Finite Group Databasebeta

← #72254366

Subgroups — #72254366

Order 4032.

716 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72254327C211yesmaximal, characteristic, complemented
2#72245556C211yesmaximal, characteristic, complemented
3#72245514C211yesmaximal, characteristic, complemented
4C3×ΓL(1,𝔽8)×#104C211yesmaximal, characteristic, complemented
5#72244540C211yesmaximal, characteristic, complemented
6#72244421C211yesmaximal, characteristic, complemented
7#72244251C211yesmaximal, characteristic, complemented
8#13056459C311yesmaximal, characteristic, complemented
9#89594⋊C3—31nomaximal
10C3×#41×ΓL(1,𝔽8)C2211yescharacteristic
11#11759493—21no—
12D4×C3⋊AGL(1,𝔽7)—22no—
13D4×C3⋊AGL(1,𝔽7)—21no—
14#66728⋊C3—21no—
15#66728⋊C3C2211yescharacteristic
16C2×C4⋊(C3⋊AGL(1,𝔽7))—21no—
17C2×C4⋊(C3⋊AGL(1,𝔽7))—22no—
18C2×C4⋊(C3⋊AGL(1,𝔽7))C2211yescharacteristic
19C2×C4⋊(C3⋊AGL(1,𝔽7))C2211yescharacteristic, complemented
20C3×M16×ΓL(1,𝔽8)C2211yescharacteristic, complemented
21C3×C42×ΓL(1,𝔽8)C2211yescharacteristic, complemented
22#66634⋊C3—21no—
23#66632⋊C3—21no—
24#66627⋊C3C2211yescharacteristic, complemented
25D168⋊C3—21no—
26#66623⋊C3—21no—
27#10621662C2×C311yescharacteristic, complemented
28#10621518—31no—
29#10621432C2×C311yescharacteristic, complemented
30#10621391C2×C311yescharacteristic, complemented
31#10621357C2×C311yescharacteristic, complemented
32#6512⋊C3—31no—
33#6471⋊C3—31no—
34#10620710—31no—
35C3×C7×#104C2×C311yescharacteristic, complemented
36#10620662C2×C311yescharacteristic, complemented
37#10620644C2×C311yescharacteristic, complemented
38ΓL(1,𝔽8)×#104—21no—
39ΓL(1,𝔽8)×#104D311yescharacteristic, complemented
40#6397⋊C3—31no—
41#6379⋊C3—31no—
42C3×#4822—71nomaximal, Hall
43C22×C3⋊AGL(1,𝔽7)—22no—
44C22×C3⋊AGL(1,𝔽7)—21no—
45C22×C3⋊AGL(1,𝔽7)D412yes—
46C3×Q8×ΓL(1,𝔽8)D411yescharacteristic, complemented
47C3×D4×ΓL(1,𝔽8)—21no—
48C3×D4×ΓL(1,𝔽8)D411yescharacteristic, complemented
49C2×C3×C4×ΓL(1,𝔽8)—21no—
50C2×C3×C4×ΓL(1,𝔽8)—21no—
51C2×C3×C4×ΓL(1,𝔽8)C2311yescharacteristic
52#4268⋊C3—22no—
53#4268⋊C3—21no—
54C4⋊(C3⋊AGL(1,𝔽7))—22no—
55C4⋊(C3⋊AGL(1,𝔽7))—21no—
56C4⋊(C3⋊AGL(1,𝔽7))—21no—
57C4⋊(C3⋊AGL(1,𝔽7))—21no—
58C4⋊(C3⋊AGL(1,𝔽7))—21no—
59C4⋊(C3⋊AGL(1,𝔽7))—44no—
60C4⋊(C3⋊AGL(1,𝔽7))D411yescharacteristic, complemented
61C4×C3⋊AGL(1,𝔽7)—22no—
62C4×C3⋊AGL(1,𝔽7)—21no—
63Dic42⋊C3D411yescharacteristic, complemented
64C3×C8×ΓL(1,𝔽8)—21no—
65C3⋊(ΓL(1,𝔽8)⋊C8)—21no—
66#89594—31noHall
67C3×C7×#41C22×C311yescharacteristic
68#66732—21no—
69D4×D21—22no—
70D4×D21—21no—
71#66728—21no—
72#66728C22×C311yescharacteristic
73C2×D84—21no—
74C2×D84—22no—
