Finite Group Databasebeta

← C22×C4×(C3⋊D3)⋊A4 #72269126

Subgroups — C22×C4×(C3⋊D3)⋊A4 #72269126

Order 3456.

11840 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C3⋊D3)⋊A4C211yesmaximal, characteristic
2C22×C4×C22⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
3C22×(C3⋊Dic3)⋊A4C211yesmaximal, characteristic, complemented
4C2×C4×(C3⋊D3)⋊A4C2112yesmaximal, direct product factor
5C22×C4×D3×A4—31nomaximal
6C24×C4×C3⋊D3C311yesmaximal, characteristic, complemented
7C23×C22⋊H(3,𝔽3)C2211yescharacteristic
8C22×(C3⋊D3)⋊A4C418yesdirect product factor
9C22×(C3⋊D3)⋊A4C2216yes—
10C22×C4×(C3⋊D3)⋊C3—41nomaximal
11C2×C4×C22⋊H(3,𝔽3)C2216yescomplemented
12C2×(C3⋊Dic3)⋊A4C2216yescomplemented
13C4×(C3⋊D3)⋊A4C22116yesdirect product factor
14C25×C3⋊D3C2×C311yescharacteristic
15C23×D3×A4—31no—
16C24×C32×C4C2×C311yescharacteristic, complemented
17C24×C3⋊Dic3C2×C311yescharacteristic, complemented
18C23×C4×C3⋊D3—31no—
19C23×C4×C3⋊D3—31no—
20C23×C4×C3⋊D3—31no—
21C23×C4×C3⋊D3—312no—
22C23×C4×C3⋊D3—31no—
23C23×C4×C3⋊D3C2×C3112yescomplemented
24C22×C3×C4×A4—21no—
25C22×C3×C4×A4D311yescharacteristic, complemented
26C22×Dic3×A4—31no—
27C2×C4×D3×A4—312no—
28C23×(C3⋊D3)⋊C3—41no—
29C22×C22⋊H(3,𝔽3)C2×C414yescomplemented
30C22×C22⋊H(3,𝔽3)C2313yes—
31C2×(C3⋊D3)⋊A4C2×C4124yesdirect product factor
32C2×(C3⋊D3)⋊A4C2314yes—
33C22×C4×H(3,𝔽3)—41no—
34C22×(C3⋊Dic3)⋊C3—41no—
35C2×C4×(C3⋊D3)⋊C3—412no—
36C4×C22⋊H(3,𝔽3)C2314yescomplemented
37(C3⋊Dic3)⋊A4C2314yescomplemented
38C24×C4×D3—31no—
39C24×C4×D3—91no—
40C23×C4×A4—91no—
41C25×C32C22×C311yescharacteristic
42C24×C3⋊D3—31no—
43C24×C3⋊D3—31no—
44C24×C3⋊D3—36no—
45C24×C3⋊D3—38no—
46C24×C3⋊D3C3×C418yescomplemented
47C24×C3⋊D3C22×C316yes—
48C23×C3×A4—21no—
49C23×C3×A4C2×D311yescharacteristic
50C22×D3×A4—38no—
51C22×D3×A4—36no—
52C23×C32×C4—31no—
53C23×C32×C4—36no—
54C23×C32×C4—31no—
55C23×C32×C4C22×C316yescomplemented
56C23×C3⋊Dic3—31no—
57C23×C3⋊Dic3—36no—
58C23×C3⋊Dic3—31no—
59C23×C3⋊Dic3C22×C316yescomplemented
60C22×C4×C3⋊D3—312no—
61C22×C4×C3⋊D3—312no—
62C22×C4×C3⋊D3—332no—
63C22×C4×C3⋊D3—32no—
64C22×C4×C3⋊D3—312no—
65C22×C4×C3⋊D3—31no—
66C22×C4×C3⋊D3—31no—
67C22×C4×C3⋊D3—312no—
68C22×C4×C3⋊D3—312no—
69C22×C4×C3⋊D3—312no—
70C22×C4×C3⋊D3—312no—
71C22×C4×C3⋊D3—312no—
72C22×C4×C3⋊D3—348no—
73C22×C4×C3⋊D3—31no—
74C22×C4×C3⋊D3A411yescharacteristic, complemented
75C22×C4×C3⋊D3C22×C3116yescomplemented
76C22×C3×C4×D3—121no—
77C2×C3×C4×A4—26no—
78C2×C3×C4×A4C2×D316yescomplemented
79C2×Dic3×A4—36no—
80C4×D3×A4—316no—
81C23×H(3,𝔽3)—41no—
