Finite Group Databasebeta

← C3×#25527 #10644134

Subgroups — C3×#25527 #10644134

Order 768.

1090 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3494C211yesmaximal, characteristic
2C3×#3095C211yesmaximal, characteristic, complemented
3C3×#3056C211yesmaximal, characteristic, complemented
4C3×#2620C211yesmaximal, characteristic, complemented
5C3×#2060C211yesmaximal, characteristic, complemented
6C3×#2037C211yesmaximal, characteristic, complemented
7C3×#2028C211yesmaximal, characteristic, complemented
8C3×#2004C211yesmaximal, characteristic, complemented
9C3×#1900C211yesmaximal, characteristic, complemented
10C3×#1897C211yesmaximal, characteristic, complemented
11C3×#1885C211yesmaximal, characteristic, complemented
12C3×#1882C211yesmaximal, characteristic, complemented
13C3×#1859C211yesmaximal, characteristic, complemented
14C3×#1856C211yesmaximal, characteristic, complemented
15C3×#1733C211yesmaximal, characteristic, complemented
16#25527C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#137C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C3×#555—21no—
20C3×#553—21no—
21C3×#553—21no—
22C3×#551—22no—
23C3×#547—21no—
24C3×#546—22no—
25C3×#544C2211yescharacteristic
26C3×#542—21no—
27C3×#540—21no—
28C3×#535C2211yescharacteristic
29C3×#532—21no—
30C3×#529—21no—
31C2×C3×#124C2211yescharacteristic
32C3×#525C2211yescharacteristic
33C2×C3×C22⋊Q8C2211yescharacteristic
34C2×C3×#121C2211yescharacteristic
35C3×#520C2211yescharacteristic
36C3×#518C2211yescharacteristic
37C2×C3×#117C2211yescharacteristic
38C2×C3×#117C2211yescharacteristic
39C3×#485—21no—
40C3×#485—21no—
41C3×#484—21no—
42C3×#483—21no—
43C3×#470—21no—
44C3×#468—21no—
45C3×#467—21no—
46C3×#465—21no—
47C3×#428C2211yescharacteristic
48C3×#428C2211yescharacteristic
49C3×#428C2211yescharacteristic
50C2×C3×#104C2211yescharacteristic
51C2×C3×#104C2211yescharacteristic
52C3×#419C2211yescharacteristic
53C3×#419C2211yescharacteristic
54C3×#419C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C2×C3×#100C2211yescharacteristic
57C2×C3×#100C2211yescharacteristic
58C3×#407C2211yescharacteristic
59C3×#396—22no—
60C3×#394—22no—
61C3×#391C2211yescharacteristic
62C3×#390C2211yescharacteristic
63C3×#384C2211yescharacteristic
64C3×#343C2211yescharacteristic
65C3×#343C2211yescharacteristic
66C3×#339C2211yescharacteristic
67C3×#339C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#339C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3494C2×C311yescharacteristic
73#3095C2×C311yescharacteristic, complemented
74#3056C2×C311yescharacteristic, complemented
75#2620C2×C311yescharacteristic, complemented
76#2060C2×C311yescharacteristic, complemented
77#2037C2×C311yescharacteristic, complemented
78#2028C2×C311yescharacteristic, complemented
79#2004C2×C311yescharacteristic, complemented
80#1900C2×C311yescharacteristic, complemented
81#1897C2×C311yescharacteristic, complemented
82#1885C2×C311yescharacteristic, complemented
83#1882C2×C311yescharacteristic, complemented
84#1859C2×C311yescharacteristic, complemented
85#1856C2×C311yescharacteristic, complemented
86#1733C2×C311yescharacteristic, complemented
87C2×C3×#41—22no—
88C2×C3×#41C2311yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C22×C3×D4D412yes—
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C3×#137—22no—
94C3×#137—41no—
95C2×C3×Q16—21no—
96C2×C3×SD16—21no—
97C2×C3×M16—21no—