75C2×D84C22×C311yescharacteristic
76C2×D84C22×C311yescharacteristic, complemented
77#41×ΓL(1,𝔽8)—21no—
78#41×ΓL(1,𝔽8)C2×D311yescharacteristic
79#66659—61no—
80D4×AGL(1,𝔽7)—62no—
81D4×AGL(1,𝔽7)—61no—
82#1157⋊C3—31no—
83#1157⋊C3—61no—
84C2×C4⋊AGL(1,𝔽7)—31no—
85C2×C4⋊AGL(1,𝔽7)—31no—
86C2×C4⋊AGL(1,𝔽7)—61no—
87C2×C4⋊AGL(1,𝔽7)—62no—
88C3×C7×M16C22×C311yescharacteristic, complemented
89C3×C42×C7C22×C311yescharacteristic, complemented
90#66634—21no—
91#66632—21no—
92#66627C22×C311yescharacteristic, complemented
93D168—21no—
94#66623—21no—
95M16×ΓL(1,𝔽8)—21no—
96M16×ΓL(1,𝔽8)C2×D311yescharacteristic, complemented
97C42×ΓL(1,𝔽8)—21no—
98C42×ΓL(1,𝔽8)C2×D311yescharacteristic, complemented
99#1143⋊C3—61no—
100#1141⋊C3—61no—
101#1136⋊C3—31no—
102D56⋊C3—61no—
103#1132⋊C3—61no—
104C3×#1009—71no—
105C3×#949—71no—
106C3×#908—71no—
107C3×#874—71no—
108C32×#104—141no—
109C3×#823—71no—
110C3×#805—71no—
111C22×C3×ΓL(1,𝔽8)—21no—
112C22×C3×ΓL(1,𝔽8)C2×D411yescharacteristic
113C2×C3⋊AGL(1,𝔽7)—21no—
114C2×C3⋊AGL(1,𝔽7)—22no—
115C2×C3⋊AGL(1,𝔽7)—42no—
116C2×C3⋊AGL(1,𝔽7)—42no—
117C2×C3⋊AGL(1,𝔽7)—41no—
118C2×C3⋊AGL(1,𝔽7)—82no—
119C3×C4×ΓL(1,𝔽8)—22no—
120C3×C4×ΓL(1,𝔽8)—21no—
121C3×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
122C3×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
123C3⋊(ΓL(1,𝔽8)⋊C4)—21no—
124#6553—31no—
125#6512—31no—
126#6471—31no—
127#6437—31no—
128C7×#104C3×D311yescharacteristic, complemented
129#6397—31no—
130#6379—31no—
131C3×#453—211no—
132#4822—71no—
133C22×D21—22no—
134C22×D21—21no—
135C22×D21C3×D412yes—
136C22×AGL(1,𝔽7)—32no—
137C22×AGL(1,𝔽7)—62no—
138C22×AGL(1,𝔽7)—61no—
139C3×C7×Q8C3×D411yescharacteristic, complemented
140C3×C7×D4—21no—
141C3×C7×D4C3×D411yescharacteristic, complemented
142C2×C3×C4×C7—21no—
143C2×C3×C4×C7—21no—
144C2×C3×C4×C7C23×C311yescharacteristic
145#4268—22no—
146#4268—21no—
147D84—22no—
148D84—21no—
149D84—21no—
150D84—21no—
151D84—21no—
152D84—44no—
153D84C3×D411yescharacteristic, complemented
154C4×D21—22no—
155C4×D21—21no—
156Dic42C3×D411yescharacteristic, complemented
157Q8×ΓL(1,𝔽8)—21no—
158Q8×ΓL(1,𝔽8)D1211yescharacteristic, complemented
159D4×ΓL(1,𝔽8)—21no—
160D4×ΓL(1,𝔽8)—21no—
161D4×ΓL(1,𝔽8)—41no—
162D4×ΓL(1,𝔽8)D1211yescharacteristic, complemented
163C2×C4×ΓL(1,𝔽8)—21no—
164C2×C4×ΓL(1,𝔽8)—21no—
165C2×C4×ΓL(1,𝔽8)—21no—
166C2×C4×ΓL(1,𝔽8)—41no—
167C2×C4×ΓL(1,𝔽8)—41no—
168C2×C4×ΓL(1,𝔽8)C22×D311yescharacteristic
169(C22⋊D7)⋊C3—62no—
170(C22⋊D7)⋊C3—61no—
171C4⋊AGL(1,𝔽7)—31no—
172C4⋊AGL(1,𝔽7)—62no—
173C4⋊AGL(1,𝔽7)—61no—
174C4⋊AGL(1,𝔽7)—61no—
175C4⋊AGL(1,𝔽7)—61no—
176C4⋊AGL(1,𝔽7)—61no—
