Finite Group Databasebeta

← C2×3−1+2×#997 #72245854

Subgroups — C2×3−1+2×#997 #72245854

Order 5184.

2116 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 2116 conjugacy classes of subgroups — too many to draw. Only its 169 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
13−1+2×#997C211yesmaximal, characteristic, direct product factor
2C2×C32×#997C311yesmaximal, characteristic
3C2×3−1+2×H(5,𝔽2)C311yesmaximal, characteristic, complemented
4C2×#11722589C312yesmaximal, complemented
5C2×C9⋊#997C316yesmaximal, complemented
6C2×C9×#997C313yesmaximal, complemented
7C22×A4×3−1+2—42nomaximal
8C22×A4×3−1+2—41nomaximal
9C2×SL(2,𝔽3)×3−1+2—42nomaximal
10C32×#997C2×C311yescharacteristic
113−1+2×H(5,𝔽2)—32no—
123−1+2×H(5,𝔽2)—31no—
133−1+2×H(5,𝔽2)—32no—
143−1+2×H(5,𝔽2)C2×C311yescharacteristic, complemented
15C2×#41×3−1+2—32no—
16C22×D4×3−1+2—32no—
17C22×D4×3−1+2—31no—
18#11722589C2×C312yescomplemented
19C9⋊#997C2×C316yescomplemented
20C9×#997C2×C313yescomplemented
21C2×A4×3−1+2—42no—
22C2×A4×3−1+2—41no—
23C2×A4×3−1+2—42no—
24C2×A4×3−1+2—41no—
25C2×A4×3−1+2—42no—
26C2×A4×3−1+2—41no—
27SL(2,𝔽3)×3−1+2—42no—
28C2×C32×H(5,𝔽2)C3211yescharacteristic
29C2×C3×#997—33no—
30C2×C3×#997C3212yes—
31C2×C3×#997C3211yescharacteristic
32C2×C9×H(5,𝔽2)C3213yescomplemented
33C2×#63703C3216yescomplemented
34C22×C32×A4—42no—
35C22×C32×A4—41no—
36C2×C32×SL(2,𝔽3)—42no—
37C24×3−1+2—31no—
38C24×3−1+2A412yescomplemented
39C24×3−1+2A411yescharacteristic, complemented
40C22×#1094—44no—
41C22×#1094—42no—
42C22×C9⋊A4—412no—
43C22×C9⋊A4—46no—
44C22×C9×A4—46no—
45C22×C9×A4—43no—
46#41×3−1+2—32no—
47#41×3−1+2—34no—
48#41×3−1+2—32no—
49#41×3−1+2—34no—
50#41×3−1+2—32no—
51#41×3−1+2—32no—
52C2×Q8×3−1+2A412yescomplemented
53C2×D4×3−1+2—32no—
54C2×D4×3−1+2—34no—
55C2×D4×3−1+2—32no—
56C2×D4×3−1+2—31no—
57C2×D4×3−1+2—34no—
58C2×D4×3−1+2—34no—
59C2×D4×3−1+2—34no—
60C2×D4×3−1+2—32no—
61C2×D4×3−1+2—31no—
62C2×D4×3−1+2—32no—
63C2×D4×3−1+2—31no—
64C2×D4×3−1+2—32no—
65C2×D4×3−1+2—31no—
66C22×C4×3−1+2—32no—
67C22×C4×3−1+2—31no—
68C2×#6204—44no—
69C2×C9⋊SL(2,𝔽3)—412no—
70C2×C9×SL(2,𝔽3)—46no—
71C22×C3×3−1+2—161no—
72A4×3−1+2—42no—
73A4×3−1+2—41no—
74C32×H(5,𝔽2)—32no—
75C32×H(5,𝔽2)—31no—
76C32×H(5,𝔽2)—32no—
77C32×H(5,𝔽2)C2×C3211yescharacteristic
78C2×C32×#41—32no—
79C22×C32×D4—32no—
80C22×C32×D4—31no—
81C3×#997—33no—
82C3×#997C2×C3212yes—
83C3×#997C2×C3211yescharacteristic
84C9×H(5,𝔽2)—36no—
