Finite Group Databasebeta

← C3×#11066 #10629673

Subgroups — C3×#11066 #10629673

Order 768.

1282 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#102C211yesmaximal, characteristic
2C22×C3×#102C211yesmaximal, characteristic
3C2×C3×#390C211yesmaximal, characteristic
4C2×C3×#389C211yesmaximal, characteristic, complemented
5C2×C3×#340C211yesmaximal, characteristic, complemented
6C2×C3×#340C211yesmaximal, characteristic, complemented
7C2×C3×#336C211yesmaximal, characteristic, complemented
8#11066C311yesmaximal, characteristic, direct product factor, Sylow
9C23×C3×D4C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C23×C3×C8C2211yescharacteristic
12C22×C3×C4⋊C4—21no—
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C22⋊C4—21no—
17C22×C3×C22⋊C4—21no—
18C22×C3×C42C2211yescharacteristic
19C2×C3×#102—22no—
20C2×C3×#102—22no—
21C2×C3×#102—22no—
22C2×C3×#102—22no—
23C2×C3×#102—22no—
24C2×C3×#102C414yescomplemented
25C3×#390—22no—
26C3×#390—22no—
27C3×#389—22no—
28C3×#389—22no—
29C2×C3×#95—21no—
30C3×#340—22no—
31C3×#340—22no—
32C3×#336—22no—
33C22×#102C2×C311yescharacteristic
34C22×#102C2×C311yescharacteristic
35C2×#390C2×C311yescharacteristic
36C2×#389C2×C311yescharacteristic, complemented
37C2×#340C2×C311yescharacteristic, complemented
38C2×#340C2×C311yescharacteristic, complemented
39C2×#336C2×C311yescharacteristic, complemented
40C25×C3—21no—
41C22×C3×D4—21no—
42C22×C3×D4—21no—
43C22×C3×D4—21no—
44C22×C3×D4—21no—
45C22×C3×D4—21no—
46C22×C3×D4—21no—
47C22×C3×D4—21no—
48C22×C3×D4—21no—
49C22×C3×D4—21no—
50C22×C3×D4—21no—
51C22×C3×D4—21no—
52C22×C3×D4C2×C412yes—
53C22×C3×D4D412yes—
54C22×C3×D4Q812yes—
55C23×C3×C4—21no—
56C23×C3×C4—21no—
57C23×C3×C4—21no—
58C23×C3×C4D411yescharacteristic
59C23×C3×C4D411yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C22×C3×C8—21no—
62C22×C3×C8—21no—
63C22×C3×C8—21no—
64C22×C3×C8—21no—
65C22×C3×C8—21no—
66C22×C3×C8—21no—
67C22×C3×C8—21no—
68C22×C3×C8—21no—
69C22×C3×C8—21no—
70C22×C3×C8—21no—
71C22×C3×C8—21no—
72C22×C3×C8—21no—
73C22×C3×C8C2×C412yes—
74C22×C3×C8D412yes—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4—21no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—24no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—42no—
90C2×C3×C4⋊C4—42no—
91C2×C3×C4⋊C4C2×C412yes—
92C2×C3×C4⋊C4D412yes—
93C2×C3×C4⋊C4D412yes—
94C2×C3×C4⋊C4D412yes—
95C2×C3×C4⋊C4D412yes—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—42no—
99C2×C3×C22⋊C4—42no—
100C2×C3×C22⋊C4—42no—
101C2×C3×C22⋊C4—42no—
102C2×C3×C42—21no—
103C2×C3×C42—21no—
104C2×C3×C42—21no—
105C2×C3×C42—21no—
106C2×C3×C42—21no—
107C2×C3×C42—21no—
108C3×#102—28no—
109C3×#102—28no—
110C3×#95—24no—
111C23×D4C22×C311yescharacteristic
112C23×C8C22×C311yescharacteristic
113C23×C8C22×C311yescharacteristic
114C22×C4⋊C4—21no—
115C22×C4⋊C4C22×C311yescharacteristic
116C22×C4⋊C4C22×C311yescharacteristic
117C22×C4⋊C4C22×C311yescharacteristic
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C42C22×C311yescharacteristic
121C2×#102—22no—
122C2×#102—22no—
123C2×#102—22no—
124C2×#102—22no—
125C2×#102—22no—
126C2×#102C3×C414yescomplemented
127#390—22no—
128#390—22no—
129#389—22no—
130#389—22no—
131C2×#95—21no—
132#340—22no—
133#340—22no—
134#336—22no—
135C24×C3—22no—
136C24×C3—22no—
