Finite Group Databasebeta

← C3×#24136 #10642743

Subgroups — C3×#24136 #10642743

Order 768.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#553C211yesmaximal, characteristic, complemented
2C2×C3×#478C211yesmaximal, characteristic, complemented
3C2×C3×#442C211yesmaximal, characteristic, complemented
4C3×#2537C211yesmaximal, characteristic, complemented
5C3×#2034C211yesmaximal, characteristic, complemented
6C3×#2033C211yesmaximal, characteristic, complemented
7C3×#1999C211yesmaximal, characteristic, complemented
8C3×#1999C211yesmaximal, characteristic, complemented
9C3×#1992C211yesmaximal, characteristic, complemented
10C3×#1955C211yesmaximal, characteristic, complemented
11C3×#1875C211yesmaximal, characteristic, complemented
12C3×#1874C211yesmaximal, characteristic, complemented
13C3×#1854C211yesmaximal, characteristic, complemented
14C3×#1853C211yesmaximal, characteristic, complemented
15C3×#1802C211yesmaximal, characteristic, complemented
16#24136C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C3×#553—24no—
19C3×#553—24no—
20C2×C3×#126—21no—
21C2×C3×#125C2211yescharacteristic
22C2×C3×#123—21no—
23C2×C3×#121—21no—
24C2×C3×#121—21no—
25C2×C3×#121C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×D4—21no—
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×#117C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C3×#478—24no—
36C3×#442—24no—
37C2×C3×#107C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×C4⋊C8C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×C3×C22⋊C8C2211yescharacteristic
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×#97C2211yescharacteristic
52C3×#394—21no—
53C3×#394—21no—
54C3×#384C2211yescharacteristic
55C3×#380—21no—
56C3×#380C2211yescharacteristic
57C3×#380C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C3×#340C2211yescharacteristic
64C2×#553C2×C311yescharacteristic, complemented
65C2×#478C2×C311yescharacteristic, complemented
66C2×#442C2×C311yescharacteristic, complemented
67#2537C2×C311yescharacteristic, complemented
68#2034C2×C311yescharacteristic, complemented
69#2033C2×C311yescharacteristic, complemented
70#1999C2×C311yescharacteristic, complemented
71#1999C2×C311yescharacteristic, complemented
72#1992C2×C311yescharacteristic, complemented
73#1955C2×C311yescharacteristic, complemented
74#1875C2×C311yescharacteristic, complemented
75#1874C2×C311yescharacteristic, complemented
76#1854C2×C311yescharacteristic, complemented
77#1853C2×C311yescharacteristic, complemented
78#1802C2×C311yescharacteristic, complemented
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4D411yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C23×C3×C4—21no—
87C23×C3×C4—21no—
88C23×C3×C4—21no—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C2×C3×D8—22no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#126—28no—
99C3×#125—22no—
100C3×#125D414yescomplemented
101C3×#123—28no—
102C3×#121—28no—
103C3×#121—22no—
104C3×#121—22no—
105C3×#121—22no—
106C3×#121—22no—
107C3×#121—22no—
108C3×#121—22no—
109C3×#121—41no—
110C3×#121—41no—
111C3×#121—44no—
112C3×C4×D4—28no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C3×C4×D4D414yescomplemented
119C3×#117—22no—
120C3×#117—22no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4D411yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4D411yescharacteristic
145C2×C3×C22⋊C4D411yescharacteristic
146C2×C3×C42—21no—
147C2×C3×C42C2311yescharacteristic
148C3×#107—22no—
149C3×#106—22no—
150C3×#106—22no—
151C3×C4⋊C8—22no—
152C3×#102—22no—
153C3×#102—22no—
154C3×#102—22no—
155C3×#102—22no—
156C3×#102—41no—
157C3×#102—41no—
158C3×C22⋊C8—22no—
159C3×C22⋊C8—22no—
160C3×C22⋊C8—41no—
161C3×C22⋊C8—41no—
162C3×#97—22no—
163C3×#95—21no—
164C3×#95—21no—
165C22×D8C22×C311yescharacteristic
166#553—24no—
167#553—24no—
168C2×#126—21no—
169C2×#125C22×C311yescharacteristic
170C2×#123—21no—
171C2×#121—21no—
172C2×#121—21no—
173C2×#121C22×C311yescharacteristic
174C2×#121C22×C311yescharacteristic
175C2×#121C22×C311yescharacteristic
176C2×#121C22×C311yescharacteristic
177C2×C4×D4—21no—
178C2×C4×D4C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×C4×D4C22×C311yescharacteristic
181C2×#117C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183#478—24no—
184#442—24no—