85C9×H(5,𝔽2)—33no—
86C9×H(5,𝔽2)—36no—
87C9×H(5,𝔽2)C2×C3213yescomplemented
88C2×C9×#41—36no—
89C22×D4×C9—36no—
90C22×D4×C9—33no—
91#63703C2×C3216yescomplemented
92C2×C32×A4—42no—
93C2×C32×A4—41no—
94C2×C32×A4—42no—
95C2×C32×A4—41no—
96C2×C32×A4—42no—
97C2×C32×A4—41no—
98C32×SL(2,𝔽3)—42no—
99C23×3−1+2—31no—
100C23×3−1+2—32no—
101C23×3−1+2—31no—
102C23×3−1+2—32no—
103C23×3−1+2—31no—
104C23×3−1+2—32no—
105C23×3−1+2—31no—
106C23×3−1+2—42no—
107C23×3−1+2—122no—
108C23×3−1+2—121no—
109C23×3−1+2—121no—
110C23×3−1+2—121no—
111C23×3−1+2—121no—
112C23×3−1+2C2×A412yescomplemented
113C23×3−1+2C2×A411yescharacteristic, complemented
114C2×#1094—44no—
115C2×#1094—42no—
116C2×#1094—44no—
117C2×#1094—42no—
118C2×#1094—44no—
119C2×#1094—42no—
120C2×C9⋊A4—412no—
121C2×C9⋊A4—46no—
122C2×C9⋊A4—412no—
123C2×C9⋊A4—46no—
124C2×C9⋊A4—412no—
125C2×C9⋊A4—46no—
126C2×C9×A4—46no—
127C2×C9×A4—43no—
128C2×C9×A4—46no—
129C2×C9×A4—43no—
130C2×C9×A4—46no—
131C2×C9×A4—43no—
132Q8×3−1+2—32no—
133Q8×3−1+2C2×A412yescomplemented
134D4×3−1+2—34no—
135D4×3−1+2—34no—
136D4×3−1+2—34no—
137D4×3−1+2—32no—
138D4×3−1+2—34no—
139D4×3−1+2—32no—
140D4×3−1+2—34no—
141C2×C4×3−1+2—32no—
142C2×C4×3−1+2—31no—
143C2×C4×3−1+2—34no—
144C2×C4×3−1+2—32no—
145C2×C4×3−1+2—32no—
146C2×C4×3−1+2—31no—
147C2×C4×3−1+2—32no—
148#6204—44no—
149C9⋊SL(2,𝔽3)—412no—
150C9×SL(2,𝔽3)—46no—
151C2×C3×H(5,𝔽2)—31no—
152C2×C3×H(5,𝔽2)C3311yescharacteristic
153C2×#997—32no—
154C2×#9973−1+213yesdirect product factor
155C2×C3×3−1+2—161no—
156C2×C3×3−1+2—161no—
157C2×C3×3−1+2—161no—
158C24×C32—31no—
159C24×C32C3×A412yes—
160C24×C32C3×A411yescharacteristic
161C22×C3×A4—42no—
162C22×C3×A4—41no—
163C22×C3×A4—44no—
164C22×C3×A4—42no—
165C22×C3×A4—126no—
166C22×C3×A4—123no—
167C32×#41—32no—
168C32×#41—34no—
169C32×#41—32no—
170C32×#41—34no—
171C32×#41—32no—
172C32×#41—32no—
173C2×C32×Q8C3×A412yes—
174C2×C32×D4—32no—
175C2×C32×D4—34no—
176C2×C32×D4—32no—
177C2×C32×D4—31no—
178C2×C32×D4—34no—
179C2×C32×D4—34no—
180C2×C32×D4—34no—
181C2×C32×D4—32no—
182C2×C32×D4—31no—
183C2×C32×D4—32no—
184C2×C32×D4—31no—
185C2×C32×D4—32no—
186C2×C32×D4—31no—
187C22×C32×C4—32no—
188C22×C32×C4—31no—
189C2×C3×SL(2,𝔽3)—42no—
190C2×C3×SL(2,𝔽3)—44no—
191C2×C3×SL(2,𝔽3)—126no—
192C24×C9—33no—
193C24×C9C3×A416yescomplemented
194C24×C9C3×A413yescomplemented
195C22×C22⋊C9—412no—
196C22×C22⋊C9—46no—
197C9×#41—36no—
198C9×#41—312no—
199C9×#41—36no—
200C9×#41—312no—
