Dic6C22×C311yescharacteristic
197C4×Dic6C22×C311yescharacteristic
198C3×#107—31no—
199C3×#106—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×#103—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#810C22×C311yescharacteristic
227#808C22×C311yescharacteristic
228#808C22×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—
238C32×Q8—21no—
239C32×Q8—21no—
240C32×Q8—41no—
241C32×D4—21no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—42no—
246C32×D4—81no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—81no—
250C2×C32×C4—81no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C3×Dic6—21no—
263C3×Dic6—42no—
264C3×Dic6#4112yes—
265C3×C3⋊C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#559C3×D311yescharacteristic
270#557—31no—
271#490—31no—
272#489—31no—
273#488—31no—
274#479—31no—
275#478—31no—
276#476—31no—
277#464—31no—
278#464—31no—
279#460—31no—
280#446—31no—
281#441—31no—
282#440—31no—
283C4×SD16—31no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8—31no—
287C2×C3×Q8—61no—
288C2×C3×Q8#6711yescharacteristic
289C2×C3×Q8C3×D411yescharacteristic
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×Q8C23×C311yescharacteristic
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C23×C311yescharacteristic
303C2×C3×D4C23×C311yescharacteristic
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C2×Dic6—21no—
311C2×Dic6C23×C311yescharacteristic
312C3×Q16—62no—
313C3×SD16—62no—
314C3×SD16—62no—
315C2×C3×C8—31no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C3×C4⋊C4—22no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4#6711yescharacteristic
338C3×C4⋊C4#6711yescharacteristic
339C3×C4⋊C4#6711yescharacteristic
340C3×C4⋊C4C3×D411yescharacteristic
341C3×C4⋊C4C3×D411yescharacteristic
342C3×C4⋊C4C3×D411yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C23×C311yescharacteristic
345C3×C22⋊C4—22no—
346C3×C22⋊C4—22no—
347C3×C22⋊C4—22no—
348C3×C22⋊C4—22no—
349C3×C22⋊C4—22no—
350C3×C22⋊C4—22no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
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×C42—22no—
364C3×C42—21no—
365C3×C42—21no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42—61no—
370C3×C42—61no—
371C3×C42—61no—
372C3×C42C22×D311yescharacteristic
373C3×C42C22×D311yescharacteristic
374C3×C42C22×D311yescharacteristic
375C3×C42C23×C311yescharacteristic
376C3×C42C23×C311yescharacteristic
377C3×C42C23×C311yescharacteristic
378#216—22no—
379#214—22no—
380#214—22no—
381C4⋊Dic3—21no—
382C4⋊Dic3C23×C311yescharacteristic
383C4⋊Dic3C23×C311yescharacteristic
384C4⋊Dic3C23×C311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C2×C3⋊C8C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397C2×C3⋊C8C23×C311yescharacteristic
398C2×C3⋊C8C23×C311yescharacteristic
399C22×C32—41no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32C22×D411yescharacteristic
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4C2×#4111yescharacteristic
415C32×C42−1+411yescharacteristic
416C3×Dic3—22no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C2×Q16—31no—
421C2×SD16—31no—
422C2×SD16—31no—
423C4⋊Q8—31no—
424C4⋊Q8—61no—
425#127C2×C3×D311yescharacteristic
426#125—31no—
427#125—31no—
428#125—61no—
429#125—61no—
430#124—21no—
431#124C2×C3×D311yescharacteristic
432#124C2×C3×D311yescharacteristic
433#123—21no—
434#123—21no—
435C4×Q8—31no—
436C4×Q8—31no—
437C4×Q8—31no—
438C4×Q8—61no—
439C4×Q8C2×C3×D311yescharacteristic
440C4×Q8C2×C3×D311yescharacteristic
441C4×D4—21no—
442C4×D4C2×C3×D311yescharacteristic
443C4×D4C2×C3×D311yescharacteristic
444#107—31no—
445#106—31no—
446#106—31no—
447C4⋊C8—31no—
448C4⋊C8—31no—
449C4⋊C8—31no—
450#103—31no—
451#103—31no—
452#103—31no—
453#103—31no—
454#102—31no—
455#102—31no—
456#102—31no—
457#102—31no—
458#102—31no—
459#102—31no—
460#97—31no—
461#97—31no—
462C4×C8—31no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C3×Q8—21no—
470C3×Q8—21no—
471C3×Q8—21no—
472C3×Q8—21no—
473C3×Q8—32no—
474C3×Q8—41no—
475C3×Q8—41no—
476C3×Q8—41no—
477C3×Q8—41no—
478C3×Q8—42no—
479C3×Q8—61no—
480C3×Q8—122no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—44no—
494C3×D4—42no—
495C3×D4—42no—
496C3×D4—81no—
497C3×D4—81no—
498C3×D4—82no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
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—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—81no—
517C2×C3×C4—81no—
518C2×C3×C4—81no—
519C2×C3×C4—81no—
520C2×C3×C4—82no—
521C2×C3×C4—82no—
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C2×#6711yescharacteristic