185C2×#107C22×C311yescharacteristic
186C2×#106C22×C311yescharacteristic
187C2×#106C22×C311yescharacteristic
188C2×C4⋊C8C22×C311yescharacteristic
189C2×#102C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196C2×C22⋊C8C22×C311yescharacteristic
197C2×C22⋊C8C22×C311yescharacteristic
198C2×C22⋊C8C22×C311yescharacteristic
199C2×#97C22×C311yescharacteristic
200#394—21no—
201#394—21no—
202#384C22×C311yescharacteristic
203#380—21no—
204#380C22×C311yescharacteristic
205#380C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#340C22×C311yescharacteristic
210#340C22×C311yescharacteristic
211#340C22×C311yescharacteristic
212C24×C3—21no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C24×C3C2×D411yescharacteristic
216C2×C3×D4—24no—
217C2×C3×D4—22no—
218C2×C3×D4—24no—
219C2×C3×D4—22no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—41no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—81no—
238C2×C3×D4—81no—
239C2×C3×D4—81no—
240C2×C3×D4—81no—
241C2×C3×D4C2×D412yes—
242C2×C3×D4#4112yes—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—24no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—24no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—42no—
264C22×C3×C4—42no—
265C22×C3×C4—42no—
266C22×C3×C4—81no—
267C22×C3×C4—81no—
268C22×C3×C4—81no—
269C22×C3×C4—81no—
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2411yescharacteristic
275C3×D8—28no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8#4112yes—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—24no—
291C3×C4⋊C4—22no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—42no—
302C3×C4⋊C4—81no—
303C3×C4⋊C4C2×D412yes—
304C3×C4⋊C4C2×D412yes—
305C3×C4⋊C4C2×D412yes—
306C3×C22⋊C4—24no—
307C3×C22⋊C4—24no—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—22no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—42no—
316C3×C22⋊C4—42no—
317C3×C42—24no—
318C3×C42C2×D412yes—
319C3×C42C2×D412yes—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4C3×D411yescharacteristic
325C22×D4C23×C311yescharacteristic
326C22×D4C23×C311yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4C23×C311yescharacteristic
331C23×C4C23×C311yescharacteristic
332C2×D8—22no—
333C2×D8—22no—
334C2×D8—22no—
335C22×C8C23×C311yescharacteristic
336C22×C8C23×C311yescharacteristic
337C22×C8C23×C311yescharacteristic
338C22×C8C23×C311yescharacteristic
339#126—28no—
340#125—22no—
341#125C3×D414yescomplemented
342#123—28no—
343#121—28no—
344#121—22no—
345#121—22no—
346#121—22no—
347#121—22no—
348#121—22no—
349#121—22no—
350#121—41no—
351#121—41no—
352#121—44no—
353C4×D4—28no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4C3×D414yescomplemented
360#117—22no—
361#117—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4C3×D411yescharacteristic
370C2×C4⋊C4C23×C311yescharacteristic
371C2×C4⋊C4C23×C311yescharacteristic
372C2×C4⋊C4C23×C311yescharacteristic
373C2×C4⋊C4C23×C311yescharacteristic
374C2×C4⋊C4C23×C311yescharacteristic
375C2×C4⋊C4C23×C311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4C3×D411yescharacteristic
386C2×C22⋊C4C3×D411yescharacteristic
387C2×C42—21no—
388C2×C42C23×C311yescharacteristic
389#107—22no—
390#106—22no—
391#106—22no—
392C4⋊C8—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—41no—
398#102—41no—
399C22⋊C8—22no—
400C22⋊C8—22no—
401C22⋊C8—41no—
402C22⋊C8—41no—
403#97—22no—
404#95—21no—
405#95—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3AGL(1,ℤ/8)12yes—
434C23×C3C22×D411yescharacteristic
435C3×D4—22no—
436C3×D4—22no—
437C3×D4—22no—
438C3×D4—22no—
439C3×D4—44no—
440C3×D4—48no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—84no—
446C3×D4—84no—
447C3×D4—84no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—84no—
485C2×C3×C4—84no—
486C2×C3×C4—84no—
487C2×C3×C4#12012yes—
488C2×C3×C4#12012yes—
489C2×C3×C4C22×D411yescharacteristic
490C2×C3×C4C22×D411yescharacteristic
491C2×C3×C4C2×#4111yescharacteristic
492C2×C3×C4C2×#4111yescharacteristic
493C2×C3×C4H(5,𝔽2)11yescharacteristic
494C2×C3×C42−1+411yescharacteristic
495C3×C8—22no—
496C3×C8—41no—
497C3×C8—41no—
498C3×C8—41no—
499C24—21no—
500C24—21no—
501C24C2×C3×D411yescharacteristic
502C24C2×C3×D411yescharacteristic
503C2×D4—24no—
504C2×D4—22no—
505C2×D4—24no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—41no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4C2×C3×D412yes—
