Finite Group Databasebeta

← #90218⋊C3 #13057264

Subgroups — #90218⋊C3 #13057264

Order 1344.

496 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1ΓL(1,𝔽8)×#117C211yesmaximal, characteristic, complemented
2#6492⋊C3C211yesmaximal, characteristic, complemented
3C2×(C2×AGL(1,𝔽7))⋊C4C211yesmaximal, characteristic, complemented
4#6461⋊C3C211yesmaximal, characteristic, complemented
5#6459⋊C3C211yesmaximal, characteristic, complemented
6#6457⋊C3C211yesmaximal, characteristic, complemented
7#6457⋊C3C211yesmaximal, characteristic, complemented
8#6445⋊C3C211yesmaximal, characteristic
9((C22⋊D7)⋊C3)⋊C4C211yesmaximal, characteristic, complemented
10C22⋊C4×AGL(1,𝔽7)C211yesmaximal, characteristic, complemented
11#6441⋊C3C211yesmaximal, characteristic, complemented
12#10620712C211yesmaximal, characteristic, complemented
13#6438⋊C3C211yesmaximal, characteristic, complemented
14C4×C4⋊AGL(1,𝔽7)C211yesmaximal, characteristic, complemented
15#6435⋊C3C211yesmaximal, characteristic, complemented
16#90218C311yesmaximal, characteristic, complemented, Hall
17C23×AGL(1,𝔽7)C2211yescharacteristic
18C22×C4×ΓL(1,𝔽8)C2211yescharacteristic
19C2×(C22⋊D7)⋊C3C2211yescharacteristic
20C22×ΓL(1,𝔽8)⋊C4C2211yescharacteristic
21C2×C4⋊AGL(1,𝔽7)C2211yescharacteristic
22C2×C4⋊AGL(1,𝔽7)C2211yescharacteristic
23C2×C4×AGL(1,𝔽7)C2211yescharacteristic
24C2×C4×AGL(1,𝔽7)C2211yescharacteristic
25C2×C4×AGL(1,𝔽7)C2211yescharacteristic, complemented
26C2×ΓL(1,𝔽8)⋊Q8C2211yescharacteristic, complemented
27C4⋊C4×ΓL(1,𝔽8)C2211yescharacteristic, complemented
28C4⋊C4×ΓL(1,𝔽8)C2211yescharacteristic, complemented
29C22⋊C4×ΓL(1,𝔽8)C2211yescharacteristic
30C22⋊C4×ΓL(1,𝔽8)C2211yescharacteristic
31C42×ΓL(1,𝔽8)C2211yescharacteristic, complemented
32C42×ΓL(1,𝔽8)C2211yescharacteristic, complemented
33(C22⋊Dic7)⋊C3C2211yescharacteristic
34(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic
35(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic
36(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic
37(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic
38(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic
39(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic
40(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic
41(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic
42(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic, complemented
43(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic, complemented
