Finite Group Databasebeta

← C22×#11722398 #72252731

Subgroups — C22×#11722398 #72252731

Order 3456.

8049 conjugacy classes of subgroups; only the 321 normal subgroups are shown.

normal subgroups only

This group has 8049 conjugacy classes of subgroups — too many to draw. Only its 321 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
1C24×C22⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C23×#6258C211yesmaximal, characteristic, complemented
3C2×#11722398C2112yesmaximal, direct product factor
4C22×#88613C211yesmaximal, characteristic, complemented
5C22×C3×GL(2,ℤ/4)—33nomaximal
6C22×C3×#953—31nomaximal
7C23×C22⋊H(3,𝔽3)—24no—
8C23×C22⋊H(3,𝔽3)C2211yescharacteristic
9C23×C22⋊H(3,𝔽3)C2216yescomplemented
10C22×#6258—24no—
11C22×#6258C2216yescomplemented
12C22×#6235—41nomaximal
13#11722398C22116yesdirect product factor
14C2×#88613C2216yescomplemented
15C26×C32D311yescharacteristic, complemented
16C24×C3×A4D313yescomplemented
17C23×C3×S4—33no—
18C23×C3×#67—31no—
19C23×C3×#67—31no—
20C23×C3×#67—31no—
21C2×C3×GL(2,ℤ/4)—336no—
22C22×C3×SL(2,ℤ/4)—33no—
23C2×C3×#953—312no—
24C2×C3×#953—312no—
25C22×C3×#217—31no—
26C22×C3×#217—31no—
27C22×C3×#217—31no—
28C24×H(3,𝔽3)—41no—
29C23×#272—41no—
30C22×C22⋊H(3,𝔽3)—212no—
31C22×C22⋊H(3,𝔽3)D414yescomplemented
32C22×C22⋊H(3,𝔽3)C2313yes—
33C22×C22⋊H(3,𝔽3)C2314yescomplemented
34C2×#6258—212no—
35C2×#6258C2314yescomplemented
36C2×#6235—412no—
37C22×#1084—41no—
38#88613C2314yescomplemented
39C22×GL(2,ℤ/4)—33no—
40C22×C3×#120—91no—
41C22×#953—31no—
42C25×C32—24no—
43C25×C32—31no—
44C25×C32—31no—
45C25×C32—36no—
46C25×C32—64no—
47C25×C32C2×D311yescharacteristic
48C25×C32C2×D316yescomplemented
49C24×C3×D3—31no—
50C23×C3×A4—212no—
51C23×C3×A4C2×D313yes—
52C23×C3×A4C2×D3118yescomplemented
53C22×C3×S4—318no—
54C22×C3×S4—612no—
55C22×C3×#67—36no—
56C22×C3×#67—312no—
57C22×C3×#67—312no—
58C22×C3×#67—36no—
59C22×C3×#67—64no—
60C22×C3×#67—68no—
61C22×C3×#67—66no—
62C22×C3×#67—61no—
63C22×C3×#67—64no—
64C22×C3×#67—61no—
65C22×C3×#67—123no—
66C23×C3×Dic3—31no—
67C23×C3×Dic3—31no—
68C23×C3×Dic3—31no—
69C3×GL(2,ℤ/4)—348no—
70C2×C3×SL(2,ℤ/4)—318no—
71C3×#953—348no—
72C3×#953—316no—
73C2×C3×#217—36no—
74C2×C3×#217—312no—
75C2×C3×#217—312no—
76C2×C3×#217—36no—
77C23×H(3,𝔽3)—41no—
78C23×H(3,𝔽3)—46no—
79C23×H(3,𝔽3)—84no—
80C22×#272—46no—
81C22×#272—84no—
82C2×C22⋊H(3,𝔽3)—24no—