529C2×D4C3×#4112yes—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4C2×C3×D411yescharacteristic
558C22×C4C2×C3×D411yescharacteristic
559C22×C4C2×C3×D411yescharacteristic
560C22×C4C2×C3×D411yescharacteristic
561C22×C4C24×C311yescharacteristic
562D8—28no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8C3×#4112yes—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—81no—
590C4⋊C4C2×C3×D412yes—
591C4⋊C4C2×C3×D412yes—
592C4⋊C4C2×C3×D412yes—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C42—24no—
605C42C2×C3×D412yes—
606C42C2×C3×D412yes—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—42no—
625C22×C3—41no—
626C22×C3—42no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3C2×#12011yescharacteristic
636C22×C3#54611yescharacteristic
637C22×C3#54711yescharacteristic
638C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
639C22×C3#57511yescharacteristic
640C22×C3#57611yescharacteristic
641C22×C3#57711yescharacteristic
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4—81no—
652C3×C4#52511yescharacteristic
653C3×C4#53711yescharacteristic
654C3×C4#54811yescharacteristic
655C3×C4#55011yescharacteristic
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23C3×AGL(1,ℤ/8)12yes—
684C23C22×C3×D411yescharacteristic
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—44no—
690D4—48no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—84no—
696D4—84no—
697D4—84no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4C3×#12012yes—
738C2×C4C3×#12012yes—
739C2×C4C22×C3×D411yescharacteristic
740C2×C4C22×C3×D411yescharacteristic
741C2×C4C2×C3×#4111yescharacteristic
742C2×C4C2×C3×#4111yescharacteristic
743C2×C4C3×H(5,𝔽2)11yescharacteristic
744C2×C4C3×2−1+411yescharacteristic
745C8—22no—
746C8—41no—
747C8—41no—
748C8—41no—
749C2×C3—42no—
750C2×C3—81no—
751C2×C3—82no—
752C2×C3—82no—
753C2×C3#240711yescharacteristic
754C2×C3#300611yescharacteristic
755C2×C3#301211yescharacteristic
756C2×C3#330711yescharacteristic
757C2×C3#331811yescharacteristic
758C2×C3#334511yescharacteristic
759C2×C3#334711yescharacteristic
760C22—22no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—42no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—41no—
779C22—41no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22C2×C3×#12011yescharacteristic
789C22C3×#54611yescharacteristic
790C22C3×#54711yescharacteristic
791C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
792C22C3×#57511yescharacteristic
793C22C3×#57611yescharacteristic
794C22C3×#57711yescharacteristic
795C4—22no—
796C4—22no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4—81no—
805C4C3×#52511yescharacteristic
806C4C3×#53711yescharacteristic
807C4C3×#54811yescharacteristic
808C4C3×#55011yescharacteristic
809C3#2413611yescharacteristic, direct product factor, Sylow
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2C3×#240711yescharacteristic
815C2C3×#300611yescharacteristic
816C2C3×#301211yescharacteristic
817C2C3×#330711yescharacteristic
818C2C3×#331811yescharacteristic
819C2C3×#334511yescharacteristic
820C2C3×#334711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#553C2semidirect
2. C2×C3×#478C2semidirect
3. C2×C3×#442C2semidirect
4. C3×#2537C2semidirect
5. C3×#2034C2semidirect
6. C3×#2033C2semidirect
7. C3×#1999C2semidirect
8. C3×#1999C2semidirect
9. C3×#1992C2semidirect
10. C3×#1955C2semidirect
11. C3×#1875C2semidirect
12. C3×#1874C2semidirect
13. C3×#1854C2semidirect
14. C3×#1853C2semidirect
15. C3×#1802C2semidirect
16. #24136C3direct (N × H)
64. C2×#553C2×C3semidirect
65. C2×#478C2×C3semidirect
66. C2×#442C2×C3semidirect
67. #2537C2×C3semidirect
68. #2034C2×C3semidirect
69. #2033C2×C3semidirect
70. #1999C2×C3semidirect
71. #1999C2×C3semidirect
72. #1992C2×C3semidirect
73. #1955C2×C3semidirect
74. #1875C2×C3semidirect
75. #1874C2×C3semidirect
76. #1854C2×C3semidirect
77. #1853C2×C3semidirect
78. #1802C2×C3semidirect
100. C3×#125D4semidirect
118. C3×C4×D4D4semidirect
341. #125C3×D4semidirect
359. C4×D4C3×D4semidirect
809. C3#24136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5532
C2×C3×#4782
C2×C3×#4422
C3×#25372
C3×#20342
C3×#20332
C3×#19992
C3×#19922
C3×#19552
C3×#18752
C3×#18742
C3×#18542
C3×#18532
C3×#18022
#241363