Finite Group Databasebeta

← #72277277

Subgroups — #72277277

Order 2688.

1340 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6548⋊C3C211yesmaximal, characteristic
2C2×ΓL(1,𝔽8)×#99C211yesmaximal, characteristic, complemented
3#89992⋊C3C211yesmaximal, characteristic, complemented
4#89730⋊C3C212yesmaximal, complemented
5C2×#6380⋊C3C212yesmaximal, complemented
6#11727787C311yesmaximal, characteristic, complemented, Hall
7C22×D4×ΓL(1,𝔽8)C2211yescharacteristic
8C22×(C22⋊D7)⋊C3—21no—
9C22×(C22⋊D7)⋊C3C2212yes—
10C23×ΓL(1,𝔽8)⋊C4C2211yescharacteristic, complemented
11#6548⋊C3—22no—
12#6548⋊C3—24no—
13#6548⋊C3C414yescomplemented
14C2×#1159⋊C3—22no—
15C2×D4×AGL(1,𝔽7)—22no—
16C2×#1157⋊C3—21no—
17C2×C22⋊C4×ΓL(1,𝔽8)C2212yescomplemented
18C2×(C22⋊Dic7)⋊C3—21no—
19C2×(C22⋊Dic7)⋊C3C2211yescharacteristic, complemented
20C2×(C2×AGL(1,𝔽7))⋊C4—22no—
21ΓL(1,𝔽8)×#99—22no—
22ΓL(1,𝔽8)⋊#95—21no—
23ΓL(1,𝔽8)⋊#95—22no—
24#6380⋊C3—24no—
25C2×#6548C2×C311yescharacteristic
26C2×C7×#99C2×C311yescharacteristic, complemented
27#89992C2×C311yescharacteristic, complemented
28#89730C2×C312yescomplemented
29C2×#6380C2×C312yescomplemented
30C3×#1790—71nomaximal, Hall
31C24×ΓL(1,𝔽8)D411yescharacteristic
32C24×ΓL(1,𝔽8)C2311yescharacteristic
33C23×AGL(1,𝔽7)—21no—
34C23×AGL(1,𝔽7)D412yes—
35C2×D4×ΓL(1,𝔽8)—22no—
36C2×D4×ΓL(1,𝔽8)—22no—
37C2×D4×ΓL(1,𝔽8)C2×C412yes—
38C2×D4×ΓL(1,𝔽8)D412yes—
39C22×C4×ΓL(1,𝔽8)—22no—
40C22×C4×ΓL(1,𝔽8)D411yescharacteristic
41C2×(C22⋊D7)⋊C3—22no—
42C2×(C22⋊D7)⋊C3—24no—
43C2×(C22⋊D7)⋊C3—24no—
44C2×(C22⋊D7)⋊C3—22no—
45C2×(C22⋊D7)⋊C3—22no—
46C2×(C22⋊D7)⋊C3—22no—
47C2×(C22⋊D7)⋊C3—22no—
48C2×(C22⋊D7)⋊C3C2×C414yes—
49C2×(C22⋊D7)⋊C3D414yes—
50C22×ΓL(1,𝔽8)⋊C4—21no—
51C22×ΓL(1,𝔽8)⋊C4—22no—
52C22×ΓL(1,𝔽8)⋊C4—21no—
53C22×ΓL(1,𝔽8)⋊C4—21no—
54C22×ΓL(1,𝔽8)⋊C4—42no—
55C22×ΓL(1,𝔽8)⋊C4D412yes—
56#1159⋊C3—28no—
57#1159⋊C3—28no—
58D4×AGL(1,𝔽7)—28no—
59D4×AGL(1,𝔽7)—28no—
60#1157⋊C3—24no—
61#1157⋊C3—24no—
62C2×C4⋊AGL(1,𝔽7)—21no—
63C2×C4×AGL(1,𝔽7)—22no—
64C2×ΓL(1,𝔽8)⋊Q8—21no—
65C22⋊C4×ΓL(1,𝔽8)—22no—
66C22⋊C4×ΓL(1,𝔽8)—22no—
67(C22⋊Dic7)⋊C3—22no—
68(C22⋊Dic7)⋊C3—42no—
69(C2×AGL(1,𝔽7))⋊C4—44no—
70C22×C7×D4C22×C311yescharacteristic
71C22×C22⋊D7—21no—
72C22×C22⋊D7C22×C312yes—
73C23×Dic7C22×C311yescharacteristic, complemented
74#6548—22no—
75#6548—24no—
76#6548C3×C414yescomplemented
77C2×#1159—22no—
78C2×D4×D7—22no—
