Finite Group Databasebeta

← C3×AGL(1,𝔽7)×C22⋊A4 #72244657

Subgroups — C3×AGL(1,𝔽7)×C22⋊A4 #72244657

Order 6048.

2224 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 2224 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C3×D7⋊(C22⋊A4)C312yesmaximal, complemented
2C3×D7×C22⋊A4C311yesmaximal, characteristic, complemented
3C3×ΓL(1,𝔽8)×C22⋊A4C211yesmaximal, characteristic, complemented
4C24×C3×AGL(1,𝔽7)C311yesmaximal, characteristic, complemented
5AGL(1,𝔽7)×C22⋊A4C319yesmaximal, direct product factor
6C3×A4×AGL(1,𝔽7)—41nomaximal
7C3×A4×AGL(1,𝔽7)—41nomaximal
8C3×A4×AGL(1,𝔽7)—41nomaximal
9C3×A4×AGL(1,𝔽7)—41nomaximal
10C3×A4×AGL(1,𝔽7)—41nomaximal
11C3×C22⋊(C22⋊ΓL(1,𝔽8))C2×C312yescomplemented
12C3×C7×C22⋊A4C2×C311yescharacteristic, complemented
13C24×C3×ΓL(1,𝔽8)C2×C311yescharacteristic, complemented
14C23×C3×AGL(1,𝔽7)—31no—
15C23×C3×AGL(1,𝔽7)—31no—
16C23×C3×AGL(1,𝔽7)—31no—
17C23×C3×AGL(1,𝔽7)—31no—
18C23×C3×AGL(1,𝔽7)—31no—
19C23×C3×AGL(1,𝔽7)—31no—
20C23×C3×AGL(1,𝔽7)—31no—
21C23×C3×AGL(1,𝔽7)—31no—
22C23×C3×AGL(1,𝔽7)—31no—
23C23×C3×AGL(1,𝔽7)—31no—
24ΓL(1,𝔽8)×C22⋊A4C2×C319yescomplemented
25C2×C32×C22⋊A4—71nomaximal, Hall
26C3×A4×ΓL(1,𝔽8)—41no—
27C3×A4×ΓL(1,𝔽8)—41no—
28C3×A4×ΓL(1,𝔽8)—41no—
29C3×A4×ΓL(1,𝔽8)—41no—
30C3×A4×ΓL(1,𝔽8)—41no—
31C24×C3×D7C3211yescharacteristic, complemented
32D7⋊(C22⋊A4)C3216yescomplemented
33D7×C22⋊A4C3213yescomplemented
34C24×AGL(1,𝔽7)C3213yescomplemented
35C23×C3×ΓL(1,𝔽8)—31no—
36C23×C3×ΓL(1,𝔽8)—31no—
37C23×C3×ΓL(1,𝔽8)—31no—
38C23×C3×ΓL(1,𝔽8)—31no—
39C23×C3×ΓL(1,𝔽8)—31no—
40C3×D7⋊A4—42no—
41C3×D7⋊A4—42no—
42C3×D7⋊A4—42no—
43C3×D7⋊A4—42no—
44C3×D7⋊A4—42no—
45C3×A4×D7—41no—
46C3×A4×D7—41no—
47C3×A4×D7—41no—
48C3×A4×D7—41no—
49C3×A4×D7—41no—
50C22×C3×AGL(1,𝔽7)—31no—
51C22×C3×AGL(1,𝔽7)—31no—
52C22×C3×AGL(1,𝔽7)—31no—
53C22×C3×AGL(1,𝔽7)—31no—
54C22×C3×AGL(1,𝔽7)—31no—
55C22×C3×AGL(1,𝔽7)—31no—
56C22×C3×AGL(1,𝔽7)—31no—
57C22×C3×AGL(1,𝔽7)—31no—
58C22×C3×AGL(1,𝔽7)—31no—
59C22×C3×AGL(1,𝔽7)—31no—
60C22×C3×AGL(1,𝔽7)—31no—
61C22×C3×AGL(1,𝔽7)—31no—
62C22×C3×AGL(1,𝔽7)—31no—
63C22×C3×AGL(1,𝔽7)—31no—
64C22×C3×AGL(1,𝔽7)—31no—
65C22×C3×AGL(1,𝔽7)—31no—
66C22×C3×AGL(1,𝔽7)—31no—
67C22×C3×AGL(1,𝔽7)—31no—
68C22×C3×AGL(1,𝔽7)—31no—
69C22×C3×AGL(1,𝔽7)—31no—
70C22×C3×AGL(1,𝔽7)—31no—
71C22×C3×AGL(1,𝔽7)—31no—
72C22×C3×AGL(1,𝔽7)—31no—
73C22×C3×AGL(1,𝔽7)—31no—
74C22×C3×AGL(1,𝔽7)—31no—
75C22×C3×AGL(1,𝔽7)—31no—
76C22×C3×AGL(1,𝔽7)—31no—
77C22×C3×AGL(1,𝔽7)—31no—
78C22×C3×AGL(1,𝔽7)—31no—
79C22×C3×AGL(1,𝔽7)—31no—
80C22×C3×AGL(1,𝔽7)—31no—
81C22×C3×AGL(1,𝔽7)—31no—
82C22×C3×AGL(1,𝔽7)—31no—
83C22×C3×AGL(1,𝔽7)—31no—
84C22×C3×AGL(1,𝔽7)—31no—
85C22×C3×AGL(1,𝔽7)—31no—
86C22×C3×AGL(1,𝔽7)—31no—
87C22×C3×AGL(1,𝔽7)—31no—
88C22×C3×AGL(1,𝔽7)—31no—
89C22×C3×AGL(1,𝔽7)—31no—
90C22×C3×AGL(1,𝔽7)—31no—
91C22×C3×AGL(1,𝔽7)—31no—
92C22×C3×AGL(1,𝔽7)—31no—
93C22×C3×AGL(1,𝔽7)—31no—
94C22×C3×AGL(1,𝔽7)—31no—
95C22×C3×AGL(1,𝔽7)A411yescharacteristic, complemented
96C22×C3×AGL(1,𝔽7)A411yescharacteristic, complemented
97C22×C3×AGL(1,𝔽7)A411yescharacteristic, complemented
98C22×C3×AGL(1,𝔽7)A411yescharacteristic, complemented
99C22×C3×AGL(1,𝔽7)A411yescharacteristic, complemented
100A4×AGL(1,𝔽7)—49no—
101A4×AGL(1,𝔽7)—49no—
102A4×AGL(1,𝔽7)—49no—
103A4×AGL(1,𝔽7)—49no—
104A4×AGL(1,𝔽7)—49no—
105C32×C22⋊A4—71no—
106C32×AGL(1,𝔽7)—161no—
107C24×C3×C7C2×C3211yescharacteristic, complemented
108C23×C3×D7—31no—
109C23×C3×D7—31no—
110C23×C3×D7—31no—
111C23×C3×D7—31no—
112C23×C3×D7—31no—
113C23×C3×D7—31no—
114C23×C3×D7—31no—
115C23×C3×D7—31no—
116C23×C3×D7—31no—
117C23×C3×D7—31no—
118C22⋊(C22⋊ΓL(1,𝔽8))C2×C3216yescomplemented
119C7×C22⋊A4C2×C3213yescomplemented
120C24×ΓL(1,𝔽8)C2×C3213yescomplemented
