Finite Group Databasebeta

← C3×#24149 #10642756

Subgroups — C3×#24149 #10642756

Order 768.

1038 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3510C211yesmaximal, characteristic
2C3×#3078C211yesmaximal, characteristic, complemented
3C3×C4×#137C211yesmaximal, characteristic, complemented
4C3×#2545C211yesmaximal, characteristic, complemented
5C3×#2038C211yesmaximal, characteristic, complemented
6C3×#2037C211yesmaximal, characteristic
7C3×#2005C211yesmaximal, characteristic, complemented
8C3×#2004C211yesmaximal, characteristic
9C3×#1986C211yesmaximal, characteristic, complemented
10C3×#1967C211yesmaximal, characteristic, complemented
11C3×#1886C211yesmaximal, characteristic, complemented
12C3×#1885C211yesmaximal, characteristic, complemented
13C3×#1857C211yesmaximal, characteristic, complemented
14C3×#1856C211yesmaximal, characteristic, complemented
15C3×#1806C211yesmaximal, characteristic, complemented
16#24149C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#137C2211yescharacteristic
18C3×#559—21no—
19C3×#559—21no—
20C3×#556—21no—
21C3×#556—21no—
22C3×#551—22no—
23C3×#551—22no—
24C3×#542—21no—
25C3×#542—21no—
26C3×#536C2211yescharacteristic
27C3×#535C2211yescharacteristic
28C3×#533C2211yescharacteristic
29C2×C3×C4⋊Q8C2211yescharacteristic
30C3×#529—21no—
31C3×#529—21no—
32C2×C3×#124C2211yescharacteristic
33C2×C3×#124C2211yescharacteristic
34C3×#519C2211yescharacteristic
35C3×#518C2211yescharacteristic
36C3×C4×#41C2211yescharacteristic
37C2×C3×C4×Q8C2211yescharacteristic
38C3×#479—21no—
39C3×#479—21no—
40C3×#477—21no—
41C3×#475—21no—
42C3×#441—21no—
43C3×#440—21no—
44C3×C4×Q16—21no—
45C3×C4×SD16—21no—
46C3×#428C2211yescharacteristic
47C3×#428C2211yescharacteristic
48C3×#428C2211yescharacteristic
49C3×#423C2211yescharacteristic
50C2×C3×#104C2211yescharacteristic
51C2×C3×#104C2211yescharacteristic
52C3×#419C2211yescharacteristic
53C3×#419C2211yescharacteristic
54C3×#419C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C2×C3×#101C2211yescharacteristic
57C2×C3×#101C2211yescharacteristic
58C2×C3×#100C2211yescharacteristic
59C2×C3×#100C2211yescharacteristic
60C3×C4×M16C2211yescharacteristic
61C3×#396—22no—
62C3×#391C2211yescharacteristic
63C3×#390C2211yescharacteristic
64C3×#388—22no—
65C3×C4×C4⋊C4C2211yescharacteristic
66C3×#339C2211yescharacteristic
67C3×#339C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#339C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3510C2×C311yescharacteristic
73#3078C2×C311yescharacteristic, complemented
74C4×#137C2×C311yescharacteristic, complemented
75#2545C2×C311yescharacteristic, complemented
76#2038C2×C311yescharacteristic, complemented
77#2037C2×C311yescharacteristic
78#2005C2×C311yescharacteristic, complemented
79#2004C2×C311yescharacteristic
80#1986C2×C311yescharacteristic, complemented
81#1967C2×C311yescharacteristic, complemented
82#1886C2×C311yescharacteristic, complemented
83#1885C2×C311yescharacteristic, complemented
84#1857C2×C311yescharacteristic, complemented
85#1856C2×C311yescharacteristic, complemented
86#1806C2×C311yescharacteristic, complemented
87C2×C3×#41C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C22×C3×D4C2311yescharacteristic
91C3×#137—22no—
92C3×#137—22no—