79C2×#1157—21no—
80C2×C7×C22⋊C4C22×C312yescomplemented
81C2×C22⋊Dic7—21no—
82C2×C22⋊Dic7C22×C311yescharacteristic, complemented
83C2×(C2×D7)⋊C4—22no—
84C7×#99—22no—
85C7⋊#95—21no—
86C7⋊#95—22no—
87#6380—24no—
88C2×C3×H(5,𝔽2)—71no—
89C2×C3×#99—72no—
90C2×C3×#99—71no—
91C3×#386—72no—
92C3×#386—71no—
93C23×ΓL(1,𝔽8)—21no—
94C23×ΓL(1,𝔽8)—21no—
95C23×ΓL(1,𝔽8)—41no—
96C23×ΓL(1,𝔽8)—41no—
97C23×ΓL(1,𝔽8)—41no—
98C23×ΓL(1,𝔽8)—41no—
99C23×ΓL(1,𝔽8)C22⋊C412yescomplemented
100C23×ΓL(1,𝔽8)C22×C411yescharacteristic
101C23×ΓL(1,𝔽8)C2×D411yescharacteristic
102C23×ΓL(1,𝔽8)C2×D412yes—
103C23×ΓL(1,𝔽8)C2×D411yescharacteristic
104C23×ΓL(1,𝔽8)C2×D412yes—
105C22×AGL(1,𝔽7)—22no—
106C22×AGL(1,𝔽7)—24no—
107C22×AGL(1,𝔽7)—22no—
108C22×AGL(1,𝔽7)—42no—
109C22×AGL(1,𝔽7)—42no—
110C22×AGL(1,𝔽7)—81no—
111C22×AGL(1,𝔽7)—81no—
112C22×AGL(1,𝔽7)C22⋊C414yescomplemented
113D4×ΓL(1,𝔽8)—24no—
114D4×ΓL(1,𝔽8)—24no—
115C2×C4×ΓL(1,𝔽8)—21no—
116C2×C4×ΓL(1,𝔽8)—21no—
117C2×C4×ΓL(1,𝔽8)—42no—
118C2×C4×ΓL(1,𝔽8)—42no—
119C2×C4×ΓL(1,𝔽8)—42no—
120C2×C4×ΓL(1,𝔽8)C22⋊C412yescomplemented
121(C22⋊D7)⋊C3—28no—
122(C22⋊D7)⋊C3—24no—
123(C22⋊D7)⋊C3—24no—
124(C22⋊D7)⋊C3—24no—
125(C22⋊D7)⋊C3—24no—
126C2×ΓL(1,𝔽8)⋊C4—24no—
127C2×ΓL(1,𝔽8)⋊C4—22no—
128C2×ΓL(1,𝔽8)⋊C4—22no—
129C2×ΓL(1,𝔽8)⋊C4—24no—
130C2×ΓL(1,𝔽8)⋊C4—22no—
131C2×ΓL(1,𝔽8)⋊C4—41no—
132C2×ΓL(1,𝔽8)⋊C4—42no—
133C2×ΓL(1,𝔽8)⋊C4—41no—
134C2×ΓL(1,𝔽8)⋊C4—41no—
135C2×ΓL(1,𝔽8)⋊C4—41no—
136C2×ΓL(1,𝔽8)⋊C4—41no—
137C2×ΓL(1,𝔽8)⋊C4C22⋊C414yescomplemented
138C4⋊AGL(1,𝔽7)—24no—
139C4×AGL(1,𝔽7)—28no—
140ΓL(1,𝔽8)⋊Q8—24no—
141#1790—71noSylow
142C24×C7C3×D411yescharacteristic
143C24×C7C23×C311yescharacteristic
144C23×D7—21no—
145C23×D7C3×D412yes—
146C2×C7×D4—22no—
147C2×C7×D4—22no—
148C2×C7×D4C2×C3×C412yes—
149C2×C7×D4C3×D412yes—
150C22×C4×C7—22no—
151C22×C4×C7C3×D411yescharacteristic
152C2×C22⋊D7—22no—
153C2×C22⋊D7—24no—
154C2×C22⋊D7—24no—
155C2×C22⋊D7—22no—
156C2×C22⋊D7—22no—
157C2×C22⋊D7—22no—
158C2×C22⋊D7—22no—
159C2×C22⋊D7C2×C3×C414yes—
160C2×C22⋊D7C3×D414yes—
161C22×Dic7—21no—
162C22×Dic7—22no—
163C22×Dic7—21no—
164C22×Dic7—21no—
165C22×Dic7—42no—
166C22×Dic7C3×D412yes—
167#1159—28no—
168#1159—28no—
169D4×D7—28no—
170D4×D7—28no—
171#1157—24no—
172#1157—24no—
173C2×D28—21no—
174C2×C4×D7—22no—
175C2×Dic14—21no—
176C7×C22⋊C4—22no—
177C7×C22⋊C4—22no—
178C22⋊Dic7—22no—
179C22⋊Dic7—42no—
180(C2×D7)⋊C4—44no—
