Finite Group Databasebeta

← C31×#33358 #21490117

Subgroups — C31×#33358 #21490117

Order 7936.

1252 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3449C211yesmaximal, characteristic
2C2×C31×#410C212yesmaximal, complemented
3C31×#2129C212yesmaximal, complemented
4C31×#2128C212yesmaximal, complemented
5C31×#2127C214yesmaximal, complemented
6C31×#2126C214yesmaximal, complemented
7C22×#41×C31C411yescharacteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C31×#537—22no—
10C31×#536C412yescomplemented
11C31×#536C411yescharacteristic, complemented
12C31×#536C2211yescharacteristic
13C31×#535C411yescharacteristic, complemented
14C31×#535C2212yes—
15C31×#535C2211yescharacteristic
16C31×#534—22no—
17C31×#532C412yescomplemented
18C31×#532C2212yes—
19C31×#525—22no—
20C31×#525—22no—
21C2×C31×#117—22no—
22C2×C31×#117C411yescharacteristic, complemented
23C31×#410—22no—
24C31×#410—22no—
25C31×#410C2214yes—
26C31×#410C2214yescomplemented
27C2×C31×#99—22no—
28C2×C31×#99C2214yescomplemented
29C31×#354C2218yescomplemented
30C31×#353C2218yescomplemented
31C2×#41×C31—21no—
32C2×#41×C31—21no—
33C2×#41×C31—42no—
34C2×#41×C31—42no—
35C2×#41×C31—42no—
36C2×#41×C31—42no—
37C2×#41×C31C2×C412yes—
38C2×#41×C31C2×C411yescharacteristic
39C2×#41×C31C2×C411yescharacteristic
40C2×#41×C31C2×C412yescomplemented
41C2×#41×C31D412yes—
42C2×#41×C31D412yes—
43C2×#41×C31C2311yescharacteristic
44C2×#41×C31C2311yescharacteristic
45C22×Q8×C31C2×C411yescharacteristic
46C22×Q8×C31C2×C411yescharacteristic, complemented
47C22×D4×C31—21no—
48C22×D4×C31C2×C411yescharacteristic, complemented
49C22×D4×C31D412yes—
50C22×D4×C31C2311yescharacteristic
51C23×C4×C31—21no—
52C23×C4×C31C2×C411yescharacteristic
53C23×C4×C31D412yes—
54C31×C4⋊Q8C2×C412yescomplemented
55C31×C4⋊Q8C2×C412yescomplemented
56C31×#127C2×C412yes—
57C31×#127C2312yes—
58C31×#124C2×C412yes—
59C31×#124C2×C412yescomplemented
60C31×#124C2×C412yescomplemented
61C31×#124C2312yes—
62C31×#123—22no—
63C31×#123—22no—
64C31×#123—24no—
65C31×C22⋊Q8—24no—
66C31×C22⋊Q8—22no—
67C31×C22⋊Q8—22no—
68C31×#121—24no—
69C31×#121—24no—
70C31×#121—24no—
71C31×#121—22no—
72C31×#121—22no—
73C31×#120—24no—
74C31×#120—22no—
75C31×#120—22no—
76C4×D4×C31—24no—
77C4×D4×C31—24no—
78C31×#117—21no—
79C31×#117—21no—
80C31×#117—24no—
81C31×#117—24no—
82C31×#117—42no—
83C31×#117—42no—
84C31×#117C2×C412yes—
85C31×#117C2×C411yescharacteristic, complemented
86C31×#117C2×C411yescharacteristic, complemented
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—42no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—24no—
91C2×C42×C31—42no—
92C2×C42×C31C2×C412yescomplemented
93C31×#99—24no—
94C31×#99—24no—
95C31×#99—24no—
96C31×#99C2318yes—
97C24×C31—21no—
98C24×C31C22⋊C411yescharacteristic
99C24×C31C2×D412yes—