93C2×C3×Q16—21no—
94C2×C3×SD16—21no—
95C2×C3×M16C2311yescharacteristic
96C2×C3×M16C2311yescharacteristic
97C2×C3×M16C2311yescharacteristic
98C2×C3×M16C2311yescharacteristic
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—22no—
101C3×C4⋊Q8—41no—
102C3×C4⋊Q8D411yescharacteristic
103C3×C4⋊Q8D411yescharacteristic
104C3×#127—21no—
105C3×#126—22no—
106C3×#126—22no—
107C3×#126—22no—
108C3×#126—22no—
109C3×#125D411yescharacteristic
110C3×#125D411yescharacteristic
111C3×#124—22no—
112C3×#124—22no—
113C3×#124—21no—
114C3×#124—21no—
115C3×#124—22no—
116C3×#124—21no—
117C3×#124—21no—
118C3×#124—21no—
119C3×#124—21no—
120C3×#124—41no—
121C3×#123—22no—
122C3×#123—22no—
123C3×#123—22no—
124C3×#123—22no—
125C3×#123—22no—
126C3×C22⋊Q8—22no—
127C3×C22⋊Q8—22no—
128C3×C22⋊Q8—21no—
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8—21no—
131C3×C22⋊Q8—21no—
132C3×#121—21no—
133C3×#121—21no—
134C3×#120—22no—
135C3×C4×Q8—21no—
136C3×C4×Q8—21no—
137C3×C4×Q8—21no—
138C3×C4×Q8—21no—
139C3×C4×Q8—21no—
140C3×C4×Q8—21no—
141C3×C4×Q8—21no—
142C3×C4×Q8—21no—
143C3×C4×Q8—21no—
144C3×C4×Q8—21no—
145C3×C4×Q8D411yescharacteristic
146C3×C4×Q8D411yescharacteristic
147C3×C4×D4—22no—
148C3×C4×D4—22no—
149C3×C4×D4—21no—
150C3×C4×D4—21no—
151C3×C4×D4—21no—
152C3×C4×D4—21no—
153C3×C4×D4—21no—
154C3×C4×D4—21no—
155C3×C4×D4D411yescharacteristic
156C3×C4×D4D411yescharacteristic
157C3×#117—22no—
158C3×#117—22no—
159C3×#117—22no—
160C3×#117—21no—
161C3×#117C2311yescharacteristic
162C3×#117C2311yescharacteristic
163C3×#117C2311yescharacteristic
164C2×C3×C4⋊C4—21no—
165C2×C3×C4⋊C4—22no—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4C2311yescharacteristic
168C2×C3×C22⋊C4—22no—
169C2×C3×C22⋊C4—22no—
170C2×C3×C22⋊C4—22no—
171C2×C3×C22⋊C4D412yes—
172C2×C3×C22⋊C4D412yes—
173C2×C3×C42—21no—
174C2×C3×C42—21no—
175C2×C3×C42C2311yescharacteristic
176C2×C3×C42C2311yescharacteristic
177C2×C3×C42C2311yescharacteristic
178C3×#107—21no—
179C3×#107—21no—
180C3×#107—21no—
181C3×#106—21no—
182C3×#106—21no—
183C3×#106—21no—
184C3×C4⋊C8—21no—
185C3×C4⋊C8—21no—
186C3×#104—41no—
187C3×#104—41no—
188C3×#103—21no—
189C3×#103—21no—
190C3×#103—21no—
191C3×#103—21no—
192C3×#103—21no—
193C3×#103—21no—
194C3×#103—21no—
195C3×#102—21no—
196C3×#101—22no—
197C3×#101—41no—
198C3×#100—22no—
199C3×#100—41no—
200C3×#97—21no—
201C3×C4×C8—21no—
202C3×#95—21no—
203C3×#95—22no—
204C2×#137C22×C311yescharacteristic
205#559—21no—
206#559—21no—
207#556—21no—
208#556—21no—
209#551—22no—
210#551—22no—
211#542—21no—
212#542—21no—
213#536C22×C311yescharacteristic
214#535C22×C311yescharacteristic
215#533C22×C311yescharacteristic
216C2×C4⋊Q8C22×C311yescharacteristic
217#529—21no—
218#529—21no—
219C2×#124C22×C311yescharacteristic
220C2×#124C22×C311yescharacteristic
221#519C22×C311yescharacteristic
222#518C22×C311yescharacteristic
223C4×#41C22×C311yescharacteristic
224C2×C4×Q8C22×C311yescharacteristic
225#479—21no—
226#479—21no—
227#477—21no—
228#475—21no—
229#441—21no—
230#440—21no—
231C4×Q16—21no—
232C4×SD16—21no—
233#428C22×C311yescharacteristic
234#428C22×C311yescharacteristic
235#428C22×C311yescharacteristic
236#423C22×C311yescharacteristic
237C2×#104C22×C311yescharacteristic
238C2×#104C22×C311yescharacteristic
239#419C22×C311yescharacteristic