98C2×C3×M16—22no—
99C2×C3×M16—41no—
100C2×C3×M16C2311yescharacteristic
101C2×C3×M16C2311yescharacteristic
102C2×C3×M16C2311yescharacteristic
103C2×C3×M16C2311yescharacteristic
104C22×C3×C8—21no—
105C3×C4⋊Q8—21no—
106C3×C4⋊Q8—21no—
107C3×#127—21no—
108C3×#126—22no—
109C3×#126—22no—
110C3×#125—21no—
111C3×#125—21no—
112C3×#124—22no—
113C3×#124—22no—
114C3×#124—21no—
115C3×#124—22no—
116C3×#124—41no—
117C3×#123—22no—
118C3×#123—22no—
119C3×#123—22no—
120C3×#123—22no—
121C3×#123—21no—
122C3×C22⋊Q8—22no—
123C3×C22⋊Q8—22no—
124C3×C22⋊Q8—21no—
125C3×C22⋊Q8—21no—
126C3×C22⋊Q8—21no—
127C3×C22⋊Q8—21no—
128C3×C22⋊Q8D411yescharacteristic
129C3×C22⋊Q8D411yescharacteristic
130C3×#121—22no—
131C3×#121—22no—
132C3×#121—22no—
133C3×#121—21no—
134C3×#121—21no—
135C3×#121—21no—
136C3×#121—21no—
137C3×#121—21no—
138C3×#121—21no—
139C3×#121D411yescharacteristic
140C3×#121D411yescharacteristic
141C3×#120—21no—
142C3×#120—22no—
143C3×C4×Q8—21no—
144C3×C4×D4—22no—
145C3×C4×D4—22no—
146C3×C4×D4—21no—
147C3×C4×D4—22no—
148C3×C4×D4—21no—
149C3×C4×D4—21no—
150C3×C4×D4—21no—
151C3×C4×D4—21no—
152C3×C4×D4—21no—
153C3×C4×D4—21no—
154C3×#117—22no—
155C3×#117—21no—
156C3×#117—21no—
157C3×#117—21no—
158C3×#117—22no—
159C3×#117—41no—
160C3×#117D411yescharacteristic
161C3×#117D411yescharacteristic
162C3×#117C2311yescharacteristic
163C3×#117C2311yescharacteristic
164C3×#117C2311yescharacteristic
165C2×C3×C4⋊C4—21no—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—22no—
169C2×C3×C4⋊C4D411yescharacteristic
170C2×C3×C4⋊C4D411yescharacteristic
171C2×C3×C4⋊C4C2311yescharacteristic
172C2×C3×C4⋊C4C2311yescharacteristic
173C2×C3×C22⋊C4—21no—
174C2×C3×C22⋊C4—22no—
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—22no—
178C2×C3×C22⋊C4—22no—
179C2×C3×C22⋊C4D412yes—
180C2×C3×C42—21no—
181C2×C3×C42C2311yescharacteristic
182C2×C3×C42C2311yescharacteristic
183C3×#107—21no—
184C3×#107—21no—
185C3×#107—21no—
186C3×#106—21no—
187C3×#106—21no—
188C3×#106—21no—
189C3×#104—22no—
190C3×#104—41no—
191C3×#103—21no—
192C3×#103—21no—
193C3×#103—21no—
194C3×#103—21no—
195C3×#103—21no—
196C3×#103—21no—
197C3×#103—21no—
198C3×#102—21no—
199C3×#100—22no—
200C3×#100—41no—
201C3×C22⋊C8—21no—
202C3×C22⋊C8—21no—
203C3×#95—22no—
204C2×#137C22×C311yescharacteristic
205C22×M16C22×C311yescharacteristic
206#555—21no—
207#553—21no—
208#553—21no—
209#551—22no—
210#547—21no—
211#546—22no—
212#544C22×C311yescharacteristic
213#542—21no—
214#540—21no—
215#535C22×C311yescharacteristic
216#532—21no—
217#529—21no—
218C2×#124C22×C311yescharacteristic
219#525C22×C311yescharacteristic
220C2×C22⋊Q8C22×C311yescharacteristic
221C2×#121C22×C311yescharacteristic
222#520C22×C311yescharacteristic
223#518C22×C311yescharacteristic
224C2×#117C22×C311yescharacteristic
225C2×#117C22×C311yescharacteristic
226#485—21no—
227#485—21no—
228#484—21no—
229#483—21no—
230#470—21no—
231#468—21no—
232#467—21no—
233#465—21no—
234#428C22×C311yescharacteristic
235#428C22×C311yescharacteristic
236#428C22×C311yescharacteristic
237C2×#104C22×C311yescharacteristic
238C2×#104C22×C311yescharacteristic
239#419C22×C311yescharacteristic
240#419C22×C311yescharacteristic
241#419C22×C311yescharacteristic
242#417C22×C311yescharacteristic
243C2×#100C22×C311yescharacteristic
244C2×#100C22×C311yescharacteristic
245#407C22×C311yescharacteristic
246#396—22no—
247#394—22no—
248#391C22×C311yescharacteristic
249#390C22×C311yescharacteristic
