Finite Group Databasebeta

← C2×C31×#2425 #21491426

Subgroups — C2×C31×#2425 #21491426

Order 7936.

3938 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic, complemented
2C22×C31×#123C211yesmaximal, characteristic, complemented
3C22×C31×#121C211yesmaximal, characteristic
4C22×C4×D4×C31C211yesmaximal, characteristic, complemented
5C31×#2425C2116yesmaximal, direct product factor
6C2×C31×#398C211yesmaximal, characteristic, complemented
7C2×C31×#397C211yesmaximal, characteristic, complemented
8C2×C31×#396C211yesmaximal, characteristic, complemented
9C2×C31×#394C211yesmaximal, characteristic, complemented
10C2×C31×#389C211yesmaximal, characteristic, complemented
11C2×C31×#388C211yesmaximal, characteristic, complemented
12C2×C31×#386C211yesmaximal, characteristic, complemented
13C2×C31×#386C211yesmaximal, characteristic, complemented
14C2×C31×#385C211yesmaximal, characteristic, complemented
15C2×C31×#380C211yesmaximal, characteristic, complemented
16C22×C31×#95C211yesmaximal, characteristic, complemented
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C23×D4×C31C2211yescharacteristic
20C24×C4×C31C2211yescharacteristic
21C24×C4×C31C2211yescharacteristic
22C24×C4×C31C2211yescharacteristic
23C24×C4×C31C2211yescharacteristic
24C2×C31×#123—28no—
25C2×C31×#123—28no—
26C2×C31×#123C2218yescomplemented
27C2×C31×#123C2218yescomplemented
28C2×C31×#121—28no—
29C2×C31×#121C2218yes—
30C2×C4×D4×C31—28no—
31C2×C4×D4×C31C2218yescomplemented
32C22×C4⋊C4×C31C2211yescharacteristic
33C22×C4⋊C4×C31C2211yescharacteristic
34C22×C4⋊C4×C31C2211yescharacteristic
35C22×C4⋊C4×C31C2211yescharacteristic
36C22×C4⋊C4×C31C2211yescharacteristic
37C22×C4⋊C4×C31C2211yescharacteristic
38C22×C4⋊C4×C31C2211yescharacteristic
39C22×C4⋊C4×C31C2211yescharacteristic
40C22×C22⋊C4×C31C2211yescharacteristic
41C22×C22⋊C4×C31C2211yescharacteristic
42C22×C22⋊C4×C31C2211yescharacteristic
43C22×C22⋊C4×C31C2211yescharacteristic
44C22×C22⋊C4×C31C2211yescharacteristic
45C22×C22⋊C4×C31C2211yescharacteristic
46C22×C22⋊C4×C31C2211yescharacteristic
47C22×C22⋊C4×C31C2211yescharacteristic
48C22×C22⋊C4×C31C2211yescharacteristic
49C22×C22⋊C4×C31C2211yescharacteristic
50C22×C22⋊C4×C31C2211yescharacteristic
51C22×C42×C31C2211yescharacteristic
52C31×#398C2218yescomplemented
53C31×#397C2218yescomplemented
54C31×#396C2218yescomplemented
55C31×#394C2218yescomplemented
56C31×#389C2218yescomplemented
57C31×#388C2218yescomplemented
58C31×#386C2218yescomplemented
59C31×#386C2218yescomplemented
60C31×#385C2218yescomplemented
61C31×#380C2218yescomplemented
62C2×C31×#95C2211yescharacteristic
63C2×C31×#95C2211yescharacteristic
64C2×C31×#95C2211yescharacteristic
65C2×C31×#95C2211yescharacteristic
66C2×C31×#95C2211yescharacteristic
67C2×C31×#95C2211yescharacteristic
68C2×C31×#95C2211yescharacteristic
69C2×C31×#95C2211yescharacteristic
70C2×C31×#95C2218yescomplemented
71C25×C31C2311yescharacteristic
