Finite Group Databasebeta

← C3×#40640 #10659247

Subgroups — C3×#40640 #10659247

Order 768.

2654 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2825C212yesmaximal, complemented
2C3×#2760C211yesmaximal, characteristic, complemented
3C3×#2752C211yesmaximal, characteristic, complemented
4C3×#2749C212yesmaximal, complemented
5C3×#2678C212yesmaximal, complemented
6C3×#2670C211yesmaximal, characteristic, complemented
7C3×#2668C211yesmaximal, characteristic, complemented
8C3×#2635C212yesmaximal, complemented
9C3×#2631C212yesmaximal, complemented
10C3×#2626C211yesmaximal, characteristic, complemented
11C3×#2510C212yesmaximal, complemented
12C3×#2472C212yesmaximal, complemented
13C3×#2456C212yesmaximal, complemented
14C3×#2412C212yesmaximal, complemented
15C3×#2410C212yesmaximal, complemented
16C3×#2403C212yesmaximal, complemented
17C2×C3×#392C211yesmaximal, characteristic, complemented
18C3×D4×C22⋊C4C212yesmaximal, complemented
19C3×#2308C211yesmaximal, characteristic, complemented
20#40640C311yesmaximal, characteristic, direct product factor, Sylow
21C23×C3×D4C2212yes—
22C23×C3×D4C2211yescharacteristic
23C23×C3×D4C2211yescharacteristic, complemented
24C2×C3×#124C2212yescomplemented
25C2×C3×#123C2212yescomplemented
26C2×C3×C22⋊Q8C2211yescharacteristic, complemented
27C2×C3×#121C2212yescomplemented
28C2×C3×#121C2212yescomplemented
29C2×C3×#120C2212yes—
30C2×C3×#120C2212yes—
31C2×C3×#120C2212yescomplemented
32C2×C3×#120C2212yescomplemented
33C2×C3×C4×D4C2212yescomplemented
34C2×C3×C4×D4C2212yescomplemented
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2212yescomplemented
38C22×C3×C22⋊C4C2212yescomplemented
39C3×#401C2212yescomplemented
40C3×#400C2212yescomplemented
41C3×#399C2211yescharacteristic, complemented
42C3×#399C2211yescharacteristic, complemented
43C3×#397C2212yescomplemented
44C3×#397C2212yescomplemented
45C3×#397C2212yescomplemented
46C3×#397C2212yescomplemented
47C3×#397C2212yescomplemented
48C3×#396C2212yescomplemented
49C3×#396C2212yescomplemented
50C3×#394C2212yescomplemented
51C3×#394C2212yescomplemented
52C3×#394C2212yescomplemented
53C3×#394C2212yescomplemented
54C3×#394C2212yescomplemented
55C3×#394C2212yescomplemented
56C3×#393C2211yescharacteristic, complemented
57C3×#393C2211yescharacteristic, complemented
58C3×#393C2212yescomplemented
59C3×#392C2211yescharacteristic
60C3×#392C2211yescharacteristic
61C3×#392C2212yes—
62C3×#392C2212yescomplemented
63C3×#392C2212yescomplemented
64C3×#392C2212yescomplemented
65C3×#392C2212yescomplemented
66C3×#392C2212yescomplemented
67C3×#392C2212yescomplemented
68C3×#392C2211yescharacteristic, complemented
69C3×#392C2211yescharacteristic, complemented
70C3×#392C2212yescomplemented
71C3×#390C2212yescomplemented
72C3×#390C2212yescomplemented
73C3×#390C2212yescomplemented
74C3×#388C2212yescomplemented
75C3×#388C2212yescomplemented
76C3×#388C2212yescomplemented
77C3×#388C2212yescomplemented
78C3×#387C2212yescomplemented
79C3×#386C2212yes—
80C3×#386C2212yes—
81C3×#386C2212yes—
82C3×#386C2212yes—
83C3×#386C2212yescomplemented
84C3×#386C2212yescomplemented
85C3×#386C2212yescomplemented
86C3×#386C2212yescomplemented
87C3×#386C2212yescomplemented
88C3×#386C2212yescomplemented
89C3×#386C2212yescomplemented
90C3×#386C2212yescomplemented