83C2×C22⋊H(3,𝔽3)C2×D416yescomplemented
84C2×C22⋊H(3,𝔽3)C2411yescharacteristic
85#6258—24no—
86#6235—416no—
87C2×#1084—46no—
88C26×C3—31no—
89C26×C3C3⋊D311yescharacteristic
90C24×A4—33no—
91C23×S4—33no—
92C23×C3×D4—91no—
93C23×C3×D4—91no—
94C23×C3×D4—91no—
95C23×#67—31no—
96C23×#67—31no—
97C23×#67—31no—
98C2×GL(2,ℤ/4)—336no—
99C22×SL(2,ℤ/4)—33no—
100C2×C3×#120—912no—
101C2×C3×#120—912no—
102C22×C3×C22⋊C4—91no—
103C22×C3×C22⋊C4—91no—
104C22×C3×C22⋊C4—91no—
105C2×#953—312no—
106C2×#953—312no—
107C22×#217—31no—
108C22×#217—31no—
109C22×#217—31no—
110C24×C32—212no—
111C24×C32—31no—
112C24×C32—33no—
113C24×C32—36no—
114C24×C32—34no—
115C24×C32—38no—
116C24×C32—31no—
117C24×C32—36no—
118C24×C32—36no—
119C24×C32—312no—
120C24×C32—43no—
121C24×C32—64no—
122C24×C32—64no—
123C24×C32—63no—
124C24×C32—64no—
125C24×C32—612no—
126C24×C32—624no—
127C24×C32—64no—
128C24×C32—624no—
129C24×C32#6714yescomplemented
130C24×C32S411yescharacteristic, complemented
131C24×C32C22×D313yes—
132C24×C32C22×D314yescomplemented
133C23×C3×D3—36no—
134C23×C3×D3—64no—
135C23×C3×D3—64no—
136C23×C3×D3—63no—
137C23×C3×D3—61no—
138C23×C3×D3—123no—
139C22×C3×A4—236no—
140C22×C3×A4#67112yescomplemented
141C22×C3×A4C22×D319yes—
142C22×C3×A4C22×D3112yescomplemented
143C2×C3×S4—312no—
144C2×C3×S4—636no—
145C2×C3×#67—312no—
146C2×C3×#67—316no—
147C2×C3×#67—316no—
148C2×C3×#67—34no—
149C2×C3×#67—624no—
150C2×C3×#67—612no—
151C2×C3×#67—648no—
152C2×C3×#67—624no—
153C2×C3×#67—612no—
154C2×C3×#67—612no—
155C2×C3×#67—612no—
156C2×C3×#67—1236no—
157C22×C3×Dic3—36no—
158C22×C3×Dic3—36no—
159C22×C3×Dic3—36no—
160C22×C3×Dic3—64no—
161C22×C3×Dic3—64no—
162C22×C3×Dic3—63no—
163C22×C3×Dic3—61no—
164C22×C3×Dic3—123no—
165C3×SL(2,ℤ/4)—312no—
166C3×#217—312no—
167C3×#217—316no—
168C3×#217—316no—
169C3×#217—34no—
170C22×#120—91noSylow
171C22×H(3,𝔽3)—44no—
172C22×H(3,𝔽3)—43no—
173C22×H(3,𝔽3)—44no—
174C22×H(3,𝔽3)—812no—
175C2×#272—44no—
176C2×#272—812no—
177C22⋊H(3,𝔽3)C22×D411yescharacteristic, complemented
178#1084—44no—
179C25×C3—24no—
180C25×C3—31no—
181C25×C3—31no—
182C25×C3—31no—
183C25×C3—31no—
184C25×C3—36no—
185C25×C3—36no—
186C25×C3—31no—
187C25×C3—36no—
188C25×C3—64no—
189C25×C3—61no—
190C25×C3—61no—
191C25×C3—66no—
192C25×C3—64no—
193C25×C3—68no—
194C25×C3—64no—
195C25×C3—91no—
196C25×C3C2×C3⋊D311yescharacteristic
197C25×C3C2×C3⋊D316yes—
198C24×D3—31no—
199C23×A4—33no—