121C23×AGL(1,𝔽7)—33no—
122C23×AGL(1,𝔽7)—33no—
123C23×AGL(1,𝔽7)—33no—
124C23×AGL(1,𝔽7)—33no—
125C23×AGL(1,𝔽7)—33no—
126C23×AGL(1,𝔽7)—33no—
127C23×AGL(1,𝔽7)—33no—
128C23×AGL(1,𝔽7)—33no—
129C23×AGL(1,𝔽7)—33no—
130C23×AGL(1,𝔽7)—33no—
131C25×C32—71no—
132C2×C3×C22⋊A4—79no—
133C2×C3×C22⋊A4—72no—
134C2×C3×C22⋊A4—211no—
135C3×C22⋊ΓL(1,𝔽8)—42no—
136C3×C22⋊ΓL(1,𝔽8)—42no—
137C3×C22⋊ΓL(1,𝔽8)—42no—
138C3×C22⋊ΓL(1,𝔽8)—42no—
139C3×C22⋊ΓL(1,𝔽8)—42no—
140C3×C7×A4—41no—
141C3×C7×A4—41no—
142C3×C7×A4—41no—
143C3×C7×A4—41no—
144C3×C7×A4—41no—
145C22×C3×ΓL(1,𝔽8)—31no—
146C22×C3×ΓL(1,𝔽8)—31no—
147C22×C3×ΓL(1,𝔽8)—31no—
148C22×C3×ΓL(1,𝔽8)—31no—
149C22×C3×ΓL(1,𝔽8)—31no—
150C22×C3×ΓL(1,𝔽8)—31no—
151C22×C3×ΓL(1,𝔽8)—31no—
152C22×C3×ΓL(1,𝔽8)—31no—
153C22×C3×ΓL(1,𝔽8)—31no—
154C22×C3×ΓL(1,𝔽8)—31no—
155C22×C3×ΓL(1,𝔽8)C2×A411yescharacteristic, complemented
156C22×C3×ΓL(1,𝔽8)C2×A411yescharacteristic, complemented
157C22×C3×ΓL(1,𝔽8)C2×A411yescharacteristic, complemented
158C22×C3×ΓL(1,𝔽8)C2×A411yescharacteristic, complemented
159C22×C3×ΓL(1,𝔽8)C2×A411yescharacteristic, complemented
160C2×C3×AGL(1,𝔽7)—31no—
161C2×C3×AGL(1,𝔽7)—31no—
162C2×C3×AGL(1,𝔽7)—31no—
163C2×C3×AGL(1,𝔽7)—31no—
164C2×C3×AGL(1,𝔽7)—31no—
165C2×C3×AGL(1,𝔽7)—31no—
166C2×C3×AGL(1,𝔽7)—31no—
167C2×C3×AGL(1,𝔽7)—31no—
168C2×C3×AGL(1,𝔽7)—31no—
169C2×C3×AGL(1,𝔽7)—31no—
170C2×C3×AGL(1,𝔽7)—31no—
171C2×C3×AGL(1,𝔽7)—31no—
172C2×C3×AGL(1,𝔽7)—31no—
173C2×C3×AGL(1,𝔽7)—31no—
174C2×C3×AGL(1,𝔽7)—31no—
175C2×C3×AGL(1,𝔽7)—31no—
176C2×C3×AGL(1,𝔽7)—31no—
177C2×C3×AGL(1,𝔽7)—31no—
178C2×C3×AGL(1,𝔽7)—31no—
179C2×C3×AGL(1,𝔽7)—31no—
180C2×C3×AGL(1,𝔽7)—31no—
181C2×C3×AGL(1,𝔽7)—31no—
182C2×C3×AGL(1,𝔽7)—31no—
183C2×C3×AGL(1,𝔽7)—31no—
184C2×C3×AGL(1,𝔽7)—31no—
185C2×C3×AGL(1,𝔽7)—31no—
186C2×C3×AGL(1,𝔽7)—31no—
187C2×C3×AGL(1,𝔽7)—31no—
188C2×C3×AGL(1,𝔽7)—31no—
189C2×C3×AGL(1,𝔽7)—31no—
190C2×C3×AGL(1,𝔽7)—31no—
191C2×C3×AGL(1,𝔽7)—31no—
192C2×C3×AGL(1,𝔽7)—31no—
193C2×C3×AGL(1,𝔽7)—31no—
194C2×C3×AGL(1,𝔽7)—31no—
195C2×C3×AGL(1,𝔽7)—31no—
196C2×C3×AGL(1,𝔽7)—31no—
197C2×C3×AGL(1,𝔽7)—31no—
198C2×C3×AGL(1,𝔽7)—31no—
199C2×C3×AGL(1,𝔽7)—31no—
200A4×ΓL(1,𝔽8)—49no—
201A4×ΓL(1,𝔽8)—49no—
202A4×ΓL(1,𝔽8)—49no—
203A4×ΓL(1,𝔽8)—49no—
204A4×ΓL(1,𝔽8)—49no—
205C24×D7C3311yescharacteristic, complemented, Hall
206C2×C32×A4—281no—
207C2×C32×A4—281no—
208C2×C32×A4—281no—
209C2×C32×A4—281no—
210C2×C32×A4—281no—
211C32×ΓL(1,𝔽8)—161noHall
212C23×C3×C7—31no—
213C23×C3×C7—31no—
214C23×C3×C7—31no—
215C23×C3×C7—31no—
216C23×C3×C7—31no—
217C22×C3×D7—31no—
218C22×C3×D7—31no—
219C22×C3×D7—31no—
220C22×C3×D7—31no—
221C22×C3×D7—31no—
222C22×C3×D7—31no—
223C22×C3×D7—31no—
224C22×C3×D7—31no—
225C22×C3×D7—31no—
226C22×C3×D7—31no—
227C22×C3×D7—31no—
228C22×C3×D7—31no—
229C22×C3×D7—31no—
230C22×C3×D7—31no—
231C22×C3×D7—31no—
232C22×C3×D7—31no—
233C22×C3×D7—31no—
234C22×C3×D7—31no—
235C22×C3×D7—31no—
236C22×C3×D7—31no—
237C22×C3×D7—31no—
238C22×C3×D7—31no—
239C22×C3×D7—31no—
240C22×C3×D7—31no—
241C22×C3×D7—31no—
242C22×C3×D7—31no—
243C22×C3×D7—31no—
244C22×C3×D7—31no—
245C22×C3×D7—31no—
246C22×C3×D7—31no—
247C22×C3×D7—31no—
248C22×C3×D7—31no—
249C22×C3×D7—31no—
250C22×C3×D7—31no—
251C22×C3×D7—31no—
252C22×C3×D7—31no—
253C22×C3×D7—31no—
254C22×C3×D7—31no—
255C22×C3×D7—31no—
256C22×C3×D7—31no—
257C22×C3×D7—31no—
258C22×C3×D7—31no—
259C22×C3×D7—31no—
260C22×C3×D7—31no—
261C22×C3×D7—31no—
262C22×C3×D7C3×A411yescharacteristic, complemented
263C22×C3×D7C3×A411yescharacteristic, complemented
264C22×C3×D7C3×A411yescharacteristic, complemented
265C22×C3×D7C3×A411yescharacteristic, complemented
266C22×C3×D7C3×A411yescharacteristic, complemented
267C23×ΓL(1,𝔽8)—33no—