201C9×#41—36no—
202C9×#41—36no—
203C2×Q8×C9C3×A416yescomplemented
204C2×D4×C9—36no—
205C2×D4×C9—312no—
206C2×D4×C9—36no—
207C2×D4×C9—33no—
208C2×D4×C9—312no—
209C2×D4×C9—312no—
210C2×D4×C9—312no—
211C2×D4×C9—36no—
212C2×D4×C9—33no—
213C2×D4×C9—36no—
214C2×D4×C9—33no—
215C2×D4×C9—36no—
216C2×D4×C9—33no—
217C22×C4×C9—36no—
218C22×C4×C9—33no—
219C2×Q8⋊C9—412no—
220C22×C33—161no—
221C32×A4—42no—
222C32×A4—41no—
223C22×3−1+2—32no—
224C22×3−1+2—31no—
225C22×3−1+2—32no—
226C22×3−1+2—31no—
227C22×3−1+2—42no—
228C22×3−1+2—41no—
229C22×3−1+2—62no—
230C22×3−1+2—62no—
231C22×3−1+2—61no—
232C22×3−1+2—61no—
233C22×3−1+2—121no—
234C22×3−1+2—122no—
235C22×3−1+2—121no—
236C22×3−1+2—122no—
237C22×3−1+2—121no—
238C22×3−1+2—162no—
239C22×3−1+2—166no—
240C22×3−1+2C22⋊A411yescharacteristic
241C22×C3×C9—163no—
242#1094—44no—
243#1094—42no—
244C9⋊A4—412no—
245C9⋊A4—46no—
246C9×A4—46no—
247C9×A4—43no—
248C4×3−1+2—32no—
249C4×3−1+2—32no—
250C3×H(5,𝔽2)—32no—
251C3×H(5,𝔽2)—31no—
252C3×H(5,𝔽2)—32no—
253C3×H(5,𝔽2)—31no—
254C3×H(5,𝔽2)—92no—
255C3×H(5,𝔽2)—92no—
256C3×H(5,𝔽2)—91no—
257C3×H(5,𝔽2)C2×C3311yescharacteristic
258C2×C3×#41—32no—
259C2×C3×#41—92no—
260C22×C3×D4—32no—
261C22×C3×D4—31no—
262C22×C3×D4—92no—
263C22×C3×D4—91no—
264#997—32no—
265#997C2×3−1+213yesdirect product factor
266C3×3−1+2—161noSylow
267C23×C32—31no—
268C23×C32—32no—
269C23×C32—31no—
270C23×C32—32no—
271C23×C32—31no—
272C23×C32—32no—
273C23×C32—31no—
274C23×C32—42no—
275C23×C32—122no—
276C23×C32—121no—
277C23×C32—121no—
278C23×C32—121no—
279C23×C32—121no—
280C23×C32C2×C3×A412yes—
281C23×C32C2×C3×A411yescharacteristic
282C2×C3×A4—42no—
283C2×C3×A4—41no—
284C2×C3×A4—42no—
285C2×C3×A4—41no—
286C2×C3×A4—42no—
287C2×C3×A4—41no—
288C2×C3×A4—44no—
289C2×C3×A4—42no—
290C2×C3×A4—44no—
291C2×C3×A4—42no—
292C2×C3×A4—44no—
293C2×C3×A4—42no—
294C2×C3×A4—126no—
295C2×C3×A4—123no—
296C2×C3×A4—126no—
297C2×C3×A4—123no—
298C2×C3×A4—126no—
299C2×C3×A4—123no—
300C32×Q8—32no—
301C32×Q8C2×C3×A412yes—
302C32×D4—34no—
303C32×D4—34no—
304C32×D4—34no—
305C32×D4—32no—
306C32×D4—34no—
307C32×D4—32no—
308C32×D4—34no—
309C2×C32×C4—32no—
310C2×C32×C4—31no—
311C2×C32×C4—34no—
312C2×C32×C4—32no—
313C2×C32×C4—32no—
314C2×C32×C4—31no—
315C2×C32×C4—32no—
316C3×SL(2,𝔽3)—42no—
317C3×SL(2,𝔽3)—44no—
318C3×SL(2,𝔽3)—126no—
319C23×C9—33no—
320C23×C9—36no—
321C23×C9—33no—
322C23×C9—36no—
323C23×C9—33no—
324C23×C9—36no—
325C23×C9—33no—