137C24×C3—22no—
138C24×C3—41no—
139C24×C3—41no—
140C24×C3—41no—
141C24×C3—41no—
142C24×C3—41no—
143C24×C3—41no—
144C24×C3—41no—
145C24×C3—41no—
146C24×C3—41no—
147C24×C3—41no—
148C24×C3—41no—
149C24×C3—41no—
150C24×C3C2×D411yescharacteristic
151C2×C3×D4—22no—
152C2×C3×D4—22no—
153C2×C3×D4—22no—
154C2×C3×D4—22no—
155C2×C3×D4—22no—
156C2×C3×D4—22no—
157C2×C3×D4—22no—
158C2×C3×D4—22no—
159C2×C3×D4—22no—
160C2×C3×D4—22no—
161C2×C3×D4—22no—
162C2×C3×D4—22no—
163C2×C3×D4—22no—
164C2×C3×D4—22no—
165C2×C3×D4—22no—
166C2×C3×D4—41no—
167C2×C3×D4—41no—
168C2×C3×D4—41no—
169C2×C3×D4—41no—
170C2×C3×D4—41no—
171C2×C3×D4—41no—
172C2×C3×D4—41no—
173C2×C3×D4—41no—
174C2×C3×D4—41no—
175C2×C3×D4—41no—
176C2×C3×D4—41no—
177C2×C3×D4—41no—
178C2×C3×D4C4⋊C414yescomplemented
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—41no—
197C22×C3×C4—41no—
198C22×C3×C4—41no—
199C22×C3×C4—41no—
200C22×C3×C4—41no—
201C22×C3×C4—41no—
202C22×C3×C4—41no—
203C22×C3×C4—41no—
204C22×C3×C4—41no—
205C22×C3×C4—41no—
206C22×C3×C4—41no—
207C22×C3×C4—41no—
208C22×C3×C4—41no—
209C22×C3×C4—41no—
210C22×C3×C4—41no—
211C22×C3×C4—41no—
212C22×C3×C4D812yes—
213C22×C3×C4SD1612yes—
214C22×C3×C4C22×C411yescharacteristic
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×Q811yescharacteristic
222C22×C3×C4#4111yescharacteristic
223C22×C3×C4#4111yescharacteristic
224C22×C3×C4#4111yescharacteristic
225C22×C3×C4#4111yescharacteristic
226C22×C3×C4#4111yescharacteristic
227C22×C3×C4#4111yescharacteristic
228C2×C3×C8—22no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—22no—
232C2×C3×C8—22no—
233C2×C3×C8—22no—
234C2×C3×C8—41no—
235C2×C3×C8—41no—
236C2×C3×C8—41no—
237C2×C3×C8—41no—
238C2×C3×C8—41no—
239C2×C3×C8—41no—
240C2×C3×C8—41no—
241C2×C3×C8—41no—
242C3×C4⋊C4—22no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—22no—
246C3×C4⋊C4—22no—
247C3×C4⋊C4—22no—
248C3×C4⋊C4—22no—
249C3×C4⋊C4—48no—
250C3×C4⋊C4—41no—
251C3×C4⋊C4—41no—
252C3×C4⋊C4—41no—
253C3×C4⋊C4—41no—
254C3×C4⋊C4C22⋊C414yescomplemented
255C3×C22⋊C4—48no—
256C3×C22⋊C4—48no—
257C3×C42—41no—
258C3×C42—41no—
259C3×C42—41no—
260C3×C42—41no—
261C25—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4C2×C3×C412yes—
274C22×D4C3×D412yes—
275C22×D4C3×Q812yes—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4C3×D411yescharacteristic
280C23×C4C3×D411yescharacteristic
281C23×C4C23×C311yescharacteristic
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8C2×C3×C412yes—
295C22×C8C3×D412yes—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4C2×C3×C412yes—
313C2×C4⋊C4C3×D412yes—
314C2×C4⋊C4C3×D412yes—
315C2×C4⋊C4C3×D412yes—
316C2×C4⋊C4C3×D412yes—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329#102—28no—
330#102—28no—
331#95—24no—
332C23×C3—24no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—81no—
352C23×C3—81no—
353C23×C3—81no—
354C23×C3—81no—
355C23×C3—81no—
356C23×C3—81no—
357C23×C3—81no—
358C23×C3—81no—
359C23×C3—81no—
360C23×C3—81no—
361C23×C3—81no—
362C23×C3—81no—
363C23×C3—81no—
364C23×C3—81no—
365C23×C3—81no—
366C23×C3—81no—
367C23×C3C4×D411yescharacteristic
368C23×C3#12011yescharacteristic
369C23×C3#12011yescharacteristic
370C23×C3#12111yescharacteristic
371C23×C3#12111yescharacteristic
372C23×C3C22⋊Q811yescharacteristic
373C23×C3#12411yescharacteristic