528C2×C3×C4C2×C3×D411yescharacteristic
529C2×C3×C4C2×C3×D411yescharacteristic
530C2×C3×C4C2×C3×D411yescharacteristic
531C2×C3×C4C2×C3×D411yescharacteristic
532C2×C3×C4C2×C3×D411yescharacteristic
533C2×C3×C4C2×C3×D411yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C24×C311yescharacteristic
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540Dic6—21no—
541Dic6—42no—
542Dic6C3×#4112yes—
543C3×C8—61no—
544C3×C8—61no—
545C3×C8—61no—
546C3×C8—61no—
547C3⋊C8—21no—
548C3⋊C8—21no—
549C3⋊C8—21no—
550C3⋊C8—21no—
551C2×C32—81no—
552C2×C32—81no—
553C2×C32#54811yescharacteristic
554C2×C32#57511yescharacteristic
555C2×C32#57711yescharacteristic
556C2×Q8—31no—
557C2×Q8—61no—
558C2×Q8C3×#6711yescharacteristic
559C2×Q8C22×C3×D311yescharacteristic
560C2×D4—21no—
561C2×D4—21no—
562C2×D4C22×C3×D311yescharacteristic
563C2×D4C22×C3×D311yescharacteristic
564C22×C4—21no—
565C22×C4—21no—
566Q16—62no—
567SD16—62no—
568SD16—62no—
569C2×C8—31no—
570C2×C8—31no—
571C2×C8—31no—
572C2×C8—31no—
573C4⋊C4—21no—
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—31no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4C3×#6711yescharacteristic
586C4⋊C4C3×#6711yescharacteristic
587C4⋊C4C3×#6711yescharacteristic
588C4⋊C4C22×C3×D311yescharacteristic
589C22⋊C4—21no—
590C22⋊C4—21no—
591C22⋊C4—21no—
592C22⋊C4—21no—
593C22⋊C4—21no—
594C22⋊C4—21no—
595C42—21no—
596C42—61no—
597C42—61no—
598C42—61no—
599C42C22×C3×D311yescharacteristic
600C42C22×C3×D311yescharacteristic
601C42C22×C3×D311yescharacteristic
602C22×C3—21no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3C22×#6711yescharacteristic
622C22×C3C22×C3×D411yescharacteristic
623C3×C4—22no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—62no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4D3×#4111yescharacteristic
654C3×C4#101011yescharacteristic
655C3×C4C2×C3×#4111yescharacteristic
656C3×C4C3×2−1+411yescharacteristic
657Dic3—22no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661C32#337111yescharacteristic, complemented, Sylow
662C23—21no—
663C23—21no—
664Q8—21no—
665Q8—21no—
666Q8—32no—
667Q8—41no—
668Q8—61no—
669Q8—122no—
670D4—21no—
671D4—21no—
672D4—21no—
673D4—21no—
674D4—42no—
675D4—81no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4C2×C3×#6711yescharacteristic
685C2×C4C2×C3×#6711yescharacteristic
686C2×C4C2×C3×#6711yescharacteristic
687C2×C4C2×C3×#6711yescharacteristic
688C2×C4C2×C3×#6711yescharacteristic
689C2×C4C2×C3×#6711yescharacteristic
690C2×C4C23×C3×D311yescharacteristic
691C8—61no—
692C8—61no—
693C8—61no—
694C8—61no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—82no—
699C2×C3—82no—
700C2×C3—81no—
701C2×C3—81no—
702C2×C3—81no—
703C2×C3—81no—
704C2×C3#582211yescharacteristic
705C2×C3#583111yescharacteristic
706C2×C3#583611yescharacteristic
707C2×C3C3×#54811yescharacteristic
708C2×C3C3×#57511yescharacteristic
709C2×C3C3×#57711yescharacteristic
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22C22×C3×#6711yescharacteristic
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—41no—
724C4—41no—
725C4—62no—
726C4—121no—
727C4—121no—
728C4—121no—
729C4C3×D3×#4111yescharacteristic
730C4C3×#101011yescharacteristic
731C3—21no—
732C3#8371811yescharacteristic, direct product factor
733C3C3×#337111yescharacteristic, complemented
734C2—81no—
735C2—81no—
736C2C3×#582211yescharacteristic
737C2C3×#583111yescharacteristic
738C2C3×#583611yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#559C2
socleC22×C32C22×D4
prime radicalC32×#127C22
hypercenterC3×#559D3
hypocenterC3C3×#3371
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
2. C3×#5567C2semidirect
5. C3×#5056C2semidirect
6. C3×#5055C2semidirect
7. C3×#5054C2semidirect
8. C3×#5054C2semidirect
9. C3×#5030C2semidirect
10. C3×#5024C2semidirect
11. C3×#5022C2semidirect
12. C3×#5018C2semidirect
13. C3×C4×#214C2semidirect
14. C3×#5009C2semidirect
15. C3×#5008C2semidirect
17. #83718C3direct (N × H)
65. #5567C2×C3semidirect
81. #5056C2×C3semidirect
82. #5055C2×C3semidirect
83. #5054C2×C3semidirect
84. #5054C2×C3semidirect
85. #5030C2×C3semidirect
86. #5024C2×C3semidirect
87. #5022C2×C3semidirect
88. #5018C2×C3semidirect
89. C4×#214C2×C3semidirect
90. #5009C2×C3semidirect
91. #5008C2×C3semidirect
661. C32#3371semidirect
732. C3#83718direct (N × H)
733. C3C3×#3371semidirect

Maximal subgroups

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

subgroupindex
C32×#5592
C3×#55672
C3×#50752
C3×#50712
C3×#50562
C3×#50552
C3×#50542
C3×#50302
C3×#50242
C3×#50222
C3×#50182
C3×C4×#2142
C3×#50092
C3×#50082
C3×#33713
#837183