326C23×C9—46no—
327C23×C9—126no—
328C23×C9—123no—
329C23×C9—123no—
330C23×C9—123no—
331C23×C9—123no—
332C23×C9C2×C3×A416yescomplemented
333C23×C9C2×C3×A413yescomplemented
334C2×C22⋊C9—412no—
335C2×C22⋊C9—46no—
336C2×C22⋊C9—412no—
337C2×C22⋊C9—46no—
338C2×C22⋊C9—412no—
339C2×C22⋊C9—46no—
340Q8×C9—36no—
341Q8×C9C2×C3×A416yescomplemented
342D4×C9—312no—
343D4×C9—312no—
344D4×C9—312no—
345D4×C9—36no—
346D4×C9—312no—
347D4×C9—36no—
348D4×C9—312no—
349C2×C4×C9—36no—
350C2×C4×C9—33no—
351C2×C4×C9—312no—
352C2×C4×C9—36no—
353C2×C4×C9—36no—
354C2×C4×C9—33no—
355C2×C4×C9—36no—
356Q8⋊C9—412no—
357C2×H(5,𝔽2)C3×3−1+211yescharacteristic, complemented, Sylow
358C2×C33—161no—
359C2×C33—161no—
360C2×C33—161no—
361C2×3−1+2—62no—
362C2×3−1+2—61no—
363C2×3−1+2—62no—
364C2×3−1+2—61no—
365C2×3−1+2—162no—
366C2×3−1+2—162no—
367C2×3−1+2—162no—
368C2×3−1+2—166no—
369C2×3−1+2—166no—
370C2×3−1+2—166no—
371C2×3−1+2#99711yescharacteristic, direct product factor
372C2×3−1+2#99711yescharacteristic, direct product factor
373C2×3−1+2C2×C22⋊A411yescharacteristic
374C2×C3×C9—163no—
375C2×C3×C9—163no—
376C2×C3×C9—163no—
377C24×C3—31no—
378C24×C3—32no—
379C24×C3—31no—
380C24×C3—91no—
381C24×C3C32×A412yes—
382C24×C3C32×A411yescharacteristic
383C22×A4—46no—
384C22×A4—43no—
385C22×A4—124no—
386C22×A4—122no—
387C3×#41—34no—
388C3×#41—32no—
389C3×#41—34no—
390C3×#41—32no—
391C3×#41—32no—
392C3×#41—32no—
393C3×#41—92no—
394C3×#41—92no—
395C3×#41—94no—
396C3×#41—92no—
397C3×#41—94no—
398C3×#41—92no—
399C2×C3×Q8—32no—
400C2×C3×Q8C32×A412yes—
401C2×C3×D4—32no—
402C2×C3×D4—34no—
403C2×C3×D4—32no—
404C2×C3×D4—31no—
405C2×C3×D4—34no—
406C2×C3×D4—34no—
407C2×C3×D4—34no—
408C2×C3×D4—32no—
409C2×C3×D4—31no—
410C2×C3×D4—32no—
411C2×C3×D4—31no—
412C2×C3×D4—32no—
413C2×C3×D4—31no—
414C2×C3×D4—92no—
415C2×C3×D4—91no—
416C2×C3×D4—92no—
417C2×C3×D4—91no—
418C2×C3×D4—92no—
419C2×C3×D4—94no—
420C2×C3×D4—92no—
421C2×C3×D4—91no—
422C2×C3×D4—94no—
423C2×C3×D4—94no—
424C2×C3×D4—94no—
425C2×C3×D4—92no—
426C2×C3×D4—91no—
427C22×C3×C4—32no—
428C22×C3×C4—31no—
429C22×C3×C4—92no—
430C22×C3×C4—91no—
431C2×SL(2,𝔽3)—46no—
432C2×SL(2,𝔽3)—124no—
433C22×C32—32no—
434C22×C32—31no—
435C22×C32—32no—
436C22×C32—31no—
437C22×C32—42no—
438C22×C32—41no—
439C22×C32—62no—
440C22×C32—62no—
441C22×C32—61no—
442C22×C32—61no—
443C22×C32—122no—
444C22×C32—121no—
445C22×C32—121no—
446C22×C32—122no—
447C22×C32—121no—
448C22×C32—161no—