44(C2×AGL(1,𝔽7))⋊C4C2211yescharacteristic, complemented
45C4⋊(ΓL(1,𝔽8)⋊C4)C2211yescharacteristic, complemented
46(ΓL(1,𝔽8)⋊C4)⋊C4C2211yescharacteristic, complemented
47(ΓL(1,𝔽8)⋊C4)⋊C4C2211yescharacteristic, complemented
48(ΓL(1,𝔽8)⋊C4)⋊C4C2211yescharacteristic, complemented
49(ΓL(1,𝔽8)⋊C4)⋊C4C2211yescharacteristic, complemented
50(ΓL(1,𝔽8)⋊C4)⋊C4C2211yescharacteristic, complemented
51C4×ΓL(1,𝔽8)⋊C4C2211yescharacteristic, complemented
52C7×#117C2×C311yescharacteristic, complemented
53#6492C2×C311yescharacteristic, complemented
54C2×(C2×D7)⋊C4C2×C311yescharacteristic, complemented
55#6461C2×C311yescharacteristic, complemented
56#6459C2×C311yescharacteristic, complemented
57#6457C2×C311yescharacteristic, complemented
58#6457C2×C311yescharacteristic, complemented
59#6445C2×C311yescharacteristic
60(C22⋊D7)⋊C4C2×C311yescharacteristic, complemented
61D7×C22⋊C4C2×C311yescharacteristic, complemented
62#6441C2×C311yescharacteristic, complemented
63#6439C2×C311yescharacteristic, complemented
64#6438C2×C311yescharacteristic, complemented
65C4×D28C2×C311yescharacteristic, complemented
66#6435C2×C311yescharacteristic, complemented
67C3×#551—71nomaximal, Hall
68C23×ΓL(1,𝔽8)C2311yescharacteristic
69C22×AGL(1,𝔽7)—22no—
70C22×AGL(1,𝔽7)—22no—
71C22×AGL(1,𝔽7)—41no—
72C22×AGL(1,𝔽7)C2311yescharacteristic
73C22×AGL(1,𝔽7)C2311yescharacteristic
74C22×AGL(1,𝔽7)C2311yescharacteristic
75C2×C4×ΓL(1,𝔽8)—22no—
76C2×C4×ΓL(1,𝔽8)C2311yescharacteristic
77C2×C4×ΓL(1,𝔽8)C2311yescharacteristic
78C2×C4×ΓL(1,𝔽8)C2311yescharacteristic
79C2×C4×ΓL(1,𝔽8)C2311yescharacteristic
80C2×C4×ΓL(1,𝔽8)C2311yescharacteristic
81C2×C4×ΓL(1,𝔽8)C2311yescharacteristic
82(C22⋊D7)⋊C3—22no—
83C2×ΓL(1,𝔽8)⋊C4—41no—
84C2×ΓL(1,𝔽8)⋊C4C2311yescharacteristic
85C2×ΓL(1,𝔽8)⋊C4C2311yescharacteristic
86C2×ΓL(1,𝔽8)⋊C4C2311yescharacteristic
87C2×ΓL(1,𝔽8)⋊C4C2311yescharacteristic
88C2×ΓL(1,𝔽8)⋊C4C2311yescharacteristic
89C4⋊AGL(1,𝔽7)—22no—
90C4⋊AGL(1,𝔽7)—41no—
91C4×AGL(1,𝔽7)—22no—
92C4×AGL(1,𝔽7)—41no—
93C4×AGL(1,𝔽7)—41no—
94ΓL(1,𝔽8)⋊Q8—41no—
95C23×D7C22×C311yescharacteristic
96C22×C4×C7C22×C311yescharacteristic
97C2×C22⋊D7C22×C311yescharacteristic
98C22×Dic7C22×C311yescharacteristic
99C2×D28C22×C311yescharacteristic
100C2×D28C22×C311yescharacteristic
101C2×C4×D7C22×C311yescharacteristic
102C2×C4×D7C22×C311yescharacteristic
103C2×C4×D7C22×C311yescharacteristic, complemented
104C2×Dic14C22×C311yescharacteristic, complemented
105C7×C4⋊C4C22×C311yescharacteristic, complemented
