Finite Group Databasebeta

← C3×#80321 #11895708

Subgroups — C3×#80321 #11895708

Order 1152.

862 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic, complemented
2C3×#5539C211yesmaximal, characteristic, complemented
3C32×#459C211yesmaximal, characteristic, complemented
4C3×#5152C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6C3×#5150C211yesmaximal, characteristic, complemented
7C3×Dic3×D8C211yesmaximal, characteristic, complemented
8C3×#5071C211yesmaximal, characteristic, complemented
9C3×#5014C211yesmaximal, characteristic, complemented
10C3×#4847C211yesmaximal, characteristic, complemented
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4766C211yesmaximal, characteristic, complemented
13C3×#4764C211yesmaximal, characteristic, complemented
14C3×#4761C211yesmaximal, characteristic, complemented
15C3×#4760C211yesmaximal, characteristic, complemented
16C3×#3366—31nomaximal
17#80321C311yesmaximal, characteristic, direct product factor
18C2×C3×#237—21no—
19C2×C32×D8C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C32×#127C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×#940C2211yescharacteristic
24C3×#940C2211yescharacteristic
25C3×#939—21no—
26C3×#939—21no—
27C3×#938—21no—
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C3×D4×Dic3C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#924—21no—
34C2×C3×Dic3⋊C4—21no—
35C3×#890C2211yescharacteristic
36C3×#888C2211yescharacteristic
37C3×#878—21no—
38C3×#878—21no—
39C3×C4×D12C2211yescharacteristic
40C3×#870C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#815C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#554—31no—
62C3×#550—31no—
63#5718C2×C311yescharacteristic, complemented
64#5539C2×C311yescharacteristic, complemented
65C3×#490—31no—
66C3×#490—31no—
67C3×#486—31no—
68C3×#478—31no—
69C3×#478—31no—
70C3×#476—31no—
71C3×#459—21no—
72C3×#459—31no—
73C3×#459—31no—
74C3×#459D311yescharacteristic, complemented
75C3×#459C2×C311yescharacteristic, complemented
76C3×#446—31no—
77C3×#442—31no—
78C3×#442—31no—
79C3×C4×D8—31no—
80#5152C2×C311yescharacteristic, complemented
81#5150C2×C311yescharacteristic, complemented
82#5150C2×C311yescharacteristic, complemented
83Dic3×D8C2×C311yescharacteristic, complemented
84#5071C2×C311yescharacteristic, complemented
85#5014C2×C311yescharacteristic, complemented
86#4847C2×C311yescharacteristic, complemented
87#4828C2×C311yescharacteristic, complemented
88#4766C2×C311yescharacteristic, complemented
89#4764C2×C311yescharacteristic, complemented
90#4761C2×C311yescharacteristic, complemented
91#4760C2×C311yescharacteristic, complemented
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#237—44no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6D411yescharacteristic
111C32×D8—22no—
112C32×D8—22no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C42C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#213—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
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⋊C4D411yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3366—31noSylow
140C2×C3×#41—61no—
141C2×#237—21no—
142C2×C3×D8—21no—
143C2×C3×D8—21no—
144C2×C3×D8—31no—
145C2×C3×D8C2×D311yescharacteristic
146C2×C3×D8C2×D311yescharacteristic
147C2×C3×D8C22×C311yescharacteristic
148C2×C3×D8C22×C311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×#127—21no—
151C3×#127—31no—
152C3×#127—31no—
153C3×#127C2×D311yescharacteristic
154C3×#127C22×C311yescharacteristic
155C3×#125—31no—
156C3×#125—31no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8—61no—
160C3×#121—61no—
161C3×#121—61no—
162C3×#121—61no—
163C3×C4×Q8—31no—
164C3×C4×D4—21no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—31no—
170C3×C4×D4C2×D311yescharacteristic
171C3×C4×D4C22×C311yescharacteristic
172C2×C3×C4⋊C4—61no—
173#940C22×C311yescharacteristic
174#940C22×C311yescharacteristic
175#939—21no—
176#939—21no—
177#938—21no—
178D4×Dic3C22×C311yescharacteristic
179D4×Dic3C22×C311yescharacteristic
180D4×Dic3C22×C311yescharacteristic
181D4×Dic3C22×C311yescharacteristic
182C2×#213C22×C311yescharacteristic
183#924—21no—
184C2×Dic3⋊C4—21no—
185#890C22×C311yescharacteristic
186#888C22×C311yescharacteristic
187#878—21no—
188#878—21no—
189C4×D12C22×C311yescharacteristic
190#870C22×C311yescharacteristic
191C4×Dic6C22×C311yescharacteristic
192C3×#107—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×C4⋊C8—21no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×C4⋊C8C2×D311yescharacteristic
199C3×C4⋊C8C22×C311yescharacteristic
200C3×#102—21no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102C2×D311yescharacteristic
211C3×#102C2×D311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×#97—31no—