449C22×C32—162no—
450C22×C32—483no—
451C22×C32C3×C22⋊A411yescharacteristic
452C3×A4—42no—
453C3×A4—41no—
454C3×A4—44no—
455C3×A4—42no—
456C3×A4—126no—
457C3×A4—123no—
458C32×C4—32no—
459C32×C4—32no—
460C22×C9—36no—
461C22×C9—33no—
462C22×C9—36no—
463C22×C9—33no—
464C22×C9—46no—
465C22×C9—43no—
466C22×C9—66no—
467C22×C9—66no—
468C22×C9—63no—
469C22×C9—63no—
470C22×C9—126no—
471C22×C9—123no—
472C22×C9—123no—
473C22×C9—126no—
474C22×C9—123no—
475C22×C9—166no—
476C22×C9C3×C22⋊A413yes—
477C22⋊C9—412no—
478C22⋊C9—46no—
479C4×C9—36no—
480C4×C9—36no—
481H(5,𝔽2)—32no—
482H(5,𝔽2)—31no—
483H(5,𝔽2)—32no—
484H(5,𝔽2)C2×C3×3−1+211yescharacteristic, complemented
485C2×#41—32no—
486C22×D4—32no—
487C22×D4—31no—
488C33—161no—
4893−1+2—162no—
4903−1+2—166no—
4913−1+2C2×#99711yescharacteristic, direct product factor
492C3×C9—163no—
493C23×C3—31no—
494C23×C3—32no—
495C23×C3—31no—
496C23×C3—32no—
497C23×C3—31no—
498C23×C3—32no—
499C23×C3—31no—
500C23×C3—32no—
501C23×C3—31no—
502C23×C3—42no—
503C23×C3—92no—
504C23×C3—91no—
505C23×C3—91no—
506C23×C3—92no—
507C23×C3—91no—
508C23×C3—92no—
509C23×C3—91no—
510C23×C3—122no—
511C23×C3—122no—
512C23×C3—121no—
513C23×C3—121no—
514C23×C3—121no—
515C23×C3—121no—
516C23×C3—362no—
517C23×C3—361no—
518C23×C3—361no—
519C23×C3—361no—
520C23×C3—361no—
521C23×C3C2×C32×A412yes—
522C23×C3C2×C32×A411yescharacteristic
523C2×A4—46no—
524C2×A4—43no—
525C2×A4—46no—
526C2×A4—43no—
527C2×A4—46no—
528C2×A4—43no—
529C2×A4—124no—
530C2×A4—122no—
531C2×A4—124no—
532C2×A4—122no—
533C2×A4—124no—
534C2×A4—122no—
535C3×Q8—32no—
536C3×Q8—32no—
537C3×Q8—92no—
538C3×Q8C2×C32×A412yes—
539C3×D4—32no—
540C3×D4—34no—
541C3×D4—32no—
542C3×D4—34no—
543C3×D4—34no—
544C3×D4—34no—
545C3×D4—34no—
546C3×D4—92no—
547C3×D4—94no—
548C3×D4—92no—
549C3×D4—94no—
550C3×D4—94no—
551C3×D4—94no—
552C3×D4—94no—
553C2×C3×C4—32no—
554C2×C3×C4—31no—
555C2×C3×C4—34no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—31no—
559C2×C3×C4—32no—
560C2×C3×C4—92no—
561C2×C3×C4—92no—
562C2×C3×C4—91no—
563C2×C3×C4—94no—
564C2×C3×C4—92no—
565C2×C3×C4—92no—
566C2×C3×C4—91no—
567SL(2,𝔽3)—46no—
568SL(2,𝔽3)—124no—
569C2×C32—62no—
570C2×C32—61no—
571C2×C32—62no—
572C2×C32—61no—
573C2×C32—161no—
574C2×C32—161no—
575C2×C32—161no—
576C2×C32—162no—
577C2×C32—162no—
578C2×C32—162no—
579C2×C32—483no—
580C2×C32—483no—
581C2×C32—483no—
582C2×C32C3×#99711yescharacteristic
583C2×C32C3×#99711yescharacteristic
