Finite Group Databasebeta

← C3×#24335 #10642942

Subgroups — C3×#24335 #10642942

Order 768.

1118 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#554C211yesmaximal, characteristic, complemented
2C2×C3×#478C211yesmaximal, characteristic, complemented
3C2×C3×C4×D8C211yesmaximal, characteristic
4C3×#2580C211yesmaximal, characteristic, complemented
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2057C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic, complemented
8C3×#2023C211yesmaximal, characteristic, complemented
9C3×#1991C211yesmaximal, characteristic, complemented
10C3×#1984C211yesmaximal, characteristic, complemented
11C3×#1879C211yesmaximal, characteristic
12C3×#1879C211yesmaximal, characteristic
13C3×#1864C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1804C211yesmaximal, characteristic, complemented
16#24335C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C3×#554—24no—
19C3×#554—24no—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×#125C2211yescharacteristic
22C2×C3×#125C2211yescharacteristic
23C2×C3×C22⋊Q8—21no—
24C2×C3×C22⋊Q8—21no—
25C2×C3×C22⋊Q8—21no—
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C22×C3×C4⋊C4—21no—
32C3×#478—24no—
33C3×C4×D8—24no—
34C2×C3×#107C2211yescharacteristic
35C2×C3×#107C2211yescharacteristic
36C2×C3×#106C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×C4×C8C2211yescharacteristic
45C3×#399—21no—
46C3×#393—21no—
47C3×#390C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#389C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#385—21no—
52C3×#385—21no—
53C3×#382C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#554C2×C311yescharacteristic, complemented
65C2×#478C2×C311yescharacteristic, complemented
66C2×C4×D8C2×C311yescharacteristic
67#2580C2×C311yescharacteristic, complemented
68#2059C2×C311yescharacteristic, complemented
69#2057C2×C311yescharacteristic, complemented
70#2025C2×C311yescharacteristic, complemented
71#2023C2×C311yescharacteristic, complemented
72#1991C2×C311yescharacteristic, complemented
73#1984C2×C311yescharacteristic, complemented
74#1879C2×C311yescharacteristic
75#1879C2×C311yescharacteristic
76#1864C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic, complemented
78#1804C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8D411yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C23×C3×C4—21no—
87C2×C3×D8—22no—
88C2×C3×D8—22no—
89C2×C3×D8Q814yescomplemented
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×C4⋊Q8—22no—
95C3×C4⋊Q8—22no—
96C3×#125—22no—
97C3×#125—22no—
98C3×#125—22no—
99C3×#125D414yes—
100C3×C22⋊Q8—28no—
101C3×C22⋊Q8—28no—
102C3×C22⋊Q8—28no—
103C3×C4×Q8—22no—
104C3×C4×Q8—22no—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C3×C4×D4—22no—
108C3×C4×D4—22no—
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C3×C4×D4—22no—
112C3×C4×D4D414yes—
113C2×C3×C4⋊C4—28no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4D411yescharacteristic
122C2×C3×C4⋊C4D411yescharacteristic
123C2×C3×C4⋊C4D411yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
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×C22⋊C4—21no—
138C2×C3×C42C2311yescharacteristic
139C2×C3×C42C2311yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C3×#107—22no—
142C3×#107—22no—
143C3×#106—22no—
144C3×C4⋊C8—22no—
145C3×#102—22no—
146C3×#102—22no—
147C3×#102—22no—
148C3×#102—22no—
149C3×#102—22no—
150C3×#102—22no—
151C3×C4×C8—22no—
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C22×D8C22×C311yescharacteristic
157#554—24no—
158#554—24no—
159C2×C4⋊Q8C22×C311yescharacteristic
160C2×#125C22×C311yescharacteristic
161C2×#125C22×C311yescharacteristic
162C2×C22⋊Q8—21no—
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C4×Q8C22×C311yescharacteristic
166C2×C4×D4C22×C311yescharacteristic
167C2×C4×D4C22×C311yescharacteristic
168C2×C4×D4C22×C311yescharacteristic
169C2×C4×D4C22×C311yescharacteristic
170C22×C4⋊C4—21no—
171#478—24no—
172C4×D8—24no—
173C2×#107C22×C311yescharacteristic
174C2×#107C22×C311yescharacteristic
175C2×#106C22×C311yescharacteristic
176C2×C4⋊C8C22×C311yescharacteristic
177C2×#102C22×C311yescharacteristic
178C2×#102C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×C4×C8C22×C311yescharacteristic