177C4⋊AGL(1,𝔽7)—124no—
178C4×AGL(1,𝔽7)—62no—
179C4×AGL(1,𝔽7)—61no—
180ΓL(1,𝔽8)⋊Q8—31no—
181C3×C7×C8—21no—
182C3⋊(C7⋊C8)—21no—
183C8×ΓL(1,𝔽8)—21no—
184C8×ΓL(1,𝔽8)—41no—
185ΓL(1,𝔽8)⋊C8—61no—
186C32×#41—141no—
187C3×#239—141no—
188C3×D3×D4—141no—
189C3×D3×D4—142no—
190C3×#235—71no—
191C3×#235—141no—
192C2×C3×D12—71no—
193C2×C3×D12—71no—
194C2×C3×D12—141no—
195C2×C3×D12—142no—
196C32×M16—141no—
197C32×C42—141no—
198C3×#215—141no—
199C3×#213—141no—
200C3×#208—71no—
201C3×D24—141no—
202C3×#204—141no—
203C2×C3×ΓL(1,𝔽8)—21no—
204C2×C3×ΓL(1,𝔽8)—41no—
205C2×C3×ΓL(1,𝔽8)#12011yescharacteristic
206C3⋊AGL(1,𝔽7)—42no—
207C3⋊AGL(1,𝔽7)—41no—
208C3⋊AGL(1,𝔽7)—81no—
209C7×#41C2×C3×D311yescharacteristic
210#1161—61no—
211D4×D7—62no—
212D4×D7—61no—
213#1157—31no—
214#1157—61no—
215C2×D28—31no—
216C2×D28—31no—
217C2×D28—61no—
218C2×D28—62no—
219C7×M16C2×C3×D311yescharacteristic, complemented
220C42×C7C2×C3×D311yescharacteristic, complemented
221#1143—61no—
222#1141—61no—
223#1136—31no—
224D56—61no—
225#1132—61no—
226C3×H(5,𝔽2)—211no—
227#1009—71no—
228C3×AGL(1,ℤ/8)—211no—
229C3×AGL(1,ℤ/8)—211no—
230C3×#127—211no—
231#949—71no—
232#908—71no—
233#874—71no—
234C3×#104—141no—
235C3×#104—141no—
236C3×#104—211no—
237C3×#104AGL(1,𝔽7)11yescharacteristic, complemented
238C3×#100—211no—
239#823—71no—
240#805—71no—
241C22×C3×C7—21no—
242C22×C3×C7C2×C3×D411yescharacteristic
243C2×D21—22no—
244C2×D21—21no—
245C2×D21—42no—
246C2×D21—42no—
247C2×D21—41no—
248C2×D21—82no—
249C22×ΓL(1,𝔽8)—21no—
250C22×ΓL(1,𝔽8)—21no—
251C22×ΓL(1,𝔽8)—41no—
252C22×ΓL(1,𝔽8)D3×D411yescharacteristic
253C2×AGL(1,𝔽7)—61no—
254C2×AGL(1,𝔽7)—62no—
255C2×AGL(1,𝔽7)—122no—
256C2×AGL(1,𝔽7)—122no—
257C2×AGL(1,𝔽7)—121no—
258C2×AGL(1,𝔽7)—242no—
259C3×C4×C7—22no—
260C3×C4×C7—21no—
261C3×C4×C7C2×C3×D411yescharacteristic
262C3×C4×C7C2×C3×D411yescharacteristic
263Dic21—21no—
264C4×ΓL(1,𝔽8)—21no—
265C4×ΓL(1,𝔽8)—21no—
266C4×ΓL(1,𝔽8)—22no—
267C4×ΓL(1,𝔽8)—21no—
268C4×ΓL(1,𝔽8)—41no—
269C4×ΓL(1,𝔽8)—42no—
270C4×ΓL(1,𝔽8)C2×D1211yescharacteristic
271C4×ΓL(1,𝔽8)D3×D411yescharacteristic
272ΓL(1,𝔽8)⋊C4—61no—
273C22×C3×D3—72no—
274C22×C3×D3—142no—
275C22×C3×D3—141no—
276C32×Q8—141no—
277C32×D4—141no—
278C32×D4—281no—
279C2×C32×C4—141no—
280C2×C32×C4—281no—
281C2×C32×C4—281no—
282C3×#67—141no—
283C3×#67—142no—
284C3×D12—71no—
285C3×D12—141no—
286C3×D12—141no—
287C3×D12—141no—
288C3×D12—141no—
289C3×D12—142no—
290C3×D12—284no—
291C3×C4×D3—141no—
292C3×C4×D3—142no—
293C3×Dic6—71no—
294C32×C8—281no—
295C3×C3⋊C8—141no—
296#453—211noSylow
297C3×ΓL(1,𝔽8)#45311yescharacteristic, complemented, Hall
298C22×D7—32no—
