Finite Group Databasebeta

← C4×#1343 #128759

Subgroups — C4×#1343 #128759

Order 512.

1172 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 1172 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#392C211yesmaximal, characteristic
2C2×#1343C212yesmaximal
3C4×#342C211yesmaximal, characteristic, complemented
4C4×#323C211yesmaximal, characteristic, complemented
5#7250C212yesmaximal, complemented
6C22×C4×D4—21no—
7C22×C4×D4C411yescharacteristic, complemented
8C2×#392C2211yescharacteristic
9C2×C4×C22⋊C4—21no—
10C2×C4×C22⋊C4—21no—
11C2×C4×C22⋊C4C2211yescharacteristic
12C4×C22⋊C8—21no—
13C2×#342—21no—
14C2×#342C2212yes—
15C2×#323C2212yes—
16#1444C411yescharacteristic, complemented
17#1439—21no—
18#1439C2211yescharacteristic
19#1438—21no—
20#1438C411yescharacteristic, complemented
21C4×#95C411yescharacteristic, complemented
22#1343C418yesdirect product factor
23#1280—21no—
24C23×D4—21no—
25C23×D4C2×C411yescharacteristic
26C24×C4—21no—
27C24×C4D411yescharacteristic
28C2×C4×D4—44no—
29C2×C4×D4—41no—
30C2×C4×D4—41no—
31C2×C4×D4—44no—
32C2×C4×D4—42no—
33C2×C4×D4—42no—
34C2×C4×D4—44no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C22⋊C4—22no—
38C22×C22⋊C4—21no—
39C22×C22⋊C4—21no—
40C22×C22⋊C4—21no—
41C22×C22⋊C4—21no—
42C22×C22⋊C4—21no—
43C22×C22⋊C4D411yescharacteristic
44C22×C22⋊C4C2311yescharacteristic
45C22×C42—21no—
46C22×C42—41no—
47C22×C42C2×C411yescharacteristic
48C22×C42D411yescharacteristic
49C2×C22⋊C8—22no—
50C2×C4×C8—41no—
51#392—22no—
52#392C2×C414yes—
53C4×C22⋊C4—24no—
54C4×C22⋊C4—41no—
55C4×C22⋊C4—41no—
56C4×C22⋊C4—44no—
57C4×C22⋊C4—42no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—41no—
62C2×#95C2×C411yescharacteristic
63C2×#95C2×C411yescharacteristic
64C2×#95C2×C411yescharacteristic
65C2×#95D411yescharacteristic
66#342—24no—
67#342—22no—
68#342C2×C414yescomplemented
69#336—41no—
70#323—22no—
71#323C2×C414yescomplemented
72C25—21no—
73C25C2×D411yescharacteristic
74C22×D4—24no—
75C22×D4—21no—
76C22×D4—41no—
77C22×D4—41no—
78C22×D4—42no—
79C22×D4—42no—
80C22×D4—42no—
81C22×D4—42no—
82C22×D4—41no—
83C22×D4—41no—
84C22×D4—42no—
85C22×D4—42no—
86C22×D4—42no—
87C22×D4C4212yescomplemented
88C23×C4—21no—
89C23×C4—21no—
90C23×C4—21no—
91C23×C4—22no—
92C23×C4—24no—
93C23×C4—21no—
94C23×C4—21no—
95C23×C4—42no—
96C23×C4—42no—
97C23×C4—42no—
98C23×C4—42no—
99C23×C4—42no—
100C23×C4—42no—
101C23×C4—41no—
102C23×C4—41no—
103C23×C4—42no—
104C23×C4—42no—
105C23×C4C22⋊C411yescharacteristic
106C23×C4C22⋊C411yescharacteristic
107C23×C4C22⋊C411yescharacteristic
108C23×C4C22⋊C411yescharacteristic
109C23×C4D812yes—
110C23×C4SD1612yes—
111C23×C4C22×C411yescharacteristic
112C23×C4C2×D411yescharacteristic
113C22×C8—42no—
114C4×D4—44no—
115C4×D4—416no—
116C4×D4—416no—
117C4×D4—44no—
118C4×D4—44no—
119C4×D4—44no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—42no—
122C2×C4⋊C4—42no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—42no—