250#384C22×C311yescharacteristic
251#343C22×C311yescharacteristic
252#343C22×C311yescharacteristic
253#339C22×C311yescharacteristic
254#339C22×C311yescharacteristic
255#339C22×C311yescharacteristic
256#339C22×C311yescharacteristic
257#339C22×C311yescharacteristic
258#339C22×C311yescharacteristic
259C24×C3C2×D412yes—
260C24×C3C2×D411yescharacteristic
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C3×#41—21no—
265C3×#41—84no—
266C2×C3×Q8—22no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8C2×D411yescharacteristic
274C2×C3×D4—21no—
275C2×C3×D4—22no—
276C2×C3×D4—21no—
277C2×C3×D4—22no—
278C2×C3×D4—22no—
279C2×C3×D4—21no—
280C2×C3×D4—22no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—82no—
288C2×C3×D4C2×D411yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—22no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4C2×D412yes—
309C22×C3×C4C2411yescharacteristic
310C3×Q16—42no—
311C3×SD16—42no—
312C3×M16—21no—
313C3×M16—21no—
314C3×M16—21no—
315C3×M16—21no—
316C3×M16—21no—
317C3×M16—21no—
318C3×M16—21no—
319C3×M16—42no—
320C3×M16#4112yescomplemented
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—42no—
326C3×C4⋊C4—22no—
327C3×C4⋊C4—22no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—42no—
339C3×C4⋊C4—41no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—82no—
342C3×C4⋊C4C2×D411yescharacteristic
343C3×C4⋊C4C2×D411yescharacteristic
344C3×C4⋊C4C2×D411yescharacteristic
345C3×C4⋊C4C2×D411yescharacteristic
346C3×C4⋊C4C2×D411yescharacteristic
347C3×C4⋊C4C2×D411yescharacteristic
348C3×C22⋊C4—22no—
349C3×C22⋊C4—22no—
350C3×C22⋊C4—22no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—22no—
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—22no—
361C3×C22⋊C4—22no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—42no—
365C3×C22⋊C4—44no—
366C3×C22⋊C4—41no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—82no—
369C3×C42—22no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42#4112yescomplemented
379C2×#41—22no—
380C2×#41C23×C311yescharacteristic
381C22×Q8C23×C311yescharacteristic
382C22×D4C3×D412yes—
383C22×D4C23×C311yescharacteristic
384C23×C4C23×C311yescharacteristic
385#137—22no—
386#137—41no—
387C2×Q16—21no—
388C2×SD16—21no—
389C2×M16—21no—
390C2×M16—22no—
391C2×M16—41no—
392C2×M16C23×C311yescharacteristic
393C2×M16C23×C311yescharacteristic
394C2×M16C23×C311yescharacteristic
395C2×M16C23×C311yescharacteristic
396C22×C8—21no—
397C4⋊Q8—21no—
398C4⋊Q8—21no—
399#127—21no—
400#126—22no—
401#126—22no—
402#125—21no—
403#125—21no—
404#124—22no—
405#124—22no—
406#124—21no—
407#124—22no—
408#124—41no—
409#123—22no—
410#123—22no—
411#123—22no—
412#123—22no—
413#123—21no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8C3×D411yescharacteristic
421C22⋊Q8C3×D411yescharacteristic
422#121—22no—
423#121—22no—
424#121—22no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121C3×D411yescharacteristic
432#121C3×D411yescharacteristic
433#120—21no—
434#120—22no—
435C4×Q8—21no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—21no—
439C4×D4—22no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446#117—22no—
447#117—21no—
448#117—21no—
449#117—21no—
450#117—22no—
451#117—41no—
452#117C3×D411yescharacteristic
453#117C3×D411yescharacteristic
454#117C23×C311yescharacteristic
455#117C23×C311yescharacteristic
456#117C23×C311yescharacteristic