82C22×(C3⋊D3)⋊C3—48no—
83C22×(C3⋊D3)⋊C3—46no—
84C2×C22⋊H(3,𝔽3)C22×C416yescomplemented
85C2×C22⋊H(3,𝔽3)C2411yescharacteristic
86(C3⋊D3)⋊A4C22×C418yesdirect product factor
87C2×C4×H(3,𝔽3)—46no—
88C2×(C3⋊Dic3)⋊C3—46no—
89C4×(C3⋊D3)⋊C3—416no—
90C25×D3—31no—
91C25×D3—91no—
92C24×A4—91no—
93C24×C3×C4—31no—
94C24×C3×C4C3×D311yescharacteristic
95C24×Dic3—31no—
96C24×Dic3—91no—
97C23×C4×D3—312no—
98C23×C4×D3—912no—
99C23×C4×D3—91no—
100C23×C4×D3—93no—
101C23×C4×D3—93no—
102C23×C4×D3—936no—
103C23×C4×D3—93no—
104C23×C4×D3—93no—
105C23×C4×D3—912no—
106C23×C4×D3—91no—
107C23×C4×D3—91no—
108C23×C4×D3—91no—
109C22×C4×A4—31no—
110C22×C4×A4—61no—
111C22×C4×A4—912no—
112C22×C4×A4—91no—
113C24×C32—31no—
114C24×C32—33no—
115C24×C32—34no—
116C24×C32C2×C3×C414yescomplemented
117C24×C32C23×C313yes—
118C23×C3⋊D3—36no—
119C23×C3⋊D3—38no—
120C23×C3⋊D3—38no—
121C23×C3⋊D3—348no—
122C23×C3⋊D3—31no—
123C23×C3⋊D3—38no—
124C23×C3⋊D3—38no—
125C23×C3⋊D3—36no—
126C23×C3⋊D3—36no—
127C23×C3⋊D3—36no—
128C23×C3⋊D3—312no—
129C23×C3⋊D3—38no—
130C23×C3⋊D3—348no—
131C23×C3⋊D3—324no—
132C23×C3⋊D3C2×C3×C4124yescomplemented
133C23×C3⋊D3C2×A411yescharacteristic
134C23×C3⋊D3C23×C314yes—
135C23×C3×D3—121no—
136C22×C3×A4—24no—
137C22×C3×A4—23no—
138C22×C3×A4C4×D314yescomplemented
139C22×C3×A4C22×D313yes—
140C2×D3×A4—324no—
141C2×D3×A4—34no—
142C22×C32×C4—36no—
143C22×C32×C4—38no—
144C22×C32×C4—31no—
145C22×C32×C4—36no—
146C22×C32×C4—36no—
147C22×C32×C4—36no—
148C22×C32×C4—312no—
149C22×C32×C4—41no—
150C22×C32×C4—81no—
151C22×C32×C4C2×A411yescharacteristic, complemented
152C22×C32×C4C23×C314yescomplemented
153C22×C3⋊Dic3—36no—
154C22×C3⋊Dic3—38no—
155C22×C3⋊Dic3—31no—
156C22×C3⋊Dic3—36no—
157C22×C3⋊Dic3—36no—
158C22×C3⋊Dic3—36no—
159C22×C3⋊Dic3—312no—
160C22×C3⋊Dic3C2×A411yescharacteristic, complemented
161C22×C3⋊Dic3C23×C314yescomplemented
162C2×C4×C3⋊D3—324no—
163C2×C4×C3⋊D3—348no—
164C2×C4×C3⋊D3—348no—
165C2×C4×C3⋊D3—348no—
166C2×C4×C3⋊D3—312no—
167C2×C4×C3⋊D3—312no—
168C2×C4×C3⋊D3—312no—
169C2×C4×C3⋊D3—348no—
170C2×C4×C3⋊D3—316no—
171C2×C4×C3⋊D3—316no—
172C2×C4×C3⋊D3—316no—
173C2×C4×C3⋊D3—316no—
174C2×C4×C3⋊D3C2×A4112yescomplemented
175C22×C3×Dic3—121no—
176C2×C3×C4×D3—1212no—
177C3×C4×A4—24no—
178C3×C4×A4C22×D314yescomplemented
179Dic3×A4—34no—
180C25×C4—91noSylow
181C22×H(3,𝔽3)—44no—
182C22×H(3,𝔽3)—43no—
183C2×(C3⋊D3)⋊C3—424no—
184C2×(C3⋊D3)⋊C3—44no—
185C22⋊H(3,𝔽3)C23×C411yescharacteristic, complemented
186C4×H(3,𝔽3)—44no—
187(C3⋊Dic3)⋊C3—44no—
188C25×C3—31no—
189C25×C3C2×C3×D311yescharacteristic