181C3×H(5,𝔽2)—74no—
182C3×H(5,𝔽2)—144no—
183C3×H(5,𝔽2)—142no—
184C2×C3×#41—141no—
185C2×C3×#41—142no—
186C22×C3×D4—72no—
187C22×C3×D4—71no—
188C22×C3×D4—142no—
189C22×C3×D4—141no—
190C23×C3×C4—71no—
191C2×C3×C22⋊C4—71no—
192C2×C3×C22⋊C4—72no—
193C2×C3×C22⋊C4—142no—
194C2×C3×C22⋊C4—141no—
195C3×#99—142no—
196C3×#99—144no—
197C3×#95—142no—
198C3×#95—141no—
199C22×ΓL(1,𝔽8)—21no—
200C22×ΓL(1,𝔽8)—22no—
201C22×ΓL(1,𝔽8)—21no—
202C22×ΓL(1,𝔽8)—22no—
203C22×ΓL(1,𝔽8)—22no—
204C22×ΓL(1,𝔽8)—41no—
205C22×ΓL(1,𝔽8)—42no—
206C22×ΓL(1,𝔽8)—41no—
207C22×ΓL(1,𝔽8)—42no—
208C22×ΓL(1,𝔽8)—41no—
209C22×ΓL(1,𝔽8)—41no—
210C22×ΓL(1,𝔽8)—81no—
211C22×ΓL(1,𝔽8)C2×C22⋊C412yes—
212C22×ΓL(1,𝔽8)C2×C22⋊C411yescharacteristic
213C22×ΓL(1,𝔽8)#12012yes—
214C22×ΓL(1,𝔽8)#12011yescharacteristic
215C22×ΓL(1,𝔽8)#12011yescharacteristic
216C2×AGL(1,𝔽7)—24no—
217C2×AGL(1,𝔽7)—42no—
218C2×AGL(1,𝔽7)—42no—
219C2×AGL(1,𝔽7)—44no—
220C2×AGL(1,𝔽7)—82no—
221C2×AGL(1,𝔽7)—84no—
222C4×ΓL(1,𝔽8)—22no—
223C4×ΓL(1,𝔽8)—82no—
224ΓL(1,𝔽8)⋊C4—24no—
225ΓL(1,𝔽8)⋊C4—42no—
226ΓL(1,𝔽8)⋊C4—81no—
227C2×H(5,𝔽2)—71no—
228C2×#99—72no—
229C2×#99AGL(1,𝔽7)11yescharacteristic, complemented
230#386—71no—
231#386—72no—
232C23×C7—21no—
233C23×C7—21no—
234C23×C7—41no—
235C23×C7—41no—
236C23×C7—41no—
237C23×C7—41no—
238C23×C7C3×C22⋊C412yescomplemented
239C23×C7C22×C3×C411yescharacteristic
240C23×C7C2×C3×D411yescharacteristic
241C23×C7C2×C3×D412yes—
242C23×C7C2×C3×D412yes—
243C23×C7C2×C3×D411yescharacteristic
244C22×D7—22no—
245C22×D7—24no—
246C22×D7—22no—
247C22×D7—42no—
248C22×D7—42no—
249C22×D7—81no—
250C22×D7—81no—
251C22×D7C3×C22⋊C414yescomplemented
252C7×D4—24no—
253C7×D4—24no—
254C2×C4×C7—21no—
255C2×C4×C7—21no—
256C2×C4×C7—42no—
257C2×C4×C7—42no—
258C2×C4×C7—42no—
259C2×C4×C7C3×C22⋊C412yescomplemented
260C22⋊D7—28no—
261C22⋊D7—24no—
262C22⋊D7—24no—
263C22⋊D7—24no—
264C22⋊D7—24no—
265C2×Dic7—24no—
266C2×Dic7—22no—
267C2×Dic7—22no—
268C2×Dic7—24no—
269C2×Dic7—22no—
270C2×Dic7—41no—
271C2×Dic7—42no—
272C2×Dic7—41no—
273C2×Dic7—41no—
274C2×Dic7—41no—
275C2×Dic7—41no—
276C2×Dic7C3×C22⋊C414yescomplemented
277D28—24no—
278C4×D7—28no—
279Dic14—24no—
280C24×C3—72no—
281C24×C3—71no—
282C24×C3—71no—
283C24×C3—141no—
284C3×#41—144no—
285C3×#41—148no—
286C3×#41—144no—
287C3×#41—148no—
288C2×C3×Q8—141no—
289C2×C3×D4—74no—
290C2×C3×D4—74no—
291C2×C3×D4—72no—
292C2×C3×D4—72no—