268C23×ΓL(1,𝔽8)—33no—
269C23×ΓL(1,𝔽8)—33no—
270C23×ΓL(1,𝔽8)—33no—
271C23×ΓL(1,𝔽8)—33no—
272D7⋊A4—46no—
273D7⋊A4—46no—
274D7⋊A4—46no—
275D7⋊A4—46no—
276D7⋊A4—46no—
277A4×D7—43no—
278A4×D7—43no—
279A4×D7—43no—
280A4×D7—43no—
281A4×D7—43no—
282C22×AGL(1,𝔽7)—33no—
283C22×AGL(1,𝔽7)—33no—
284C22×AGL(1,𝔽7)—33no—
285C22×AGL(1,𝔽7)—33no—
286C22×AGL(1,𝔽7)—33no—
287C22×AGL(1,𝔽7)—33no—
288C22×AGL(1,𝔽7)—33no—
289C22×AGL(1,𝔽7)—33no—
290C22×AGL(1,𝔽7)—33no—
291C22×AGL(1,𝔽7)—33no—
292C22×AGL(1,𝔽7)—33no—
293C22×AGL(1,𝔽7)—33no—
294C22×AGL(1,𝔽7)—33no—
295C22×AGL(1,𝔽7)—33no—
296C22×AGL(1,𝔽7)—33no—
297C22×AGL(1,𝔽7)—33no—
298C22×AGL(1,𝔽7)—33no—
299C22×AGL(1,𝔽7)—33no—
300C22×AGL(1,𝔽7)—33no—
301C22×AGL(1,𝔽7)—33no—
302C22×AGL(1,𝔽7)—33no—
303C22×AGL(1,𝔽7)—33no—
304C22×AGL(1,𝔽7)—33no—
305C22×AGL(1,𝔽7)—33no—
306C22×AGL(1,𝔽7)—33no—
307C22×AGL(1,𝔽7)—33no—
308C22×AGL(1,𝔽7)—33no—
309C22×AGL(1,𝔽7)—33no—
310C22×AGL(1,𝔽7)—33no—
311C22×AGL(1,𝔽7)—33no—
312C22×AGL(1,𝔽7)—33no—
313C22×AGL(1,𝔽7)—33no—
314C22×AGL(1,𝔽7)—33no—
315C22×AGL(1,𝔽7)—33no—
316C22×AGL(1,𝔽7)—33no—
317C22×AGL(1,𝔽7)—33no—
318C22×AGL(1,𝔽7)—33no—
319C22×AGL(1,𝔽7)—33no—
320C22×AGL(1,𝔽7)—33no—
321C22×AGL(1,𝔽7)—33no—
322C22×AGL(1,𝔽7)—33no—
323C22×AGL(1,𝔽7)—33no—
324C22×AGL(1,𝔽7)—33no—
325C22×AGL(1,𝔽7)—33no—
326C22×AGL(1,𝔽7)—33no—
327C22×AGL(1,𝔽7)C3×A413yescomplemented
328C22×AGL(1,𝔽7)C3×A413yescomplemented
329C22×AGL(1,𝔽7)C3×A413yescomplemented
330C22×AGL(1,𝔽7)C3×A413yescomplemented
331C22×AGL(1,𝔽7)C3×A413yescomplemented
332C24×C32—71no—
333C24×C32—211no—
334C24×C32—211no—
335C24×C32—211no—
336C24×C32—211no—
337C24×C32—211no—
338C24×C32—211no—
339C24×C32—211no—
340C24×C32—211no—
341C24×C32—211no—
342C24×C32—211no—
343C3×C22⋊A4—72no—
344C3×C22⋊A4—79no—
345C3×C22⋊A4AGL(1,𝔽7)11yescharacteristic, direct product factor
346C32×D7—161no—
347C2×C3×ΓL(1,𝔽8)—31no—
348C2×C3×ΓL(1,𝔽8)—31no—
349C2×C3×ΓL(1,𝔽8)—31no—
350C2×C3×ΓL(1,𝔽8)—31no—
351C2×C3×ΓL(1,𝔽8)—31no—
352C3×AGL(1,𝔽7)—31no—
353C3×AGL(1,𝔽7)—31no—
354C3×AGL(1,𝔽7)—31no—
355C3×AGL(1,𝔽7)—31no—
356C3×AGL(1,𝔽7)—31no—
357C3×AGL(1,𝔽7)—162no—
358C3×AGL(1,𝔽7)—169no—
359C3×AGL(1,𝔽7)C22⋊A411yescharacteristic, direct product factor
360C24×C7C2×C3311yescharacteristic, complemented
361C23×D7—31no—
362C23×D7—31no—
363C23×D7—31no—
364C23×D7—31no—
365C23×D7—31no—
366C23×D7—31no—
367C23×D7—31no—
368C23×D7—31no—
369C23×D7—31no—
370C23×D7—31no—
371C32×A4—281no—
372C32×A4—281no—
373C32×A4—281no—
374C32×A4—281no—
375C32×A4—281no—
376C25×C3—73no—
377C25×C3—211no—
378C2×C22⋊A4—76no—
379C2×C22⋊A4—213no—
380C22×C3×C7—31no—
381C22×C3×C7—31no—
382C22×C3×C7—31no—
383C22×C3×C7—31no—
384C22×C3×C7—31no—
385C22×C3×C7—31no—
386C22×C3×C7—31no—
387C22×C3×C7—31no—
388C22×C3×C7—31no—
389C22×C3×C7—31no—
390C22×C3×C7C2×C3×A411yescharacteristic, complemented
391C22×C3×C7C2×C3×A411yescharacteristic, complemented
392C22×C3×C7C2×C3×A411yescharacteristic, complemented
393C22×C3×C7C2×C3×A411yescharacteristic, complemented
394C22×C3×C7C2×C3×A411yescharacteristic, complemented
395C2×C3×D7—31no—
396C2×C3×D7—31no—
397C2×C3×D7—31no—
398C2×C3×D7—31no—
399C2×C3×D7—31no—
400C2×C3×D7—31no—
401C2×C3×D7—31no—
402C2×C3×D7—31no—
403C2×C3×D7—31no—
404C2×C3×D7—31no—
405C2×C3×D7—31no—
406C2×C3×D7—31no—
407C2×C3×D7—31no—
408C2×C3×D7—31no—
409C2×C3×D7—31no—
410C2×C3×D7—31no—
411C2×C3×D7—31no—
412C2×C3×D7—31no—
413C2×C3×D7—31no—
414C2×C3×D7—31no—
415C2×C3×D7—31no—
416C2×C3×D7—31no—
417C2×C3×D7—31no—
418C2×C3×D7—31no—
419C2×C3×D7—31no—
420C2×C3×D7—31no—
421C2×C3×D7—31no—
422C2×C3×D7—31no—
423C2×C3×D7—31no—
424C2×C3×D7—31no—
425C2×C3×D7—31no—
426C2×C3×D7—31no—
427C2×C3×D7—31no—
428C2×C3×D7—31no—
429C2×C3×D7—31no—
430C2×C3×D7—31no—