184#399—21no—
185#393—21no—
186#390C22×C311yescharacteristic
187#390C22×C311yescharacteristic
188#389C22×C311yescharacteristic
189#389C22×C311yescharacteristic
190#385—21no—
191#385—21no—
192#382C22×C311yescharacteristic
193#340C22×C311yescharacteristic
194#340C22×C311yescharacteristic
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199#336C22×C311yescharacteristic
200#336C22×C311yescharacteristic
201#336C22×C311yescharacteristic
202#336C22×C311yescharacteristic
203C24×C3—21no—
204C24×C3—21no—
205C2×C3×Q8—24no—
206C2×C3×Q8—22no—
207C2×C3×Q8—22no—
208C2×C3×Q8—41no—
209C2×C3×Q8—81no—
210C2×C3×Q8—81no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4C2×D412yes—
220C2×C3×D4C2×Q812yes—
221C2×C3×D4C2×Q812yes—
222C2×C3×D4#4112yes—
223C22×C3×C4—24no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—24no—
228C22×C3×C4—24no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—42no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4—81no—
236C22×C3×C4—81no—
237C22×C3×C4—81no—
238C22×C3×C4—81no—
239C22×C3×C4—81no—
240C22×C3×C4—81no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2411yescharacteristic
248C3×D8—28no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8C2×Q812yes—
261C3×C4⋊C4—24no—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—24no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—81no—
279C3×C4⋊C4—81no—
280C3×C4⋊C4C2×D412yes—
281C3×C4⋊C4C2×D412yes—
282C3×C4⋊C4C2×D412yes—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—42no—
289C3×C22⋊C4—81no—
290C3×C22⋊C4—81no—
291C3×C42—21no—
292C3×C42—21no—
293C3×C42—21no—
294C3×C42—21no—
295C3×C42C2×D412yes—
296C3×C42C2×D412yes—
297C22×Q8—21no—
298C22×Q8C3×D411yescharacteristic
299C22×D4C23×C311yescharacteristic
300C22×D4C23×C311yescharacteristic
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C2×D8—22no—
306C2×D8—22no—
307C2×D8C3×Q814yescomplemented
308C22×C8C23×C311yescharacteristic
309C22×C8C23×C311yescharacteristic
310C22×C8C23×C311yescharacteristic
311C22×C8C23×C311yescharacteristic
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314#125—22no—
315#125—22no—
316#125—22no—
317#125C3×D414yes—
318C22⋊Q8—28no—
319C22⋊Q8—28no—
320C22⋊Q8—28no—
321C4×Q8—22no—
322C4×Q8—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4C3×D414yes—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4C3×D411yescharacteristic
340C2×C4⋊C4C3×D411yescharacteristic
341C2×C4⋊C4C3×D411yescharacteristic
342C2×C4⋊C4C23×C311yescharacteristic
343C2×C4⋊C4C23×C311yescharacteristic
344C2×C4⋊C4C23×C311yescharacteristic
345C2×C4⋊C4C23×C311yescharacteristic
346C2×C4⋊C4C23×C311yescharacteristic
347C2×C4⋊C4C23×C311yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C42C23×C311yescharacteristic
357C2×C42C23×C311yescharacteristic
358C2×C42C23×C311yescharacteristic
359#107—22no—
360#107—22no—
361#106—22no—
362C4⋊C8—22no—
363#102—22no—
364#102—22no—
365#102—22no—
366#102—22no—
367#102—22no—
368#102—22no—
369C4×C8—22no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3C22×D411yescharacteristic
389C3×Q8—44no—
390C3×Q8—84no—
391C3×D4—22no—
392C3×D4—22no—
393C3×D4—22no—
394C3×D4—22no—
395C3×D4—22no—
396C3×D4—41no—
397C3×D4—41no—
398C3×D4C22⋊Q814yes—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—48no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—84no—
434C2×C3×C4—84no—
435C2×C3×C4—84no—
436C2×C3×C4#12012yes—
437C2×C3×C4#12012yes—
438C2×C3×C4#13512yes—
439C2×C3×C4C22×D411yescharacteristic
440C2×C3×C4C22×D411yescharacteristic
441C2×C3×C4C22×Q811yescharacteristic
442C2×C3×C4C2×#4111yescharacteristic
443C2×C3×C42−1+411yescharacteristic
444C2×C3×C42−1+411yescharacteristic
445C3×C8—22no—
446C3×C8—41no—
447C3×C8—41no—
448C3×C8—41no—
449C24—21no—
450C24—21no—
451C2×Q8—24no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—41no—
455C2×Q8—81no—
456C2×Q8—81no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4C2×C3×D412yes—
466C2×D4C2×C3×Q812yes—
467C2×D4C2×C3×Q812yes—
468C2×D4C3×#4112yes—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4C2×C3×D411yescharacteristic
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C2×C3×D411yescharacteristic
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C24×C311yescharacteristic