125C2×C22⋊C4—24no—
126C2×C22⋊C4—24no—
127C2×C22⋊C4—24no—
128C2×C22⋊C4—22no—
129C2×C22⋊C4—22no—
130C2×C22⋊C4—24no—
131C2×C22⋊C4—41no—
132C2×C22⋊C4—41no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—42no—
135C2×C22⋊C4—42no—
136C2×C22⋊C4—42no—
137C2×C22⋊C4—42no—
138C2×C22⋊C4—42no—
139C2×C22⋊C4—42no—
140C2×C22⋊C4—42no—
141C2×C22⋊C4—42no—
142C2×C22⋊C4—42no—
143C2×C22⋊C4—42no—
144C2×C22⋊C4—42no—
145C2×C22⋊C4—42no—
146C2×C22⋊C4—41no—
147C2×C22⋊C4—42no—
148C2×C22⋊C4—41no—
149C2×C22⋊C4—42no—
150C2×C22⋊C4—42no—
151C2×C22⋊C4—42no—
152C2×C22⋊C4C22×C412yes—
153C2×C22⋊C4#4112yes—
154C2×C42—24no—
155C2×C42—21no—
156C2×C42—21no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—42no—
160C2×C42—42no—
161C2×C42—42no—
162C2×C42—42no—
163C2×C42—44no—
164C2×C42—82no—
165C2×C42—82no—
166C22⋊C8—24no—
167C22⋊C8—42no—
168C4×C8—82no—
169#95—21no—
170#95—41no—
171#95—41no—
172#95—41no—
173#95—42no—
174#95—42no—
175#95—42no—
176#95—44no—
177#95C4212yescomplemented
178C24—21no—
179C24—21no—
180C24—21no—
181C24—21no—
182C24—22no—
183C24—22no—
184C24—22no—
185C24—41no—
186C24—41no—
187C24—41no—
188C24—41no—
189C24—41no—
190C24—41no—
191C24—41no—
192C24—41no—
193C24—41no—
194C24—41no—
195C24—41no—
196C24—41no—
197C24—41no—
198C24—41no—
199C24—41no—
200C24—41no—
201C24C2×C22⋊C411yescharacteristic
202C24C4×D412yes—
203C24C2×D811yescharacteristic
204C24C2×SD1611yescharacteristic
205C24#13512yes—
206C2×D4—42no—
207C2×D4—48no—
208C2×D4—42no—
209C2×D4—48no—
210C2×D4—44no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—44no—
214C2×D4—44no—
215C2×D4—42no—
216C2×D4—48no—
217C2×D4—44no—
218C2×D4—44no—
219C2×D4—48no—
220C2×D4—48no—
221C2×D4—42no—
222C2×D4—44no—
223C2×D4—44no—
224C2×D4—44no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—48no—
251C22×C4—48no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—44no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—44no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—84no—
285C22×C4—81no—
286C22×C4—81no—
287C22×C4—82no—
288C22×C4—84no—
289C22×C4—84no—
290C22×C4—82no—
291C22×C4—82no—
292C22×C4—82no—
293C22×C4—82no—
294C22×C4—82no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4#9911yescharacteristic
298C22×C4#9911yescharacteristic
299C22×C4#10212yes—
300C22×C4#10212yes—
301C22×C4#10412yes—
302C22×C4#10412yes—
303C22×C4C2×C4211yescharacteristic
304C22×C4#11711yescharacteristic
305C22×C4C4×D412yes—
306C2×C8—44no—
307C2×C8—82no—
308C2×C8—82no—
309C4⋊C4—42no—
310C4⋊C4—48no—
311C4⋊C4—42no—
312C22⋊C4—28no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—44no—
316C22⋊C4—48no—
317C22⋊C4—44no—
318C22⋊C4—44no—
319C22⋊C4—48no—
320C22⋊C4—48no—
321C22⋊C4—44no—
322C22⋊C4—44no—
323C22⋊C4—48no—
324C22⋊C4—44no—
325C42—42no—
326C42—48no—
327C42—42no—
328C42—42no—
329C42—81no—
330C42—88no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—22no—
338C23—22no—
339C23—22no—
340C23—21no—
341C23—21no—
342C23—22no—
343C23—24no—
344C23—41no—