431C2×C3×D7—31no—
432C2×C3×D7—31no—
433C2×C3×D7—31no—
434C2×C3×D7—31no—
435C22⋊ΓL(1,𝔽8)—46no—
436C22⋊ΓL(1,𝔽8)—46no—
437C22⋊ΓL(1,𝔽8)—46no—
438C22⋊ΓL(1,𝔽8)—46no—
439C22⋊ΓL(1,𝔽8)—46no—
440C7×A4—43no—
441C7×A4—43no—
442C7×A4—43no—
443C7×A4—43no—
444C7×A4—43no—
445C22×ΓL(1,𝔽8)—33no—
446C22×ΓL(1,𝔽8)—33no—
447C22×ΓL(1,𝔽8)—33no—
448C22×ΓL(1,𝔽8)—33no—
449C22×ΓL(1,𝔽8)—33no—
450C22×ΓL(1,𝔽8)—33no—
451C22×ΓL(1,𝔽8)—33no—
452C22×ΓL(1,𝔽8)—33no—
453C22×ΓL(1,𝔽8)—33no—
454C22×ΓL(1,𝔽8)—33no—
455C22×ΓL(1,𝔽8)C2×C3×A413yescomplemented
456C22×ΓL(1,𝔽8)C2×C3×A413yescomplemented
457C22×ΓL(1,𝔽8)C2×C3×A413yescomplemented
458C22×ΓL(1,𝔽8)C2×C3×A413yescomplemented
459C22×ΓL(1,𝔽8)C2×C3×A413yescomplemented
460C2×AGL(1,𝔽7)—33no—
461C2×AGL(1,𝔽7)—33no—
462C2×AGL(1,𝔽7)—33no—
463C2×AGL(1,𝔽7)—33no—
464C2×AGL(1,𝔽7)—33no—
465C2×AGL(1,𝔽7)—33no—
466C2×AGL(1,𝔽7)—33no—
467C2×AGL(1,𝔽7)—33no—
468C2×AGL(1,𝔽7)—33no—
469C2×AGL(1,𝔽7)—33no—
470C2×AGL(1,𝔽7)—33no—
471C2×AGL(1,𝔽7)—33no—
472C2×AGL(1,𝔽7)—33no—
473C2×AGL(1,𝔽7)—33no—
474C2×AGL(1,𝔽7)—33no—
475C2×AGL(1,𝔽7)—33no—
476C2×AGL(1,𝔽7)—33no—
477C2×AGL(1,𝔽7)—33no—
478C2×AGL(1,𝔽7)—33no—
479C2×AGL(1,𝔽7)—33no—
480C2×AGL(1,𝔽7)—33no—
481C2×AGL(1,𝔽7)—33no—
482C2×AGL(1,𝔽7)—33no—
483C2×AGL(1,𝔽7)—33no—
484C2×AGL(1,𝔽7)—33no—
485C2×AGL(1,𝔽7)—33no—
486C2×AGL(1,𝔽7)—33no—
487C2×AGL(1,𝔽7)—33no—
488C2×AGL(1,𝔽7)—33no—
489C2×AGL(1,𝔽7)—33no—
490C2×AGL(1,𝔽7)—33no—
491C2×AGL(1,𝔽7)—33no—
492C2×AGL(1,𝔽7)—33no—
493C2×AGL(1,𝔽7)—33no—
494C2×AGL(1,𝔽7)—33no—
495C2×AGL(1,𝔽7)—33no—
496C2×AGL(1,𝔽7)—33no—
497C2×AGL(1,𝔽7)—33no—
498C2×AGL(1,𝔽7)—33no—
499C2×AGL(1,𝔽7)—33no—
500C23×C32—71no—
501C23×C32—71no—
502C23×C32—71no—
503C23×C32—71no—
504C23×C32—71no—
505C23×C32—211no—
506C23×C32—211no—
507C23×C32—211no—
508C23×C32—211no—
509C23×C32—211no—
510C23×C32—211no—
511C23×C32—211no—
512C23×C32—211no—
513C23×C32—211no—
514C23×C32—211no—
515C23×C32—211no—
516C23×C32—211no—
517C23×C32—211no—
518C23×C32—211no—
519C23×C32—211no—
520C23×C32—211no—
521C23×C32—211no—
522C23×C32—211no—
523C23×C32—211no—
524C23×C32—211no—
525C23×C32—211no—
526C23×C32—211no—
527C23×C32—211no—
528C23×C32—211no—
529C23×C32—211no—
530C23×C32—211no—
531C23×C32—211no—
532C23×C32—211no—
533C23×C32—211no—
534C23×C32—211no—
535C23×C32—211no—
536C23×C32—211no—
537C23×C32—211no—
538C23×C32—211no—
539C23×C32—211no—
540C23×C32—211no—
541C23×C32—211no—
542C23×C32—211no—
543C23×C32—211no—
544C23×C32—211no—
545C23×C32—211no—
546C23×C32—211no—
547C23×C32—211no—
548C23×C32—211no—
549C23×C32—211no—
550C23×C32—211no—
551C23×C32—211no—
552C23×C32—211no—
553C23×C32—211no—
554C23×C32—211no—
555C2×C3×A4—282no—
556C2×C3×A4—282no—
557C2×C3×A4—282no—
558C2×C3×A4—282no—
559C2×C3×A4—282no—
560C2×C3×A4—289no—
561C2×C3×A4—289no—
562C2×C3×A4—289no—
563C2×C3×A4—289no—
564C2×C3×A4—289no—
565C2×C3×A4—841no—
566C2×C3×A4—841no—
567C2×C3×A4—841no—
568C2×C3×A4—841no—
569C2×C3×A4—841no—
570C32×C7—161no—
571C3×ΓL(1,𝔽8)—162no—
572C3×ΓL(1,𝔽8)—169no—
573C3×ΓL(1,𝔽8)C2×C22⋊A411yescharacteristic, complemented
574C23×C7—31no—
575C23×C7—31no—
576C23×C7—31no—
577C23×C7—31no—
578C23×C7—31no—
579C22×D7—31no—
580C22×D7—31no—
581C22×D7—31no—
582C22×D7—31no—
583C22×D7—31no—
584C22×D7—31no—
585C22×D7—31no—
586C22×D7—31no—
587C22×D7—31no—
588C22×D7—31no—
589C22×D7—31no—
590C22×D7—31no—
591C22×D7—31no—
592C22×D7—31no—
593C22×D7—31no—
594C22×D7—31no—
595C22×D7—31no—
596C22×D7—31no—
597C22×D7—31no—
598C22×D7—31no—
599C22×D7—31no—
600C22×D7—31no—
601C22×D7—31no—
602C22×D7—31no—
603C22×D7—31no—
604C22×D7—31no—
605C22×D7—31no—
606C22×D7—31no—
607C22×D7—31no—
608C22×D7—31no—
609C22×D7—31no—
610C22×D7—31no—
611C22×D7—31no—
612C22×D7—31no—
613C22×D7—31no—
614C22×D7—31no—