299C22×D7—62no—
300C22×D7—61no—
301C7×Q8C3×D1211yescharacteristic, complemented
302C7×D4—21no—
303C7×D4C3×D1211yescharacteristic, complemented
304C2×C4×C7—21no—
305C2×C4×C7—21no—
306C2×C4×C7C22×C3×D311yescharacteristic
307C22⋊D7—62no—
308C22⋊D7—61no—
309D28—31no—
310D28—62no—
311D28—61no—
312D28—61no—
313D28—61no—
314D28—61no—
315D28—124no—
316C4×D7—62no—
317C4×D7—61no—
318Dic14—31no—
319C7×C8—21no—
320C7⋊C8—61no—
321C3×#41—141no—
322C3×#41—141no—
323C3×#41—211no—
324C3×#41—421no—
325C3×#41—421no—
326C3×#41C2×AGL(1,𝔽7)11yescharacteristic
327C2×C3×D4—211no—
328C2×C3×D4—211no—
329C2×C3×D4—421no—
330C2×C3×D4—422no—
331C2×C3×D4—421no—
332C2×C3×D4—422no—
333#239—141no—
334D3×D4—142no—
335D3×D4—141no—
336#235—71no—
337#235—141no—
338C2×D12—71no—
339C2×D12—71no—
340C2×D12—141no—
341C2×D12—142no—
342C3×SD16—421no—
343C3×SD16—421no—
344C3×D8—421no—
345C3×D8—421no—
346C3×M16—141no—
347C3×M16—141no—
348C3×M16—211no—
349C3×M16C2×AGL(1,𝔽7)11yescharacteristic, complemented
350C3×C42—141no—
351C3×C42—141no—
352C3×C42C2×AGL(1,𝔽7)11yescharacteristic, complemented
353#215—141no—
354#213—141no—
355#208—71no—
356D24—141no—
357#204—141no—
358C2×C3×C7—21no—
359C2×C3×C7—41no—
360C2×C3×C7C3×#12011yescharacteristic
361D21—42no—
362D21—41no—
363D21—81no—
364C2×ΓL(1,𝔽8)—21no—
365C2×ΓL(1,𝔽8)—21no—
366C2×ΓL(1,𝔽8)—41no—
367C2×ΓL(1,𝔽8)—41no—
368C2×ΓL(1,𝔽8)—81no—
369C2×ΓL(1,𝔽8)#88211yescharacteristic
370AGL(1,𝔽7)—122no—
371AGL(1,𝔽7)—121no—
372AGL(1,𝔽7)—241no—
373C22×C32—141no—
374C22×C32—281no—
375C2×C3×D3—141no—
376C2×C3×D3—142no—
377C2×C3×D3—282no—
378C2×C3×D3—281no—
379C2×C3×D3—282no—
380C2×C3×D3—562no—
381C32×C4—141no—
382C32×C4—141no—
383C32×C4—281no—
384C32×C4—282no—
385C3×Dic3—141no—
386H(5,𝔽2)—211no—
387AGL(1,ℤ/8)—211no—
388AGL(1,ℤ/8)—211no—
389#127—211no—
390#104—211no—
391#104C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
392#100—211no—
393C22×C7—21no—
394C22×C7C3×D3×D411yescharacteristic
395C2×D7—61no—
396C2×D7—62no—
397C2×D7—122no—
398C2×D7—122no—
399C2×D7—121no—
400C2×D7—242no—
401C4×C7—22no—
402C4×C7—21no—
403C4×C7C2×C3×D1211yescharacteristic
404C4×C7C3×D3×D411yescharacteristic
405Dic7—61no—
406C23×C3—212no—
407C23×C3—421no—
408C23×C3—422no—
409C22×D3—72no—
410C22×D3—142no—
411C22×D3—141no—
412C3×Q8—141no—
413C3×Q8—141no—
414C3×Q8—211no—
415C3×Q8C4⋊AGL(1,𝔽7)11yescharacteristic, complemented
416C3×D4—21no—
417C3×D4—141no—
418C3×D4—141no—
419C3×D4—211no—
420C3×D4—281no—
421C3×D4—281no—
422C3×D4—421no—
423C3×D4—421no—
424C3×D4—421no—
425C3×D4—421no—
426C3×D4—422no—
427C3×D4—421no—
428C3×D4—422no—
429C3×D4—844no—