190C24×D3—38no—
191C24×D3—36no—
192C24×D3—96no—
193C24×D3—98no—
194C24×D3—91no—
195C24×D3—93no—
196C24×D3—918no—
197C24×D3—93no—
198C24×D3—924no—
199C24×D3—96no—
200C24×D3—91no—
201C24×D3—98no—
202C23×A4—31no—
203C23×A4—61no—
204C23×A4—96no—
205C23×A4—98no—
206C23×C3×C4—33no—
207C23×C3×C4—33no—
208C23×C3×C4—318no—
209C23×C3×C4—31no—
210C23×C3×C4—31no—
211C23×C3×C4—36no—
212C23×C3×C4—36no—
213C23×C3×C4—361no—
214C23×C3×C4C2×C3×D316yes—
215C23×Dic3—36no—
216C23×Dic3—96no—
217C23×Dic3—91no—
218C23×Dic3—93no—
219C23×Dic3—918no—
220C23×Dic3—93no—
221C23×Dic3—96no—
222C23×Dic3—91no—
223C22×C4×D3—31no—
224C22×C4×D3—316no—
225C22×C4×D3—91no—
226C22×C4×D3—916no—
227C22×C4×D3—912no—
228C22×C4×D3—912no—
229C22×C4×D3—91no—
230C22×C4×D3—91no—
231C22×C4×D3—936no—
232C22×C4×D3—936no—
233C22×C4×D3—93no—
234C22×C4×D3—93no—
235C22×C4×D3—932no—
236C22×C4×D3—912no—
237C22×C4×D3—912no—
238C22×C4×D3—996no—
239C22×C4×D3—936no—
240C22×C4×D3—936no—
241C22×C4×D3—96no—
242C22×C4×D3—936no—
243C22×C4×D3—92no—
244C22×C4×D3—912no—
245C22×C4×D3—936no—
246C22×C4×D3—9144no—
247C22×C4×D3—936no—
248C22×C4×D3—936no—
249C22×C4×D3—93no—
250C22×C4×D3—91no—
251C22×C4×D3—948no—
252C22×C4×D3—912no—
253C22×C4×D3—912no—
254C22×C4×D3—912no—
255C2×C4×A4—36no—
256C2×C4×A4—66no—
257C2×C4×A4—916no—
258C2×C4×A4—96no—
259C23×C32—312no—
260C23×C32—36no—
261C23×C32—33no—
262C23×C32—312no—
263C23×C32—32no—
264C23×C32—34no—
265C23×C32—34no—
266C23×C32—33no—
267C23×C32—33no—
268C23×C32—41no—
269C23×C32—81no—
270C23×C32C22×C3×C416yescomplemented
271C23×C32C22×A411yescharacteristic
272C23×C32C24×C311yescharacteristic
273C22×C3⋊D3—348no—
274C22×C3⋊D3—324no—
275C22×C3⋊D3—364no—
276C22×C3⋊D3—348no—
277C22×C3⋊D3—312no—
278C22×C3⋊D3—38no—
279C22×C3⋊D3—36no—
280C22×C3⋊D3—324no—
281C22×C3⋊D3—348no—
282C22×C3⋊D3—324no—
283C22×C3⋊D3—34no—
284C22×C3⋊D3—312no—
285C22×C3⋊D3—324no—
286C22×C3⋊D3—348no—
287C22×C3⋊D3—38no—
288C22×C3⋊D3—34no—
289C22×C3⋊D3C4×A418yescomplemented
290C22×C3⋊D3C22×C3×C418yescomplemented
291C22×C3⋊D3C22×A416yes—
292C22×C3×D3—128no—
293C22×C3×D3—126no—
294C2×C3×A4—21no—
295C2×C3×A4—26no—
296C2×C3×A4C2×C4×D316yescomplemented
297C2×C3×A4C23×D311yescharacteristic
298D3×A4—38no—
299C2×C32×C4—312no—
300C2×C32×C4—36no—
301C2×C32×C4—312no—
302C2×C32×C4—34no—
303C2×C32×C4—34no—
304C2×C32×C4—46no—
305C2×C32×C4—86no—
306C2×C32×C4C22×A416yescomplemented
307C2×C3⋊Dic3—312no—
308C2×C3⋊Dic3—36no—
309C2×C3⋊Dic3—312no—
310C2×C3⋊Dic3—34no—
311C2×C3⋊Dic3—34no—
312C2×C3⋊Dic3C22×A416yescomplemented