615C22×D7—31no—
616C22×D7—31no—
617C22×D7—31no—
618C22×D7—31no—
619C22×D7—31no—
620C22×D7—31no—
621C22×D7—31no—
622C22×D7—31no—
623C22×D7—31no—
624C22×D7C32×A411yescharacteristic, complemented
625C22×D7C32×A411yescharacteristic, complemented
626C22×D7C32×A411yescharacteristic, complemented
627C22×D7C32×A411yescharacteristic, complemented
628C22×D7C32×A411yescharacteristic, complemented
629C2×C33—1121no—
630C24×C3—73no—
631C24×C3—211no—
632C24×C3—213no—
633C24×C3—213no—
634C24×C3—213no—
635C24×C3—213no—
636C24×C3—213no—
637C24×C3—213no—
638C24×C3—213no—
639C24×C3—213no—
640C24×C3—213no—
641C24×C3—213no—
642C24×C3—631no—
643C24×C3—631no—
644C24×C3—631no—
645C24×C3—631no—
646C24×C3—631no—
647C24×C3—631no—
648C24×C3—631no—
649C24×C3—631no—
650C24×C3—631no—
651C24×C3C3×AGL(1,𝔽7)11yescharacteristic, complemented
652C22⋊A4—76no—
653C22⋊A4C3×AGL(1,𝔽7)13yesdirect product factor
654C2×C3×C7—31no—
655C2×C3×C7—31no—
656C2×C3×C7—31no—
657C2×C3×C7—31no—
658C2×C3×C7—31no—
659C3×D7—31no—
660C3×D7—31no—
661C3×D7—31no—
662C3×D7—31no—
663C3×D7—31no—
664C3×D7—163no—
665C3×D7C3×C22⋊A411yescharacteristic, complemented
666C2×ΓL(1,𝔽8)—33no—
667C2×ΓL(1,𝔽8)—33no—
668C2×ΓL(1,𝔽8)—33no—
669C2×ΓL(1,𝔽8)—33no—
670C2×ΓL(1,𝔽8)—33no—
671AGL(1,𝔽7)—33no—
672AGL(1,𝔽7)—33no—
673AGL(1,𝔽7)—33no—
674AGL(1,𝔽7)—33no—
675AGL(1,𝔽7)—33no—
676AGL(1,𝔽7)—166no—
677AGL(1,𝔽7)C3×C22⋊A413yesdirect product factor
678C22×C32—71no—
679C22×C32—71no—
680C22×C32—71no—
681C22×C32—71no—
682C22×C32—71no—
683C22×C32—211no—
684C22×C32—211no—
685C22×C32—211no—
686C22×C32—211no—
687C22×C32—211no—
688C22×C32—211no—
689C22×C32—211no—
690C22×C32—211no—
691C22×C32—211no—
692C22×C32—211no—
693C22×C32—211no—
694C22×C32—211no—
695C22×C32—211no—
696C22×C32—211no—
697C22×C32—211no—
698C22×C32—211no—
699C22×C32—211no—
700C22×C32—211no—
701C22×C32—211no—
702C22×C32—211no—
703C22×C32—211no—
704C22×C32—211no—
705C22×C32—211no—
706C22×C32—211no—
707C22×C32—211no—
708C22×C32—211no—
709C22×C32—211no—
710C22×C32—211no—
711C22×C32—211no—
712C22×C32—211no—
713C22×C32—211no—
714C22×C32—211no—
715C22×C32—211no—
716C22×C32—211no—
717C22×C32—211no—
718C22×C32—211no—
719C22×C32—211no—
720C22×C32—211no—
721C22×C32—211no—
722C22×C32—211no—
723C22×C32—211no—
724C22×C32—211no—
725C22×C32—211no—
726C22×C32—211no—
727C22×C32—211no—
728C22×C32—211no—
729C22×C32—211no—
730C22×C32—211no—
731C22×C32—211no—
732C22×C32—211no—
733C3×A4—41no—
734C3×A4—41no—
735C3×A4—41no—
736C3×A4—41no—
737C3×A4—41no—
738C3×A4—289no—
739C3×A4—289no—
740C3×A4—289no—
741C3×A4—289no—
742C3×A4—289no—
743C3×A4—282no—
744C3×A4—282no—
745C3×A4—282no—
746C3×A4—282no—
747C3×A4—282no—
748C25—211noSylow
749C22×C7—31no—
750C22×C7—31no—
751C22×C7—31no—
752C22×C7—31no—
753C22×C7—31no—
754C22×C7—31no—
755C22×C7—31no—
756C22×C7—31no—
757C22×C7—31no—
758C22×C7—31no—
759C22×C7C2×C32×A411yescharacteristic, complemented
760C22×C7C2×C32×A411yescharacteristic, complemented
761C22×C7C2×C32×A411yescharacteristic, complemented
762C22×C7C2×C32×A411yescharacteristic, complemented
763C22×C7C2×C32×A411yescharacteristic, complemented
764C2×D7—31no—
765C2×D7—31no—
766C2×D7—31no—
767C2×D7—31no—
768C2×D7—31no—
769C2×D7—31no—
770C2×D7—31no—
771C2×D7—31no—
772C2×D7—31no—
773C2×D7—31no—
774C2×D7—31no—
775C2×D7—31no—
776C2×D7—31no—
777C2×D7—31no—
778C2×D7—31no—
779C2×D7—31no—
780C2×D7—31no—
781C2×D7—31no—
782C2×D7—31no—
783C2×D7—31no—
784C2×D7—31no—
785C2×D7—31no—
786C2×D7—31no—
787C2×D7—31no—
788C2×D7—31no—
789C2×D7—31no—
790C2×D7—31no—
791C2×D7—31no—
792C2×D7—31no—
793C2×D7—31no—
794C2×D7—31no—
795C2×D7—31no—
796C2×D7—31no—
797C2×D7—31no—
798C2×D7—31no—
799C2×D7—31no—