584C2×C32C2×C3×C22⋊A411yescharacteristic
585C2×C9—66no—
586C2×C9—63no—
587C2×C9—66no—
588C2×C9—63no—
589C2×C9—166no—
590C2×C9—166no—
591C2×C9—166no—
592C2×C9C3×#99713yescomplemented
593C2×C9C3×#99713yescomplemented
594C2×C9C2×C3×C22⋊A413yes—
595C24—31no—
596C24A4×3−1+212yescomplemented
597C24A4×3−1+211yescharacteristic, complemented
598#41—34no—
599#41—32no—
600#41—34no—
601#41—32no—
602#41—32no—
603#41—32no—
604C2×Q8A4×3−1+212yescomplemented
605C2×D4—32no—
606C2×D4—34no—
607C2×D4—32no—
608C2×D4—31no—
609C2×D4—34no—
610C2×D4—34no—
611C2×D4—34no—
612C2×D4—32no—
613C2×D4—31no—
614C2×D4—32no—
615C2×D4—31no—
616C2×D4—32no—
617C2×D4—31no—
618C22×C4—32no—
619C22×C4—31no—
620C22×C3—32no—
621C22×C3—31no—
622C22×C3—32no—
623C22×C3—31no—
624C22×C3—31no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—62no—
628C22×C3—62no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—92no—
632C22×C3—91no—
633C22×C3—92no—
634C22×C3—91no—
635C22×C3—122no—
636C22×C3—121no—
637C22×C3—122no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—122no—
641C22×C3—121no—
642C22×C3—163no—
643C22×C3—182no—
644C22×C3—181no—
645C22×C3—182no—
646C22×C3—181no—
647C22×C3—362no—
648C22×C3—361no—
649C22×C3—361no—
650C22×C3—362no—
651C22×C3—361no—
652C22×C3—482no—
653C22×C3C32×C22⋊A411yescharacteristic
654A4—46no—
655A4—43no—
656A4—124no—
657A4—122no—
658C3×C4—32no—
659C3×C4—32no—
660C3×C4—92no—
661C3×C4—92no—
662C32—161no—
663C32—162no—
664C32—483no—
665C32C2×C3×#99711yescharacteristic
666C9—166no—
667C9C2×C3×#99713yescomplemented
668C23—31no—
669C23—32no—
670C23—31no—
671C23—32no—
672C23—31no—
673C23—32no—
674C23—31no—
675C23—42no—
676C23—122no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23C2×A4×3−1+212yescomplemented
682C23C2×A4×3−1+211yescharacteristic, complemented
683Q8—32no—
684Q8C2×A4×3−1+212yescomplemented
685D4—32no—
686D4—34no—
687D4—32no—
688D4—34no—
689D4—34no—
690D4—34no—
691D4—34no—
692C2×C4—32no—
693C2×C4—31no—
694C2×C4—34no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—31no—
698C2×C4—32no—
699C2×C3—31no—
700C2×C3—31no—
701C2×C3—31no—
702C2×C3—62no—
703C2×C3—61no—
704C2×C3—62no—
705C2×C3—61no—
706C2×C3—163no—
707C2×C3—163no—
708C2×C3—163no—
709C2×C3—182no—
710C2×C3—181no—
711C2×C3—182no—
712C2×C3—181no—
713C2×C3—482no—
714C2×C3—482no—
715C2×C3—482no—
716C2×C3C32×#99711yescharacteristic
717C2×C3C32×#99711yescharacteristic