72C25×C31C2311yescharacteristic
73C25×C31C2311yescharacteristic
74C22×D4×C31—24no—
75C22×D4×C31—24no—
76C22×D4×C31—24no—
77C22×D4×C31—24no—
78C22×D4×C31—24no—
79C22×D4×C31—24no—
80C22×D4×C31—24no—
81C22×D4×C31—42no—
82C22×D4×C31D418yes—
83C22×D4×C31C2314yes—
84C22×D4×C31C2314yes—
85C22×D4×C31C2314yes—
86C23×C4×C31—24no—
87C23×C4×C31—24no—
88C23×C4×C31—24no—
89C23×C4×C31—24no—
90C23×C4×C31—24no—
91C23×C4×C31—24no—
92C23×C4×C31—24no—
93C23×C4×C31—24no—
94C23×C4×C31—24no—
95C23×C4×C31—42no—
96C23×C4×C31—42no—
97C23×C4×C31—42no—
98C23×C4×C31C2314yes—
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2311yescharacteristic
101C23×C4×C31C2311yescharacteristic
102C23×C4×C31C2311yescharacteristic
103C23×C4×C31C2311yescharacteristic
104C23×C4×C31C2311yescharacteristic
105C23×C4×C31C2311yescharacteristic
106C23×C4×C31C2314yes—
107C23×C4×C31C2314yes—
108C23×C4×C31C2314yes—
109C23×C4×C31C2311yescharacteristic
110C23×C4×C31C2311yescharacteristic
111C23×C4×C31C2311yescharacteristic
112C23×C4×C31C2311yescharacteristic
113C23×C4×C31C2311yescharacteristic
114C31×#123—232no—
115C31×#123—232no—
116C31×#121—232no—
117C4×D4×C31—232no—
118C2×C4⋊C4×C31—24no—
119C2×C4⋊C4×C31—24no—
120C2×C4⋊C4×C31—24no—
121C2×C4⋊C4×C31—24no—
122C2×C4⋊C4×C31—24no—
123C2×C4⋊C4×C31—24no—
124C2×C4⋊C4×C31—24no—
125C2×C4⋊C4×C31—42no—
126C2×C4⋊C4×C31C2314yes—
127C2×C4⋊C4×C31C2314yes—
128C2×C4⋊C4×C31C2314yes—
129C2×C4⋊C4×C31C2314yes—
130C2×C4⋊C4×C31C2314yes—
131C2×C4⋊C4×C31C2314yes—
132C2×C4⋊C4×C31C2314yes—
133C2×C4⋊C4×C31C2314yes—
134C2×C22⋊C4×C31—24no—
135C2×C22⋊C4×C31—24no—
136C2×C22⋊C4×C31—24no—
137C2×C22⋊C4×C31—24no—
138C2×C22⋊C4×C31—24no—
139C2×C22⋊C4×C31—24no—
140C2×C22⋊C4×C31—24no—
141C2×C22⋊C4×C31—24no—
142C2×C22⋊C4×C31—24no—
143C2×C22⋊C4×C31—42no—
144C2×C22⋊C4×C31D418yescomplemented
145C2×C22⋊C4×C31C2314yes—
146C2×C22⋊C4×C31C2314yes—
147C2×C22⋊C4×C31C2314yes—
148C2×C22⋊C4×C31C2314yes—
149C2×C22⋊C4×C31C2314yes—
150C2×C22⋊C4×C31C2314yes—
151C2×C22⋊C4×C31C2314yes—
152C2×C22⋊C4×C31C2314yes—
153C2×C22⋊C4×C31C2314yes—
154C2×C22⋊C4×C31C2314yes—
155C2×C22⋊C4×C31C2314yes—
156C2×C42×C31—24no—
157C2×C42×C31C2314yes—
158C31×#95C2314yes—
159C31×#95C2314yes—
160C31×#95C2314yes—
161C31×#95C2314yes—
162C31×#95C2314yes—
163C31×#95C2314yes—
164C31×#95C2314yes—
165C31×#95C2314yes—
166C24×C31—22no—
167C24×C31—22no—
168C24×C31—22no—
169C24×C31—22no—
170C24×C31—22no—
171C24×C31—22no—
172C24×C31—22no—
173C24×C31—22no—
174C24×C31—22no—
175C24×C31—22no—
176C24×C31—22no—
177C24×C31—22no—
178C24×C31—22no—
179C24×C31—22no—
180C24×C31—22no—
181C24×C31—22no—
182C24×C31—22no—
183C24×C31C2×D414yes—
184C24×C31C2×D414yes—
185C24×C31C2×D414yes—
186C24×C31#4114yes—
187C24×C31C2412yes—
188C24×C31C2412yes—
189C24×C31C2412yes—
190C24×C31C2411yescharacteristic
191C2×D4×C31—232no—
192C2×D4×C31—28no—
193C2×D4×C31—28no—
194C2×D4×C31—28no—
195C2×D4×C31—28no—
196C2×D4×C31—28no—
197C2×D4×C31—28no—
198C2×D4×C31—28no—
199C2×D4×C31—44no—