91C3×#386C2212yescomplemented
92C3×#386C2212yescomplemented
93C3×#386C2212yescomplemented
94C3×#385C2212yescomplemented
95C3×#385C2212yescomplemented
96C3×#383C2212yescomplemented
97C3×#381C2212yescomplemented
98C3×#381C2211yescharacteristic, complemented
99C3×#381C2211yescharacteristic, complemented
100C3×#380C2211yescharacteristic, complemented
101C3×#380C2212yescomplemented
102C3×#379C2212yes—
103C3×#379C2212yescomplemented
104C3×#379C2211yescharacteristic, complemented
105C3×#379C2211yescharacteristic, complemented
106C3×C4×C22⋊C4C2212yescomplemented
107C2×C3×#95C2211yescharacteristic, complemented
108#2825C2×C312yescomplemented
109#2760C2×C311yescharacteristic, complemented
110#2752C2×C311yescharacteristic, complemented
111#2749C2×C312yescomplemented
112#2678C2×C312yescomplemented
113#2670C2×C311yescharacteristic, complemented
114#2668C2×C311yescharacteristic, complemented
115#2635C2×C312yescomplemented
116#2631C2×C312yescomplemented
117#2626C2×C311yescharacteristic, complemented
118#2510C2×C312yescomplemented
119#2472C2×C312yescomplemented
120#2456C2×C312yescomplemented
121#2412C2×C312yescomplemented
122#2410C2×C312yescomplemented
123#2403C2×C312yescomplemented
124C2×#392C2×C311yescharacteristic, complemented
125D4×C22⋊C4C2×C312yescomplemented
126#2308C2×C311yescharacteristic, complemented
127C25×C3C2312yes—
128C25×C3C2311yescharacteristic
129C25×C3C2311yescharacteristic
130C22×C3×Q8C2311yescharacteristic
131C22×C3×D4—28no—
132C22×C3×D4—24no—
133C22×C3×D4—44no—
134C22×C3×D4—42no—
135C22×C3×D4—44no—
136C22×C3×D4—42no—
137C22×C3×D4—42no—
138C22×C3×D4—44no—
139C22×C3×D4C2312yes—
140C22×C3×D4C2312yes—
141C22×C3×D4C2312yes—
142C22×C3×D4C2312yes—
143C22×C3×D4C2311yescharacteristic
144C22×C3×D4C2312yes—
145C22×C3×D4C2312yes—
146C22×C3×D4C2312yes—
147C22×C3×D4C2312yes—
148C22×C3×D4C2312yes—
149C22×C3×D4C2311yescharacteristic
150C22×C3×D4C2312yes—
151C22×C3×D4C2312yes—
152C23×C3×C4C2312yes—
153C23×C3×C4C2311yescharacteristic
154C23×C3×C4C2311yescharacteristic
155C23×C3×C4C2311yescharacteristic
156C23×C3×C4C2312yes—
157C23×C3×C4C2312yes—
158C23×C3×C4C2312yes—
159C3×#124—44no—
160C3×#123—44no—
161C3×C22⋊Q8—42no—
162C3×#121—44no—
163C3×#121—44no—
164C3×#120—44no—
165C3×#120—44no—
166C3×#120—44no—
167C3×#120—44no—
168C3×C4×D4—44no—
169C3×C4×D4—44no—
170C2×C3×C4⋊C4C2312yes—
171C2×C3×C4⋊C4C2312yes—
172C2×C3×C4⋊C4C2312yes—
173C2×C3×C4⋊C4C2312yes—
174C2×C3×C4⋊C4C2312yes—
175C2×C3×C4⋊C4C2311yescharacteristic
176C2×C3×C4⋊C4C2312yes—
177C2×C3×C22⋊C4—44no—
178C2×C3×C22⋊C4—42no—
179C2×C3×C22⋊C4—44no—
180C2×C3×C22⋊C4—42no—
181C2×C3×C22⋊C4C2312yes—
182C2×C3×C22⋊C4C2312yes—
183C2×C3×C22⋊C4C2312yes—
184C2×C3×C22⋊C4C2312yes—
185C2×C3×C22⋊C4C2312yes—
186C2×C3×C22⋊C4C2312yes—
187C2×C3×C22⋊C4C2312yes—
188C2×C3×C22⋊C4C2312yes—
189C2×C3×C22⋊C4C2312yes—
190C2×C3×C22⋊C4C2312yes—
191C2×C3×C22⋊C4C2312yes—
192C2×C3×C22⋊C4C2312yes—
193C2×C3×C22⋊C4C2311yescharacteristic
194C2×C3×C22⋊C4C2311yescharacteristic
195C2×C3×C22⋊C4C2311yescharacteristic
196C2×C3×C22⋊C4C2311yescharacteristic
197C2×C3×C22⋊C4C2312yes—
198C2×C3×C22⋊C4C2312yes—
199C2×C3×C22⋊C4C2312yes—
200C2×C3×C22⋊C4C2312yes—
201C2×C3×C22⋊C4C2312yes—
202C2×C3×C22⋊C4C2312yes—
203C2×C3×C22⋊C4C2312yes—
204C2×C3×C22⋊C4C2312yes—
205C2×C3×C22⋊C4C2312yes—