800C2×D7—31no—
801C2×D7—31no—
802C2×D7—31no—
803C2×D7—31no—
804C33—1121noSylow
805C23×C3—31no—
806C23×C3—31no—
807C23×C3—31no—
808C23×C3—31no—
809C23×C3—31no—
810C23×C3—73no—
811C23×C3—73no—
812C23×C3—73no—
813C23×C3—73no—
814C23×C3—73no—
815C23×C3—213no—
816C23×C3—213no—
817C23×C3—213no—
818C23×C3—213no—
819C23×C3—213no—
820C23×C3—211no—
821C23×C3—211no—
822C23×C3—211no—
823C23×C3—213no—
824C23×C3—213no—
825C23×C3—213no—
826C23×C3—213no—
827C23×C3—211no—
828C23×C3—211no—
829C23×C3—211no—
830C23×C3—211no—
831C23×C3—211no—
832C23×C3—211no—
833C23×C3—213no—
834C23×C3—213no—
835C23×C3—213no—
836C23×C3—213no—
837C23×C3—213no—
838C23×C3—213no—
839C23×C3—213no—
840C23×C3—213no—
841C23×C3—213no—
842C23×C3—213no—
843C23×C3—213no—
844C23×C3—213no—
845C23×C3—213no—
846C23×C3—213no—
847C23×C3—213no—
848C23×C3—213no—
849C23×C3—213no—
850C23×C3—213no—
851C23×C3—213no—
852C23×C3—213no—
853C23×C3—213no—
854C23×C3—213no—
855C23×C3—213no—
856C23×C3—213no—
857C23×C3—213no—
858C23×C3—213no—
859C23×C3—213no—
860C23×C3—213no—
861C23×C3—213no—
862C23×C3—213no—
863C23×C3—213no—
864C23×C3—213no—
865C23×C3—213no—
866C23×C3—213no—
867C23×C3—213no—
868C23×C3—213no—
869C23×C3—213no—
870C23×C3—213no—
871C23×C3—213no—
872C23×C3—213no—
873C23×C3—213no—
874C23×C3—631no—
875C23×C3—631no—
876C23×C3—631no—
877C23×C3—631no—
878C23×C3—631no—
879C23×C3—631no—
880C23×C3—631no—
881C23×C3—631no—
882C23×C3—631no—
883C23×C3—631no—
884C23×C3—631no—
885C23×C3—631no—
886C23×C3—631no—
887C23×C3—631no—
888C23×C3—631no—
889C23×C3—631no—
890C23×C3—631no—
891C23×C3—631no—
892C23×C3—631no—
893C23×C3—631no—
894C23×C3—631no—
895C23×C3—631no—
896C23×C3—631no—
897C23×C3—631no—
898C23×C3—631no—
899C23×C3—631no—
900C23×C3—631no—
901C23×C3—631no—
902C23×C3—631no—
903C23×C3—631no—
904C23×C3—631no—
905C23×C3—631no—
906C23×C3—631no—
907C23×C3—631no—
908C23×C3—631no—
909C23×C3—631no—
910C23×C3—631no—
911C23×C3—631no—
912C23×C3—631no—
913C23×C3—631no—
914C23×C3—631no—
915C2×A4—286no—
916C2×A4—286no—
917C2×A4—286no—
918C2×A4—286no—
919C2×A4—286no—
920C2×A4—843no—
921C2×A4—843no—
922C2×A4—843no—
923C2×A4—843no—
924C2×A4—843no—
925C3×C7—163no—
926C3×C7C2×C3×C22⋊A411yescharacteristic, complemented
927ΓL(1,𝔽8)—166no—
928ΓL(1,𝔽8)C2×C3×C22⋊A413yescomplemented
929C2×C32—71no—
930C2×C32—211no—
931C2×C32—211no—
932C2×C32—211no—
933C2×C32—211no—
934C2×C32—211no—
935C2×C32—211no—
936C2×C32—211no—
937C2×C32—211no—
938C2×C32—211no—
939C2×C32—211no—
940C2×C32—3361no—
941C2×C32—1129no—
942C2×C32—1122no—
943C24—211no—
944C24—631no—
945C24—631no—
946C24—631no—
947C24—631no—
948C24—631no—
949C24—631no—
950C24—631no—
951C24—631no—
952C24—631no—
953C24C32×AGL(1,𝔽7)11yescharacteristic, complemented
954C2×C7—31no—
955C2×C7—31no—
956C2×C7—31no—
957C2×C7—31no—
958C2×C7—31no—
959D7—31no—
960D7—31no—
961D7—31no—
962D7—31no—
963D7—31no—
964D7C32×C22⋊A411yescharacteristic, complemented
965C22×C3—31no—
966C22×C3—31no—
967C22×C3—31no—
968C22×C3—31no—
969C22×C3—31no—
970C22×C3—31no—
971C22×C3—31no—
972C22×C3—31no—
973C22×C3—31no—
974C22×C3—31no—
975C22×C3—73no—
976C22×C3—73no—
977C22×C3—73no—
978C22×C3—73no—
979C22×C3—73no—
980C22×C3—213no—
981C22×C3—213no—
982C22×C3—213no—
983C22×C3—213no—
984C22×C3—213no—
985C22×C3—213no—
986C22×C3—213no—
987C22×C3—213no—
988C22×C3—213no—
989C22×C3—213no—
990C22×C3—211no—
991C22×C3—211no—
992C22×C3—211no—
993C22×C3—211no—
994C22×C3—211no—
995C22×C3—213no—
996C22×C3—213no—
997C22×C3—213no—
998C22×C3—213no—
999C22×C3—213no—
1000C22×C3—213no—
1001C22×C3—213no—
1002C22×C3—213no—
1003C22×C3—213no—
1004C22×C3—213no—
1005C22×C3—213no—
1006C22×C3—213no—
1007C22×C3—213no—
1008C22×C3—213no—
1009C22×C3—213no—