200C23×A4—318no—
201C23×A4—612no—
202C22×S4—318no—
203C22×S4—612no—
204C22×C3×D4—912no—
205C22×C3×D4—96no—
206C22×C3×D4—912no—
207C22×C3×D4—96no—
208C22×C3×D4—184no—
209C22×C3×D4—188no—
210C22×C3×D4—186no—
211C22×C3×D4—181no—
212C22×C3×D4—184no—
213C22×C3×D4—181no—
214C23×C3×C4—91no—
215C23×C3×C4—91no—
216C23×C3×C4—91no—
217C22×#67—36no—
218C22×#67—312no—
219C22×#67—312no—
220C22×#67—36no—
221C22×#67—64no—
222C22×#67—68no—
223C22×#67—66no—
224C22×#67—61no—
225C22×#67—64no—
226C22×#67—61no—
227C22×#67—123no—
228C23×Dic3—31no—
229C23×Dic3—31no—
230C23×Dic3—31no—
231GL(2,ℤ/4)—348no—
232C2×SL(2,ℤ/4)—318no—
233C3×#120—948no—
234C3×#120—916no—
235C2×C3×C22⋊C4—912no—
236C2×C3×C22⋊C4—96no—
237C2×C3×C22⋊C4—912no—
238C2×C3×C22⋊C4—96no—
239#953—348no—
240#953—316no—
241C2×#217—36no—
242C2×#217—312no—
243C2×#217—312no—
244C2×#217—36no—
245C23×C32—24no—
246C23×C32—24no—
247C23×C32—34no—
248C23×C32—34no—
249C23×C32—33no—
250C23×C32—33no—
251C23×C32—33no—
252C23×C32—34no—
253C23×C32—312no—
254C23×C32—36no—
255C23×C32—324no—
256C23×C32—36no—
257C23×C32—34no—
258C23×C32—312no—
259C23×C32—418no—
260C23×C32—43no—
261C23×C32—612no—
262C23×C32—612no—
263C23×C32—624no—
264C23×C32—64no—
265C23×C32—66no—
266C23×C32—61no—
267C23×C32—66no—
268C23×C32—624no—
269C23×C32—612no—
270C23×C32—624no—
271C23×C32—624no—
272C23×C32—632no—
273C23×C32—64no—
274C23×C32—812no—
275C23×C32C2×#6716yescomplemented
276C23×C32C2×S411yescharacteristic
277C23×C32C2×S416yescomplemented
278C23×C32C23×D311yescharacteristic
279C22×C3×D3—34no—
280C22×C3×D3—612no—
281C22×C3×D3—612no—
282C22×C3×D3—66no—
283C22×C3×D3—66no—
284C22×C3×D3—1218no—
285C22×C3×D3—1212no—
286C22×C3×D3—124no—
287C22×C3×D3—2412no—
288C2×C3×A4—212no—
289C2×C3×A4C2×#67118yescomplemented
290C2×C3×A4C23×D313yes—
291C3×S4—612no—
292C3×#67—624no—
293C3×#67—64no—
294C3×#67—632no—
295C3×#67—616no—
296C3×#67—64no—
297C3×#67—616no—
298C3×#67—1248no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3—612no—
303C2×C3×Dic3—612no—
304C2×C3×Dic3—66no—
305C2×C3×Dic3—66no—
306C2×C3×Dic3—1218no—
307C26#27211yescharacteristic, complemented
308C23×D4—91no—
309C23×D4—91no—
310C23×D4—91no—
311C2×#120—912no—
312C2×#120—912no—
313C22×C22⋊C4—91no—
314C22×C22⋊C4—91no—
315C22×C22⋊C4—91no—
316C2×H(3,𝔽3)—46no—
317C2×H(3,𝔽3)—41no—
318C2×H(3,𝔽3)—84no—
319#272—84no—
320C24×C3—212no—
321C24×C3—31no—
322C24×C3—31no—