100#41×C31—42no—
101#41×C31—41no—
102#41×C31—41no—
103#41×C31—42no—
104#41×C31—42no—
105#41×C31—42no—
106#41×C31—42no—
107#41×C31—42no—
108#41×C31—41no—
109#41×C31—41no—
110#41×C31—44no—
111#41×C31—44no—
112#41×C31—42no—
113#41×C31—42no—
114#41×C31—42no—
115#41×C31—42no—
116C2×Q8×C31—21no—
117C2×Q8×C31—42no—
118C2×Q8×C31—42no—
119C2×Q8×C31C22⋊C412yes—
120C2×Q8×C31C22×C412yes—
121C2×Q8×C31C22×C411yescharacteristic
122C2×Q8×C31C22×C411yescharacteristic
123C2×D4×C31—22no—
124C2×D4×C31—22no—
125C2×D4×C31—24no—
126C2×D4×C31—24no—
127C2×D4×C31—21no—
128C2×D4×C31—42no—
129C2×D4×C31—42no—
130C2×D4×C31—42no—
131C2×D4×C31—42no—
132C2×D4×C31—44no—
133C2×D4×C31C22⋊C412yes—
134C2×D4×C31C22⋊C412yes—
135C2×D4×C31C22×C412yes—
136C2×D4×C31C22×C411yescharacteristic
137C2×D4×C31C2×D412yes—
138C2×D4×C31C2×D412yes—
139C2×D4×C31C2×D412yes—
140C2×D4×C31C2411yescharacteristic
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—21no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—42no—
152C22×C4×C31—42no—
153C22×C4×C31—44no—
154C22×C4×C31C22⋊C411yescharacteristic
155C22×C4×C31C22⋊C411yescharacteristic
156C22×C4×C31C22⋊C412yes—
157C22×C4×C31C22⋊C412yes—
158C22×C4×C31C22⋊C412yes—
159C22×C4×C31C22⋊C411yescharacteristic
160C22×C4×C31C22×C411yescharacteristic
161C22×C4×C31C22×C411yescharacteristic
162C22×C4×C31C22×C411yescharacteristic
163C22×C4×C31C2×D412yes—
164C22×C4×C31C2×D412yes—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31—24no—
169C4⋊C4×C31—24no—
170C4⋊C4×C31—44no—
171C4⋊C4×C31—44no—
172C22⋊C4×C31—22no—
173C22⋊C4×C31—21no—
174C22⋊C4×C31—21no—
175C22⋊C4×C31—24no—
176C22⋊C4×C31—24no—
177C22⋊C4×C31—24no—
178C22⋊C4×C31—24no—
179C22⋊C4×C31—28no—
180C22⋊C4×C31—44no—
181C42×C31—22no—
182C42×C31—44no—
183C42×C31—44no—
184C42×C31C22×C412yes—
185C42×C31C22×C412yes—
186#33358C3111yesmaximal, characteristic, direct product factor, Sylow
187C23×C31—22no—
188C23×C31—22no—
189C23×C31—22no—
190C23×C31—22no—
191C23×C31—42no—
192C23×C31—82no—
193C23×C31—81no—
194C23×C31—82no—
195C23×C31C2×C22⋊C411yescharacteristic
196C23×C31C2×C22⋊C412yes—
197C23×C31C2×C22⋊C411yescharacteristic
198C23×C31C2×C22⋊C411yescharacteristic
199C23×C31C22×D412yes—
200Q8×C31—42no—
201Q8×C31—41no—
202Q8×C31—41no—
203Q8×C31—42no—
204Q8×C31—42no—
205D4×C31—42no—
206D4×C31—42no—
207D4×C31—41no—
208D4×C31—42no—
209D4×C31—42no—
210D4×C31—42no—
211D4×C31—41no—
212D4×C31—42no—
213D4×C31—44no—
214D4×C31—44no—
215D4×C31—42no—
216D4×C31—84no—
217D4×C31—84no—
218C2×C4×C31—22no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—22no—
223C2×C4×C31—22no—
224C2×C4×C31—21no—
225C2×C4×C31—22no—
226C2×C4×C31—22no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—22no—
230C2×C4×C31—21no—
231C2×C4×C31—22no—
232C2×C4×C31—21no—
233C2×C4×C31—22no—
234C2×C4×C31—21no—