206C2×C3×C22⋊C4C2312yes—
207C2×C3×C22⋊C4C2312yes—
208C2×C3×C22⋊C4C2312yes—
209C2×C3×C22⋊C4C2311yescharacteristic
210C2×C3×C22⋊C4C2311yescharacteristic
211C2×C3×C22⋊C4C2312yes—
212C2×C3×C22⋊C4C2312yes—
213C2×C3×C22⋊C4C2312yes—
214C2×C3×C22⋊C4C2312yes—
215C2×C3×C22⋊C4C2312yes—
216C2×C3×C42C2312yes—
217C2×C3×C42C2312yes—
218C3×#95C2312yes—
219C3×#95C2311yescharacteristic
220C3×#95C2311yescharacteristic
221C3×#95C2312yes—
222C3×#95C2312yes—
223C3×#95C2311yescharacteristic
224C3×#95C2312yes—
225C3×#95C2312yes—
226C3×#95C2311yescharacteristic
227C3×#95C2312yes—
228C3×#95C2312yes—
229C3×#95C2312yes—
230C3×#95C2312yes—
231C3×#95C2312yes—
232C3×#95C2312yes—
233C3×#95C2312yes—
234C3×#95C2312yes—
235C3×#95C2312yes—
236C3×#95C2312yes—
237C23×D4C22×C311yescharacteristic
238C23×D4C22×C312yes—
239C23×D4C22×C311yescharacteristic, complemented
240C2×#124C22×C312yescomplemented
241C2×#123C22×C312yescomplemented
242C2×C22⋊Q8C22×C311yescharacteristic, complemented
243C2×#121C22×C312yescomplemented
244C2×#121C22×C312yescomplemented
245C2×#120C22×C312yes—
246C2×#120C22×C312yes—
247C2×#120C22×C312yescomplemented
248C2×#120C22×C312yescomplemented
249C2×C4×D4C22×C312yescomplemented
250C2×C4×D4C22×C312yescomplemented
251C22×C22⋊C4C22×C311yescharacteristic
252C22×C22⋊C4C22×C311yescharacteristic
253C22×C22⋊C4C22×C312yescomplemented
254C22×C22⋊C4C22×C312yescomplemented
255#401C22×C312yescomplemented
256#400C22×C312yescomplemented
257#399C22×C311yescharacteristic, complemented
258#399C22×C311yescharacteristic, complemented
259#397C22×C312yescomplemented
260#397C22×C312yescomplemented
261#397C22×C312yescomplemented
262#397C22×C312yescomplemented
263#397C22×C312yescomplemented
264#396C22×C312yescomplemented
265#396C22×C312yescomplemented
266#394C22×C312yescomplemented
267#394C22×C312yescomplemented
268#394C22×C312yescomplemented
269#394C22×C312yescomplemented
270#394C22×C312yescomplemented
271#394C22×C312yescomplemented
272#393C22×C311yescharacteristic, complemented
273#393C22×C311yescharacteristic, complemented
274#393C22×C312yescomplemented
275#392C22×C311yescharacteristic
276#392C22×C311yescharacteristic
277#392C22×C312yes—
278#392C22×C311yescharacteristic, complemented
279#392C22×C312yescomplemented
280#392C22×C312yescomplemented
281#392C22×C312yescomplemented
282#392C22×C312yescomplemented
283#392C22×C312yescomplemented
284#392C22×C312yescomplemented
285#392C22×C312yescomplemented
286#392C22×C311yescharacteristic, complemented
287#390C22×C312yescomplemented
288#390C22×C312yescomplemented
289#390C22×C312yescomplemented
290#388C22×C312yescomplemented
291#388C22×C312yescomplemented
292#388C22×C312yescomplemented
293#388C22×C312yescomplemented
294#387C22×C312yescomplemented
295#386C22×C312yes—
296#386C22×C312yes—
297#386C22×C312yes—
298#386C22×C312yes—
299#386C22×C312yescomplemented
300#386C22×C312yescomplemented
301#386C22×C312yescomplemented
302#386C22×C312yescomplemented
303#386C22×C312yescomplemented
304#386C22×C312yescomplemented
305#386C22×C312yescomplemented
306#386C22×C312yescomplemented
307#386C22×C312yescomplemented
308#386C22×C312yescomplemented
309#386C22×C312yescomplemented
310#385C22×C312yescomplemented
311#385C22×C312yescomplemented
312#383C22×C312yescomplemented
313#381C22×C311yescharacteristic, complemented
