Finite Group Databasebeta

← C3×#24195 #10642802

Subgroups — C3×#24195 #10642802

Order 768.

1074 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#556C211yesmaximal, characteristic
2C2×C3×#464C211yesmaximal, characteristic
3C2×C3×C4×Q16C211yesmaximal, characteristic, complemented
4C3×#2581C211yesmaximal, characteristic, complemented
5C3×#2043C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic
7C3×#2016C211yesmaximal, characteristic, complemented
8C3×#2015C211yesmaximal, characteristic
9C3×#1984C211yesmaximal, characteristic, complemented
10C3×#1958C211yesmaximal, characteristic
11C3×#1878C211yesmaximal, characteristic, complemented
12C3×#1877C211yesmaximal, characteristic
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic
15C3×#1805C211yesmaximal, characteristic, complemented
16#24195C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C3×#556—24no—
21C3×#556—24no—
22C2×C3×C4⋊Q8C2211yescharacteristic
23C2×C3×#126—21no—
24C2×C3×#126—21no—
25C2×C3×#124C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×C22⋊Q8—21no—
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×Q8C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×#117—21no—
34C3×#464—24no—
35C3×C4×Q16—24no—
36C2×C3×#107C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×C4×C8C2211yescharacteristic
49C3×#400—21no—
50C3×#395—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#387—21no—
56C3×#387—21no—
57C3×#382C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#556C2×C311yescharacteristic
65C2×#464C2×C311yescharacteristic
66C2×C4×Q16C2×C311yescharacteristic, complemented
67#2581C2×C311yescharacteristic, complemented
68#2043C2×C311yescharacteristic, complemented
69#2042C2×C311yescharacteristic
70#2016C2×C311yescharacteristic, complemented
71#2015C2×C311yescharacteristic
72#1984C2×C311yescharacteristic, complemented
73#1958C2×C311yescharacteristic
74#1878C2×C311yescharacteristic, complemented
75#1877C2×C311yescharacteristic
76#1863C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic
78#1805C2×C311yescharacteristic, complemented
79C22×C3×Q8D411yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C2×C3×Q16—22no—
86C2×C3×Q16—22no—
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—22no—
90C2×C3×Q16—41no—
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×C4⋊Q8—22no—
99C3×C4⋊Q8—22no—
100C3×#126—28no—
101C3×#126—28no—
102C3×#124—22no—
103C3×#124—22no—
104C3×#124—22no—
105C3×#124D414yes—
106C3×C22⋊Q8—28no—
107C3×C4×Q8—22no—
108C3×C4×Q8—22no—
109C3×C4×Q8—22no—
110C3×C4×Q8—22no—
111C3×C4×Q8—22no—
112C3×C4×Q8—22no—
113C3×C4×Q8—22no—
114C3×C4×Q8D414yes—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×#117—28no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4D411yescharacteristic
126C2×C3×C4⋊C4D411yescharacteristic
127C2×C3×C4⋊C4D411yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C42—21no—
138C2×C3×C42—21no—
139C2×C3×C42—21no—
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2311yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C3×#107—22no—
144C3×C4⋊C8—22no—
145C3×#103—22no—
146C3×#103—22no—
147C3×#103—22no—
148C3×#103—22no—
149C3×#103—41no—
150C3×#103—41no—
151C3×#103—41no—
152C3×#102—22no—
153C3×#102—22no—
154C3×#102—41no—
155C3×C4×C8—22no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×Q16C22×C311yescharacteristic
165C22×Q16C22×C311yescharacteristic
166C22×SD16C22×C311yescharacteristic
167#556—24no—
168#556—24no—
169C2×C4⋊Q8C22×C311yescharacteristic
170C2×#126—21no—
171C2×#126—21no—
172C2×#124C22×C311yescharacteristic
173C2×#124C22×C311yescharacteristic
174C2×C22⋊Q8—21no—
175C2×C4×Q8C22×C311yescharacteristic
176C2×C4×Q8C22×C311yescharacteristic
177C2×C4×Q8C22×C311yescharacteristic
178C2×C4×Q8C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×#117—21no—
181#464—24no—
182C4×Q16—24no—