240#419C22×C311yescharacteristic
241#419C22×C311yescharacteristic
242#417C22×C311yescharacteristic
243C2×#101C22×C311yescharacteristic
244C2×#101C22×C311yescharacteristic
245C2×#100C22×C311yescharacteristic
246C2×#100C22×C311yescharacteristic
247C4×M16C22×C311yescharacteristic
248#396—22no—
249#391C22×C311yescharacteristic
250#390C22×C311yescharacteristic
251#388—22no—
252C4×C4⋊C4C22×C311yescharacteristic
253#339C22×C311yescharacteristic
254#339C22×C311yescharacteristic
255#339C22×C311yescharacteristic
256#339C22×C311yescharacteristic
257#339C22×C311yescharacteristic
258#339C22×C311yescharacteristic
259C24×C3C2×D412yes—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C2×C3×Q8—21no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
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×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8—21no—
277C2×C3×Q8C2×D411yescharacteristic
278C2×C3×Q8#4112yes—
279C2×C3×D4—21no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4C2×D411yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4C2×D412yes—
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2411yescharacteristic
302C3×Q16—24no—
303C3×SD16—24no—
304C3×M16—21no—
305C3×M16—21no—
306C3×M16—21no—
307C3×M16—21no—
308C3×M16—21no—
309C3×M16—21no—
310C3×M16—21no—
311C3×M16#4112yes—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—22no—
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—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—44no—
331C3×C4⋊C4—42no—
332C3×C4⋊C4—41no—
333C3×C4⋊C4—41no—
334C3×C4⋊C4C2×D411yescharacteristic
335C3×C4⋊C4C2×D411yescharacteristic
336C3×C4⋊C4C2×D411yescharacteristic
337C3×C4⋊C4C2×D411yescharacteristic
338C3×C4⋊C4C2×D411yescharacteristic
339C3×C4⋊C4C2×D411yescharacteristic
340C3×C22⋊C4—22no—
341C3×C22⋊C4—22no—
342C3×C22⋊C4—22no—
343C3×C22⋊C4—22no—
344C3×C22⋊C4—22no—
345C3×C22⋊C4—22no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
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—44no—
356C3×C22⋊C4—44no—
357C3×C42—22no—
358C3×C42—22no—
359C3×C42—21no—
360C3×C42—21no—
361C3×C42—21no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—21no—
365C3×C42—21no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—41no—
369C3×C42—41no—
370C3×C42C2×D411yescharacteristic
371C3×C42C2×D411yescharacteristic
372C3×C42C2×D411yescharacteristic
373C3×C42C2×D411yescharacteristic
374C2×#41C23×C311yescharacteristic
375C22×Q8C23×C311yescharacteristic
376C22×Q8C23×C311yescharacteristic
377C22×D4C23×C311yescharacteristic
378#137—22no—
379#137—22no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×M16C23×C311yescharacteristic
383C2×M16C23×C311yescharacteristic
384C2×M16C23×C311yescharacteristic
385C2×M16C23×C311yescharacteristic
386C4⋊Q8—21no—
387C4⋊Q8—22no—
388C4⋊Q8—41no—
389C4⋊Q8C3×D411yescharacteristic
390C4⋊Q8C3×D411yescharacteristic
391#127—21no—
392#126—22no—
393#126—22no—
394#126—22no—
395#126—22no—
396#125C3×D411yescharacteristic
397#125C3×D411yescharacteristic
398#124—22no—
399#124—22no—
400#124—21no—
401#124—21no—
402#124—22no—
403#124—21no—
404#124—21no—
405#124—21no—
406#124—21no—
407#124—41no—
408#123—22no—
409#123—22no—
410#123—22no—
411#123—22no—
412#123—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419#121—21no—