718C2×C3C2×C32×C22⋊A411yescharacteristic
719C22—32no—
720C22—31no—
721C22—32no—
722C22—31no—
723C22—42no—
724C22—41no—
725C22—62no—
726C22—62no—
727C22—61no—
728C22—61no—
729C22—122no—
730C22—121no—
731C22—121no—
732C22—122no—
733C22—121no—
734C223−1+2×C22⋊A411yescharacteristic
735C4—32no—
736C4—32no—
737C3—31no—
738C3—163no—
739C3—482no—
740C3C2×C32×#99711yescharacteristic
741C2—62no—
742C2—61no—
743C2—62no—
744C2—61no—
745C23−1+2×#99711yescharacteristic, direct product factor
746C23−1+2×#99711yescharacteristic, direct product factor
747C2C2×3−1+2×C22⋊A411yescharacteristic
subgroupG/H
center, socleC22×C3C32×C22⋊A4
commutator, cosocleC3×H(5,𝔽2)C2×C33
FrattiniC2×C3C2×C32×C22⋊A4
FittingC2×3−1+2×H(5,𝔽2)C3
prime radicalC2×C32×#997C3
hypercenterC22×3−1+2C22⋊A4
hypocenterH(5,𝔽2)C2×C3×3−1+2
LCSG ▷ C3×H(5,𝔽2) ▷ H(5,𝔽2)
UCSC1 ◁ C22×C3 ◁ C22×3−1+2

Complements

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

NH ≅ G/Ntype
1. 3−1+2×#997C2direct (N × H)
3. C2×3−1+2×H(5,𝔽2)C3semidirect
4. C2×#11722589C3semidirect
5. C2×C9⋊#997C3semidirect
6. C2×C9×#997C3semidirect
14. 3−1+2×H(5,𝔽2)C2×C3semidirect
18. #11722589C2×C3semidirect
19. C9⋊#997C2×C3semidirect
20. C9×#997C2×C3semidirect
32. C2×C9×H(5,𝔽2)C32semidirect
33. C2×#63703C32semidirect
38. C24×3−1+2A4semidirect
39. C24×3−1+2A4semidirect
52. C2×Q8×3−1+2A4semidirect
87. C9×H(5,𝔽2)C2×C32semidirect
91. #63703C2×C32semidirect
112. C23×3−1+2C2×A4semidirect
113. C23×3−1+2C2×A4semidirect
133. Q8×3−1+2C2×A4semidirect
154. C2×#9973−1+2direct (N × H)
193. C24×C9C3×A4semidirect
194. C24×C9C3×A4semidirect
203. C2×Q8×C9C3×A4semidirect
265. #997C2×3−1+2direct (N × H)
332. C23×C9C2×C3×A4semidirect
333. C23×C9C2×C3×A4semidirect
341. Q8×C9C2×C3×A4semidirect
357. C2×H(5,𝔽2)C3×3−1+2semidirect
371. C2×3−1+2#997direct (N × H)
372. C2×3−1+2#997direct (N × H)
484. H(5,𝔽2)C2×C3×3−1+2semidirect
491. 3−1+2C2×#997direct (N × H)
592. C2×C9C3×#997semidirect
593. C2×C9C3×#997semidirect
596. C24A4×3−1+2semidirect
597. C24A4×3−1+2semidirect
604. C2×Q8A4×3−1+2semidirect
667. C9C2×C3×#997semidirect
681. C23C2×A4×3−1+2semidirect
682. C23C2×A4×3−1+2semidirect
684. Q8C2×A4×3−1+2semidirect
745. C23−1+2×#997direct (N × H)
746. C23−1+2×#997direct (N × H)

Maximal subgroups

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

subgroupindex
3−1+2×#9972
C2×C32×#9973
C2×3−1+2×H(5,𝔽2)3
C2×#117225893
C2×C9⋊#9973
C2×C9×#9973
C22×A4×3−1+24
C2×SL(2,𝔽3)×3−1+24