313C4×C3⋊D3—332no—
314C4×C3⋊D3—316no—
315C4×C3⋊D3—316no—
316C4×C3⋊D3—316no—
317C4×C3⋊D3C22×A4116yescomplemented
318C2×C3×Dic3—126no—
319C3×C4×D3—1216no—
320C26—91no—
321C24×C4—91no—
322C24×C4—912no—
323C24×C4—271no—
324C24×C4—271no—
325C24×C4—2712no—
326C24×C4—271no—
327C24×C4—271no—
328C24×C4(C3⋊D3)⋊C311yescharacteristic, complemented
329C2×H(3,𝔽3)—46no—
330C2×H(3,𝔽3)—41no—
331(C3⋊D3)⋊C3—48no—
332C24×C3—33no—
333C24×C3—34no—
334C24×C3—39no—
335C24×C3—33no—
336C24×C3—312no—
337C24×C3—31no—
338C24×C3—34no—
339C24×C3—33no—
340C24×C3—361no—
341C24×C3C3×C4×D314yes—
342C24×C3C22×C3×D313yes—
343C23×D3—31no—
344C23×D3—34no—
345C23×D3—324no—
346C23×D3—924no—
347C23×D3—91no—
348C23×D3—94no—
349C23×D3—96no—
350C23×D3—96no—
351C23×D3—98no—
352C23×D3—98no—
353C23×D3—918no—
354C23×D3—918no—
355C23×D3—936no—
356C23×D3—918no—
357C23×D3—98no—
358C23×D3—924no—
359C23×D3—918no—
360C23×D3—96no—
361C23×D3—93no—
362C23×D3—924no—
363C23×D3—924no—
364C23×D3—9144no—
365C23×D3—924no—
366C23×D3—972no—
367C23×D3—948no—
368C23×D3—9144no—
369C23×D3—924no—
370C23×D3—98no—
371C23×D3—91no—
372C23×D3—912no—
373C23×D3—96no—
374C23×D3—948no—
375C23×D3—924no—
376C23×D3—98no—
377C22×A4—34no—
378C22×A4—33no—
379C22×A4—64no—
380C22×A4—63no—
381C22×A4—94no—
382C22×A4—924no—
383C22×C3×C4—318no—
384C22×C3×C4—324no—
385C22×C3×C4—36no—
386C22×C3×C4—38no—
387C22×C3×C4—33no—
388C22×C3×C4—318no—
389C22×C3×C4—318no—
390C22×C3×C4—318no—
391C22×C3×C4—336no—
392C22×C3×C4—31no—
393C22×C3×C4—36no—
394C22×C3×C4—36no—
395C22×C3×C4—36no—
396C22×C3×C4—312no—
397C22×C3×C4—31no—
398C22×C3×C4—34no—
399C22×C3×C4—121no—
400C22×C3×C4—241no—
401C22×C3×C4—3612no—
402C22×C3×C4—361no—
403C22×C3×C4D3×A411yescharacteristic
404C22×C3×C4C22×C3×D314yes—
405C22×Dic3—31no—
406C22×Dic3—34no—
407C22×Dic3—91no—
408C22×Dic3—94no—
409C22×Dic3—96no—
410C22×Dic3—96no—
411C22×Dic3—918no—
412C22×Dic3—918no—
413C22×Dic3—98no—
414C22×Dic3—924no—
415C22×Dic3—918no—
416C22×Dic3—96no—
417C22×Dic3—93no—
418C22×Dic3—936no—
419C22×Dic3—918no—
420C22×Dic3—91no—
421C22×Dic3—912no—
422C22×Dic3—96no—
423C2×C4×D3—312no—
424C2×C4×D3—912no—
425C2×C4×D3—916no—
426C2×C4×D3—948no—
427C2×C4×D3—912no—
428C2×C4×D3—912no—
429C2×C4×D3—948no—
430C2×C4×D3—9144no—
431C2×C4×D3—936no—
432C2×C4×D3—936no—
433C2×C4×D3—948no—
434C2×C4×D3—948no—
435C2×C4×D3—9144no—
436C2×C4×D3—9144no—
437C2×C4×D3—972no—
438C2×C4×D3—9144no—
439C2×C4×D3—924no—
440C2×C4×D3—948no—
441C2×C4×D3—948no—
442C2×C4×D3—948no—
443C2×C4×D3—948no—
444C2×C4×D3—936no—
445C2×C4×D3—912no—
446C2×C4×D3—916no—