200C2×D4×C31—416no—
201C2×D4×C31—416no—
202C2×D4×C31C2×D4116yes—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—22no—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—28no—
224C22×C4×C31—28no—
225C22×C4×C31—28no—
226C22×C4×C31—28no—
227C22×C4×C31—22no—
228C22×C4×C31—22no—
229C22×C4×C31—28no—
230C22×C4×C31—22no—
231C22×C4×C31—22no—
232C22×C4×C31—22no—
233C22×C4×C31—22no—
234C22×C4×C31—22no—
235C22×C4×C31—22no—
236C22×C4×C31—22no—
237C22×C4×C31—22no—
238C22×C4×C31—22no—
239C22×C4×C31—28no—
240C22×C4×C31—28no—
241C22×C4×C31—28no—
242C22×C4×C31—28no—
243C22×C4×C31—44no—
244C22×C4×C31—44no—
245C22×C4×C31—44no—
246C22×C4×C31—416no—
247C22×C4×C31—416no—
248C22×C4×C31—416no—
249C22×C4×C31—416no—
250C22×C4×C31C2×D414yes—
251C22×C4×C31C2×D414yes—
252C22×C4×C31C2×D414yes—
253C22×C4×C31#4114yes—
254C22×C4×C31#4114yes—
255C22×C4×C31C2412yes—
256C22×C4×C31C2412yes—
257C22×C4×C31C2412yes—
258C22×C4×C31C2412yes—
259C22×C4×C31C2412yes—
260C22×C4×C31C2412yes—
261C22×C4×C31C2412yes—
262C22×C4×C31C2412yes—
263C22×C4×C31C2412yes—
264C22×C4×C31C2412yes—
265C22×C4×C31C2412yes—
266C22×C4×C31C2412yes—
267C4⋊C4×C31—28no—
268C4⋊C4×C31—28no—
269C4⋊C4×C31—28no—
270C4⋊C4×C31—28no—
271C4⋊C4×C31—28no—
272C4⋊C4×C31—28no—
273C4⋊C4×C31—28no—
274C4⋊C4×C31—44no—
275C22⋊C4×C31—28no—
276C22⋊C4×C31—28no—
277C22⋊C4×C31—28no—
278C22⋊C4×C31—28no—
279C22⋊C4×C31—28no—
280C22⋊C4×C31—28no—
281C22⋊C4×C31—28no—
282C22⋊C4×C31—28no—
283C22⋊C4×C31—28no—
284C22⋊C4×C31—44no—
285C22⋊C4×C31C2×D4116yescomplemented
286C42×C31—28no—
287C2×#2425C3111yesmaximal, characteristic, direct product factor, Sylow
288C23×C31—28no—
289C23×C31—28no—
290C23×C31—28no—
291C23×C31—28no—
292C23×C31—28no—
293C23×C31—28no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—22no—
297C23×C31—22no—
298C23×C31—28no—
299C23×C31—28no—
300C23×C31—28no—
301C23×C31—22no—
302C23×C31—22no—
303C23×C31—22no—
304C23×C31—22no—
305C23×C31—22no—
306C23×C31—22no—
307C23×C31—22no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—22no—
311C23×C31—22no—
312C23×C31—22no—
313C23×C31—22no—
314C23×C31—44no—
315C23×C31—44no—
316C23×C31—44no—
317C23×C31—44no—
318C23×C31—44no—
319C23×C31—44no—
320C23×C31—44no—
321C23×C31—44no—
322C23×C31—44no—
323C23×C31—44no—
324C23×C31—44no—
325C23×C31#121116yes—
326C23×C31C22×D414yes—
327C23×C31C22×D414yes—
328C23×C31C22×D414yes—
329C23×C31C22×D412yes—
330C23×C31C22×D412yes—
331C23×C31C2×#4114yes—
332C23×C31C2×#4112yes—
333C23×C31C2×#4112yes—
334C23×C31C2×#4112yes—
335C23×C31H(5,𝔽2)12yes—
336C23×C312−1+412yes—
337C23×C31C2511yescharacteristic
338D4×C31—232no—
339D4×C31—416no—
340D4×C31—416no—
341C2×C4×C31—28no—
342C2×C4×C31—28no—
343C2×C4×C31—28no—
344C2×C4×C31—28no—
345C2×C4×C31—28no—
346C2×C4×C31—22no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—22no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—22no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—22no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—22no—