314#381C22×C311yescharacteristic, complemented
315#381C22×C312yescomplemented
316#380C22×C312yescomplemented
317#380C22×C311yescharacteristic, complemented
318#379C22×C312yes—
319#379C22×C311yescharacteristic, complemented
320#379C22×C311yescharacteristic, complemented
321#379C22×C312yescomplemented
322C4×C22⋊C4C22×C312yescomplemented
323C2×#95C22×C311yescharacteristic, complemented
324C24×C3—22no—
325C24×C3—22no—
326C24×C3—24no—
327C24×C3—24no—
328C24×C3—24no—
329C24×C3—24no—
330C24×C3—22no—
331C24×C3—42no—
332C24×C3—42no—
333C24×C3—42no—
334C24×C3—42no—
335C24×C3—42no—
336C24×C3—41no—
337C24×C3—41no—
338C24×C3—42no—
339C24×C3—42no—
340C24×C3#4114yes—
341C24×C3C2412yes—
342C24×C3C2412yes—
343C24×C3C2411yescharacteristic
344C24×C3C2411yescharacteristic
345C24×C3C2412yes—
346C24×C3C2411yescharacteristic
347C2×C3×Q8—41no—
348C2×C3×Q8—42no—
349C2×C3×D4—24no—
350C2×C3×D4—24no—
351C2×C3×D4—24no—
352C2×C3×D4—24no—
353C2×C3×D4—24no—
354C2×C3×D4—24no—
355C2×C3×D4—24no—
356C2×C3×D4—24no—
357C2×C3×D4—24no—
358C2×C3×D4—24no—
359C2×C3×D4—24no—
360C2×C3×D4—24no—
361C2×C3×D4—24no—
362C2×C3×D4—24no—
363C2×C3×D4—24no—
364C2×C3×D4—24no—
365C2×C3×D4—42no—
366C2×C3×D4—42no—
367C2×C3×D4—41no—
368C2×C3×D4—42no—
369C2×C3×D4—42no—
370C2×C3×D4—41no—
371C2×C3×D4—42no—
372C2×C3×D4—42no—
373C2×C3×D4—42no—
374C2×C3×D4—42no—
375C2×C3×D4—42no—
376C2×C3×D4—42no—
377C2×C3×D4—42no—
378C2×C3×D4—42no—
379C2×C3×D4—42no—
380C2×C3×D4—42no—
381C2×C3×D4—42no—
382C2×C3×D4—42no—
383C2×C3×D4—42no—
384C2×C3×D4—42no—
385C2×C3×D4—42no—
386C2×C3×D4—432no—
387C2×C3×D4—416no—
388C2×C3×D4—416no—
389C22×C3×C4—24no—
390C22×C3×C4—22no—
391C22×C3×C4—22no—
392C22×C3×C4—22no—
393C22×C3×C4—24no—
394C22×C3×C4—24no—
395C22×C3×C4—42no—
396C22×C3×C4—41no—
397C22×C3×C4—41no—
398C22×C3×C4—42no—
399C22×C3×C4—42no—
400C22×C3×C4—42no—
401C22×C3×C4—42no—
402C22×C3×C4—42no—
403C22×C3×C4—42no—
404C22×C3×C4—42no—
405C22×C3×C4—42no—
406C22×C3×C4—42no—
407C22×C3×C4—42no—
408C22×C3×C4C2412yes—
409C22×C3×C4C2412yes—
410C22×C3×C4C2411yescharacteristic
411C22×C3×C4C2411yescharacteristic
412C22×C3×C4C2412yes—
413C22×C3×C4C2412yes—
414C22×C3×C4C2412yes—
415C22×C3×C4C2411yescharacteristic
416C22×C3×C4C2412yes—
417C22×C3×C4C2412yes—
418C22×C3×C4C2412yes—
419C22×C3×C4C2411yescharacteristic
420C22×C3×C4C2412yes—
421C3×C4⋊C4—24no—
422C3×C4⋊C4—42no—
423C3×C4⋊C4—42no—
424C3×C4⋊C4—42no—
425C3×C4⋊C4—41no—
426C3×C4⋊C4—42no—
427C3×C4⋊C4—42no—
428C3×C22⋊C4—24no—
429C3×C22⋊C4—24no—
430C3×C22⋊C4—24no—
431C3×C22⋊C4—24no—
432C3×C22⋊C4—24no—
433C3×C22⋊C4—24no—
434C3×C22⋊C4—24no—
435C3×C22⋊C4—24no—
436C3×C22⋊C4—42no—
437C3×C22⋊C4—41no—
438C3×C22⋊C4—41no—
439C3×C22⋊C4—42no—
440C3×C22⋊C4—42no—
441C3×C22⋊C4—42no—
442C3×C22⋊C4—41no—
443C3×C22⋊C4—41no—
444C3×C22⋊C4—41no—
445C3×C22⋊C4—41no—
446C3×C22⋊C4—42no—
447C3×C22⋊C4—42no—
448C3×C22⋊C4—42no—
449C3×C22⋊C4—42no—
450C3×C22⋊C4—42no—
451C3×C22⋊C4—42no—
452C3×C22⋊C4—42no—
453C3×C22⋊C4—42no—
454C3×C22⋊C4—42no—
455C3×C22⋊C4—42no—
456C3×C22⋊C4—42no—
457C3×C22⋊C4—42no—
458C3×C22⋊C4—42no—
459C3×C22⋊C4—42no—
460C3×C22⋊C4—42no—
461C3×C22⋊C4—42no—
462C3×C22⋊C4—42no—
463C3×C42—24no—
464C3×C42—42no—
465C25C23×C312yes—
466C25C23×C311yescharacteristic
467C25C23×C311yescharacteristic
468C22×Q8C23×C311yescharacteristic
469C22×D4—28no—