1010C22×C3—213no—
1011C22×C3—213no—
1012C22×C3—213no—
1013C22×C3—213no—
1014C22×C3—213no—
1015C22×C3—213no—
1016C22×C3—213no—
1017C22×C3—213no—
1018C22×C3—213no—
1019C22×C3—213no—
1020C22×C3—213no—
1021C22×C3—213no—
1022C22×C3—213no—
1023C22×C3—213no—
1024C22×C3—213no—
1025C22×C3—213no—
1026C22×C3—213no—
1027C22×C3—213no—
1028C22×C3—213no—
1029C22×C3—213no—
1030C22×C3—213no—
1031C22×C3—213no—
1032C22×C3—213no—
1033C22×C3—213no—
1034C22×C3—213no—
1035C22×C3—631no—
1036C22×C3—631no—
1037C22×C3—631no—
1038C22×C3—631no—
1039C22×C3—631no—
1040C22×C3—631no—
1041C22×C3—631no—
1042C22×C3—631no—
1043C22×C3—631no—
1044C22×C3—631no—
1045C22×C3—631no—
1046C22×C3—631no—
1047C22×C3—631no—
1048C22×C3—631no—
1049C22×C3—631no—
1050C22×C3—631no—
1051C22×C3—631no—
1052C22×C3—631no—
1053C22×C3—631no—
1054C22×C3—631no—
1055C22×C3—631no—
1056C22×C3—631no—
1057C22×C3—631no—
1058C22×C3—631no—
1059C22×C3—631no—
1060C22×C3—631no—
1061C22×C3—631no—
1062C22×C3—631no—
1063C22×C3—631no—
1064C22×C3—631no—
1065C22×C3—631no—
1066C22×C3—631no—
1067C22×C3—631no—
1068C22×C3—631no—
1069C22×C3—631no—
1070C22×C3A4×AGL(1,𝔽7)11yescharacteristic, complemented
1071C22×C3A4×AGL(1,𝔽7)11yescharacteristic, complemented
1072C22×C3A4×AGL(1,𝔽7)11yescharacteristic, complemented
1073C22×C3A4×AGL(1,𝔽7)11yescharacteristic, complemented
1074C22×C3A4×AGL(1,𝔽7)11yescharacteristic, complemented
1075A4—43no—
1076A4—43no—
1077A4—43no—
1078A4—43no—
1079A4—43no—
1080A4—286no—
1081A4—286no—
1082A4—286no—
1083A4—286no—
1084A4—286no—
1085C32—71no—
1086C32—161no—
1087C32—1129no—
1088C32—1122no—
1089C23—31no—
1090C23—31no—
1091C23—31no—
1092C23—31no—
1093C23—31no—
1094C23—211no—
1095C23—211no—
1096C23—211no—
1097C23—211no—
1098C23—211no—
1099C23—211no—
1100C23—211no—
1101C23—211no—
1102C23—211no—
1103C23—631no—
1104C23—631no—
1105C23—631no—
1106C23—631no—
1107C23—631no—
1108C23—631no—
1109C23—631no—
1110C23—631no—
1111C23—631no—
1112C23—631no—
1113C23—631no—
1114C23—631no—
1115C23—631no—
1116C23—631no—
1117C23—631no—
1118C23—631no—
1119C23—631no—
1120C23—631no—
1121C23—631no—
1122C23—631no—
1123C23—631no—
1124C23—631no—
1125C23—631no—
1126C23—631no—
1127C23—631no—
1128C23—631no—
1129C23—631no—
1130C23—631no—
1131C23—631no—
1132C23—631no—
1133C23—631no—
1134C23—631no—
1135C23—631no—
1136C23—631no—
1137C23—631no—
1138C23—631no—
1139C23—631no—
1140C23—631no—
1141C23—631no—
1142C23—631no—
1143C23—631no—
1144C7C2×C32×C22⋊A411yescharacteristic, complemented, Sylow
1145C2×C3—31no—
1146C2×C3—31no—
1147C2×C3—31no—
1148C2×C3—31no—
1149C2×C3—31no—
1150C2×C3—73no—
1151C2×C3—213no—
1152C2×C3—213no—
1153C2×C3—213no—
1154C2×C3—213no—
1155C2×C3—213no—
1156C2×C3—213no—
1157C2×C3—211no—
1158C2×C3—211no—
1159C2×C3—213no—
1160C2×C3—213no—
1161C2×C3—213no—
1162C2×C3—213no—
1163C2×C3—631no—
1164C2×C3—631no—
1165C2×C3—631no—
1166C2×C3—631no—
1167C2×C3—3363no—
1168C2×C3—1126no—
1169C22—31no—
1170C22—31no—
1171C22—31no—
1172C22—31no—
1173C22—31no—
1174C22—31no—
1175C22—31no—
1176C22—31no—
1177C22—31no—
1178C22—31no—
1179C22—211no—
1180C22—211no—
1181C22—211no—
1182C22—211no—
1183C22—211no—
1184C22—631no—
1185C22—631no—
1186C22—631no—
1187C22—631no—
1188C22—631no—
1189C22—631no—
1190C22—631no—
1191C22—631no—
1192C22—631no—
1193C22—631no—
1194C22—631no—
1195C22—631no—
1196C22—631no—
1197C22—631no—
1198C22—631no—
1199C22—631no—
1200C22—631no—
1201C22—631no—
1202C22—631no—
1203C22—631no—
1204C22—631no—
1205C22—631no—
1206C22—631no—
1207C22—631no—
1208C22—631no—
1209C22—631no—
1210C22—631no—
1211C22—631no—
1212C22—631no—
1213C22—631no—
1214C22—631no—
1215C22—631no—
1216C22—631no—
1217C22—631no—
1218C22—631no—