376C2×C4×C31—22no—
377C2×C4×C31—416no—
378C2×C4×C31—416no—
379C2×C4×C31—416no—
380C2×C4×C31—416no—
381C2×C4×C31—44no—
382C2×C4×C31—44no—
383C2×C4×C31—44no—
384C2×C4×C31—44no—
385C2×C4×C31—44no—
386C2×C4×C31—44no—
387C2×C4×C31—44no—
388C2×C4×C31C22×D414yes—
389C2×C4×C31C22×D414yes—
390C2×C4×C31C22×D414yes—
391C2×C4×C31C2×#4114yes—
392C2×C4×C31C2×#4114yes—
393C22×#123C2×C3111yescharacteristic, complemented
394C22×#123C2×C3111yescharacteristic, complemented
395C22×#121C2×C3111yescharacteristic
396C22×C4×D4C2×C3111yescharacteristic, complemented
397#2425C2×C31116yesdirect product factor
398C2×#398C2×C3111yescharacteristic, complemented
399C2×#397C2×C3111yescharacteristic, complemented
400C2×#396C2×C3111yescharacteristic, complemented
401C2×#394C2×C3111yescharacteristic, complemented
402C2×#389C2×C3111yescharacteristic, complemented
403C2×#388C2×C3111yescharacteristic, complemented
404C2×#386C2×C3111yescharacteristic, complemented
405C2×#386C2×C3111yescharacteristic, complemented
406C2×#385C2×C3111yescharacteristic, complemented
407C2×#380C2×C3111yescharacteristic, complemented
408C22×#95C2×C3111yescharacteristic, complemented
409C22×C31—24no—
410C22×C31—232no—
411C22×C31—24no—
412C22×C31—24no—
413C22×C31—24no—
414C22×C31—24no—
415C22×C31—24no—
416C22×C31—24no—
417C22×C31—24no—
418C22×C31—24no—
419C22×C31—42no—
420C22×C31—416no—
421C22×C31—42no—
422C22×C31—42no—
423C22×C31—42no—
424C22×C31—42no—
425C22×C31—42no—
426C22×C31—42no—
427C22×C31—42no—
428C22×C31—42no—
429C22×C31—42no—
430C22×C31—42no—
431C22×C31—88no—
432C22×C31C2×#12118yes—
433C22×C31C2×#12114yes—
434C22×C31#52914yes—
435C22×C31#53914yes—
436C22×C31#54614yes—
437C22×C31#54614yes—
438C22×C31#54714yes—
439C22×C31#54714yes—
440C22×C31C23×D411yescharacteristic
441C22×C31C23×D411yescharacteristic
442C22×C31C22×#4111yescharacteristic
443C22×C31C22×#4111yescharacteristic
444C22×C31C22×#4111yescharacteristic
445C22×C31C2×H(5,𝔽2)11yescharacteristic
446C22×C31C2×2−1+411yescharacteristic
447C4×C31—24no—
448C4×C31—24no—
449C4×C31—24no—
450C4×C31—24no—
451C4×C31—24no—
452C4×C31—42no—
453C4×C31—42no—
454C4×C31—42no—
455C4×C31—42no—
456C4×C31—42no—
457C4×C31—42no—
458C4×C31—42no—
459C23×D4C22×C3111yescharacteristic
460C23×D4C22×C3111yescharacteristic
461C23×D4C22×C3111yescharacteristic
462C24×C4C22×C3111yescharacteristic
463C24×C4C22×C3111yescharacteristic
464C24×C4C22×C3111yescharacteristic
465C24×C4C22×C3111yescharacteristic
466C2×#123—28no—
467C2×#123—28no—
468C2×#123C22×C3118yescomplemented
469C2×#123C22×C3118yescomplemented
470C2×#121—28no—
471C2×#121C22×C3118yes—
472C2×C4×D4—28no—
473C2×C4×D4C22×C3118yescomplemented
474C22×C4⋊C4C22×C3111yescharacteristic
475C22×C4⋊C4C22×C3111yescharacteristic
476C22×C4⋊C4C22×C3111yescharacteristic
477C22×C4⋊C4C22×C3111yescharacteristic
478C22×C4⋊C4C22×C3111yescharacteristic
479C22×C4⋊C4C22×C3111yescharacteristic