345C23—41no—
346C23—42no—
347C23—42no—
348C23—41no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—81no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23—81no—
383C23—81no—
384C23—81no—
385C23—81no—
386C23—81no—
387C23—81no—
388C23—81no—
389C23—81no—
390C23—81no—
391C23—81no—
392C23—81no—
393C23—81no—
394C23—81no—
395C23—81no—
396C23C4×C22⋊C411yescharacteristic
397C23C2×#9911yescharacteristic
398C23#41011yescharacteristic
399C23C2×#10211yescharacteristic
400C23#41611yescharacteristic
401C23C2×#10411yescharacteristic
402C23C2×#10411yescharacteristic
403C23C4×D812yes—
404C23C4×SD1612yes—
405D4—44no—
406D4—416no—
407D4—416no—
408D4—44no—
409D4—44no—
410D4—44no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—48no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—88no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—84no—
465C2×C4—84no—
466C2×C4—84no—
467C2×C4—84no—
468C2×C4—84no—
469C2×C4—84no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—88no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4#32712yes—
477C2×C4#32712yes—
478C2×C4AΣL(1,𝔽16)12yes—
479C2×C4#35312yes—
480C8—84no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—22no—
494C22—22no—
495C22—42no—
496C22—42no—
497C22—44no—
498C22—44no—
499C22—42no—
500C22—42no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—42no—
506C22—42no—
507C22—44no—
508C22—81no—
509C22—81no—
510C22—82no—
511C22—82no—
512C22—82no—
513C22—82no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—82no—
523C22—82no—
524C22C2×#32711yescharacteristic
525C22#150011yescharacteristic
526C22#150111yescharacteristic
527C22#150211yescharacteristic
528C22C4×#9911yescharacteristic
529C22C4×#10411yescharacteristic
530C22C4×#10211yescharacteristic
531C22C2×AΣL(1,𝔽16)11yescharacteristic
532C22#212011yescharacteristic
533C22C2×#35311yescharacteristic
534C22#212611yescharacteristic
535C4—22no—
536C4—44no—
537C4—41no—
538C4—41no—
539C4—42no—
540C4—42no—
541C4—42no—
542C4—82no—
543C4—88no—
544C4—82no—
545C4—81no—
546C4#134314yesdirect product factor
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—42no—
552C2—42no—
553C2—84no—
554C2C4×#32711yescharacteristic
555C2C2×#134311yescharacteristic
556C2#1169111yescharacteristic
557C2#1172511yescharacteristic
558C2#1172611yescharacteristic
559C2C4×AΣL(1,𝔽16)11yescharacteristic
560C2C4×#35311yescharacteristic
subgroupG/H
centerC22×C4#99
commutatorC22×C4C2×C42
Frattini, cosocleC22×C22⋊C4C23
socleC23C2×#99
prime radicalC2×#392C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C4×#342C2semidirect
4. C4×#323C2semidirect
5. #7250C2semidirect
7. C22×C4×D4C4semidirect
16. #1444C4semidirect
20. #1438C4semidirect
21. C4×#95C4semidirect
22. #1343C4direct (N × H)
68. #342C2×C4semidirect
71. #323C2×C4semidirect
87. C22×D4C42semidirect
177. #95C42semidirect
546. C4#1343direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#3922
C2×#13432
C4×#3422
C4×#3232
#72502