293C2×C3×D4—142no—
294C2×C3×D4—142no—
295C2×C3×D4—148no—
296C2×C3×D4—142no—
297C2×C3×D4—142no—
298C2×C3×D4—142no—
299C2×C3×D4—142no—
300C2×C3×D4—144no—
301C2×C3×D4—141no—
302C2×C3×D4—148no—
303C2×C3×D4—142no—
304C2×C3×D4—144no—
305C22×C3×C4—72no—
306C22×C3×C4—71no—
307C22×C3×C4—142no—
308C22×C3×C4—142no—
309C22×C3×C4—141no—
310C22×C3×C4—141no—
311C22×C3×C4—142no—
312C22×C3×C4—141no—
313C22×C3×C4—282no—
314C3×C22⋊C4—142no—
315C3×C22⋊C4—142no—
316C3×C22⋊C4—142no—
317C3×C22⋊C4—284no—
318C3×C22⋊C4—282no—
319C2×ΓL(1,𝔽8)—21no—
320C2×ΓL(1,𝔽8)—22no—
321C2×ΓL(1,𝔽8)—22no—
322C2×ΓL(1,𝔽8)—21no—
323C2×ΓL(1,𝔽8)—42no—
324C2×ΓL(1,𝔽8)#37911yescharacteristic
325C2×ΓL(1,𝔽8)B(4,𝔽2)11yescharacteristic
326C2×ΓL(1,𝔽8)#45811yescharacteristic
327AGL(1,𝔽7)—44no—
328H(5,𝔽2)—74no—
329H(5,𝔽2)—144no—
330H(5,𝔽2)—142no—
331C2×#41—142no—
332C2×#41—141no—
333C22×D4—72no—
334C22×D4—142no—
335C22×D4—141no—
336C22×D4C2×AGL(1,𝔽7)11yescharacteristic
337C23×C4—71no—
338C2×C22⋊C4—71no—
339C2×C22⋊C4—142no—
340C2×C22⋊C4—141no—
341C2×C22⋊C4C2×AGL(1,𝔽7)12yescomplemented
342#99—22no—
343#99—144no—
344#95—142no—
345#95—141no—
346C22×C7—21no—
347C22×C7—22no—
348C22×C7—21no—
349C22×C7—22no—
350C22×C7—22no—
351C22×C7—41no—
352C22×C7—42no—
353C22×C7—41no—
354C22×C7—42no—
355C22×C7—41no—
356C22×C7—41no—
357C22×C7—81no—
358C22×C7C2×C3×C22⋊C412yes—
359C22×C7C2×C3×C22⋊C411yescharacteristic
360C22×C7C3×#12011yescharacteristic
361C22×C7C3×#12011yescharacteristic
362C22×C7C3×#12012yes—
363C2×D7—24no—
364C2×D7—42no—
365C2×D7—42no—
366C2×D7—44no—
367C2×D7—82no—
368C2×D7—84no—
369C4×C7—22no—
370C4×C7—82no—
371Dic7—24no—
372Dic7—42no—
373Dic7—81no—
374C23×C3—74no—
375C23×C3—71no—
376C23×C3—71no—
377C23×C3—72no—
378C23×C3—72no—
379C23×C3—71no—
380C23×C3—72no—
381C23×C3—141no—
382C23×C3—141no—
383C23×C3—142no—
384C23×C3—142no—
385C23×C3—144no—
386C23×C3—281no—
387C23×C3—281no—
388C23×C3—281no—
389C23×C3—281no—
390C23×C3—282no—
391C23×C3—282no—
392C23×C3—561no—
393C23×C3—561no—
394C3×Q8—144no—
395C3×D4—144no—
396C3×D4—144no—
397C3×D4—144no—
398C3×D4—144no—
399C3×D4—144no—
400C3×D4—144no—
401C3×D4—144no—
402C3×D4—148no—
403C2×C3×C4—74no—
404C2×C3×C4—72no—
405C2×C3×C4—141no—
406C2×C3×C4—141no—
407C2×C3×C4—142no—
408C2×C3×C4—142no—
409C2×C3×C4—148no—
410C2×C3×C4—144no—
411C2×C3×C4—144no—
412C2×C3×C4—142no—
413C2×C3×C4—282no—
414C2×C3×C4—282no—