480C22×C4⋊C4C22×C3111yescharacteristic
481C22×C4⋊C4C22×C3111yescharacteristic
482C22×C22⋊C4C22×C3111yescharacteristic
483C22×C22⋊C4C22×C3111yescharacteristic
484C22×C22⋊C4C22×C3111yescharacteristic
485C22×C22⋊C4C22×C3111yescharacteristic
486C22×C22⋊C4C22×C3111yescharacteristic
487C22×C22⋊C4C22×C3111yescharacteristic
488C22×C22⋊C4C22×C3111yescharacteristic
489C22×C22⋊C4C22×C3111yescharacteristic
490C22×C22⋊C4C22×C3111yescharacteristic
491C22×C22⋊C4C22×C3111yescharacteristic
492C22×C22⋊C4C22×C3111yescharacteristic
493C22×C42C22×C3111yescharacteristic
494#398C22×C3118yescomplemented
495#397C22×C3118yescomplemented
496#396C22×C3118yescomplemented
497#394C22×C3118yescomplemented
498#389C22×C3118yescomplemented
499#388C22×C3118yescomplemented
500#386C22×C3118yescomplemented
501#386C22×C3118yescomplemented
502#385C22×C3118yescomplemented
503#380C22×C3118yescomplemented
504C2×#95C22×C3111yescharacteristic
505C2×#95C22×C3111yescharacteristic
506C2×#95C22×C3111yescharacteristic
507C2×#95C22×C3111yescharacteristic
508C2×#95C22×C3111yescharacteristic
509C2×#95C22×C3111yescharacteristic
510C2×#95C22×C3111yescharacteristic
511C2×#95C22×C3111yescharacteristic
512C2×#95C22×C3118yescomplemented
513C2×C31—28no—
514C2×C31—44no—
515C2×C31—82no—
516C2×C31#242518yesdirect product factor
517C2×C31C22×#12111yescharacteristic
518C2×C31C2×#52911yescharacteristic
519C2×C31C2×#53911yescharacteristic
520C2×C31C2×#54611yescharacteristic
521C2×C31C2×#54611yescharacteristic
522C2×C31C2×#54711yescharacteristic
523C2×C31C2×#54711yescharacteristic
524C25C23×C3111yescharacteristic
525C25C23×C3111yescharacteristic
526C25C23×C3111yescharacteristic
527C22×D4—24no—
528C22×D4—24no—
529C22×D4—24no—
530C22×D4—24no—
531C22×D4—24no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—42no—
535C22×D4D4×C3118yes—
536C22×D4C23×C3114yes—
537C22×D4C23×C3114yes—
538C22×D4C23×C3114yes—
539C23×C4—24no—
540C23×C4—24no—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—24no—
546C23×C4—24no—
547C23×C4—24no—
548C23×C4—42no—
549C23×C4—42no—
550C23×C4—42no—
551C23×C4C23×C3111yescharacteristic
552C23×C4C23×C3111yescharacteristic
553C23×C4C23×C3111yescharacteristic
554C23×C4C23×C3111yescharacteristic
555C23×C4C23×C3111yescharacteristic
556C23×C4C23×C3111yescharacteristic
557C23×C4C23×C3111yescharacteristic
558C23×C4C23×C3114yes—
559C23×C4C23×C3114yes—
560C23×C4C23×C3114yes—
561C23×C4C23×C3114yes—
562C23×C4C23×C3111yescharacteristic
563C23×C4C23×C3111yescharacteristic
564C23×C4C23×C3111yescharacteristic
565C23×C4C23×C3111yescharacteristic
566C23×C4C23×C3111yescharacteristic
567#123—232no—
568#123—232no—
569#121—232no—
570C4×D4—232no—
571C2×C4⋊C4—24no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4—24no—
578C2×C4⋊C4—42no—
579C2×C4⋊C4C23×C3114yes—
580C2×C4⋊C4C23×C3114yes—
581C2×C4⋊C4C23×C3114yes—
582C2×C4⋊C4C23×C3114yes—
583C2×C4⋊C4C23×C3114yes—
584C2×C4⋊C4C23×C3114yes—
585C2×C4⋊C4C23×C3114yes—