374C23×C3C2×D811yescharacteristic
375C23×C3C2×SD1611yescharacteristic
376C23×C3#13511yescharacteristic
377C23×C3#13511yescharacteristic
378C23×C3AGL(1,ℤ/8)11yescharacteristic
379C23×C3AGL(1,ℤ/8)11yescharacteristic
380C23×C3AGL(1,ℤ/8)11yescharacteristic
381C23×C3#13711yescharacteristic
382C3×D4—24no—
383C3×D4—24no—
384C3×D4—42no—
385C3×D4—42no—
386C3×D4—42no—
387C3×D4—42no—
388C3×D4—42no—
389C3×D4—42no—
390C2×C3×C4—24no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—42no—
406C2×C3×C4—41no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—81no—
418C2×C3×C4—81no—
419C2×C3×C4—81no—
420C2×C3×C4—81no—
421C2×C3×C4—81no—
422C2×C3×C4—81no—
423C2×C3×C4—81no—
424C2×C3×C4—81no—
425C2×C3×C4C2×C22⋊C411yescharacteristic
426C2×C3×C4C2×C4⋊C411yescharacteristic
427C2×C3×C4#11711yescharacteristic
428C2×C3×C4C4×D411yescharacteristic
429C2×C3×C4C4×D411yescharacteristic
430C2×C3×C4C4×D411yescharacteristic
431C2×C3×C4#12011yescharacteristic
432C2×C3×C4#12111yescharacteristic
433C2×C3×C4#12111yescharacteristic
434C2×C3×C4#12111yescharacteristic
435C2×C3×C4#12111yescharacteristic
436C2×C3×C4#12111yescharacteristic
437C2×C3×C4#12111yescharacteristic
438C2×C3×C4C22⋊Q811yescharacteristic
439C2×C3×C4C22⋊Q811yescharacteristic
440C2×C3×C4C22⋊Q811yescharacteristic
441C2×C3×C4C22⋊Q811yescharacteristic
442C2×C3×C4C22⋊Q811yescharacteristic
443C2×C3×C4#12311yescharacteristic
444C2×C3×C4#12311yescharacteristic
445C2×C3×C4#12311yescharacteristic
446C2×C3×C4#12311yescharacteristic
447C2×C3×C4#12311yescharacteristic
448C2×C3×C4#12411yescharacteristic
449C2×C3×C4#12411yescharacteristic
450C2×C3×C4#12611yescharacteristic
451C2×C3×C4#12611yescharacteristic
452C2×C3×C4#12711yescharacteristic
453C3×C8—42no—
454C3×C8—42no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24—41no—
462C24—41no—
463C24—41no—
464C24—41no—
465C24—41no—
466C24—41no—
467C24—41no—
468C24—41no—
469C24—41no—
470C24C2×C3×D411yescharacteristic
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4C3×C4⋊C414yescomplemented
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4C3×D812yes—
533C22×C4C3×SD1612yes—
534C22×C4C22×C3×C411yescharacteristic
535C22×C4C2×C3×D411yescharacteristic
536C22×C4C2×C3×D411yescharacteristic
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D411yescharacteristic
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C2×C3×Q811yescharacteristic
542C22×C4C3×#4111yescharacteristic
543C22×C4C3×#4111yescharacteristic
544C22×C4C3×#4111yescharacteristic
545C22×C4C3×#4111yescharacteristic
546C22×C4C3×#4111yescharacteristic
547C22×C4C3×#4111yescharacteristic
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—48no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4C3×C22⋊C414yescomplemented
575C22⋊C4—48no—
576C22⋊C4—48no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—82no—
585C22×C3—82no—
586C22×C3—82no—
587C22×C3—82no—
588C22×C3—82no—
589C22×C3—82no—
590C22×C3—82no—
591C22×C3—82no—
592C22×C3—82no—
593C22×C3—82no—
594C22×C3—82no—
595C22×C3—82no—
596C22×C3#38511yescharacteristic
597C22×C3#38611yescharacteristic
598C22×C3#38811yescharacteristic
599C22×C3#39211yescharacteristic
600C22×C3#39311yescharacteristic
601C22×C3#39411yescharacteristic
602C22×C3#39611yescharacteristic
603C22×C3C4×D811yescharacteristic