470C22×D4—24no—
471C22×D4—44no—
472C22×D4—42no—
473C22×D4—44no—
474C22×D4—42no—
475C22×D4—42no—
476C22×D4—44no—
477C22×D4C23×C312yes—
478C22×D4C23×C312yes—
479C22×D4C23×C312yes—
480C22×D4C23×C312yes—
481C22×D4C23×C311yescharacteristic
482C22×D4C23×C312yes—
483C22×D4C23×C312yes—
484C22×D4C23×C312yes—
485C22×D4C23×C312yes—
486C22×D4C23×C312yes—
487C22×D4C23×C312yes—
488C22×D4C23×C312yes—
489C22×D4C23×C311yescharacteristic
490C23×C4C23×C312yes—
491C23×C4C23×C311yescharacteristic
492C23×C4C23×C311yescharacteristic
493C23×C4C23×C312yes—
494C23×C4C23×C311yescharacteristic
495C23×C4C23×C312yes—
496C23×C4C23×C312yes—
497#124—44no—
498#123—44no—
499C22⋊Q8—42no—
500#121—44no—
501#121—44no—
502#120—44no—
503#120—44no—
504#120—44no—
505#120—44no—
506C4×D4—44no—
507C4×D4—44no—
508C2×C4⋊C4C23×C312yes—
509C2×C4⋊C4C23×C312yes—
510C2×C4⋊C4C23×C312yes—
511C2×C4⋊C4C23×C312yes—
512C2×C4⋊C4C23×C311yescharacteristic
513C2×C4⋊C4C23×C312yes—
514C2×C4⋊C4C23×C312yes—
515C2×C22⋊C4—44no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—44no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4C23×C312yes—
520C2×C22⋊C4C23×C312yes—
521C2×C22⋊C4C23×C312yes—
522C2×C22⋊C4C23×C312yes—
523C2×C22⋊C4C23×C312yes—
524C2×C22⋊C4C23×C312yes—
525C2×C22⋊C4C23×C312yes—
526C2×C22⋊C4C23×C312yes—
527C2×C22⋊C4C23×C311yescharacteristic
528C2×C22⋊C4C23×C311yescharacteristic
529C2×C22⋊C4C23×C311yescharacteristic
530C2×C22⋊C4C23×C311yescharacteristic
531C2×C22⋊C4C23×C311yescharacteristic
532C2×C22⋊C4C23×C311yescharacteristic
533C2×C22⋊C4C23×C312yes—
534C2×C22⋊C4C23×C312yes—
535C2×C22⋊C4C23×C312yes—
536C2×C22⋊C4C23×C312yes—
537C2×C22⋊C4C23×C312yes—
538C2×C22⋊C4C23×C312yes—
539C2×C22⋊C4C23×C312yes—
540C2×C22⋊C4C23×C312yes—
541C2×C22⋊C4C23×C312yes—
542C2×C22⋊C4C23×C312yes—
543C2×C22⋊C4C23×C312yes—
544C2×C22⋊C4C23×C312yes—
545C2×C22⋊C4C23×C312yes—
546C2×C22⋊C4C23×C312yes—
547C2×C22⋊C4C23×C312yes—
548C2×C22⋊C4C23×C312yes—
549C2×C22⋊C4C23×C312yes—
550C2×C22⋊C4C23×C312yes—
551C2×C22⋊C4C23×C312yes—
552C2×C22⋊C4C23×C312yes—
553C2×C22⋊C4C23×C312yes—
554C2×C42C23×C312yes—
555C2×C42C23×C312yes—
556#95C23×C312yes—
557#95C23×C311yescharacteristic
558#95C23×C311yescharacteristic
559#95C23×C312yes—
560#95C23×C312yes—
561#95C23×C311yescharacteristic
562#95C23×C312yes—
563#95C23×C312yes—
564#95C23×C311yescharacteristic
565#95C23×C312yes—
566#95C23×C312yes—
567#95C23×C312yes—
568#95C23×C312yes—
569#95C23×C312yes—
570#95C23×C312yes—
571#95C23×C312yes—
572#95C23×C312yes—
573#95C23×C312yes—
574#95C23×C312yes—
575C23×C3—22no—
576C23×C3—22no—
577C23×C3—22no—
578C23×C3—22no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—21no—
590C23×C3—22no—
591C23×C3—28no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—48no—
607C23×C3—48no—
608C23×C3—48no—
609C23×C3—48no—
610C23×C3—44no—
611C23×C3—48no—
612C23×C3—84no—
613C23×C3—82no—
614C23×C3—84no—
615C23×C3—84no—
616C23×C3—82no—
617C23×C3—84no—
618C23×C3—84no—
619C23×C3—82no—
620C23×C3—84no—
621C23×C3—82no—
622C23×C3C2×#4112yes—
623C23×C3C2×#4112yes—
624C23×C3C2×#4112yes—
625C23×C3H(5,𝔽2)14yes—
626C23×C3H(5,𝔽2)12yes—
627C23×C3H(5,𝔽2)12yes—
628C23×C3C2511yescharacteristic
629C3×Q8—82no—
630C3×D4—216no—
631C3×D4—48no—
632C3×D4—48no—
633C3×D4—44no—
634C3×D4—48no—
635C3×D4—48no—
636C3×D4—48no—
637C3×D4—44no—