447C2×C4×D3—916no—
448C2×C4×D3—916no—
449C4×A4—34no—
450C4×A4—64no—
451C4×A4—94no—
452C22×C32—36no—
453C22×C32—31no—
454C22×C32—38no—
455C22×C32—36no—
456C22×C32—312no—
457C22×C32—36no—
458C22×C32—36no—
459C22×C32—33no—
460C22×C32—31no—
461C22×C32—44no—
462C22×C32—43no—
463C22×C32—84no—
464C22×C32—83no—
465C22×C32C2×C4×A414yescomplemented
466C22×C32C23×C3×C411yescharacteristic, complemented
467C22×C32C23×A413yes—
468C2×C3⋊D3—38no—
469C2×C3⋊D3—348no—
470C2×C3⋊D3—324no—
471C2×C3⋊D3—34no—
472C2×C3⋊D3—38no—
473C2×C3⋊D3—348no—
474C2×C3⋊D3—38no—
475C2×C3⋊D3—38no—
476C2×C3⋊D3C2×C4×A4124yescomplemented
477C2×C3⋊D3C23×A414yes—
478C2×C3×D3—124no—
479C2×C3×D3—1224no—
480C3×A4—21no—
481C3×A4C22×C4×D311yescharacteristic, complemented
482C32×C4—34no—
483C32×C4—44no—
484C32×C4—84no—
485C32×C4C23×A414yescomplemented
486C3⋊Dic3—34no—
487C3⋊Dic3C23×A414yescomplemented
488C3×Dic3—124no—
489C25—98no—
490C25—96no—
491C25—271no—
492C25—276no—
493C25—271no—
494C25—278no—
495C25C2×(C3⋊D3)⋊C311yescharacteristic
496C23×C4—31no—
497C23×C4—31no—
498C23×C4—36no—
499C23×C4—91no—
500C23×C4—96no—
501C23×C4—916no—
502C23×C4—2712no—
503C23×C4—271no—
504C23×C4—2712no—
505C23×C4—271no—
506C23×C4—2732no—
507C23×C4—2712no—
508C23×C4—2712no—
509C23×C4—272no—
510C23×C4—2712no—
511C23×C4—2712no—
512C23×C4—2748no—
513C23×C4—2712no—
514C23×C4—2712no—
515C23×C4—271no—
516C23×C4—271no—
517C23×C4—276no—
518C23×C4—271no—
519C23×C4C2×(C3⋊D3)⋊C316yescomplemented
520H(3,𝔽3)—41noSylow
521C23×C3—33no—
522C23×C3—312no—
523C23×C3—36no—
524C23×C3—39no—
525C23×C3—36no—
526C23×C3—32no—
527C23×C3—39no—
528C23×C3—39no—
529C23×C3—336no—
530C23×C3—318no—
531C23×C3—336no—
532C23×C3—312no—
533C23×C3—312no—
534C23×C3—312no—
535C23×C3—34no—
536C23×C3—34no—
537C23×C3—33no—
538C23×C3—33no—
539C23×C3—31no—
540C23×C3—31no—
541C23×C3—36no—
542C23×C3—121no—
543C23×C3—241no—
544C23×C3—366no—
545C23×C3—368no—
546C23×C3C2×C3×C4×D316yes—
547C23×C3C2×D3×A411yescharacteristic
548C23×C3C23×C3×D311yescharacteristic
549C22×D3—38no—
550C22×D3—36no—
551C22×D3—38no—
552C22×D3—98no—
553C22×D3—98no—
554C22×D3—96no—
555C22×D3—94no—
556C22×D3—912no—
557C22×D3—924no—
558C22×D3—924no—
559C22×D3—948no—
560C22×D3—912no—
561C22×D3—936no—
562C22×D3—912no—
563C22×D3—936no—
564C22×D3—912no—
565C22×D3—918no—
566C22×D3—972no—
567C22×D3—972no—
568C22×D3—9144no—
569C22×D3—9144no—
570C22×D3—972no—
571C22×D3—924no—
572C22×D3—964no—
573C22×D3—948no—
574C22×D3—9144no—
575C22×D3—9192no—
576C22×D3—972no—
577C22×D3—9144no—
578C22×D3—948no—