323C24×C3—33no—
324C24×C3—36no—
325C24×C3—34no—
326C24×C3—33no—
327C24×C3—36no—
328C24×C3—36no—
329C24×C3—34no—
330C24×C3—38no—
331C24×C3—31no—
332C24×C3—36no—
333C24×C3—38no—
334C24×C3—36no—
335C24×C3—36no—
336C24×C3—31no—
337C24×C3—312no—
338C24×C3—312no—
339C24×C3—34no—
340C24×C3—31no—
341C24×C3—33no—
342C24×C3—34no—
343C24×C3—612no—
344C24×C3—61no—
345C24×C3—63no—
346C24×C3—66no—
347C24×C3—64no—
348C24×C3—61no—
349C24×C3—66no—
350C24×C3—66no—
351C24×C3—612no—
352C24×C3—68no—
353C24×C3—64no—
354C24×C3—64no—
355C24×C3—612no—
356C24×C3—63no—
357C24×C3—64no—
358C24×C3—64no—
359C24×C3—624no—
360C24×C3—64no—
361C24×C3—64no—
362C24×C3—624no—
363C24×C3—612no—
364C24×C3—63no—
365C24×C3—66no—
366C24×C3—612no—
367C24×C3—64no—
368C24×C3—624no—
369C24×C3—624no—
370C24×C3—624no—
371C24×C3—68no—
372C24×C3—68no—
373C24×C3—68no—
374C24×C3—648no—
375C24×C3—648no—
376C24×C3—96no—
377C24×C3—123no—
378C24×C3—184no—
379C24×C3—184no—
380C24×C3—183no—
381C24×C3—181no—
382C24×C3#63814yes—
383C24×C3C3⋊S411yescharacteristic
384C24×C3C22×C3⋊D313yes—
385C24×C3C22×C3⋊D314yes—
386C23×D3—36no—
387C23×D3—63no—
388C23×D3—64no—
389C23×D3—64no—
390C23×D3—61no—
391C23×D3—123no—
392C22×A4—312no—
393C22×A4—39no—
394C22×A4—312no—
395C22×A4—636no—
396C2×S4—312no—
397C2×S4—636no—
398C2×C3×D4—912no—
399C2×C3×D4—916no—
400C2×C3×D4—916no—
401C2×C3×D4—94no—
402C2×C3×D4—1824no—
403C2×C3×D4—1812no—
404C2×C3×D4—1848no—
405C2×C3×D4—1824no—
406C2×C3×D4—1812no—
407C2×C3×D4—1812no—
408C2×C3×D4—1812no—
409C22×C3×C4—96no—
410C22×C3×C4—96no—
411C22×C3×C4—96no—
412C22×C3×C4—184no—
413C22×C3×C4—184no—
414C22×C3×C4—183no—
415C22×C3×C4—181no—
416C2×#67—312no—
417C2×#67—316no—
418C2×#67—316no—
419C2×#67—34no—
420C2×#67—624no—
421C2×#67—612no—
422C2×#67—648no—
423C2×#67—624no—
424C2×#67—612no—
425C2×#67—612no—
426C2×#67—612no—
427C2×#67—1236no—
428C22×Dic3—36no—
429C22×Dic3—36no—
430C22×Dic3—36no—
431C22×Dic3—64no—
432C22×Dic3—64no—
433C22×Dic3—63no—
434C22×Dic3—61no—
435C22×Dic3—123no—
436SL(2,ℤ/4)—312no—
437C3×C22⋊C4—916no—
438C3×C22⋊C4—912no—
439C3×C22⋊C4—916no—
440C3×C22⋊C4—94no—
441#217—312no—
442#217—316no—
443#217—316no—
444#217—34no—
445C22×C32—212no—
446C22×C32—36no—
447C22×C32—31no—
448C22×C32—36no—
449C22×C32—36no—
450C22×C32—312no—
451C22×C32—31no—
452C22×C32—33no—
453C22×C32—38no—
454C22×C32—34no—
455C22×C32—412no—
456C22×C32—49no—
457C22×C32—412no—