604C22×C3C4×SD1611yescharacteristic
605C22×C3#44011yescharacteristic
606C22×C3#44211yescharacteristic
607C22×C3#44711yescharacteristic
608C22×C3#44711yescharacteristic
609C22×C3#44811yescharacteristic
610C22×C3#44911yescharacteristic
611C22×C3#44911yescharacteristic
612C22×C3#44911yescharacteristic
613C22×C3#45011yescharacteristic
614C22×C3#45211yescharacteristic
615C22×C3#45911yescharacteristic
616C22×C3#46011yescharacteristic
617C22×C3#46311yescharacteristic
618C22×C3#46411yescharacteristic
619C22×C3#46511yescharacteristic
620C22×C3#46611yescharacteristic
621C22×C3#46811yescharacteristic
622C22×C3#46911yescharacteristic
623C22×C3#47411yescharacteristic
624C22×C3#47611yescharacteristic
625C22×C3#47811yescharacteristic
626C22×C3#47811yescharacteristic
627C22×C3#48611yescharacteristic
628C22×C3#48811yescharacteristic
629C22×C3#48911yescharacteristic
630C22×C3#49011yescharacteristic
631C3×C4—44no—
632C3×C4—42no—
633C3×C4—42no—
634C3×C4—82no—
635C3×C4—82no—
636C3×C4#38011yescharacteristic
637C3×C4#38511yescharacteristic
638C3×C4#38811yescharacteristic
639C3×C4#39011yescharacteristic
640C3×C4#39411yescharacteristic
641C3×C4#39611yescharacteristic
642C3×C4#39711yescharacteristic
643C3×C4#39911yescharacteristic
644C23—24no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—81no—
664C23—81no—
665C23—81no—
666C23—81no—
667C23—81no—
668C23—81no—
669C23—81no—
670C23—81no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23—81no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—81no—
679C23C3×C4×D411yescharacteristic
680C23C3×#12011yescharacteristic
681C23C3×#12011yescharacteristic
682C23C3×#12111yescharacteristic
683C23C3×#12111yescharacteristic
684C23C3×C22⋊Q811yescharacteristic
685C23C3×#12411yescharacteristic
686C23C2×C3×D811yescharacteristic
687C23C2×C3×SD1611yescharacteristic
688C23C3×#13511yescharacteristic
689C23C3×#13511yescharacteristic
690C23C3×AGL(1,ℤ/8)11yescharacteristic
691C23C3×AGL(1,ℤ/8)11yescharacteristic
692C23C3×AGL(1,ℤ/8)11yescharacteristic
693C23C3×#13711yescharacteristic
694D4—24no—
695D4—24no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4C2×C3×C22⋊C411yescharacteristic
738C2×C4C2×C3×C4⋊C411yescharacteristic
739C2×C4C3×#11711yescharacteristic
740C2×C4C3×C4×D411yescharacteristic
741C2×C4C3×C4×D411yescharacteristic
742C2×C4C3×C4×D411yescharacteristic
743C2×C4C3×#12011yescharacteristic
744C2×C4C3×#12111yescharacteristic
745C2×C4C3×#12111yescharacteristic
746C2×C4C3×#12111yescharacteristic
747C2×C4C3×#12111yescharacteristic
748C2×C4C3×#12111yescharacteristic
749C2×C4C3×#12111yescharacteristic
750C2×C4C3×C22⋊Q811yescharacteristic
751C2×C4C3×C22⋊Q811yescharacteristic
752C2×C4C3×C22⋊Q811yescharacteristic
753C2×C4C3×C22⋊Q811yescharacteristic
754C2×C4C3×C22⋊Q811yescharacteristic
755C2×C4C3×#12311yescharacteristic
756C2×C4C3×#12311yescharacteristic
757C2×C4C3×#12311yescharacteristic
758C2×C4C3×#12311yescharacteristic
759C2×C4C3×#12311yescharacteristic
760C2×C4C3×#12411yescharacteristic
761C2×C4C3×#12411yescharacteristic
762C2×C4C3×#12611yescharacteristic
763C2×C4C3×#12611yescharacteristic
764C2×C4C3×#12711yescharacteristic
765C8—42no—
766C8—42no—
767C2×C3—84no—
768C2×C3#143911yescharacteristic
769C2×C3#186211yescharacteristic
770C2×C3#186411yescharacteristic