183C2×#107C22×C311yescharacteristic
184C2×C4⋊C8C22×C311yescharacteristic
185C2×#103C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#103C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×C4×C8C22×C311yescharacteristic
196#400—21no—
197#395—21no—
198#391C22×C311yescharacteristic
199#391C22×C311yescharacteristic
200#389C22×C311yescharacteristic
201#389C22×C311yescharacteristic
202#387—21no—
203#387—21no—
204#382C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#336C22×C311yescharacteristic
208#336C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211C24×C3—21no—
212C2×C3×Q8—22no—
213C2×C3×Q8—22no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—41no—
230C2×C3×Q8C2×D412yes—
231C2×C3×Q8C2×D412yes—
232C2×C3×Q8#4112yes—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4C2×D412yes—
239C22×C3×C4—24no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—42no—
248C22×C3×C4—42no—
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2411yescharacteristic
256C3×Q16—28no—
257C3×Q16—44no—
258C3×SD16—44no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8#4112yes—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—42no—
286C3×C4⋊C4—42no—
287C3×C4⋊C4—42no—
288C3×C4⋊C4C2×D412yes—
289C3×C22⋊C4—24no—
290C3×C22⋊C4—24no—
291C3×C22⋊C4—24no—
292C3×C22⋊C4—24no—
293C3×C22⋊C4—24no—
294C3×C42—24no—
295C3×C42—24no—
296C3×C42—21no—
297C3×C42—21no—
298C3×C42—21no—
299C3×C42—21no—
300C3×C42—42no—
301C3×C42C2×D412yes—
302C3×C42C2×D412yes—
303C22×Q8C3×D411yescharacteristic
304C22×Q8C23×C311yescharacteristic
305C22×Q8C23×C311yescharacteristic
306C22×Q8C23×C311yescharacteristic
307C22×D4C23×C311yescharacteristic
308C23×C4—21no—
309C2×Q16—22no—
310C2×Q16—22no—
311C2×Q16—22no—
312C2×Q16—22no—
313C2×Q16—22no—
314C2×Q16—41no—
315C2×SD16—22no—
316C2×SD16—22no—
317C2×SD16—41no—
318C22×C8C23×C311yescharacteristic
319C22×C8C23×C311yescharacteristic
320C22×C8C23×C311yescharacteristic
321C22×C8C23×C311yescharacteristic
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324#126—28no—
325#126—28no—
326#124—22no—
327#124—22no—
328#124—22no—
329#124C3×D414yes—
330C22⋊Q8—28no—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8C3×D414yes—
339C4×D4—22no—
340C4×D4—22no—
341#117—28no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C3×D411yescharacteristic
350C2×C4⋊C4C3×D411yescharacteristic
351C2×C4⋊C4C3×D411yescharacteristic
352C2×C4⋊C4C23×C311yescharacteristic
353C2×C4⋊C4C23×C311yescharacteristic
354C2×C4⋊C4C23×C311yescharacteristic
355C2×C4⋊C4C23×C311yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42C23×C311yescharacteristic
365C2×C42C23×C311yescharacteristic
366C2×C42C23×C311yescharacteristic
367#107—22no—
368C4⋊C8—22no—
369#103—22no—
370#103—22no—
371#103—22no—
372#103—22no—
373#103—41no—
374#103—41no—
375#103—41no—
376#102—22no—
377#102—22no—
378#102—41no—
379C4×C8—22no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388C23×C3—22no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3C22×D411yescharacteristic
396C3×Q8—22no—
397C3×Q8—22no—
398C3×Q8—22no—
399C3×Q8—22no—
400C3×Q8—22no—
401C3×Q8—22no—
402C3×Q8—44no—
403C3×Q8—41no—
404C3×Q8—41no—
405C3×Q8—41no—
406C3×Q8—41no—
407C3×Q8—41no—
408C3×Q8—41no—
409C3×D4—22no—
410C3×D4—22no—
411C3×D4—41no—
412C3×D4—41no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—48no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4#12012yes—
451C2×C3×C4#12012yes—
452C2×C3×C4#13512yes—
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4H(5,𝔽2)11yescharacteristic
458C2×C3×C42−1+411yescharacteristic
459C3×C8—22no—
460C3×C8—41no—
461C3×C8—41no—
462C3×C8—41no—
463C24—21no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—41no—
482C2×Q8C2×C3×D412yes—
483C2×Q8C2×C3×D412yes—
484C2×Q8C3×#4112yes—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4C2×C3×D412yes—