430C3×D4C4⋊AGL(1,𝔽7)11yescharacteristic, complemented
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—141no—
434C2×C3×C4—141no—
435C2×C3×C4—281no—
436C2×C3×C4—281no—
437C2×C3×C4—281no—
438C2×C3×C4—281no—
439C2×C3×C4—421no—
440C2×C3×C4—422no—
441C2×C3×C4C22×AGL(1,𝔽7)11yescharacteristic
442#67—142no—
443#67—141no—
444D12—71no—
445D12—142no—
446D12—141no—
447D12—141no—
448D12—141no—
449D12—141no—
450D12—284no—
451C4×D3—142no—
452C4×D3—141no—
453Dic6—71no—
454C3×C8—21no—
455C3×C8—281no—
456C3×C8—281no—
457C3×C8—421no—
458C3⋊C8—141no—
459C3×C7C3×#45311yescharacteristic, complemented
460ΓL(1,𝔽8)—21no—
461ΓL(1,𝔽8)#482211yescharacteristic, complemented
462C2×C32—141no—
463C2×C32—281no—
464C2×C32—561no—
465C3×D3—282no—
466C3×D3—281no—
467C3×D3—561no—
468#41—211no—
469#41—421no—
470#41—421no—
471#41C2×C3⋊AGL(1,𝔽7)11yescharacteristic
472C2×D4—211no—
473C2×D4—211no—
474C2×D4—421no—
475C2×D4—422no—
476C2×D4—422no—
477C2×D4—421no—
478SD16—421no—
479SD16—421no—
480D8—421no—
481D8—421no—
482M16—211no—
483M16C2×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
484C42C2×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
485C2×C7—21no—
486C2×C7—41no—
487C2×C7C3×#88211yescharacteristic
488D7—122no—
489D7—121no—
490D7—241no—
491C22×C3—21no—
492C22×C3—141no—
493C22×C3—141no—
494C22×C3—281no—
495C22×C3—281no—
496C22×C3—421no—
497C22×C3—422no—
498C22×C3—841no—
499C22×C3—842no—
500C22×C3—842no—
501C22×C3—1682no—
502C22×C3D4×AGL(1,𝔽7)11yescharacteristic
503C2×D3—141no—
504C2×D3—142no—
505C2×D3—282no—
506C2×D3—282no—
507C2×D3—281no—
508C2×D3—562no—
509C3×C4—22no—
510C3×C4—21no—
511C3×C4—141no—
512C3×C4—141no—
513C3×C4—141no—
514C3×C4—141no—
515C3×C4—281no—
516C3×C4—281no—
517C3×C4—282no—
518C3×C4—282no—
519C3×C4—421no—
520C3×C4C2×C4⋊AGL(1,𝔽7)11yescharacteristic
521C3×C4D4×AGL(1,𝔽7)11yescharacteristic
522Dic3—141no—
523C32—141noSylow
524C23—212no—
525C23—422no—
526C23—421no—
527Q8—211no—
528Q8C4⋊(C3⋊AGL(1,𝔽7))11yescharacteristic, complemented
529D4—21no—
530D4—211no—
531D4—422no—
532D4—422no—
533D4—421no—
534D4—421no—
535D4—421no—
536D4—421no—
537D4—421no—
538D4—844no—
539D4C4⋊(C3⋊AGL(1,𝔽7))11yescharacteristic, complemented
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—422no—
543C2×C4—421no—
544C2×C4C22×C3⋊AGL(1,𝔽7)11yescharacteristic
545C8—21no—
546C8—421no—
547C7C3×#482211yescharacteristic, complemented, Sylow
548C2×C3—21no—
549C2×C3—41no—
550C2×C3—141no—
551C2×C3—141no—
552C2×C3—281no—
553C2×C3—281no—
554C2×C3—561no—
555C2×C3—561no—
556C2×C3—842no—
557C2×C3—841no—
558C2×C3—1681no—
559C2×C3#6445⋊C311yescharacteristic
560D3—282no—
561D3—281no—