579C22×D3—924no—
580C22×D3—924no—
581C22×D3—98no—
582C22×D3—96no—
583C22×D3—94no—
584C22×D3—98no—
585C22×D3—948no—
586C22×D3—924no—
587C2×A4—31no—
588C2×A4—36no—
589C2×A4—61no—
590C2×A4—66no—
591C2×A4—98no—
592C2×C3×C4—336no—
593C2×C3×C4—312no—
594C2×C3×C4—318no—
595C2×C3×C4—312no—
596C2×C3×C4—336no—
597C2×C3×C4—312no—
598C2×C3×C4—36no—
599C2×C3×C4—312no—
600C2×C3×C4—34no—
601C2×C3×C4—34no—
602C2×C3×C4—36no—
603C2×C3×C4—126no—
604C2×C3×C4—246no—
605C2×C3×C4—3616no—
606C2×C3×C4—366no—
607C2×C3×C4C2×D3×A416yes—
608C2×Dic3—36no—
609C2×Dic3—96no—
610C2×Dic3—94no—
611C2×Dic3—912no—
612C2×Dic3—912no—
613C2×Dic3—936no—
614C2×Dic3—936no—
615C2×Dic3—912no—
616C2×Dic3—918no—
617C2×Dic3—912no—
618C2×Dic3—96no—
619C2×Dic3—94no—
620C4×D3—316no—
621C4×D3—916no—
622C4×D3—916no—
623C4×D3—916no—
624C4×D3—948no—
625C4×D3—948no—
626C4×D3—996no—
627C4×D3—932no—
628C4×D3—948no—
629C4×D3—916no—
630C2×C32—36no—
631C2×C32—31no—
632C2×C32—31no—
633C2×C32—46no—
634C2×C32—41no—
635C2×C32—86no—
636C2×C32—81no—
637C2×C32C22×C4×A416yescomplemented
638C2×C32C24×A411yescharacteristic
639C3⋊D3—38no—
640C3⋊D3C22×C4×A418yescomplemented
641C3×D3—128no—
642C24—33no—
643C24—34no—
644C24—31no—
645C24—91no—
646C24—94no—
647C24—924no—
648C24—276no—
649C24—276no—
650C24—278no—
651C24—278no—
652C24—2712no—
653C24—276no—
654C24—2748no—
655C24—2724no—
656C24—278no—
657C24—278no—
658C24—276no—
659C24—2748no—
660C24—278no—
661C24—271no—
662C24C4×(C3⋊D3)⋊C314yescomplemented
663C24C22×(C3⋊D3)⋊C313yes—
664C22×C4—36no—
665C22×C4—38no—
666C22×C4—31no—
667C22×C4—36no—
668C22×C4—36no—
669C22×C4—36no—
670C22×C4—312no—
671C22×C4—91no—
672C22×C4—912no—
673C22×C4—94no—
674C22×C4—2716no—
675C22×C4—2712no—
676C22×C4—2748no—
677C22×C4—2712no—
678C22×C4—2748no—
679C22×C4—2748no—
680C22×C4—2724no—
681C22×C4—2748no—
682C22×C4—2716no—
683C22×C4—2716no—
684C22×C4—2716no—
685C22×C4—276no—
686C22×C4—276no—
687C22×C4—278no—
688C22×C4—276no—
689C22×C4—271no—
690C22×C4—2712no—
691C22×C4—2712no—
692C22×C4—276no—
693C22×C4(C3⋊D3)⋊A411yescharacteristic, direct product factor
694C22×C4C22×(C3⋊D3)⋊C314yescomplemented
695C22×C3—31no—
696C22×C3—36no—
697C22×C3—33no—
698C22×C3—39no—
699C22×C3—33no—
700C22×C3—318no—
701C22×C3—318no—
702C22×C3—324no—
703C22×C3—36no—
704C22×C3—38no—
705C22×C3—318no—
706C22×C3—336no—
707C22×C3—318no—
708C22×C3—36no—
709C22×C3—312no—
710C22×C3—36no—
711C22×C3—31no—
712C22×C3—33no—
713C22×C3—33no—
714C22×C3—31no—
715C22×C3—34no—
716C22×C3—123no—
717C22×C3—124no—
718C22×C3—243no—
719C22×C3—244no—