420#121—21no—
421#120—22no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8C3×D411yescharacteristic
433C4×Q8C3×D411yescharacteristic
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4C3×D411yescharacteristic
443C4×D4C3×D411yescharacteristic
444#117—22no—
445#117—22no—
446#117—22no—
447#117—21no—
448#117C23×C311yescharacteristic
449#117C23×C311yescharacteristic
450#117C23×C311yescharacteristic
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4C23×C311yescharacteristic
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4C3×D412yes—
459C2×C22⋊C4C3×D412yes—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C311yescharacteristic
463C2×C42C23×C311yescharacteristic
464C2×C42C23×C311yescharacteristic
465#107—21no—
466#107—21no—
467#107—21no—
468#106—21no—
469#106—21no—
470#106—21no—
471C4⋊C8—21no—
472C4⋊C8—21no—
473#104—41no—
474#104—41no—
475#103—21no—
476#103—21no—
477#103—21no—
478#103—21no—
479#103—21no—
480#103—21no—
481#103—21no—
482#102—21no—
483#101—22no—
484#101—41no—
485#100—22no—
486#100—41no—
487#97—21no—
488C4×C8—21no—
489#95—21no—
490#95—22no—
491C23×C3—22no—
492C23×C3—21no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—42no—
496C23×C3—42no—
497C23×C3C22×D411yescharacteristic
498C3×Q8—22no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—22no—
502C3×Q8—41no—
503C3×Q8—41no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×Q8—41no—
507C3×Q8—41no—
508C3×Q8—81no—
509C3×Q8—81no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—82no—
519C3×D4—82no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—22no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—42no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—81no—
546C2×C3×C4—81no—
547C2×C3×C4—82no—
548C2×C3×C4—82no—
549C2×C3×C4#12011yescharacteristic
550C2×C3×C4#12011yescharacteristic
551C2×C3×C4#12011yescharacteristic
552C2×C3×C4#12011yescharacteristic
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C22×D411yescharacteristic
555C2×C3×C4C2×#4111yescharacteristic
556C2×C3×C4C2×#4111yescharacteristic
557C2×C3×C4H(5,𝔽2)11yescharacteristic
558C2×C3×C42−1+411yescharacteristic
559C3×C8—22no—
560C3×C8—41no—
561C3×C8—41no—
562C3×C8—41no—
563C24C2×C3×D412yes—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×C3×D411yescharacteristic
582C2×Q8C3×#4112yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4C2×C3×D411yescharacteristic
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4C2×C3×D412yes—
603C22×C4C2×C3×D411yescharacteristic
604C22×C4C2×C3×D411yescharacteristic
605C22×C4C24×C311yescharacteristic
606Q16—24no—
607SD16—24no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16C3×#4112yes—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—44no—
635C4⋊C4—42no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4C2×C3×D411yescharacteristic
639C4⋊C4C2×C3×D411yescharacteristic
640C4⋊C4C2×C3×D411yescharacteristic
641C4⋊C4C2×C3×D411yescharacteristic
642C4⋊C4C2×C3×D411yescharacteristic
643C4⋊C4C2×C3×D411yescharacteristic
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C42—22no—
662C42—22no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—41no—
673C42—41no—
674C42C2×C3×D411yescharacteristic
675C42C2×C3×D411yescharacteristic