562D3—561no—
563C22—21no—
564C22—421no—
565C22—422no—
566C22—842no—
567C22—842no—
568C22—841no—
569C22—1682no—
570C22D4×C3⋊AGL(1,𝔽7)11yescharacteristic
571C4—22no—
572C4—21no—
573C4—421no—
574C4C2×C4⋊(C3⋊AGL(1,𝔽7))11yescharacteristic
575C4D4×C3⋊AGL(1,𝔽7)11yescharacteristic
576C3—141no—
577C3—141no—
578C3#89594⋊C311yescharacteristic, complemented
579C2—21no—
580C2—41no—
581C2—842no—
582C2—841no—
583C2—1681no—
584C2#7224417211yescharacteristic
subgroupG/H
centerC2#72244172
commutator, cosocleC2×C3×C4×C7C23×C3
FrattiniC2×C4C22×C3⋊AGL(1,𝔽7)
FittingC3×C7×#104C2×C3
socleC2×C3×C7C3×#120
hypercenter#104C3⋊AGL(1,𝔽7)
hypocenterC3×C7C3×#453
LCSG ▷ C2×C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #72254327C2semidirect
2. #72245556C2semidirect
3. #72245514C2semidirect
4. C3×ΓL(1,𝔽8)×#104C2semidirect
5. #72244540C2semidirect
6. #72244421C2semidirect
7. #72244251C2semidirect
8. #13056459C3semidirect
19. C2×C4⋊(C3⋊AGL(1,𝔽7))C22semidirect
20. C3×M16×ΓL(1,𝔽8)C22semidirect
21. C3×C42×ΓL(1,𝔽8)C22semidirect
24. #66627⋊C3C22semidirect
27. #10621662C2×C3semidirect
29. #10621432C2×C3semidirect
30. #10621391C2×C3semidirect
31. #10621357C2×C3semidirect
35. C3×C7×#104C2×C3semidirect
36. #10620662C2×C3semidirect
37. #10620644C2×C3semidirect
39. ΓL(1,𝔽8)×#104D3semidirect
46. C3×Q8×ΓL(1,𝔽8)D4semidirect
48. C3×D4×ΓL(1,𝔽8)D4semidirect
60. C4⋊(C3⋊AGL(1,𝔽7))D4semidirect
63. Dic42⋊C3D4semidirect
76. C2×D84C22×C3semidirect
88. C3×C7×M16C22×C3semidirect
89. C3×C42×C7C22×C3semidirect
92. #66627C22×C3semidirect
96. M16×ΓL(1,𝔽8)C2×D3semidirect
98. C42×ΓL(1,𝔽8)C2×D3semidirect
128. C7×#104C3×D3semidirect
139. C3×C7×Q8C3×D4semidirect
141. C3×C7×D4C3×D4semidirect
153. D84C3×D4semidirect
156. Dic42C3×D4semidirect
158. Q8×ΓL(1,𝔽8)D12semidirect
162. D4×ΓL(1,𝔽8)D12semidirect
219. C7×M16C2×C3×D3semidirect
220. C42×C7C2×C3×D3semidirect
237. C3×#104AGL(1,𝔽7)semidirect
297. C3×ΓL(1,𝔽8)#453semidirect
301. C7×Q8C3×D12semidirect
303. C7×D4C3×D12semidirect
349. C3×M16C2×AGL(1,𝔽7)semidirect
352. C3×C42C2×AGL(1,𝔽7)semidirect
391. #104C3⋊AGL(1,𝔽7)semidirect
415. C3×Q8C4⋊AGL(1,𝔽7)semidirect
430. C3×D4C4⋊AGL(1,𝔽7)semidirect
459. C3×C7C3×#453semidirect
461. ΓL(1,𝔽8)#4822semidirect
483. M16C2×C3⋊AGL(1,𝔽7)semidirect
484. C42C2×C3⋊AGL(1,𝔽7)semidirect
528. Q8C4⋊(C3⋊AGL(1,𝔽7))semidirect
539. D4C4⋊(C3⋊AGL(1,𝔽7))semidirect
547. C7C3×#4822semidirect
578. C3#89594⋊C3semidirect

Maximal subgroups

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

subgroupindex
#722543272
#722455562
#722455142
C3×ΓL(1,𝔽8)×#1042
#722445402
#722444212
#722442512
#130564593
#89594⋊C33
C3×#48227