1219C22C3×A4×AGL(1,𝔽7)11yescharacteristic, complemented
1220C22C3×A4×AGL(1,𝔽7)11yescharacteristic, complemented
1221C22C3×A4×AGL(1,𝔽7)11yescharacteristic, complemented
1222C22C3×A4×AGL(1,𝔽7)11yescharacteristic, complemented
1223C22C3×A4×AGL(1,𝔽7)11yescharacteristic, complemented
1224C3—73no—
1225C3—163no—
1226C3—1126no—
1227C3AGL(1,𝔽7)×C22⋊A411yescharacteristic, direct product factor
1228C2—31no—
1229C2—31no—
1230C2—31no—
1231C2—31no—
1232C2—31no—
1233C2—211no—
1234C2—211no—
1235C2—631no—
1236C2—631no—
1237C2—631no—
1238C2—631no—
subgroupG/H
center, hypercenterC3AGL(1,𝔽7)×C22⋊A4
commutator, cosocle, hypocenterC24×C7C2×C33
FrattiniC1G
Fitting, socleC24×C3×C7C2×C32
LCSG ▷ C24×C7
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×D7⋊(C22⋊A4)C3semidirect
2. C3×D7×C22⋊A4C3semidirect
3. C3×ΓL(1,𝔽8)×C22⋊A4C2semidirect
4. C24×C3×AGL(1,𝔽7)C3semidirect
5. AGL(1,𝔽7)×C22⋊A4C3direct (N × H)
11. C3×C22⋊(C22⋊ΓL(1,𝔽8))C2×C3semidirect
12. C3×C7×C22⋊A4C2×C3semidirect
13. C24×C3×ΓL(1,𝔽8)C2×C3semidirect
24. ΓL(1,𝔽8)×C22⋊A4C2×C3semidirect
31. C24×C3×D7C32semidirect
32. D7⋊(C22⋊A4)C32semidirect
33. D7×C22⋊A4C32semidirect
34. C24×AGL(1,𝔽7)C32semidirect
95. C22×C3×AGL(1,𝔽7)A4semidirect
96. C22×C3×AGL(1,𝔽7)A4semidirect
97. C22×C3×AGL(1,𝔽7)A4semidirect
98. C22×C3×AGL(1,𝔽7)A4semidirect
99. C22×C3×AGL(1,𝔽7)A4semidirect
107. C24×C3×C7C2×C32semidirect
118. C22⋊(C22⋊ΓL(1,𝔽8))C2×C32semidirect
119. C7×C22⋊A4C2×C32semidirect
120. C24×ΓL(1,𝔽8)C2×C32semidirect
155. C22×C3×ΓL(1,𝔽8)C2×A4semidirect
156. C22×C3×ΓL(1,𝔽8)C2×A4semidirect
157. C22×C3×ΓL(1,𝔽8)C2×A4semidirect
158. C22×C3×ΓL(1,𝔽8)C2×A4semidirect
159. C22×C3×ΓL(1,𝔽8)C2×A4semidirect
205. C24×D7C33semidirect
262. C22×C3×D7C3×A4semidirect
263. C22×C3×D7C3×A4semidirect
264. C22×C3×D7C3×A4semidirect
265. C22×C3×D7C3×A4semidirect
266. C22×C3×D7C3×A4semidirect
327. C22×AGL(1,𝔽7)C3×A4semidirect
328. C22×AGL(1,𝔽7)C3×A4semidirect
329. C22×AGL(1,𝔽7)C3×A4semidirect
330. C22×AGL(1,𝔽7)C3×A4semidirect
331. C22×AGL(1,𝔽7)C3×A4semidirect
345. C3×C22⋊A4AGL(1,𝔽7)direct (N × H)
359. C3×AGL(1,𝔽7)C22⋊A4direct (N × H)
360. C24×C7C2×C33semidirect
390. C22×C3×C7C2×C3×A4semidirect
391. C22×C3×C7C2×C3×A4semidirect
392. C22×C3×C7C2×C3×A4semidirect
393. C22×C3×C7C2×C3×A4semidirect
394. C22×C3×C7C2×C3×A4semidirect
455. C22×ΓL(1,𝔽8)C2×C3×A4semidirect
456. C22×ΓL(1,𝔽8)C2×C3×A4semidirect
457. C22×ΓL(1,𝔽8)C2×C3×A4semidirect
458. C22×ΓL(1,𝔽8)C2×C3×A4semidirect
459. C22×ΓL(1,𝔽8)C2×C3×A4semidirect
573. C3×ΓL(1,𝔽8)C2×C22⋊A4semidirect
624. C22×D7C32×A4semidirect
625. C22×D7C32×A4semidirect
626. C22×D7C32×A4semidirect
627. C22×D7C32×A4semidirect
628. C22×D7C32×A4semidirect
651. C24×C3C3×AGL(1,𝔽7)semidirect
653. C22⋊A4C3×AGL(1,𝔽7)direct (N × H)
665. C3×D7C3×C22⋊A4semidirect
677. AGL(1,𝔽7)C3×C22⋊A4direct (N × H)
759. C22×C7C2×C32×A4semidirect
760. C22×C7C2×C32×A4semidirect
761. C22×C7C2×C32×A4semidirect
762. C22×C7C2×C32×A4semidirect
763. C22×C7C2×C32×A4semidirect
926. C3×C7C2×C3×C22⋊A4semidirect
928. ΓL(1,𝔽8)C2×C3×C22⋊A4semidirect
953. C24C32×AGL(1,𝔽7)semidirect
964. D7C32×C22⋊A4semidirect
1070. C22×C3A4×AGL(1,𝔽7)semidirect
1071. C22×C3A4×AGL(1,𝔽7)semidirect
1072. C22×C3A4×AGL(1,𝔽7)semidirect
1073. C22×C3A4×AGL(1,𝔽7)semidirect
1074. C22×C3A4×AGL(1,𝔽7)semidirect
1144. C7C2×C32×C22⋊A4semidirect
1219. C22C3×A4×AGL(1,𝔽7)semidirect
1220. C22C3×A4×AGL(1,𝔽7)semidirect
1221. C22C3×A4×AGL(1,𝔽7)semidirect
1222. C22C3×A4×AGL(1,𝔽7)semidirect
1223. C22C3×A4×AGL(1,𝔽7)semidirect
1227. C3AGL(1,𝔽7)×C22⋊A4direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D7⋊(C22⋊A4)3
C3×D7×C22⋊A43
C3×ΓL(1,𝔽8)×C22⋊A42
C24×C3×AGL(1,𝔽7)3
AGL(1,𝔽7)×C22⋊A43
C3×A4×AGL(1,𝔽7)4
C2×C32×C22⋊A47