638C3×D4—48no—
639C3×D4—84no—
640C3×D4—84no—
641C3×D4—84no—
642C3×D4—84no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—48no—
678C2×C3×C4—44no—
679C2×C3×C4—44no—
680C2×C3×C4—84no—
681C2×C3×C4—82no—
682C2×C3×C4—84no—
683C2×C3×C4—84no—
684C2×C3×C4H(5,𝔽2)14yes—
685C24—22no—
686C24—22no—
687C24—24no—
688C24—24no—
689C24—24no—
690C24—24no—
691C24—22no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—41no—
698C24—41no—
699C24—42no—
700C24—42no—
701C24C3×#4114yes—
702C24C24×C312yes—
703C24C24×C312yes—
704C24C24×C311yescharacteristic
705C24C24×C311yescharacteristic
706C24C24×C312yes—
707C24C24×C311yescharacteristic
708C2×Q8—41no—
709C2×Q8—42no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—41no—
729C2×D4—42no—
730C2×D4—42no—
731C2×D4—41no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—432no—
748C2×D4—416no—
749C2×D4—416no—
750C22×C4—24no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—42no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4C24×C312yes—
770C22×C4C24×C312yes—
771C22×C4C24×C311yescharacteristic
772C22×C4C24×C311yescharacteristic
773C22×C4C24×C312yes—
774C22×C4C24×C312yes—
775C22×C4C24×C312yes—
776C22×C4C24×C311yescharacteristic
777C22×C4C24×C312yes—
778C22×C4C24×C312yes—
779C22×C4C24×C312yes—
780C22×C4C24×C311yescharacteristic
781C22×C4C24×C312yes—
782C4⋊C4—24no—
783C4⋊C4—42no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—41no—
787C4⋊C4—42no—
788C4⋊C4—42no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—24no—
795C22⋊C4—24no—
796C22⋊C4—24no—
797C22⋊C4—42no—
798C22⋊C4—41no—
799C22⋊C4—41no—
800C22⋊C4—42no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—41no—
807C22⋊C4—42no—
808C22⋊C4—42no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—42no—
812C22⋊C4—42no—
813C22⋊C4—42no—
814C22⋊C4—42no—
815C22⋊C4—42no—
816C22⋊C4—42no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—42no—
824C42—24no—
825C42—42no—
826C22×C3—24no—
827C22×C3—22no—
828C22×C3—24no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—24no—
833C22×C3—24no—
834C22×C3—24no—
835C22×C3—24no—
836C22×C3—24no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3—42no—
861C22×C3—88no—
862C22×C3—816no—
863C22×C3—88no—
864C22×C3#53814yes—
865C22×C3C22×#4111yescharacteristic
866C22×C3C2×H(5,𝔽2)11yescharacteristic
867C22×C3C2×H(5,𝔽2)11yescharacteristic
868C22×C3C2×H(5,𝔽2)12yes—
869C22×C3C2×H(5,𝔽2)12yes—
870C3×C4—24no—
871C3×C4—42no—
872C3×C4—42no—
873C3×C4—41no—
874C3×C4—41no—
875C3×C4—42no—
876C3×C4—42no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—42no—
880C3×C4—41no—
881C3×C4—41no—
882C3×C4—42no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—21no—
898C23—22no—
899C23—28no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—48no—
915C23—48no—
916C23—48no—
917C23—48no—
918C23—44no—
919C23—48no—
920C23—84no—
921C23—82no—
922C23—84no—
923C23—84no—
924C23—82no—
925C23—84no—
926C23—84no—
927C23—82no—
928C23—84no—
929C23—82no—
930C23C2×C3×#4112yes—
931C23C2×C3×#4112yes—
932C23C2×C3×#4112yes—
933C23C3×H(5,𝔽2)14yes—
934C23C3×H(5,𝔽2)12yes—
935C23C3×H(5,𝔽2)12yes—
936C23C25×C311yescharacteristic
937Q8—82no—
938D4—216no—
939D4—48no—
940D4—48no—
941D4—44no—
942D4—48no—
943D4—48no—
944D4—48no—
945D4—44no—
946D4—48no—
947D4—84no—
948D4—84no—
949D4—84no—