106C7×C4⋊C4C22×C311yescharacteristic, complemented
107C7×C22⋊C4C22×C311yescharacteristic
108C7×C22⋊C4C22×C311yescharacteristic
109C42×C7C22×C311yescharacteristic, complemented
110C42×C7C22×C311yescharacteristic, complemented
111C22⋊Dic7C22×C311yescharacteristic
112(C2×D7)⋊C4C22×C311yescharacteristic
113(C2×D7)⋊C4C22×C311yescharacteristic
114(C2×D7)⋊C4C22×C311yescharacteristic
115(C2×D7)⋊C4C22×C311yescharacteristic
116(C2×D7)⋊C4C22×C311yescharacteristic
117(C2×D7)⋊C4C22×C311yescharacteristic
118(C2×D7)⋊C4C22×C311yescharacteristic
119(C2×D7)⋊C4C22×C311yescharacteristic
120(C2×D7)⋊C4C22×C311yescharacteristic, complemented
121(C2×D7)⋊C4C22×C311yescharacteristic, complemented
122(C2×D7)⋊C4C22×C311yescharacteristic, complemented
123C4⋊Dic7C22×C311yescharacteristic, complemented
124Dic7⋊C4C22×C311yescharacteristic, complemented
125Dic7⋊C4C22×C311yescharacteristic, complemented
126Dic7⋊C4C22×C311yescharacteristic, complemented
127Dic7⋊C4C22×C311yescharacteristic, complemented
128Dic7⋊C4C22×C311yescharacteristic, complemented
129C4×Dic7C22×C311yescharacteristic, complemented
130C3×#126—71no—
131C3×#126—71no—
132C3×#124—71no—
133C3×#123—71no—
134C3×#123—71no—
135C3×#123—71no—
136C3×C22⋊Q8—71no—
137C3×C22⋊Q8—71no—
138C3×#120—71no—
139C3×C4×D4—71no—
140C3×C4×D4—71no—
141C3×#117—71no—
142C3×#117—71no—
143C2×C3×C22⋊C4—71no—
144C2×C3×C22⋊C4—71no—
145C22×ΓL(1,𝔽8)—21no—
146C22×ΓL(1,𝔽8)—21no—
147C22×ΓL(1,𝔽8)#4112yes—
148C22×ΓL(1,𝔽8)C2411yescharacteristic
149C2×AGL(1,𝔽7)—21no—
150C2×AGL(1,𝔽7)—21no—
151C2×AGL(1,𝔽7)—21no—
152C2×AGL(1,𝔽7)—21no—
153C2×AGL(1,𝔽7)—21no—
154C2×AGL(1,𝔽7)—21no—
155C2×AGL(1,𝔽7)—21no—
156C2×AGL(1,𝔽7)—21no—
157C2×AGL(1,𝔽7)—44no—
158C2×AGL(1,𝔽7)#4112yes—
159C4×ΓL(1,𝔽8)—21no—
160C4×ΓL(1,𝔽8)—21no—
161C4×ΓL(1,𝔽8)—21no—
162C4×ΓL(1,𝔽8)—21no—
163C4×ΓL(1,𝔽8)—21no—
164C4×ΓL(1,𝔽8)—21no—
165ΓL(1,𝔽8)⋊C4—21no—
166ΓL(1,𝔽8)⋊C4—21no—
167ΓL(1,𝔽8)⋊C4—21no—
168ΓL(1,𝔽8)⋊C4—21no—
169ΓL(1,𝔽8)⋊C4—21no—
170#551—71noSylow
171C23×C7C23×C311yescharacteristic
172C22×D7—22no—
173C22×D7—22no—
174C22×D7—41no—
175C22×D7C23×C311yescharacteristic
176C22×D7C23×C311yescharacteristic
177C22×D7C23×C311yescharacteristic
178C2×C4×C7—22no—
179C2×C4×C7C23×C311yescharacteristic
180C2×C4×C7C23×C311yescharacteristic
181C2×C4×C7C23×C311yescharacteristic
182C2×C4×C7C23×C311yescharacteristic
183C2×C4×C7C23×C311yescharacteristic
184C2×C4×C7C23×C311yescharacteristic
185C22⋊D7—22no—
186C2×Dic7—41no—
187C2×Dic7C23×C311yescharacteristic
188C2×Dic7C23×C311yescharacteristic