458C22×C32—64no—
459C22×C32—64no—
460C22×C32—624no—
461C22×C32—63no—
462C22×C32—64no—
463C22×C32—64no—
464C22×C32—624no—
465C22×C32—612no—
466C22×C32—836no—
467C22×C32GL(2,ℤ/4)14yescomplemented
468C22×C32C22×#6711yescharacteristic, complemented
469C22×C32C22×S413yes—
470C22×C32C22×S414yescomplemented
471C2×C3×D3—64no—
472C2×C3×D3—64no—
473C2×C3×D3—64no—
474C2×C3×D3—1212no—
475C2×C3×D3—1212no—
476C2×C3×D3—1212no—
477C2×C3×D3—2436no—
478C3×A4C22×#6713yescomplemented
479C3×Dic3—64no—
480C3×Dic3—64no—
481C3×Dic3—64no—
482C3×Dic3—1212no—
483C25—24no—
484C25—31no—
485C25—31no—
486C25—36no—
487C25—64no—
488C25—91no—
489C25C2×#27211yescharacteristic
490C25C2×#27216yescomplemented
491C22×D4—96no—
492C22×D4—912no—
493C22×D4—912no—
494C22×D4—96no—
495C22×D4—184no—
496C22×D4—188no—
497C22×D4—186no—
498C22×D4—181no—
499C22×D4—184no—
500C22×D4—181no—
501C23×C4—91no—
502C23×C4—91no—
503C23×C4—91no—
504#120—948no—
505#120—916no—
506C2×C22⋊C4—96no—
507C2×C22⋊C4—912no—
508C2×C22⋊C4—912no—
509C2×C22⋊C4—96no—
510H(3,𝔽3)—41noSylow
511C23×C3—24no—
512C23×C3—24no—
513C23×C3—33no—
514C23×C3—33no—
515C23×C3—34no—
516C23×C3—34no—
517C23×C3—34no—
518C23×C3—34no—
519C23×C3—33no—
520C23×C3—33no—
521C23×C3—33no—
522C23×C3—34no—
523C23×C3—312no—
524C23×C3—36no—
525C23×C3—33no—
526C23×C3—34no—
527C23×C3—34no—
528C23×C3—312no—
529C23×C3—36no—
530C23×C3—324no—
531C23×C3—36no—
532C23×C3—312no—
533C23×C3—324no—
534C23×C3—34no—
535C23×C3—36no—
536C23×C3—312no—
537C23×C3—31no—
538C23×C3—36no—
539C23×C3—31no—
540C23×C3—36no—
541C23×C3—64no—
542C23×C3—64no—
543C23×C3—63no—
544C23×C3—63no—
545C23×C3—64no—
546C23×C3—64no—
547C23×C3—63no—
548C23×C3—64no—
549C23×C3—612no—
550C23×C3—66no—
551C23×C3—66no—
552C23×C3—64no—
553C23×C3—612no—
554C23×C3—624no—
555C23×C3—612no—
556C23×C3—612no—
557C23×C3—624no—
558C23×C3—64no—
559C23×C3—61no—
560C23×C3—66no—
561C23×C3—66no—
562C23×C3—624no—
563C23×C3—612no—
564C23×C3—612no—
565C23×C3—612no—
566C23×C3—624no—
567C23×C3—68no—
568C23×C3—64no—
569C23×C3—63no—
570C23×C3—66no—
571C23×C3—66no—
572C23×C3—612no—
573C23×C3—612no—
574C23×C3—612no—
575C23×C3—624no—
576C23×C3—624no—
577C23×C3—624no—
578C23×C3—624no—
579C23×C3—624no—
580C23×C3—68no—
581C23×C3—64no—
582C23×C3—624no—
583C23×C3—624no—
584C23×C3—648no—
585C23×C3—648no—
586C23×C3—624no—
587C23×C3—648no—
588C23×C3—648no—
589C23×C3—632no—
590C23×C3—696no—