950D4—84no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—48no—
986C2×C4—44no—
987C2×C4—44no—
988C2×C4—84no—
989C2×C4—82no—
990C2×C4—84no—
991C2×C4—84no—
992C2×C4C3×H(5,𝔽2)14yes—
993C2×C3—24no—
994C2×C3—42no—
995C2×C3—44no—
996C2×C3—42no—
997C2×C3—82no—
998C2×C3—82no—
999C2×C3C2×#53811yescharacteristic
1000C2×C3#349012yes—
1001C2×C3#353211yescharacteristic
1002C2×C3#353712yes—
1003C2×C3#354311yescharacteristic
1004C22—24no—
1005C22—22no—
1006C22—24no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22—42no—
1016C22—42no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—88no—
1040C22—816no—
1041C22—88no—
1042C22C3×#53814yes—
1043C22C22×C3×#4111yescharacteristic
1044C22C2×C3×H(5,𝔽2)11yescharacteristic
1045C22C2×C3×H(5,𝔽2)11yescharacteristic
1046C22C2×C3×H(5,𝔽2)12yes—
1047C22C2×C3×H(5,𝔽2)12yes—
1048C4—24no—
1049C4—42no—
1050C4—42no—
1051C4—41no—
1052C4—41no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—42no—
1058C4—41no—
1059C4—41no—
1060C4—42no—
1061C3#4064011yescharacteristic, direct product factor, Sylow
1062C2—24no—
1063C2—42no—
1064C2—42no—
1065C2—44no—
1066C2—82no—
1067C2—82no—
1068C2C2×C3×#53811yescharacteristic
1069C2C3×#349012yes—
1070C2C3×#353211yescharacteristic
1071C2C3×#353712yes—
1072C2C3×#354311yescharacteristic
subgroupG/H
center, socleC23×C3C25
commutator, Frattini, cosocleC23C25×C3
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2825C2semidirect
2. C3×#2760C2semidirect
3. C3×#2752C2semidirect
4. C3×#2749C2semidirect
5. C3×#2678C2semidirect
6. C3×#2670C2semidirect
7. C3×#2668C2semidirect
8. C3×#2635C2semidirect
9. C3×#2631C2semidirect
10. C3×#2626C2semidirect
11. C3×#2510C2semidirect
12. C3×#2472C2semidirect
13. C3×#2456C2semidirect
14. C3×#2412C2semidirect
15. C3×#2410C2semidirect
16. C3×#2403C2semidirect
17. C2×C3×#392C2semidirect
18. C3×D4×C22⋊C4C2semidirect
19. C3×#2308C2semidirect
20. #40640C3direct (N × H)
23. C23×C3×D4C22semidirect
24. C2×C3×#124C22semidirect
25. C2×C3×#123C22semidirect
26. C2×C3×C22⋊Q8C22semidirect
27. C2×C3×#121C22semidirect
28. C2×C3×#121C22semidirect
31. C2×C3×#120C22semidirect
32. C2×C3×#120C22semidirect
33. C2×C3×C4×D4C22semidirect
34. C2×C3×C4×D4C22semidirect
37. C22×C3×C22⋊C4C22semidirect
38. C22×C3×C22⋊C4C22semidirect
39. C3×#401C22semidirect
40. C3×#400C22semidirect
41. C3×#399C22semidirect
42. C3×#399C22semidirect
43. C3×#397C22semidirect
44. C3×#397C22semidirect
45. C3×#397C22semidirect
46. C3×#397C22semidirect
47. C3×#397C22semidirect
48. C3×#396C22semidirect
49. C3×#396C22semidirect
50. C3×#394C22semidirect
51. C3×#394C22semidirect
52. C3×#394C22semidirect
53. C3×#394C22semidirect
54. C3×#394C22semidirect
55. C3×#394C22semidirect
56. C3×#393C22semidirect
57. C3×#393C22semidirect
58. C3×#393C22semidirect
62. C3×#392C22semidirect
63. C3×#392C22semidirect
64. C3×#392C22semidirect
65. C3×#392C22semidirect
66. C3×#392C22semidirect
67. C3×#392C22semidirect
68. C3×#392C22semidirect
69. C3×#392C22semidirect
70. C3×#392C22semidirect
71. C3×#390C22semidirect
72. C3×#390C22semidirect
73. C3×#390C22semidirect
74. C3×#388C22semidirect
75. C3×#388C22semidirect
76. C3×#388C22semidirect
77. C3×#388C22semidirect
78. C3×#387C22semidirect
83. C3×#386C22semidirect
84. C3×#386C22semidirect
85. C3×#386C22semidirect
86. C3×#386C22semidirect