586C2×C4⋊C4C23×C3114yes—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4D4×C3118yescomplemented
598C2×C22⋊C4C23×C3114yes—
599C2×C22⋊C4C23×C3114yes—
600C2×C22⋊C4C23×C3114yes—
601C2×C22⋊C4C23×C3114yes—
602C2×C22⋊C4C23×C3114yes—
603C2×C22⋊C4C23×C3114yes—
604C2×C22⋊C4C23×C3114yes—
605C2×C22⋊C4C23×C3114yes—
606C2×C22⋊C4C23×C3114yes—
607C2×C22⋊C4C23×C3114yes—
608C2×C22⋊C4C23×C3114yes—
609C2×C42—24no—
610C2×C42C23×C3114yes—
611#95C23×C3114yes—
612#95C23×C3114yes—
613#95C23×C3114yes—
614#95C23×C3114yes—
615#95C23×C3114yes—
616#95C23×C3114yes—
617#95C23×C3114yes—
618#95C23×C3114yes—
619C31C2×#242511yescharacteristic, direct product factor, Sylow
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24C2×D4×C3114yes—
638C24C2×D4×C3114yes—
639C24C2×D4×C3114yes—
640C24#41×C3114yes—
641C24C24×C3112yes—
642C24C24×C3112yes—
643C24C24×C3112yes—
644C24C24×C3111yescharacteristic
645C2×D4—232no—
646C2×D4—28no—
647C2×D4—28no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—44no—
654C2×D4—416no—
655C2×D4—416no—
656C2×D4C2×D4×C31116yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—28no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—28no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—416no—
701C22×C4—416no—
702C22×C4—416no—
703C22×C4—416no—
704C22×C4C2×D4×C3114yes—
705C22×C4C2×D4×C3114yes—
706C22×C4C2×D4×C3114yes—
707C22×C4#41×C3114yes—
708C22×C4#41×C3114yes—
709C22×C4C24×C3112yes—
710C22×C4C24×C3112yes—
711C22×C4C24×C3112yes—
712C22×C4C24×C3112yes—
713C22×C4C24×C3112yes—
714C22×C4C24×C3112yes—
715C22×C4C24×C3112yes—
716C22×C4C24×C3112yes—
717C22×C4C24×C3112yes—
718C22×C4C24×C3112yes—
719C22×C4C24×C3112yes—
720C22×C4C24×C3112yes—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—44no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—28no—
736C22⋊C4—28no—
737C22⋊C4—28no—
738C22⋊C4—44no—
739C22⋊C4C2×D4×C31116yescomplemented
740C42—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23C31×#121116yes—
779C23C22×D4×C3114yes—
780C23C22×D4×C3114yes—
781C23C22×D4×C3114yes—
782C23C22×D4×C3112yes—
783C23C22×D4×C3112yes—
784C23C2×#41×C3114yes—
785C23C2×#41×C3112yes—
786C23C2×#41×C3112yes—
787C23C2×#41×C3112yes—
788C23C31×H(5,𝔽2)12yes—
789C23C31×2−1+412yes—
790C23C25×C3111yescharacteristic
791D4—232no—
792D4—416no—
793D4—416no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—416no—
831C2×C4—416no—
832C2×C4—416no—
833C2×C4—416no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4C22×D4×C3114yes—
842C2×C4C22×D4×C3114yes—
843C2×C4C22×D4×C3114yes—
844C2×C4C2×#41×C3114yes—
845C2×C4C2×#41×C3114yes—
846C22—24no—
847C22—232no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—416no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—88no—
869C22C2×C31×#12118yes—
870C22C2×C31×#12114yes—
871C22C31×#52914yes—
872C22C31×#53914yes—
873C22C31×#54614yes—
874C22C31×#54614yes—
875C22C31×#54714yes—
876C22C31×#54714yes—
877C22C23×D4×C3111yescharacteristic