491C22×C4—24no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4C2×C3×D411yescharacteristic
502C22×C4C2×C3×D411yescharacteristic
503C22×C4C2×C3×D411yescharacteristic
504C22×C4C2×C3×D411yescharacteristic
505C22×C4C2×C3×D411yescharacteristic
506C22×C4C2×C3×D411yescharacteristic
507C22×C4C24×C311yescharacteristic
508Q16—28no—
509Q16—44no—
510SD16—44no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8C3×#4112yes—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4C2×C3×D412yes—
541C22⋊C4—24no—
542C22⋊C4—24no—
543C22⋊C4—24no—
544C22⋊C4—24no—
545C22⋊C4—24no—
546C42—24no—
547C42—24no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—42no—
553C42C2×C3×D412yes—
554C42C2×C3×D412yes—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—81no—
559C22×C3—81no—
560C22×C3—81no—
561C22×C3—81no—
562C22×C3C2×#12011yescharacteristic
563C22×C3#54811yescharacteristic
564C22×C3#55011yescharacteristic
565C22×C3C2×#13511yescharacteristic
566C22×C3#57511yescharacteristic
567C22×C3#57811yescharacteristic
568C22×C3#57811yescharacteristic
569C3×C4—22no—
570C3×C4—22no—
571C3×C4—22no—
572C3×C4—42no—
573C3×C4—42no—
574C3×C4—42no—
575C3×C4—41no—
576C3×C4—42no—
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—81no—
580C3×C4—81no—
581C3×C4—81no—
582C3×C4#52511yescharacteristic
583C3×C4#53711yescharacteristic
584C3×C4#54611yescharacteristic
585C3×C4#54711yescharacteristic
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C22×C3×D411yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—22no—
597Q8—22no—
598Q8—22no—
599Q8—22no—
600Q8—44no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—48no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4C3×#12012yes—
649C2×C4C3×#12012yes—
650C2×C4C3×#13512yes—
651C2×C4C22×C3×D411yescharacteristic
652C2×C4C22×C3×D411yescharacteristic
653C2×C4C2×C3×#4111yescharacteristic
654C2×C4C2×C3×#4111yescharacteristic
655C2×C4C3×H(5,𝔽2)11yescharacteristic
656C2×C4C3×2−1+411yescharacteristic
657C8—22no—
658C8—41no—
659C8—41no—
660C8—41no—
661C2×C3—82no—
662C2×C3#240711yescharacteristic
663C2×C3#300211yescharacteristic
664C2×C3#301111yescharacteristic
665C2×C3#336411yescharacteristic
666C2×C3#337711yescharacteristic
667C2×C3#339311yescharacteristic
668C2×C3#340211yescharacteristic
669C22—42no—
670C22—42no—
671C22—42no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22C2×C3×#12011yescharacteristic
677C22C3×#54811yescharacteristic
678C22C3×#55011yescharacteristic
679C22C2×C3×#13511yescharacteristic
680C22C3×#57511yescharacteristic
681C22C3×#57811yescharacteristic
682C22C3×#57811yescharacteristic
683C4—22no—
684C4—22no—
685C4—22no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4C3×#52511yescharacteristic
697C4C3×#53711yescharacteristic
698C4C3×#54611yescharacteristic
699C4C3×#54711yescharacteristic
700C3#2419511yescharacteristic, direct product factor, Sylow
701C2—82no—
702C2C3×#240711yescharacteristic
703C2C3×#300211yescharacteristic
704C2C3×#301111yescharacteristic
705C2C3×#336411yescharacteristic
706C2C3×#337711yescharacteristic
707C2C3×#339311yescharacteristic
708C2C3×#340211yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4×Q16C2semidirect
4. C3×#2581C2semidirect
5. C3×#2043C2semidirect
7. C3×#2016C2semidirect
9. C3×#1984C2semidirect
11. C3×#1878C2semidirect
13. C3×#1863C2semidirect
15. C3×#1805C2semidirect
16. #24195C3direct (N × H)
66. C2×C4×Q16C2×C3semidirect
67. #2581C2×C3semidirect
68. #2043C2×C3semidirect
70. #2016C2×C3semidirect
72. #1984C2×C3semidirect
74. #1878C2×C3semidirect
76. #1863C2×C3semidirect
78. #1805C2×C3semidirect
700. C3#24195direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5562
C2×C3×#4642
C2×C3×C4×Q162
C3×#25812
C3×#20432
C3×#20422
C3×#20162
C3×#20152
C3×#19842
C3×#19582
C3×#18782
C3×#18772
C3×#18632
C3×#18622
C3×#18052
#241953