235C2×C4×C31—22no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—44no—
239C2×C4×C31—42no—
240C2×C4×C31—42no—
241C2×C4×C31—42no—
242C2×C4×C31—48no—
243C2×C4×C31—82no—
244C2×C4×C31—88no—
245C2×C4×C31#9912yes—
246C2×C4×C31#9912yes—
247C2×C4×C31C2×C22⋊C412yes—
248C2×C4×C31C2×C22⋊C412yes—
249C2×C4×C31C2×C22⋊C411yescharacteristic
250C2×C4×C31C2×C22⋊C411yescharacteristic
251C2×C4×C31C2×C22⋊C411yescharacteristic
252C2×C4×C31C23×C411yescharacteristic
253#3449C2×C3111yescharacteristic
254C2×#410C2×C3112yescomplemented
255#2129C2×C3112yescomplemented
256#2128C2×C3112yescomplemented
257#2127C2×C3114yescomplemented
258#2126C2×C3114yescomplemented
259C22×C31—22no—
260C22×C31—21no—
261C22×C31—21no—
262C22×C31—22no—
263C22×C31—41no—
264C22×C31—41no—
265C22×C31—42no—
266C22×C31—42no—
267C22×C31—41no—
268C22×C31—44no—
269C22×C31—44no—
270C22×C31—42no—
271C22×C31—82no—
272C22×C31—82no—
273C22×C31—84no—
274C22×C31C2×#9912yes—
275C22×C31C22×C22⋊C411yescharacteristic
276C4×C31—21no—
277C4×C31—22no—
278C4×C31—22no—
279C4×C31—21no—
280C4×C31—42no—
281C4×C31—42no—
282C4×C31—42no—
283C4×C31—88no—
284C4×C31C2×#9911yescharacteristic
285C4×C31C2×#9912yes—
286C4×C31C2×#9911yescharacteristic
287C22×#41C4×C3111yescharacteristic, complemented
288C22×#41C22×C3111yescharacteristic
289#537—22no—
290#536C4×C3112yescomplemented
291#536C4×C3111yescharacteristic, complemented
292#536C22×C3111yescharacteristic
293#535C4×C3111yescharacteristic, complemented
294#535C22×C3112yes—
295#535C22×C3111yescharacteristic
296#534—22no—
297#532C4×C3112yescomplemented
298#532C22×C3112yes—
299#525—22no—
300#525—22no—
301C2×#117—22no—
302C2×#117C4×C3111yescharacteristic, complemented
303#410—22no—
304#410—22no—
305#410C22×C3114yes—
306#410C22×C3114yescomplemented
307C2×#99—22no—
308C2×#99C22×C3114yescomplemented
309#354C22×C3118yescomplemented
310#353C22×C3118yescomplemented
311C2×C31—21no—
312C2×C31—22no—
313C2×C31—42no—
314C2×C31—42no—
315C2×C31—41no—
316C2×C31—41no—
317C2×C31—82no—
318C2×C31C22×#9911yescharacteristic
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—42no—
322C2×#41—42no—
323C2×#41—42no—
324C2×#41—42no—
325C2×#41C2×C4×C3112yes—
326C2×#41C2×C4×C3111yescharacteristic
327C2×#41C2×C4×C3111yescharacteristic
328C2×#41C2×C4×C3112yescomplemented
329C2×#41D4×C3112yes—
330C2×#41D4×C3112yes—
331C2×#41C23×C3111yescharacteristic
332C2×#41C23×C3111yescharacteristic
333C22×Q8C2×C4×C3111yescharacteristic
334C22×Q8C2×C4×C3111yescharacteristic, complemented
335C22×D4—21no—
336C22×D4C2×C4×C3111yescharacteristic, complemented
337C22×D4D4×C3112yes—
338C22×D4C23×C3111yescharacteristic
339C23×C4—21no—
340C23×C4C2×C4×C3111yescharacteristic
341C23×C4D4×C3112yes—
342C4⋊Q8C2×C4×C3112yescomplemented
343C4⋊Q8C2×C4×C3112yescomplemented