189C2×Dic7C23×C311yescharacteristic
190C2×Dic7C23×C311yescharacteristic
191C2×Dic7C23×C311yescharacteristic
192D28—22no—
193D28—41no—
194C4×D7—22no—
195C4×D7—41no—
196C4×D7—41no—
197Dic14—41no—
198C24×C3—71no—
199C2×C3×Q8—71no—
200C2×C3×D4—71no—
201C2×C3×D4—71no—
202C2×C3×D4—71no—
203C22×C3×C4—71no—
204C22×C3×C4—71no—
205C22×C3×C4—71no—
206C22×C3×C4—71no—
207C22×C3×C4—71no—
208C3×C4⋊C4—71no—
209C3×C4⋊C4—71no—
210C3×C4⋊C4—71no—
211C3×C4⋊C4—71no—
212C3×C4⋊C4—71no—
213C3×C4⋊C4—71no—
214C3×C4⋊C4—71no—
215C3×C4⋊C4—71no—
216C3×C22⋊C4—71no—
217C3×C22⋊C4—71no—
218C3×C22⋊C4—71no—
219C3×C22⋊C4—71no—
220C3×C22⋊C4—71no—
221C3×C22⋊C4—71no—
222C3×C22⋊C4—71no—
223C3×C22⋊C4—71no—
224C3×C22⋊C4—71no—
225C3×C22⋊C4—71no—
226C3×C22⋊C4—71no—
227C3×C22⋊C4—71no—
228C3×C22⋊C4—71no—
229C3×C22⋊C4—71no—
230C3×C42—71no—
231C3×C42—71no—
232C3×C42—71no—
233C2×ΓL(1,𝔽8)—22no—
234C2×ΓL(1,𝔽8)C2×#4111yescharacteristic
235C2×ΓL(1,𝔽8)C2×#4111yescharacteristic
236C2×ΓL(1,𝔽8)H(5,𝔽2)11yescharacteristic
237AGL(1,𝔽7)—22no—
238AGL(1,𝔽7)—41no—
239AGL(1,𝔽7)—41no—
240#126—71no—
241#126—71no—
242#124—71no—
243#123—71no—
244#123—71no—
245#123—71no—
246C22⋊Q8—71no—
247C22⋊Q8—71no—
248#120—71no—
249C4×D4—71no—
250C4×D4—71no—
251#117—71no—
252#117AGL(1,𝔽7)11yescharacteristic, complemented
253C2×C22⋊C4—71no—
254C2×C22⋊C4—71no—
255C22×C7—21no—
256C22×C7—21no—
257C22×C7C3×#4112yes—
258C22×C7C24×C311yescharacteristic
259C2×D7—21no—
260C2×D7—21no—
261C2×D7—21no—
262C2×D7—21no—
263C2×D7—21no—
264C2×D7—21no—
265C2×D7—21no—
266C2×D7—21no—
267C2×D7—44no—
268C2×D7C3×#4112yes—
269C4×C7—21no—
270C4×C7—21no—
271C4×C7—21no—
272C4×C7—21no—
273C4×C7—21no—
274C4×C7—21no—
275Dic7—21no—
276Dic7—21no—
277Dic7—21no—
278Dic7—21no—
279Dic7—21no—
280C23×C3—71no—
281C23×C3—71no—
282C23×C3—71no—
283C23×C3—71no—
284C23×C3—142no—
285C23×C3—142no—
286C23×C3—281no—
287C3×Q8—281no—
288C3×D4—142no—
289C3×D4—142no—
290C3×D4—281no—
291C2×C3×C4—71no—
292C2×C3×C4—71no—
293C2×C3×C4—71no—
294C2×C3×C4—71no—
295C2×C3×C4—71no—
296C2×C3×C4—71no—
297C2×C3×C4—71no—
298C2×C3×C4—71no—
299C2×C3×C4—71no—
300C2×C3×C4—71no—
301C2×C3×C4—71no—
302C2×C3×C4—142no—
303C2×C3×C4—142no—
304C2×C3×C4—281no—
305C2×C3×C4—281no—
306C2×C3×C4—281no—
307ΓL(1,𝔽8)#55111yescharacteristic, complemented, Hall
308C24—71no—
309C2×Q8—71no—
310C2×D4—71no—
311C2×D4—71no—
312C2×D4—71no—
313C22×C4—71no—
314C22×C4—71no—
315C22×C4—71no—
316C22×C4—71no—
317C22×C4C2×AGL(1,𝔽7)11yescharacteristic
318C4⋊C4—71no—