878C22C23×D4×C3111yescharacteristic
879C22C22×#41×C3111yescharacteristic
880C22C22×#41×C3111yescharacteristic
881C22C22×#41×C3111yescharacteristic
882C22C2×C31×H(5,𝔽2)11yescharacteristic
883C22C2×C31×2−1+411yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—24no—
889C4—42no—
890C4—42no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—42no—
896C2—28no—
897C2—44no—
898C2—82no—
899C2C31×#242518yesdirect product factor
900C2C22×C31×#12111yescharacteristic
901C2C2×C31×#52911yescharacteristic
902C2C2×C31×#53911yescharacteristic
903C2C2×C31×#54611yescharacteristic
904C2C2×C31×#54611yescharacteristic
905C2C2×C31×#54711yescharacteristic
906C2C2×C31×#54711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC23C25×C31
prime radicalC22×C31×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#123C2semidirect
2. C22×C31×#123C2semidirect
4. C22×C4×D4×C31C2semidirect
5. C31×#2425C2direct (N × H)
6. C2×C31×#398C2semidirect
7. C2×C31×#397C2semidirect
8. C2×C31×#396C2semidirect
9. C2×C31×#394C2semidirect
10. C2×C31×#389C2semidirect
11. C2×C31×#388C2semidirect
12. C2×C31×#386C2semidirect
13. C2×C31×#386C2semidirect
14. C2×C31×#385C2semidirect
15. C2×C31×#380C2semidirect
16. C22×C31×#95C2semidirect
26. C2×C31×#123C22semidirect
27. C2×C31×#123C22semidirect
31. C2×C4×D4×C31C22semidirect
52. C31×#398C22semidirect
53. C31×#397C22semidirect
54. C31×#396C22semidirect
55. C31×#394C22semidirect
56. C31×#389C22semidirect
57. C31×#388C22semidirect
58. C31×#386C22semidirect
59. C31×#386C22semidirect
60. C31×#385C22semidirect
61. C31×#380C22semidirect
70. C2×C31×#95C22semidirect
144. C2×C22⋊C4×C31D4semidirect
285. C22⋊C4×C31C2×D4semidirect
287. C2×#2425C31direct (N × H)
393. C22×#123C2×C31semidirect
394. C22×#123C2×C31semidirect
396. C22×C4×D4C2×C31semidirect
397. #2425C2×C31direct (N × H)
398. C2×#398C2×C31semidirect
399. C2×#397C2×C31semidirect
400. C2×#396C2×C31semidirect
401. C2×#394C2×C31semidirect
402. C2×#389C2×C31semidirect
403. C2×#388C2×C31semidirect
404. C2×#386C2×C31semidirect
405. C2×#386C2×C31semidirect
406. C2×#385C2×C31semidirect
407. C2×#380C2×C31semidirect
408. C22×#95C2×C31semidirect
468. C2×#123C22×C31semidirect
469. C2×#123C22×C31semidirect
473. C2×C4×D4C22×C31semidirect
494. #398C22×C31semidirect
495. #397C22×C31semidirect
496. #396C22×C31semidirect
497. #394C22×C31semidirect
498. #389C22×C31semidirect
499. #388C22×C31semidirect
500. #386C22×C31semidirect
501. #386C22×C31semidirect
502. #385C22×C31semidirect
503. #380C22×C31semidirect
512. C2×#95C22×C31semidirect
516. C2×C31#2425direct (N × H)
597. C2×C22⋊C4D4×C31semidirect
619. C31C2×#2425direct (N × H)
739. C22⋊C4C2×D4×C31semidirect
899. C2C31×#2425direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C22×C31×#1212
C22×C4×D4×C312
C31×#24252
C2×C31×#3982
C2×C31×#3972
C2×C31×#3962
C2×C31×#3942
C2×C31×#3892
C2×C31×#3882
C2×C31×#3862
C2×C31×#3852
C2×C31×#3802
C22×C31×#952
C2×#242531