344#127C2×C4×C3112yes—
345#127C23×C3112yes—
346#124C2×C4×C3112yes—
347#124C2×C4×C3112yescomplemented
348#124C2×C4×C3112yescomplemented
349#124C23×C3112yes—
350#123—22no—
351#123—22no—
352#123—24no—
353C22⋊Q8—24no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356#121—24no—
357#121—24no—
358#121—24no—
359#121—22no—
360#121—22no—
361#120—24no—
362#120—22no—
363#120—22no—
364C4×D4—24no—
365C4×D4—24no—
366#117—21no—
367#117—21no—
368#117—24no—
369#117—24no—
370#117—42no—
371#117—42no—
372#117C2×C4×C3112yes—
373#117C2×C4×C3111yescharacteristic, complemented
374#117C2×C4×C3111yescharacteristic, complemented
375C2×C4⋊C4—21no—
376C2×C4⋊C4—42no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—24no—
379C2×C42—42no—
380C2×C42C2×C4×C3112yescomplemented
381#99—24no—
382#99—24no—
383#99—24no—
384#99C23×C3118yes—
385C31#3335811yescharacteristic, direct product factor, Sylow
386C24—21no—
387C24C22⋊C4×C3111yescharacteristic
388C24C2×D4×C3112yes—
389#41—42no—
390#41—41no—
391#41—41no—
392#41—42no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—41no—
397#41—42no—
398#41—41no—
399#41—44no—
400#41—44no—
401#41—42no—
402#41—42no—
403#41—42no—
404#41—42no—
405C2×Q8—21no—
406C2×Q8—42no—
407C2×Q8—42no—
408C2×Q8C22⋊C4×C3112yes—
409C2×Q8C22×C4×C3112yes—
410C2×Q8C22×C4×C3111yescharacteristic
411C2×Q8C22×C4×C3111yescharacteristic
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—44no—
422C2×D4C22⋊C4×C3112yes—
423C2×D4C22⋊C4×C3112yes—
424C2×D4C22×C4×C3112yes—
425C2×D4C22×C4×C3111yescharacteristic
426C2×D4C2×D4×C3112yes—
427C2×D4C2×D4×C3112yes—
428C2×D4C2×D4×C3112yes—
429C2×D4C24×C3111yescharacteristic
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—44no—
443C22×C4C22⋊C4×C3111yescharacteristic
444C22×C4C22⋊C4×C3111yescharacteristic
445C22×C4C22⋊C4×C3112yes—
446C22×C4C22⋊C4×C3112yes—
447C22×C4C22⋊C4×C3112yes—
448C22×C4C22⋊C4×C3111yescharacteristic
449C22×C4C22×C4×C3111yescharacteristic
450C22×C4C22×C4×C3111yescharacteristic
451C22×C4C22×C4×C3111yescharacteristic
452C22×C4C2×D4×C3112yes—
453C22×C4C2×D4×C3112yes—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—44no—
460C4⋊C4—44no—
461C22⋊C4—22no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—28no—
469C22⋊C4—44no—
470C42—22no—
471C42—44no—
472C42—44no—
473C42C22×C4×C3112yes—
474C42C22×C4×C3112yes—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—42no—
480C23—82no—
481C23—81no—
482C23—82no—
483C23C2×C22⋊C4×C3111yescharacteristic
484C23C2×C22⋊C4×C3112yes—
485C23C2×C22⋊C4×C3111yescharacteristic
486C23C2×C22⋊C4×C3111yescharacteristic
487C23C22×D4×C3112yes—
488Q8—42no—
489Q8—41no—
490Q8—41no—
491Q8—42no—
492Q8—42no—
493D4—42no—
494D4—42no—
495D4—41no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—41no—
500D4—42no—
501D4—44no—
502D4—44no—