720C22×C3—364no—
721C22×C3—3624no—
722C22×C3C4×D3×A414yes—
723C22×C3C22×C3×C4×D311yescharacteristic
724C22×C3C22×D3×A413yes—
725C2×D3—324no—
726C2×D3—34no—
727C2×D3—94no—
728C2×D3—924no—
729C2×D3—98no—
730C2×D3—98no—
731C2×D3—948no—
732C2×D3—912no—
733C2×D3—924no—
734C2×D3—924no—
735C2×D3—9144no—
736C2×D3—924no—
737C2×D3—924no—
738C2×D3—9144no—
739C2×D3—948no—
740C2×D3—98no—
741C2×D3—972no—
742C2×D3—924no—
743C2×D3—94no—
744C2×D3—98no—
745A4—31no—
746A4—61no—
747C3×C4—312no—
748C3×C4—34no—
749C3×C4—34no—
750C3×C4—124no—
751C3×C4—244no—
752C3×C4—364no—
753C3×C4C22×D3×A414yes—
754Dic3—34no—
755Dic3—94no—
756Dic3—912no—
757Dic3—94no—
758C32—41no—
759C32—81no—
760C32C23×C4×A411yescharacteristic, complemented
761C23—33no—
762C23—312no—
763C23—36no—
764C23—32no—
765C23—312no—
766C23—33no—
767C23—33no—
768C23—34no—
769C23—34no—
770C23—96no—
771C23—98no—
772C23—98no—
773C23—274no—
774C23—2712no—
775C23—2724no—
776C23—2724no—
777C23—2748no—
778C23—274no—
779C23—278no—
780C23—2748no—
781C23—2724no—
782C23—2712no—
783C23—2748no—
784C23—2764no—
785C23—2724no—
786C23—2748no—
787C23—276no—
788C23—278no—
789C23C2×C4×(C3⋊D3)⋊C316yescomplemented
790C23C2×(C3⋊D3)⋊A411yescharacteristic
791C23C23×(C3⋊D3)⋊C311yescharacteristic
792C2×C4—312no—
793C2×C4—36no—
794C2×C4—34no—
795C2×C4—312no—
796C2×C4—34no—
797C2×C4—96no—
798C2×C4—916no—
799C2×C4—2716no—
800C2×C4—2716no—
801C2×C4—2732no—
802C2×C4—274no—
803C2×C4—2712no—
804C2×C4—2712no—
805C2×C4—276no—
806C2×C4—2716no—
807C2×C4—274no—
808C2×C4C2×(C3⋊D3)⋊A416yesdirect product factor
809C2×C3—33no—
810C2×C3—33no—
811C2×C3—318no—
812C2×C3—31no—
813C2×C3—31no—
814C2×C3—36no—
815C2×C3—36no—
816C2×C3—31no—
817C2×C3—126no—
818C2×C3—121no—
819C2×C3—246no—
820C2×C3—241no—
821C2×C3—368no—
822C2×C3C2×C4×D3×A416yes—
823C2×C3C23×D3×A411yescharacteristic
824D3—38no—
825D3—98no—
826D3—924no—
827D3—98no—
828C22—31no—
829C22—36no—
830C22—36no—
831C22—38no—
832C22—36no—
833C22—312no—
834C22—36no—
835C22—31no—
836C22—33no—
837C22—924no—
838C22—94no—
839C22—278no—
840C22—278no—
841C22—2748no—
842C22—278no—
843C22—278no—
844C22—2748no—
845C22—2724no—
846C22—274no—
847C22C4×(C3⋊D3)⋊A414yesdirect product factor
848C22C22×C4×(C3⋊D3)⋊C311yescharacteristic, complemented
849C22C22×(C3⋊D3)⋊A413yes—
850C4—34no—
851C4—94no—
852C4—274no—
853C4C22×(C3⋊D3)⋊A414yesdirect product factor
854C3—31no—
855C3—121no—
856C3—241no—
857C3C22×C4×D3×A411yescharacteristic
858C2—31no—
859C2—31no—
860C2—36no—
861C2—98no—
862C2—278no—
863C2C2×C4×(C3⋊D3)⋊A416yesdirect product factor