591C23×C3—64no—
592C23×C3—94no—
593C23×C3—123no—
594C23×C3—1218no—
595C23×C3—186no—
596C23×C3—1812no—
597C23×C3—1812no—
598C23×C3—186no—
599C23×C3—2412no—
600C23×C3—3612no—
601C23×C3—364no—
602C23×C3C2×#63816yes—
603C23×C3C2×C3⋊S416yes—
604C23×C3C2×C3⋊S411yescharacteristic
605C23×C3C23×C3⋊D311yescharacteristic
606C22×D3—34no—
607C22×D3—66no—
608C22×D3—612no—
609C22×D3—612no—
610C22×D3—66no—
611C22×D3—1218no—
612C22×D3—1212no—
613C22×D3—124no—
614C22×D3—2412no—
615C2×A4—33no—
616C2×A4—318no—
617C2×A4—612no—
618S4—612no—
619C3×D4—184no—
620C3×D4—1824no—
621C3×D4—1832no—
622C3×D4—1816no—
623C3×D4—184no—
624C3×D4—1816no—
625C2×C3×C4—94no—
626C2×C3×C4—94no—
627C2×C3×C4—94no—
628C2×C3×C4—1812no—
629C2×C3×C4—1812no—
630C2×C3×C4—186no—
631C2×C3×C4—186no—
632#67—64no—
633#67—624no—
634#67—632no—
635#67—616no—
636#67—616no—
637#67—64no—
638#67—1248no—
639C2×Dic3—34no—
640C2×Dic3—34no—
641C2×Dic3—34no—
642C2×Dic3—612no—
643C2×Dic3—612no—
644C2×Dic3—66no—
645C2×Dic3—66no—
646C2×Dic3—1218no—
647C2×C32—24no—
648C2×C32—31no—
649C2×C32—31no—
650C2×C32—36no—
651C2×C32—43no—
652C2×C32—418no—
653C2×C32—64no—
654C2×C32—812no—
655C2×C32C2×GL(2,ℤ/4)16yescomplemented
656C2×C32C23×S411yescharacteristic
657C3×D3—124no—
658C3×D3—2412no—
659C24—212no—
660C24—31no—
661C24—33no—
662C24—36no—
663C24—34no—
664C24—38no—
665C24—31no—
666C24—36no—
667C24—36no—
668C24—312no—
669C24—64no—
670C24—64no—
671C24—612no—
672C24—63no—
673C24—64no—
674C24—64no—
675C24—624no—
676C24—624no—
677C24—96no—
678C24—183no—
679C24—184no—
680C24—184no—
681C24—181no—
682C24#623514yescomplemented
683C24#625811yescharacteristic, complemented
684C24C22×#27213yes—
685C24C22×#27214yescomplemented
686C2×D4—912no—
687C2×D4—916no—
688C2×D4—916no—
689C2×D4—94no—
690C2×D4—1824no—
691C2×D4—1812no—
692C2×D4—1848no—
693C2×D4—1824no—
694C2×D4—1812no—
695C2×D4—1812no—
696C2×D4—1812no—
697C22×C4—96no—
698C22×C4—96no—
699C22×C4—96no—
700C22×C4—184no—
701C22×C4—184no—
702C22×C4—183no—
703C22×C4—181no—
704C22⋊C4—912no—
705C22⋊C4—916no—
706C22⋊C4—916no—
707C22⋊C4—94no—
708C22×C3—212no—
709C22×C3—31no—
710C22×C3—36no—
711C22×C3—31no—
712C22×C3—33no—
713C22×C3—36no—
714C22×C3—36no—
715C22×C3—312no—
716C22×C3—31no—
717C22×C3—33no—
718C22×C3—36no—
719C22×C3—36no—
720C22×C3—312no—
721C22×C3—31no—
722C22×C3—36no—
723C22×C3—38no—
724C22×C3—34no—
725C22×C3—38no—
726C22×C3—34no—