415C2×C3×C4—282no—
416C2×C3×C4—281no—
417C2×C3×C4—282no—
418C2×C3×C4—281no—
419C2×C3×C4—281no—
420C2×C3×C4—281no—
421C2×C3×C4—281no—
422ΓL(1,𝔽8)#179011yescharacteristic, complemented, Hall
423C24—72no—
424C24—141no—
425C24C4⋊AGL(1,𝔽7)11yescharacteristic
426C24C22×AGL(1,𝔽7)11yescharacteristic
427#41—144no—
428#41—148no—
429#41—148no—
430#41—144no—
431C2×Q8—141no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—74no—
435C2×D4—74no—
436C2×D4—141no—
437C2×D4—148no—
438C2×D4—148no—
439C2×D4—142no—
440C2×D4—144no—
441C2×D4—142no—
442C2×D4—142no—
443C2×D4—142no—
444C2×D4—142no—
445C2×D4—144no—
446C2×D4C4×AGL(1,𝔽7)12yes—
447C2×D4(C22⋊D7)⋊C312yes—
448C22×C4—22no—
449C22×C4—72no—
450C22×C4—142no—
451C22×C4—141no—
452C22×C4—141no—
453C22×C4—142no—
454C22×C4—141no—
455C22×C4—282no—
456C22×C4C4⋊AGL(1,𝔽7)11yescharacteristic
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—142no—
460C22⋊C4—284no—
461C22⋊C4—282no—
462C2×C7—21no—
463C2×C7—22no—
464C2×C7—22no—
465C2×C7—21no—
466C2×C7—42no—
467C2×C7C3×#37911yescharacteristic
468C2×C7C3×B(4,𝔽2)11yescharacteristic
469C2×C7C3×#45811yescharacteristic
470D7—44no—
471C22×C3—72no—
472C22×C3—71no—
473C22×C3—71no—
474C22×C3—71no—
475C22×C3—72no—
476C22×C3—142no—
477C22×C3—141no—
478C22×C3—142no—
479C22×C3—141no—
480C22×C3—142no—
481C22×C3—144no—
482C22×C3—281no—
483C22×C3—281no—
484C22×C3—281no—
485C22×C3—282no—
486C22×C3—281no—
487C22×C3—282no—
488C22×C3—282no—
489C22×C3—282no—
490C22×C3—284no—
491C22×C3—561no—
492C22×C3—562no—
493C22×C3—564no—
494C3×C4—142no—
495C3×C4—144no—
496C3×C4—282no—
497C3×C4—562no—
498C3×C4—561no—
499C23—21no—
500C23—21no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—74no—
506C23—144no—
507C23—142no—
508C23—142no—
509C23—282no—
510C23—282no—
511C23—561no—
512C23—561no—
513C23(C2×AGL(1,𝔽7))⋊C412yescomplemented
514C23C2×C4×AGL(1,𝔽7)11yescharacteristic
515C23C2×C4⋊AGL(1,𝔽7)11yescharacteristic
516C23D4×AGL(1,𝔽7)12yes—
517C23D4×AGL(1,𝔽7)12yes—
518C23C2×(C22⋊D7)⋊C311yescharacteristic
519Q8—144no—
520D4—24no—
521D4—24no—
522D4—144no—
523D4—148no—
524D4—144no—
525D4—144no—
526D4—144no—
527D4—144no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—74no—
534C2×C4—148no—
535C2×C4—144no—
536C2×C4—142no—
537C2×C4—142no—
538C2×C4—144no—
539C2×C4—142no—
540C2×C4—282no—
541C2×C4—281no—
542C2×C4—281no—
543C2×C4—281no—