676C42C2×C3×D411yescharacteristic
677C42C2×C3×D411yescharacteristic
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—41no—
681C22×C3—42no—
682C22×C3—41no—
683C22×C3—42no—
684C22×C3—41no—
685C22×C3—42no—
686C22×C3—82no—
687C22×C3—82no—
688C22×C3C2×#12011yescharacteristic
689C22×C3#54611yescharacteristic
690C22×C3#54711yescharacteristic
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—42no—
696C3×C4—42no—
697C3×C4—41no—
698C3×C4—42no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—81no—
706C3×C4—81no—
707C3×C4#52511yescharacteristic
708C3×C4#53711yescharacteristic
709C3×C4#54811yescharacteristic
710C3×C4#55011yescharacteristic
711C23—22no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—42no—
716C23—42no—
717C23C22×C3×D411yescharacteristic
718Q8—22no—
719Q8—21no—
720Q8—21no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727Q8—41no—
728Q8—81no—
729Q8—81no—
730D4—21no—
731D4—21no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—82no—
739D4—82no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—82no—
768C2×C4—82no—
769C2×C4C3×#12011yescharacteristic
770C2×C4C3×#12011yescharacteristic
771C2×C4C3×#12011yescharacteristic
772C2×C4C3×#12011yescharacteristic
773C2×C4C22×C3×D411yescharacteristic
774C2×C4C22×C3×D411yescharacteristic
775C2×C4C2×C3×#4111yescharacteristic
776C2×C4C2×C3×#4111yescharacteristic
777C2×C4C3×H(5,𝔽2)11yescharacteristic
778C2×C4C3×2−1+411yescharacteristic
779C8—22no—
780C8—41no—
781C8—41no—
782C8—41no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—81no—
786C2×C3—82no—
787C2×C3#240711yescharacteristic
788C2×C3#301811yescharacteristic
789C2×C3#302211yescharacteristic
790C22—21no—
791C22—21no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—82no—
799C22—82no—
800C22C2×C3×#12011yescharacteristic
801C22C3×#54611yescharacteristic
802C22C3×#54711yescharacteristic
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—42no—
808C4—42no—
809C4—41no—
810C4—42no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4C3×#52511yescharacteristic
820C4C3×#53711yescharacteristic
821C4C3×#54811yescharacteristic
822C4C3×#55011yescharacteristic
823C3#2414911yescharacteristic, direct product factor, Sylow
824C2—21no—
825C2—21no—
826C2—82no—
827C2—81no—
828C2C3×#240711yescharacteristic
829C2C3×#301811yescharacteristic
830C2C3×#302211yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3078C2semidirect
3. C3×C4×#137C2semidirect
4. C3×#2545C2semidirect
5. C3×#2038C2semidirect
7. C3×#2005C2semidirect
9. C3×#1986C2semidirect
10. C3×#1967C2semidirect
11. C3×#1886C2semidirect
12. C3×#1885C2semidirect
13. C3×#1857C2semidirect
14. C3×#1856C2semidirect
15. C3×#1806C2semidirect
16. #24149C3direct (N × H)
73. #3078C2×C3semidirect
74. C4×#137C2×C3semidirect
75. #2545C2×C3semidirect
76. #2038C2×C3semidirect
78. #2005C2×C3semidirect
80. #1986C2×C3semidirect
81. #1967C2×C3semidirect
82. #1886C2×C3semidirect
83. #1885C2×C3semidirect
84. #1857C2×C3semidirect
85. #1856C2×C3semidirect
86. #1806C2×C3semidirect
823. C3#24149direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35102
C3×#30782
C3×C4×#1372
C3×#25452
C3×#20382
C3×#20372
C3×#20052
C3×#20042
C3×#19862
C3×#19672
C3×#18862
C3×#18852
C3×#18572
C3×#18562
C3×#18062
#241493