727C22×C3—33no—
728C22×C3—34no—
729C22×C3—34no—
730C22×C3—31no—
731C22×C3—612no—
732C22×C3—61no—
733C22×C3—66no—
734C22×C3—61no—
735C22×C3—63no—
736C22×C3—66no—
737C22×C3—66no—
738C22×C3—612no—
739C22×C3—64no—
740C22×C3—68no—
741C22×C3—64no—
742C22×C3—64no—
743C22×C3—624no—
744C22×C3—63no—
745C22×C3—64no—
746C22×C3—64no—
747C22×C3—64no—
748C22×C3—64no—
749C22×C3—624no—
750C22×C3—63no—
751C22×C3—66no—
752C22×C3—612no—
753C22×C3—64no—
754C22×C3—624no—
755C22×C3—624no—
756C22×C3—624no—
757C22×C3—612no—
758C22×C3—68no—
759C22×C3—68no—
760C22×C3—648no—
761C22×C3—68no—
762C22×C3—648no—
763C22×C3—612no—
764C22×C3—129no—
765C22×C3—1212no—
766C22×C3—1212no—
767C22×C3—184no—
768C22×C3—184no—
769C22×C3—184no—
770C22×C3—2436no—
771C22×C3—3612no—
772C22×C3—3612no—
773C22×C3#6426914yes—
774C22×C3C22×#63811yescharacteristic
775C22×C3C22×C3⋊S413yes—
776C22×C3C22×C3⋊S414yes—
777C2×D3—64no—
778C2×D3—64no—
779C2×D3—64no—
780C2×D3—1212no—
781C2×D3—1212no—
782C2×D3—1212no—
783C2×D3—2436no—
784A4—33no—
785C3×C4—184no—
786C3×C4—184no—
787C3×C4—184no—
788Dic3—64no—
789Dic3—64no—
790Dic3—64no—
791Dic3—1212no—
792C32—43no—
793C32C22×GL(2,ℤ/4)11yescharacteristic, complemented
794C23—24no—
795C23—24no—
796C23—33no—
797C23—33no—
798C23—34no—
799C23—34no—
800C23—33no—
801C23—34no—
802C23—312no—
803C23—36no—
804C23—324no—
805C23—36no—
806C23—34no—
807C23—312no—
808C23—612no—
809C23—612no—
810C23—624no—
811C23—64no—
812C23—61no—
813C23—66no—
814C23—66no—
815C23—624no—
816C23—612no—
817C23—624no—
818C23—624no—
819C23—632no—
820C23—64no—
821C23—94no—
822C23—186no—
823C23—1812no—
824C23—1812no—
825C23—186no—
826C23—3612no—
827C23—364no—
828C23C2×#623516yescomplemented
829C23C2×#625811yescharacteristic
830C23C2×#625816yescomplemented
831C23C23×#27211yescharacteristic
832D4—184no—
833D4—1824no—
834D4—1832no—
835D4—1816no—
836D4—1816no—
837D4—184no—
838C2×C4—94no—
839C2×C4—94no—
840C2×C4—94no—
841C2×C4—1812no—
842C2×C4—1812no—
843C2×C4—186no—
844C2×C4—186no—
845C2×C3—24no—
846C2×C3—31no—
847C2×C3—31no—
848C2×C3—36no—
849C2×C3—31no—
850C2×C3—31no—
851C2×C3—36no—
852C2×C3—31no—
853C2×C3—36no—
854C2×C3—64no—
855C2×C3—61no—
856C2×C3—61no—
857C2×C3—66no—
858C2×C3—68no—
859C2×C3—64no—
860C2×C3—64no—
861C2×C3—123no—
862C2×C3—1218no—
863C2×C3—2412no—
864C2×C3—364no—
865C2×C3C2×#6426916yes—
866C2×C3C23×C3⋊S411yescharacteristic
867D3—124no—
868D3—2412no—