319C4⋊C4—71no—
320C4⋊C4—71no—
321C4⋊C4—71no—
322C4⋊C4—71no—
323C4⋊C4—71no—
324C4⋊C4C2×AGL(1,𝔽7)11yescharacteristic, complemented
325C4⋊C4C2×AGL(1,𝔽7)11yescharacteristic, complemented
326C22⋊C4—71no—
327C22⋊C4—71no—
328C22⋊C4—71no—
329C22⋊C4—71no—
330C22⋊C4—71no—
331C22⋊C4—71no—
332C22⋊C4—71no—
333C22⋊C4—71no—
334C22⋊C4—71no—
335C22⋊C4—71no—
336C22⋊C4—71no—
337C22⋊C4—71no—
338C22⋊C4C2×AGL(1,𝔽7)11yescharacteristic
339C22⋊C4C2×AGL(1,𝔽7)11yescharacteristic
340C42—71no—
341C42C2×AGL(1,𝔽7)11yescharacteristic, complemented
342C42C2×AGL(1,𝔽7)11yescharacteristic, complemented
343C2×C7—22no—
344C2×C7C2×C3×#4111yescharacteristic
345C2×C7C2×C3×#4111yescharacteristic
346C2×C7C3×H(5,𝔽2)11yescharacteristic
347D7—22no—
348D7—41no—
349D7—41no—
350C22×C3—72no—
351C22×C3—72no—
352C22×C3—71no—
353C22×C3—141no—
354C22×C3—141no—
355C22×C3—141no—
356C22×C3—141no—
357C22×C3—141no—
358C22×C3—141no—
359C22×C3—141no—
360C22×C3—141no—
361C22×C3—141no—
362C22×C3—141no—
363C22×C3—284no—
364C3×C4—141no—
365C3×C4—141no—
366C3×C4—141no—
367C3×C4—141no—
368C3×C4—141no—
369C3×C4—141no—
370C3×C4—141no—
371C3×C4—141no—
372C3×C4—141no—
373C3×C4—141no—
374C3×C4—141no—
375C23—71no—
376C23—71no—
377C23—71no—
378C23—142no—
379C23—142no—
380C23—281no—
381C23C22×AGL(1,𝔽7)11yescharacteristic
382Q8—281no—
383D4—142no—
384D4—142no—
385D4—281no—
386C2×C4—22no—
387C2×C4—71no—
388C2×C4—71no—
389C2×C4—71no—
390C2×C4—71no—
391C2×C4—71no—
392C2×C4—142no—
393C2×C4—281no—
394C2×C4—281no—
395C2×C4—281no—
396C2×C4C22×AGL(1,𝔽7)11yescharacteristic
397C2×C4C22×AGL(1,𝔽7)11yescharacteristic
398C2×C4C22×AGL(1,𝔽7)11yescharacteristic
399C2×C4C22×AGL(1,𝔽7)11yescharacteristic
400C2×C4C22×AGL(1,𝔽7)11yescharacteristic
401C2×C4C22×AGL(1,𝔽7)11yescharacteristic
402C7C3×#55111yescharacteristic, complemented, Sylow
403C2×C3—71no—
404C2×C3—71no—
405C2×C3—71no—
406C2×C3—142no—
407C2×C3—142no—
408C2×C3—281no—
409C2×C3—281no—
410C22—21no—
411C22—21no—
412C22—72no—
413C22—141no—
414C22—141no—
415C22—141no—
416C22—141no—
417C22—141no—
418C22—141no—
419C22—141no—
420C22—141no—
421C22—284no—
422C22#1157⋊C312yes—
423C22C23×AGL(1,𝔽7)11yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—141no—
431C4—141no—
432C4—141no—
433C4—141no—
434C4—141no—
435C3—71noSylow
436C2—22no—
437C2—142no—
438C2—281no—
439C2—281no—
440C2C2×#1157⋊C311yescharacteristic
441C2#41×AGL(1,𝔽7)11yescharacteristic
442C2#1062151811yescharacteristic
subgroupG/H
center, FrattiniC22C23×AGL(1,𝔽7)