771C2×C3#187911yescharacteristic
772C2×C3#188011yescharacteristic
773C2×C3#193411yescharacteristic
774C2×C3#193611yescharacteristic
775C2×C3#199911yescharacteristic
776C2×C3#200011yescharacteristic
777C2×C3#202311yescharacteristic
778C2×C3#202511yescharacteristic
779C2×C3#204111yescharacteristic
780C2×C3#204211yescharacteristic
781C2×C3#206511yescharacteristic
782C2×C3#206711yescharacteristic
783C22—44no—
784C22—44no—
785C22—44no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22C3×#38511yescharacteristic
799C22C3×#38611yescharacteristic
800C22C3×#38811yescharacteristic
801C22C3×#39211yescharacteristic
802C22C3×#39311yescharacteristic
803C22C3×#39411yescharacteristic
804C22C3×#39611yescharacteristic
805C22C3×C4×D811yescharacteristic
806C22C3×C4×SD1611yescharacteristic
807C22C3×#44011yescharacteristic
808C22C3×#44211yescharacteristic
809C22C3×#44711yescharacteristic
810C22C3×#44711yescharacteristic
811C22C3×#44811yescharacteristic
812C22C3×#44911yescharacteristic
813C22C3×#44911yescharacteristic
814C22C3×#44911yescharacteristic
815C22C3×#45011yescharacteristic
816C22C3×#45211yescharacteristic
817C22C3×#45911yescharacteristic
818C22C3×#46011yescharacteristic
819C22C3×#46311yescharacteristic
820C22C3×#46411yescharacteristic
821C22C3×#46511yescharacteristic
822C22C3×#46611yescharacteristic
823C22C3×#46811yescharacteristic
824C22C3×#46911yescharacteristic
825C22C3×#47411yescharacteristic
826C22C3×#47611yescharacteristic
827C22C3×#47811yescharacteristic
828C22C3×#47811yescharacteristic
829C22C3×#48611yescharacteristic
830C22C3×#48811yescharacteristic
831C22C3×#48911yescharacteristic
832C22C3×#49011yescharacteristic
833C4—42no—
834C4—42no—
835C4—44no—
836C4—82no—
837C4—82no—
838C4C3×#38011yescharacteristic
839C4C3×#38511yescharacteristic
840C4C3×#38811yescharacteristic
841C4C3×#39011yescharacteristic
842C4C3×#39411yescharacteristic
843C4C3×#39611yescharacteristic
844C4C3×#39711yescharacteristic
845C4C3×#39911yescharacteristic
846C3#1106611yescharacteristic, direct product factor, Sylow
847C2—84no—
848C2C3×#143911yescharacteristic
849C2C3×#186211yescharacteristic
850C2C3×#186411yescharacteristic
851C2C3×#187911yescharacteristic
852C2C3×#188011yescharacteristic
853C2C3×#193411yescharacteristic
854C2C3×#193611yescharacteristic
855C2C3×#199911yescharacteristic
856C2C3×#200011yescharacteristic
857C2C3×#202311yescharacteristic
858C2C3×#202511yescharacteristic
859C2C3×#204111yescharacteristic
860C2C3×#204211yescharacteristic
861C2C3×#206511yescharacteristic
862C2C3×#206711yescharacteristic
subgroupG/H
center, socleC24×C3C2×D4
commutatorC22×C4C22×C3×C4
Frattini, cosocleC23×C4C23×C3
prime radicalC23×C3×D4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C3×#389C2semidirect
5. C2×C3×#340C2semidirect
6. C2×C3×#340C2semidirect
7. C2×C3×#336C2semidirect
8. #11066C3direct (N × H)
24. C2×C3×#102C4semidirect
36. C2×#389C2×C3semidirect
37. C2×#340C2×C3semidirect
38. C2×#340C2×C3semidirect
39. C2×#336C2×C3semidirect
126. C2×#102C3×C4semidirect
178. C2×C3×D4C4⋊C4semidirect
254. C3×C4⋊C4C22⋊C4semidirect
498. C2×D4C3×C4⋊C4semidirect
574. C4⋊C4C3×C22⋊C4semidirect
846. C3#11066direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1022
C2×C3×#3902
C2×C3×#3892
C2×C3×#3402
C2×C3×#3362
#110663