869C22—212no—
870C22—31no—
871C22—36no—
872C22—31no—
873C22—33no—
874C22—36no—
875C22—36no—
876C22—312no—
877C22—38no—
878C22—34no—
879C22—64no—
880C22—64no—
881C22—624no—
882C22—63no—
883C22—64no—
884C22—64no—
885C22—624no—
886C22—612no—
887C22—184no—
888C22—184no—
889C22—184no—
890C22—3612no—
891C22—3612no—
892C22#1172239814yesdirect product factor
893C22C22×#623511yescharacteristic, complemented
894C22C22×#625813yes—
895C22C22×#625814yescomplemented
896C4—184no—
897C4—184no—
898C4—184no—
899C3—31no—
900C3—123no—
901C3C22×#6426911yescharacteristic
902C2—24no—
903C2—31no—
904C2—31no—
905C2—36no—
906C2—64no—
907C2—364no—
908C2C2×#1172239816yesdirect product factor
909C2C23×#625811yescharacteristic
subgroupG/H
centerC23×C3C2×C3⋊S4
commutator, cosocleC2×C22⋊H(3,𝔽3)C24
FrattiniC2×C3C23×C3⋊S4
FittingC26×C32D3
socleC25×C3C2×C3⋊D3
hypercenterC24×C3C3⋊S4
hypocenterC22⋊H(3,𝔽3)C22×D4
LCSG ▷ C2×C22⋊H(3,𝔽3) ▷ C22⋊H(3,𝔽3)
UCSC1 ◁ C23×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C24×C22⋊H(3,𝔽3)C2semidirect
2. C23×#6258C2semidirect
3. C2×#11722398C2direct (N × H)
4. C22×#88613C2semidirect
9. C23×C22⋊H(3,𝔽3)C22semidirect
11. C22×#6258C22semidirect
13. #11722398C22direct (N × H)
14. C2×#88613C22semidirect
15. C26×C32D3semidirect
16. C24×C3×A4D3semidirect
31. C22×C22⋊H(3,𝔽3)D4semidirect
33. C22×C22⋊H(3,𝔽3)C23semidirect
35. C2×#6258C23semidirect
38. #88613C23semidirect
48. C25×C32C2×D3semidirect
52. C23×C3×A4C2×D3semidirect
83. C2×C22⋊H(3,𝔽3)C2×D4semidirect
129. C24×C32#67semidirect
130. C24×C32S4semidirect
132. C24×C32C22×D3semidirect
140. C22×C3×A4#67semidirect
142. C22×C3×A4C22×D3semidirect
177. C22⋊H(3,𝔽3)C22×D4semidirect
275. C23×C32C2×#67semidirect
277. C23×C32C2×S4semidirect
289. C2×C3×A4C2×#67semidirect
307. C26#272semidirect
467. C22×C32GL(2,ℤ/4)semidirect
468. C22×C32C22×#67semidirect
470. C22×C32C22×S4semidirect
478. C3×A4C22×#67semidirect
490. C25C2×#272semidirect
655. C2×C32C2×GL(2,ℤ/4)semidirect
682. C24#6235semidirect
683. C24#6258semidirect
685. C24C22×#272semidirect
793. C32C22×GL(2,ℤ/4)semidirect
828. C23C2×#6235semidirect
830. C23C2×#6258semidirect
892. C22#11722398direct (N × H)
893. C22C22×#6235semidirect
895. C22C22×#6258semidirect
908. C2C2×#11722398direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C22⋊H(3,𝔽3)2
C23×#62582
C2×#117223982
C22×#886132
C22×C3×GL(2,ℤ/4)3
C22×C3×#9533
C22×#62354