503D4—42no—
504D4—84no—
505D4—84no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—48no—
531C2×C4—82no—
532C2×C4—88no—
533C2×C4C31×#9912yes—
534C2×C4C31×#9912yes—
535C2×C4C2×C22⋊C4×C3112yes—
536C2×C4C2×C22⋊C4×C3112yes—
537C2×C4C2×C22⋊C4×C3111yescharacteristic
538C2×C4C2×C22⋊C4×C3111yescharacteristic
539C2×C4C2×C22⋊C4×C3111yescharacteristic
540C2×C4C23×C4×C3111yescharacteristic
541C22—22no—
542C22—21no—
543C22—21no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—42no—
549C22—41no—
550C22—44no—
551C22—44no—
552C22—42no—
553C22—82no—
554C22—82no—
555C22—84no—
556C22C2×C31×#9912yes—
557C22C22×C22⋊C4×C3111yescharacteristic
558C4—21no—
559C4—22no—
560C4—22no—
561C4—21no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—88no—
566C4C2×C31×#9911yescharacteristic
567C4C2×C31×#9911yescharacteristic
568C4C2×C31×#9912yes—
569C2—21no—
570C2—22no—
571C2—42no—
572C2—42no—
573C2—41no—
574C2—41no—
575C2—82no—
576C2C22×C31×#9911yescharacteristic
subgroupG/H
centerC4×C31C2×#99
commutatorC2×C4C23×C4×C31
Frattini, cosocleC2×D4C24×C31
socleC2×C31C22×#99
prime radicalC31×#3449C2
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C22×C4×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#410C2semidirect
3. C31×#2129C2semidirect
4. C31×#2128C2semidirect
5. C31×#2127C2semidirect
6. C31×#2126C2semidirect
7. C22×#41×C31C4semidirect
10. C31×#536C4semidirect
11. C31×#536C4semidirect
13. C31×#535C4semidirect
17. C31×#532C4semidirect
22. C2×C31×#117C4semidirect
26. C31×#410C22semidirect
28. C2×C31×#99C22semidirect
29. C31×#354C22semidirect
30. C31×#353C22semidirect
40. C2×#41×C31C2×C4semidirect
46. C22×Q8×C31C2×C4semidirect
48. C22×D4×C31C2×C4semidirect
54. C31×C4⋊Q8C2×C4semidirect
55. C31×C4⋊Q8C2×C4semidirect
59. C31×#124C2×C4semidirect
60. C31×#124C2×C4semidirect
85. C31×#117C2×C4semidirect
86. C31×#117C2×C4semidirect
92. C2×C42×C31C2×C4semidirect
186. #33358C31direct (N × H)
254. C2×#410C2×C31semidirect
255. #2129C2×C31semidirect
256. #2128C2×C31semidirect
257. #2127C2×C31semidirect
258. #2126C2×C31semidirect
287. C22×#41C4×C31semidirect
290. #536C4×C31semidirect
291. #536C4×C31semidirect
293. #535C4×C31semidirect
297. #532C4×C31semidirect
302. C2×#117C4×C31semidirect
306. #410C22×C31semidirect
308. C2×#99C22×C31semidirect
309. #354C22×C31semidirect
310. #353C22×C31semidirect
328. C2×#41C2×C4×C31semidirect
334. C22×Q8C2×C4×C31semidirect
336. C22×D4C2×C4×C31semidirect
342. C4⋊Q8C2×C4×C31semidirect
343. C4⋊Q8C2×C4×C31semidirect
347. #124C2×C4×C31semidirect
348. #124C2×C4×C31semidirect
373. #117C2×C4×C31semidirect
374. #117C2×C4×C31semidirect
380. C2×C42C2×C4×C31semidirect
385. C31#33358direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34492
C2×C31×#4102
C31×#21292
C31×#21282
C31×#21272
C31×#21262
#3335831