215C3×#97—31no—
216C3×C4×C8—31no—
217#832C22×C311yescharacteristic
218#832C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#832C22×C311yescharacteristic
221#832C22×C311yescharacteristic
222#821C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224#818C22×C311yescharacteristic
225#817C22×C311yescharacteristic
226#815C22×C311yescharacteristic
227Dic3⋊C8C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229C8×Dic3C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#808C22×C311yescharacteristic
232#803C22×C311yescharacteristic
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C32×D4—21no—
238C32×D4—21no—
239C32×D4—21no—
240C32×D4—21no—
241C32×D4—21no—
242C32×D4—42no—
243C32×D4—81no—
244C32×D4#4112yescomplemented
245C2×C32×C4—21no—
246C2×C32×C4—81no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C3×#67—42no—
251C3×#67—42no—
252C3×#67—81no—
253C3×#67—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×C4×D3—42no—
268C3×Dic6—22no—
269C3×Dic6—81no—
270C32×C8—21no—
271C32×C8—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274#554—31no—
275#550—31no—
276#490—31no—
277#490—31no—
278#486—31no—
279#478—31no—
280#478—31no—
281#476—31no—
282#459—31no—
283#459—31no—
284#459C3×D311yescharacteristic, complemented
285#446—31no—
286#442—31no—
287#442—31no—
288C4×D8—31no—
289C3×#41—124no—
290C2×C3×Q8—31no—
291C2×C3×Q8—61no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—31no—
300C2×C3×D4—41no—
301C2×C3×D4—41no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C23×C311yescharacteristic
310C2×C3×D4C23×C311yescharacteristic
311C2×C3×D4C23×C311yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—41no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C2×#67—21no—
321C2×#67—21no—
322C2×#67—21no—
323C2×#67—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328#237—44no—
329C2×D12C23×C311yescharacteristic
330C2×C4×D3—21no—
331C2×Dic6—21no—
332C2×Dic6C3×D411yescharacteristic
333C3×D8—22no—
334C3×D8—22no—
335C3×D8—22no—
336C3×D8—22no—
337C3×D8—42no—
338C3×D8—42no—
339C3×D8—62no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C23×C311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C42—21no—
371C3×C42—31no—
372C3×C42—31no—
373C3×C42C22×D311yescharacteristic
374C3×C42C23×C311yescharacteristic
375#217—21no—
376#217—21no—
377#217—21no—
378#217—21no—
379#213—22no—
380(C2×D3)⋊C4—21no—
381C4⋊Dic3—21no—
382C4⋊Dic3C3×D411yescharacteristic
383C4⋊Dic3C23×C311yescharacteristic
384C4⋊Dic3C23×C311yescharacteristic
385C4⋊Dic3C23×C311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4C3×D411yescharacteristic
391Dic3⋊C4C3×D411yescharacteristic
392C4×Dic3C23×C311yescharacteristic
393C4×Dic3C23×C311yescharacteristic
394C2×C3⋊C8C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396C22×C32—22no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C42−1+411yescharacteristic
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3AGL(1,ℤ/8)12yes—
421C2×#41—61no—
422C2×D8—31no—
423C2×D8C2×C3×D311yescharacteristic
424C2×D8C2×C3×D311yescharacteristic
425C4⋊Q8—31no—
426#127—31no—
427#127—31no—
428#127C2×C3×D311yescharacteristic
429#125—31no—
430#125—31no—
431C22⋊Q8—61no—
432C22⋊Q8—61no—
433C22⋊Q8—61no—
434#121—61no—
435#121—61no—
436#121—61no—
437C4×Q8—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4C2×C3×D311yescharacteristic
444C2×C4⋊C4—61no—
445#107—31no—
446#106—31no—
447#106—31no—
448C4⋊C8—31no—
449C4⋊C8—31no—
450C4⋊C8C2×C3×D311yescharacteristic
451#102—31no—
452#102—31no—
453#102—31no—
454#102—31no—
455#102—31no—
456#102—31no—
457#102—31no—
458#102—31no—
459#102C2×C3×D311yescharacteristic
460#102C2×C3×D311yescharacteristic
461#97—31no—
462#97—31no—
463C4×C8—31no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—61no—
474C22×D3—21no—
475C3×Q8—62no—
476C3×Q8—241no—
477C3×D4—21no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—22no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—42no—
494C3×D4—42no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—82no—
498C3×D4—81no—
499C3×D4—81no—
500C3×D4—82no—
501C3×D4—122no—
502C3×D4—122no—
503C3×D4—241no—
504C3×D4—241no—
505C3×D4#23712yescomplemented
506C3×D4C3×#4112yescomplemented
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—81no—
521C2×C3×C4—81no—
522C2×C3×C4—82no—
523C2×C3×C4—122no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4—241no—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×C3×D411yescharacteristic
531C2×C3×C4C2×C3×D411yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C24×C311yescharacteristic
534#67—42no—
535#67—42no—
536#67—81no—
537#67—81no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—42no—
542C2×Dic3—42no—
543C2×Dic3—42no—