544C2×C4—281no—
545C2×C4—281no—
546C2×C4(C2×AGL(1,𝔽7))⋊C412yescomplemented
547C7C3×#179011yescharacteristic, complemented, Sylow
548C2×C3—71no—
549C2×C3—71no—
550C2×C3—71no—
551C2×C3—142no—
552C2×C3—141no—
553C2×C3—141no—
554C2×C3—142no—
555C2×C3—282no—
556C2×C3—284no—
557C22—22no—
558C22—21no—
559C22—22no—
560C22—21no—
561C22—22no—
562C22—41no—
563C22—42no—
564C22—41no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—81no—
569C22—144no—
570C22—284no—
571C22—282no—
572C22—282no—
573C22—562no—
574C22—564no—
575C22C22⋊C4×AGL(1,𝔽7)12yes—
576C22#6445⋊C311yescharacteristic
577C22#6445⋊C311yescharacteristic
578C22C2×(C2×AGL(1,𝔽7))⋊C411yescharacteristic
579C22#6500⋊C312yes—
580C4—22no—
581C4—82no—
582C4—144no—
583C4—282no—
584C4—561no—
585C3—71noSylow
586C2—22no—
587C2—21no—
588C2—21no—
589C2—22no—
590C2—42no—
591C2—284no—
592C2#89513⋊C311yescharacteristic
593C2#89514⋊C311yescharacteristic
594C2#89727⋊C311yescharacteristic
subgroupG/H
centerC22#6445⋊C3
commutatorC23×C7C22×C3×C4
FrattiniC24C22×AGL(1,𝔽7)
FittingC2×C7×#99C2×C3
socleC22×C7C3×#120
prime radicalC2×#6548⋊C3C2
cosocleC24×C7C23×C3
hypercenterC2×#99AGL(1,𝔽7)
hypocenterC7C3×#1790
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×ΓL(1,𝔽8)×#99C2semidirect
3. #89992⋊C3C2semidirect
4. #89730⋊C3C2semidirect
5. C2×#6380⋊C3C2semidirect
6. #11727787C3semidirect
10. C23×ΓL(1,𝔽8)⋊C4C22semidirect
13. #6548⋊C3C4semidirect
17. C2×C22⋊C4×ΓL(1,𝔽8)C22semidirect
19. C2×(C22⋊Dic7)⋊C3C22semidirect
26. C2×C7×#99C2×C3semidirect
27. #89992C2×C3semidirect
28. #89730C2×C3semidirect
29. C2×#6380C2×C3semidirect
73. C23×Dic7C22×C3semidirect
76. #6548C3×C4semidirect
80. C2×C7×C22⋊C4C22×C3semidirect
82. C2×C22⋊Dic7C22×C3semidirect
99. C23×ΓL(1,𝔽8)C22⋊C4semidirect
112. C22×AGL(1,𝔽7)C22⋊C4semidirect
120. C2×C4×ΓL(1,𝔽8)C22⋊C4semidirect
137. C2×ΓL(1,𝔽8)⋊C4C22⋊C4semidirect
229. C2×#99AGL(1,𝔽7)semidirect
238. C23×C7C3×C22⋊C4semidirect
251. C22×D7C3×C22⋊C4semidirect
259. C2×C4×C7C3×C22⋊C4semidirect
276. C2×Dic7C3×C22⋊C4semidirect
341. C2×C22⋊C4C2×AGL(1,𝔽7)semidirect
422. ΓL(1,𝔽8)#1790semidirect
513. C23(C2×AGL(1,𝔽7))⋊C4semidirect
546. C2×C4(C2×AGL(1,𝔽7))⋊C4semidirect
547. C7C3×#1790semidirect

Maximal subgroups

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

subgroupindex
C2×#6548⋊C32
C2×ΓL(1,𝔽8)×#992
#89992⋊C32
#89730⋊C32
C2×#6380⋊C32
#117277873
C3×#17907