commutator, socle, cosocleC22×C7C24×C3
FittingC7×#117C2×C3
prime radical#6445⋊C3C2
hypercenter#117AGL(1,𝔽7)
hypocenterC7C3×#551
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. ΓL(1,𝔽8)×#117C2semidirect
2. #6492⋊C3C2semidirect
3. C2×(C2×AGL(1,𝔽7))⋊C4C2semidirect
4. #6461⋊C3C2semidirect
5. #6459⋊C3C2semidirect
6. #6457⋊C3C2semidirect
7. #6457⋊C3C2semidirect
9. ((C22⋊D7)⋊C3)⋊C4C2semidirect
10. C22⋊C4×AGL(1,𝔽7)C2semidirect
11. #6441⋊C3C2semidirect
12. #10620712C2semidirect
13. #6438⋊C3C2semidirect
14. C4×C4⋊AGL(1,𝔽7)C2semidirect
15. #6435⋊C3C2semidirect
16. #90218C3semidirect
25. C2×C4×AGL(1,𝔽7)C22semidirect
26. C2×ΓL(1,𝔽8)⋊Q8C22semidirect
27. C4⋊C4×ΓL(1,𝔽8)C22semidirect
28. C4⋊C4×ΓL(1,𝔽8)C22semidirect
31. C42×ΓL(1,𝔽8)C22semidirect
32. C42×ΓL(1,𝔽8)C22semidirect
42. (C2×AGL(1,𝔽7))⋊C4C22semidirect
43. (C2×AGL(1,𝔽7))⋊C4C22semidirect
44. (C2×AGL(1,𝔽7))⋊C4C22semidirect
45. C4⋊(ΓL(1,𝔽8)⋊C4)C22semidirect
46. (ΓL(1,𝔽8)⋊C4)⋊C4C22semidirect
47. (ΓL(1,𝔽8)⋊C4)⋊C4C22semidirect
48. (ΓL(1,𝔽8)⋊C4)⋊C4C22semidirect
49. (ΓL(1,𝔽8)⋊C4)⋊C4C22semidirect
50. (ΓL(1,𝔽8)⋊C4)⋊C4C22semidirect
51. C4×ΓL(1,𝔽8)⋊C4C22semidirect
52. C7×#117C2×C3semidirect
53. #6492C2×C3semidirect
54. C2×(C2×D7)⋊C4C2×C3semidirect
55. #6461C2×C3semidirect
56. #6459C2×C3semidirect
57. #6457C2×C3semidirect
58. #6457C2×C3semidirect
60. (C22⋊D7)⋊C4C2×C3semidirect
61. D7×C22⋊C4C2×C3semidirect
62. #6441C2×C3semidirect
63. #6439C2×C3semidirect
64. #6438C2×C3semidirect
65. C4×D28C2×C3semidirect
66. #6435C2×C3semidirect
103. C2×C4×D7C22×C3semidirect
104. C2×Dic14C22×C3semidirect
105. C7×C4⋊C4C22×C3semidirect
106. C7×C4⋊C4C22×C3semidirect
109. C42×C7C22×C3semidirect
110. C42×C7C22×C3semidirect
120. (C2×D7)⋊C4C22×C3semidirect
121. (C2×D7)⋊C4C22×C3semidirect
122. (C2×D7)⋊C4C22×C3semidirect
123. C4⋊Dic7C22×C3semidirect
124. Dic7⋊C4C22×C3semidirect
125. Dic7⋊C4C22×C3semidirect
126. Dic7⋊C4C22×C3semidirect
127. Dic7⋊C4C22×C3semidirect
128. Dic7⋊C4C22×C3semidirect
129. C4×Dic7C22×C3semidirect
252. #117AGL(1,𝔽7)semidirect
307. ΓL(1,𝔽8)#551semidirect
324. C4⋊C4C2×AGL(1,𝔽7)semidirect
325. C4⋊C4C2×AGL(1,𝔽7)semidirect
341. C42C2×AGL(1,𝔽7)semidirect
342. C42C2×AGL(1,𝔽7)semidirect
402. C7C3×#551semidirect

Maximal subgroups

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

subgroupindex
ΓL(1,𝔽8)×#1172
#6492⋊C32
C2×(C2×AGL(1,𝔽7))⋊C42
#6461⋊C32
#6459⋊C32
#6457⋊C32
#6445⋊C32
((C22⋊D7)⋊C3)⋊C42
C22⋊C4×AGL(1,𝔽7)2
#6441⋊C32
#106207122
#6438⋊C32
C4×C4⋊AGL(1,𝔽7)2
#6435⋊C32
#902183
C3×#5517