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4C3×D411yescharacteristic
462C2×C4⋊C4C3×D411yescharacteristic
463C2×C4⋊C4C23×C311yescharacteristic
464C2×C4⋊C4C23×C311yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4C3×D412yes—
472C2×C42—21no—
473C2×C42C23×C311yescharacteristic
474C2×C42C23×C311yescharacteristic
475#107—21no—
476#107—21no—
477#107—21no—
478#106—21no—
479#106—21no—
480#106—21no—
481#104—22no—
482#104—41no—
483#103—21no—
484#103—21no—
485#103—21no—
486#103—21no—
487#103—21no—
488#103—21no—
489#103—21no—
490#102—21no—
491#100—22no—
492#100—41no—
493C22⋊C8—21no—
494C22⋊C8—21no—
495#95—22no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—42no—
505C23×C3—42no—
506C23×C3#12011yescharacteristic
507C23×C3#12011yescharacteristic
508C23×C3C22×D411yescharacteristic
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—41no—
512C3×Q8—41no—
513C3×Q8—41no—
514C3×Q8—41no—
515C3×Q8—82no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—44no—
519C3×D4—42no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—81no—
527C3×D4—82no—
528C3×D4—82no—
529C3×D4—82no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—42no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—42no—
555C2×C3×C4—41no—
556C2×C3×C4—42no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—81no—
564C2×C3×C4—82no—
565C2×C3×C4—82no—
566C2×C3×C4—82no—
567C2×C3×C4#12011yescharacteristic
568C2×C3×C4#12011yescharacteristic
569C2×C3×C4C22×D411yescharacteristic
570C2×C3×C4C22×D411yescharacteristic
571C2×C3×C4C2×#4111yescharacteristic
572C2×C3×C4C2×#4111yescharacteristic
573C2×C3×C4H(5,𝔽2)11yescharacteristic
574C2×C3×C42−1+411yescharacteristic
575C3×C8—22no—
576C3×C8—41no—
577C3×C8—41no—
578C3×C8—41no—
579C24C2×C3×D412yes—
580C24C2×C3×D411yescharacteristic
581#41—21no—
582#41—21no—
583#41—21no—
584#41—21no—
585#41—84no—
586C2×Q8—22no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C2×C3×D411yescharacteristic
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—82no—
608C2×D4C2×C3×D411yescharacteristic
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4C2×C3×D411yescharacteristic
624C22×C4C2×C3×D411yescharacteristic
625C22×C4C2×C3×D411yescharacteristic
626C22×C4C2×C3×D411yescharacteristic
627C22×C4C2×C3×D411yescharacteristic
628C22×C4C2×C3×D412yes—
629C22×C4C24×C311yescharacteristic
630Q16—42no—
631SD16—42no—
632M16—21no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—21no—
639M16—42no—
640M16C3×#4112yescomplemented
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—42no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—42no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4—82no—
662C4⋊C4C2×C3×D411yescharacteristic
663C4⋊C4C2×C3×D411yescharacteristic
664C4⋊C4C2×C3×D411yescharacteristic
665C4⋊C4C2×C3×D411yescharacteristic
666C4⋊C4C2×C3×D411yescharacteristic
667C4⋊C4C2×C3×D411yescharacteristic
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—42no—
685C22⋊C4—44no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—82no—
689C42—22no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42C3×#4112yescomplemented
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—41no—
708C22×C3—42no—
709C22×C3—41no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—41no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—82no—
716C22×C3—82no—
717C22×C3C2×#12011yescharacteristic
718C22×C3#54611yescharacteristic