494D8—28no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8C2×C3×Q812yes—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—24no—
510C4⋊C4—22no—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—81no—
525C4⋊C4—81no—
526C4⋊C4C2×C3×D412yes—
527C4⋊C4C2×C3×D412yes—
528C4⋊C4C2×C3×D412yes—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—24no—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—81no—
536C22⋊C4—81no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42C2×C3×D412yes—
542C42C2×C3×D412yes—
543C22×C3—24no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—81no—
554C22×C3—81no—
555C22×C3—81no—
556C22×C3—81no—
557C22×C3C2×#12011yescharacteristic
558C22×C3#54811yescharacteristic
559C22×C3D4×Q811yescharacteristic
560C22×C3C2×#13511yescharacteristic
561C22×C3#57511yescharacteristic
562C22×C3#57611yescharacteristic
563C22×C3#57611yescharacteristic
564C3×C4—22no—
565C3×C4—22no—
566C3×C4—22no—
567C3×C4—41no—
568C3×C4—42no—
569C3×C4—41no—
570C3×C4—41no—
571C3×C4—42no—
572C3×C4—42no—
573C3×C4—81no—
574C3×C4—81no—
575C3×C4—81no—
576C3×C4C2×C22⋊Q811yescharacteristic
577C3×C4#53611yescharacteristic
578C3×C4#54811yescharacteristic
579C3×C4D4×Q811yescharacteristic
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23C22×C3×D411yescharacteristic
595Q8—44no—
596Q8—84no—
597D4—22no—
598D4—22no—
599D4—22no—
600D4—22no—
601D4—22no—
602D4—41no—
603D4—41no—
604D4C3×C22⋊Q814yes—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
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—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—48no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
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—84no—
640C2×C4—84no—
641C2×C4—84no—
642C2×C4C3×#12012yes—
643C2×C4C3×#12012yes—
644C2×C4C3×#13512yes—
645C2×C4C22×C3×D411yescharacteristic
646C2×C4C22×C3×D411yescharacteristic
647C2×C4C22×C3×Q811yescharacteristic
648C2×C4C2×C3×#4111yescharacteristic
649C2×C4C3×2−1+411yescharacteristic
650C2×C4C3×2−1+411yescharacteristic
651C8—22no—
652C8—41no—
653C8—41no—
654C8—41no—
655C2×C3—44no—
656C2×C3—82no—
657C2×C3#240911yescharacteristic
658C2×C3#300211yescharacteristic
659C2×C3#300811yescharacteristic
660C2×C3#336111yescharacteristic
661C2×C3#337011yescharacteristic
662C2×C3#338011yescharacteristic
663C2×C3#338911yescharacteristic
664C22—24no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22C2×C3×#12011yescharacteristic
679C22C3×#54811yescharacteristic
680C22C3×D4×Q811yescharacteristic
681C22C2×C3×#13511yescharacteristic
682C22C3×#57511yescharacteristic
683C22C3×#57611yescharacteristic
684C22C3×#57611yescharacteristic
685C4—22no—
686C4—22no—
687C4—22no—
688C4—41no—
689C4—42no—
690C4—41no—
691C4—41no—
692C4—42no—
693C4—42no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4C2×C3×C22⋊Q811yescharacteristic
698C4C3×#53611yescharacteristic
699C4C3×#54811yescharacteristic
700C4C3×D4×Q811yescharacteristic
701C3#2433511yescharacteristic, direct product factor, Sylow
702C2—44no—
703C2—82no—
704C2C3×#240911yescharacteristic
705C2C3×#300211yescharacteristic
706C2C3×#300811yescharacteristic
707C2C3×#336111yescharacteristic
708C2C3×#337011yescharacteristic
709C2C3×#338011yescharacteristic
710C2C3×#338911yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D8C22
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
1. C2×C3×#554C2semidirect
2. C2×C3×#478C2semidirect
4. C3×#2580C2semidirect
5. C3×#2059C2semidirect
6. C3×#2057C2semidirect
7. C3×#2025C2semidirect
8. C3×#2023C2semidirect
9. C3×#1991C2semidirect
10. C3×#1984C2semidirect
13. C3×#1864C2semidirect
14. C3×#1862C2semidirect
15. C3×#1804C2semidirect
16. #24335C3direct (N × H)
64. C2×#554C2×C3semidirect
65. C2×#478C2×C3semidirect
67. #2580C2×C3semidirect
68. #2059C2×C3semidirect
69. #2057C2×C3semidirect
70. #2025C2×C3semidirect
71. #2023C2×C3semidirect
72. #1991C2×C3semidirect
73. #1984C2×C3semidirect
76. #1864C2×C3semidirect
77. #1862C2×C3semidirect
78. #1804C2×C3semidirect
89. C2×C3×D8Q8semidirect
307. C2×D8C3×Q8semidirect
701. C3#24335direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5542
C2×C3×#4782
C2×C3×C4×D82
C3×#25802
C3×#20592
C3×#20572
C3×#20252
C3×#20232
C3×#19912
C3×#19842
C3×#18792
C3×#18642
C3×#18622
C3×#18042
#243353