544C2×Dic3—81no—
545C2×Dic3C2×C3×D411yescharacteristic
546C2×Dic3C2×C3×D411yescharacteristic
547C2×Dic3C2×C3×D411yescharacteristic
548C2×Dic3C2×C3×D411yescharacteristic
549D12—21no—
550D12—21no—
551C4×D3—42no—
552Dic6—22no—
553Dic6—81no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—41no—
560C3×C8—61no—
561C3×C8—61no—
562C3⋊C8—21no—
563C3⋊C8—21no—
564C2×C32—42no—
565C2×C32—81no—
566C2×C32—81no—
567C2×C32#54811yescharacteristic
568C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
569C2×C32#57611yescharacteristic
570C3×D3—81no—
571#41—124no—
572C2×Q8—31no—
573C2×Q8—61no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4C22×C3×D311yescharacteristic
582C2×D4C22×C3×D311yescharacteristic
583C2×D4C22×C3×D311yescharacteristic
584C22×C4—21no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590D8—22no—
591D8—22no—
592D8—62no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8C22×C3×D311yescharacteristic
596C2×C8C22×C3×D311yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4C22×C3×D311yescharacteristic
609C22⋊C4—21no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C42—31no—
616C42—31no—
617C42C22×C3×D311yescharacteristic
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
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×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C22×C3×D411yescharacteristic
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C3×C4—22no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—32no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4C2×#23711yescharacteristic
673C3×C4#101011yescharacteristic
674C3×C4C2×C3×#4111yescharacteristic
675C3×C4C3×2−1+411yescharacteristic
676Dic3—21no—
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3C3×AGL(1,ℤ/8)12yes—
683C32#336611yescharacteristic, complemented, Sylow
684C23—21no—
685C23—21no—
686C23—21no—
687C23—61no—
688Q8—62no—
689Q8—241no—
690D4—21no—
691D4—21no—
692D4—21no—
693D4—21no—
694D4—21no—
695D4—42no—
696D4—61no—
697D4—61no—
698D4—81no—
699D4—122no—
700D4—122no—
701D4—241no—
702D4—241no—
703D4C3×#23712yescomplemented
704C2×C4—21no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—81no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4—241no—
718C2×C4C3×D3×D411yescharacteristic
719C2×C4C3×D3×D411yescharacteristic
720C2×C4C23×C3×D311yescharacteristic
721C8—21no—
722C8—21no—
723C8—61no—
724C8—61no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—42no—
729C2×C3—42no—
730C2×C3—82no—
731C2×C3—81no—
732C2×C3—81no—
733C2×C3—81no—
734C2×C3—81no—
735C2×C3—161no—
736C2×C3—161no—
737C2×C3—241no—
738C2×C3#559811yescharacteristic
739C2×C3#575711yescharacteristic
740C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
741C2×C3C3×#54811yescharacteristic
742C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
743C2×C3C3×#57611yescharacteristic
744D3—81no—
745C22—22no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22C2×C3×D3×D411yescharacteristic
758C4—21no—
759C4—21no—
760C4—32no—
761C4—41no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4C2×C3×#23711yescharacteristic
769C4C3×#101011yescharacteristic
770C3—21no—
771C3#8032111yescharacteristic, direct product factor
772C3C3×#336611yescharacteristic, complemented
773C2—42no—
774C2—81no—
775C2—81no—
776C2—241no—
777C2C3×#559811yescharacteristic
778C2C3×#575711yescharacteristic
779C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenterC3×#459D3
hypocenterC3C3×#3366
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×#5718C2semidirect
2. C3×#5539C2semidirect
3. C32×#459C2semidirect
4. C3×#5152C2semidirect
5. C3×#5150C2semidirect
6. C3×#5150C2semidirect
7. C3×Dic3×D8C2semidirect
8. C3×#5071C2semidirect
9. C3×#5014C2semidirect
10. C3×#4847C2semidirect
11. C3×#4828C2semidirect
12. C3×#4766C2semidirect
13. C3×#4764C2semidirect
14. C3×#4761C2semidirect
15. C3×#4760C2semidirect
17. #80321C3direct (N × H)
63. #5718C2×C3semidirect
64. #5539C2×C3semidirect
74. C3×#459D3semidirect
75. C3×#459C2×C3semidirect
80. #5152C2×C3semidirect
81. #5150C2×C3semidirect
82. #5150C2×C3semidirect
83. Dic3×D8C2×C3semidirect
84. #5071C2×C3semidirect
85. #5014C2×C3semidirect
86. #4847C2×C3semidirect
87. #4828C2×C3semidirect
88. #4766C2×C3semidirect
89. #4764C2×C3semidirect
90. #4761C2×C3semidirect
91. #4760C2×C3semidirect
244. C32×D4#41semidirect
284. #459C3×D3semidirect
505. C3×D4#237semidirect
506. C3×D4C3×#41semidirect
683. C32#3366semidirect
703. D4C3×#237semidirect
771. C3#80321direct (N × H)
772. C3C3×#3366semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
C3×#55392
C32×#4592
C3×#51522
C3×#51502
C3×Dic3×D82
C3×#50712
C3×#50142
C3×#48472
C3×#48282
C3×#47662
C3×#47642
C3×#47612
C3×#47602
C3×#33663
#803213