719C22×C3#54711yescharacteristic
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—42no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—42no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—81no—
732C3×C4—81no—
733C3×C4—81no—
734C3×C4#53211yescharacteristic
735C3×C4#53711yescharacteristic
736C3×C4#54611yescharacteristic
737C3×C4#54711yescharacteristic
738C23—21no—
739C23—21no—
740C23—22no—
741C23—21no—
742C23—22no—
743C23—22no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23—42no—
748C23C3×#12011yescharacteristic
749C23C3×#12011yescharacteristic
750C23C22×C3×D411yescharacteristic
751Q8—21no—
752Q8—21no—
753Q8—41no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8—82no—
758D4—21no—
759D4—21no—
760D4—44no—
761D4—42no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—82no—
769D4—81no—
770D4—82no—
771D4—82no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—81no—
806C2×C4—82no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4C3×#12011yescharacteristic
810C2×C4C3×#12011yescharacteristic
811C2×C4C22×C3×D411yescharacteristic
812C2×C4C22×C3×D411yescharacteristic
813C2×C4C2×C3×#4111yescharacteristic
814C2×C4C2×C3×#4111yescharacteristic
815C2×C4C3×H(5,𝔽2)11yescharacteristic
816C2×C4C3×2−1+411yescharacteristic
817C8—22no—
818C8—41no—
819C8—41no—
820C8—41no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—41no—
824C2×C3—41no—
825C2×C3—81no—
826C2×C3—82no—
827C2×C3#243011yescharacteristic
828C2×C3#301911yescharacteristic
829C2×C3#302211yescharacteristic
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—41no—
844C22—81no—
845C22—81no—
846C22—82no—
847C22—82no—
848C22C2×C3×#12011yescharacteristic
849C22C3×#54611yescharacteristic
850C22C3×#54711yescharacteristic
851C4—21no—
852C4—21no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—42no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—81no—
863C4—81no—
864C4—81no—
865C4C3×#53211yescharacteristic
866C4C3×#53711yescharacteristic
867C4C3×#54611yescharacteristic
868C4C3×#54711yescharacteristic
869C3#2552711yescharacteristic, direct product factor, Sylow
870C2—21no—
871C2—21no—
872C2—41no—
873C2—41no—
874C2—82no—
875C2—81no—
876C2C3×#243011yescharacteristic
877C2C3×#301911yescharacteristic
878C2C3×#302211yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#3494C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3095C2semidirect
3. C3×#3056C2semidirect
4. C3×#2620C2semidirect
5. C3×#2060C2semidirect
6. C3×#2037C2semidirect
7. C3×#2028C2semidirect
8. C3×#2004C2semidirect
9. C3×#1900C2semidirect
10. C3×#1897C2semidirect
11. C3×#1885C2semidirect
12. C3×#1882C2semidirect
13. C3×#1859C2semidirect
14. C3×#1856C2semidirect
15. C3×#1733C2semidirect
16. #25527C3direct (N × H)
73. #3095C2×C3semidirect
74. #3056C2×C3semidirect
75. #2620C2×C3semidirect
76. #2060C2×C3semidirect
77. #2037C2×C3semidirect
78. #2028C2×C3semidirect
79. #2004C2×C3semidirect
80. #1900C2×C3semidirect
81. #1897C2×C3semidirect
82. #1885C2×C3semidirect
83. #1882C2×C3semidirect
84. #1859C2×C3semidirect
85. #1856C2×C3semidirect
86. #1733C2×C3semidirect
320. C3×M16#41semidirect
378. C3×C42#41semidirect
640. M16C3×#41semidirect
698. C42C3×#41semidirect
869. C3#25527direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34942
C3×#30952
C3×#30562
C3×#26202
C3×#20602
C3×#20372
C3×#20282
C3×#20042
C3×#19002
C3×#18972
C3×#18852
C3×#18822
C3×#18592
C3×#18562
C3×#17332
#255273