87. C3×#386C22semidirect
88. C3×#386C22semidirect
89. C3×#386C22semidirect
90. C3×#386C22semidirect
91. C3×#386C22semidirect
92. C3×#386C22semidirect
93. C3×#386C22semidirect
94. C3×#385C22semidirect
95. C3×#385C22semidirect
96. C3×#383C22semidirect
97. C3×#381C22semidirect
98. C3×#381C22semidirect
99. C3×#381C22semidirect
100. C3×#380C22semidirect
101. C3×#380C22semidirect
103. C3×#379C22semidirect
104. C3×#379C22semidirect
105. C3×#379C22semidirect
106. C3×C4×C22⋊C4C22semidirect
107. C2×C3×#95C22semidirect
108. #2825C2×C3semidirect
109. #2760C2×C3semidirect
110. #2752C2×C3semidirect
111. #2749C2×C3semidirect
112. #2678C2×C3semidirect
113. #2670C2×C3semidirect
114. #2668C2×C3semidirect
115. #2635C2×C3semidirect
116. #2631C2×C3semidirect
117. #2626C2×C3semidirect
118. #2510C2×C3semidirect
119. #2472C2×C3semidirect
120. #2456C2×C3semidirect
121. #2412C2×C3semidirect
122. #2410C2×C3semidirect
123. #2403C2×C3semidirect
124. C2×#392C2×C3semidirect
125. D4×C22⋊C4C2×C3semidirect
126. #2308C2×C3semidirect
239. C23×D4C22×C3semidirect
240. C2×#124C22×C3semidirect
241. C2×#123C22×C3semidirect
242. C2×C22⋊Q8C22×C3semidirect
243. C2×#121C22×C3semidirect
244. C2×#121C22×C3semidirect
247. C2×#120C22×C3semidirect
248. C2×#120C22×C3semidirect
249. C2×C4×D4C22×C3semidirect
250. C2×C4×D4C22×C3semidirect
253. C22×C22⋊C4C22×C3semidirect
254. C22×C22⋊C4C22×C3semidirect
255. #401C22×C3semidirect
256. #400C22×C3semidirect
257. #399C22×C3semidirect
258. #399C22×C3semidirect
259. #397C22×C3semidirect
260. #397C22×C3semidirect
261. #397C22×C3semidirect
262. #397C22×C3semidirect
263. #397C22×C3semidirect
264. #396C22×C3semidirect
265. #396C22×C3semidirect
266. #394C22×C3semidirect
267. #394C22×C3semidirect
268. #394C22×C3semidirect
269. #394C22×C3semidirect
270. #394C22×C3semidirect
271. #394C22×C3semidirect
272. #393C22×C3semidirect
273. #393C22×C3semidirect
274. #393C22×C3semidirect
278. #392C22×C3semidirect
279. #392C22×C3semidirect
280. #392C22×C3semidirect
281. #392C22×C3semidirect
282. #392C22×C3semidirect
283. #392C22×C3semidirect
284. #392C22×C3semidirect
285. #392C22×C3semidirect
286. #392C22×C3semidirect
287. #390C22×C3semidirect
288. #390C22×C3semidirect
289. #390C22×C3semidirect
290. #388C22×C3semidirect
291. #388C22×C3semidirect
292. #388C22×C3semidirect
293. #388C22×C3semidirect
294. #387C22×C3semidirect
299. #386C22×C3semidirect
300. #386C22×C3semidirect
301. #386C22×C3semidirect
302. #386C22×C3semidirect
303. #386C22×C3semidirect
304. #386C22×C3semidirect
305. #386C22×C3semidirect
306. #386C22×C3semidirect
307. #386C22×C3semidirect
308. #386C22×C3semidirect
309. #386C22×C3semidirect
310. #385C22×C3semidirect
311. #385C22×C3semidirect
312. #383C22×C3semidirect
313. #381C22×C3semidirect
314. #381C22×C3semidirect
315. #381C22×C3semidirect
316. #380C22×C3semidirect
317. #380C22×C3semidirect
319. #379C22×C3semidirect
320. #379C22×C3semidirect
321. #379C22×C3semidirect
322. C4×C22⋊C4C22×C3semidirect
323. C2×#95C22×C3semidirect
1061. C3#40640direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#28252
C3×#27602
C3×#27522
C3×#27492
C3×#26782
C3×#26702
C3×#26682
C3×#26352
C3×#26312
C3×#26262
C3×#25102
C3×#24722
C3×#24562
C3×#24122
C3×#24102
C3×#24032
C2×C3×#3922
C3×D4×C22⋊C42
C3×#23082
#406403