864C2C23×(C3⋊D3)⋊A411yescharacteristic
subgroupG/H
center, hypercenterC22×C4(C3⋊D3)⋊A4
commutator, hypocenterC22×C32C23×C3×C4
FrattiniC2×C3C23×D3×A4
FittingC24×C32×C4C2×C3
socleC25×C3C2×C3×D3
prime radicalC23×(C3⋊D3)⋊A4C2
cosocleC23×C32C24×C3
LCSG ▷ C22×C32
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊H(3,𝔽3)C2semidirect
3. C22×(C3⋊Dic3)⋊A4C2semidirect
4. C2×C4×(C3⋊D3)⋊A4C2direct (N × H)
6. C24×C4×C3⋊D3C3semidirect
8. C22×(C3⋊D3)⋊A4C4direct (N × H)
11. C2×C4×C22⋊H(3,𝔽3)C22semidirect
12. C2×(C3⋊Dic3)⋊A4C22semidirect
13. C4×(C3⋊D3)⋊A4C22direct (N × H)
16. C24×C32×C4C2×C3semidirect
17. C24×C3⋊Dic3C2×C3semidirect
23. C23×C4×C3⋊D3C2×C3semidirect
25. C22×C3×C4×A4D3semidirect
29. C22×C22⋊H(3,𝔽3)C2×C4semidirect
31. C2×(C3⋊D3)⋊A4C2×C4direct (N × H)
36. C4×C22⋊H(3,𝔽3)C23semidirect
37. (C3⋊Dic3)⋊A4C23semidirect
46. C24×C3⋊D3C3×C4semidirect
55. C23×C32×C4C22×C3semidirect
59. C23×C3⋊Dic3C22×C3semidirect
74. C22×C4×C3⋊D3A4semidirect
75. C22×C4×C3⋊D3C22×C3semidirect
78. C2×C3×C4×A4C2×D3semidirect
84. C2×C22⋊H(3,𝔽3)C22×C4semidirect
86. (C3⋊D3)⋊A4C22×C4direct (N × H)
116. C24×C32C2×C3×C4semidirect
132. C23×C3⋊D3C2×C3×C4semidirect
138. C22×C3×A4C4×D3semidirect
151. C22×C32×C4C2×A4semidirect
152. C22×C32×C4C23×C3semidirect
160. C22×C3⋊Dic3C2×A4semidirect
161. C22×C3⋊Dic3C23×C3semidirect
174. C2×C4×C3⋊D3C2×A4semidirect
178. C3×C4×A4C22×D3semidirect
185. C22⋊H(3,𝔽3)C23×C4semidirect
270. C23×C32C22×C3×C4semidirect
289. C22×C3⋊D3C4×A4semidirect
290. C22×C3⋊D3C22×C3×C4semidirect
296. C2×C3×A4C2×C4×D3semidirect
306. C2×C32×C4C22×A4semidirect
312. C2×C3⋊Dic3C22×A4semidirect
317. C4×C3⋊D3C22×A4semidirect
328. C24×C4(C3⋊D3)⋊C3semidirect
465. C22×C32C2×C4×A4semidirect
466. C22×C32C23×C3×C4semidirect
476. C2×C3⋊D3C2×C4×A4semidirect
481. C3×A4C22×C4×D3semidirect
485. C32×C4C23×A4semidirect
487. C3⋊Dic3C23×A4semidirect
519. C23×C4C2×(C3⋊D3)⋊C3semidirect
637. C2×C32C22×C4×A4semidirect
640. C3⋊D3C22×C4×A4semidirect
662. C24C4×(C3⋊D3)⋊C3semidirect
693. C22×C4(C3⋊D3)⋊A4direct (N × H)
694. C22×C4C22×(C3⋊D3)⋊C3semidirect
760. C32C23×C4×A4semidirect
789. C23C2×C4×(C3⋊D3)⋊C3semidirect
808. C2×C4C2×(C3⋊D3)⋊A4direct (N × H)
847. C22C4×(C3⋊D3)⋊A4direct (N × H)
848. C22C22×C4×(C3⋊D3)⋊C3semidirect
853. C4C22×(C3⋊D3)⋊A4direct (N × H)
863. C2C2×C4×(C3⋊D3)⋊A4direct (N × H)

Maximal subgroups

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

subgroupindex
C23×(C3⋊D3)⋊A42
C22×C4×C22⋊H(3,𝔽3)2
C22×(C3⋊Dic3)⋊A42
C2×C4×(C3⋊D3)⋊A42
C22×C4×D3×A43
C24×C4×C3⋊D33
C22×C4×(C3⋊D3)⋊C34