Finite Group Databasebeta

← #72277443

Subgroups — #72277443

Order 2688.

1532 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13062154C211yesmaximal, characteristic, complemented
2#90519⋊C3C211yesmaximal, characteristic, complemented
3#90215⋊C3C212yesmaximal, complemented
4ΓL(1,𝔽8)×#410C211yesmaximal, characteristic, complemented
5#89778⋊C3C212yesmaximal, complemented
6#89514⋊C3C214yesmaximal, complemented
7#89513⋊C3C214yesmaximal, complemented
8#11736135C311yesmaximal, characteristic, complemented, Hall
9C2×#41×ΓL(1,𝔽8)C2211yescharacteristic
10#10621519—22no—
11#10621518—22no—
12#41×AGL(1,𝔽7)—24no—
13#10621516—21no—
14#6548⋊C3—21no—
15#6548⋊C3C2214yes—
16C2×#1157⋊C3—22no—
17C2×#1157⋊C3C2212yes—
18C22×C4×AGL(1,𝔽7)C2211yescharacteristic, complemented
19ΓL(1,𝔽8)×#117C2212yescomplemented
20#6509⋊C3—21no—
21#6501⋊C3—21no—
22#6500⋊C3C2212yescomplemented
23#6498⋊C3C2212yescomplemented
24C4×(C22⋊D7)⋊C3—22no—
25#6489⋊C3C2211yescharacteristic, complemented
26#6460⋊C3—22no—
27#6458⋊C3—22no—
28#6449⋊C3C2214yescomplemented
29#6445⋊C3C2214yescomplemented
30C4×C4⋊AGL(1,𝔽7)—24no—
31ΓL(1,𝔽8)×#99C2214yescomplemented
32#6380⋊C3C2218yescomplemented
33#90616C2×C311yescharacteristic, complemented
34#90519C2×C311yescharacteristic, complemented
35#90215C2×C312yescomplemented
36C7×#410C2×C311yescharacteristic, complemented
37#89778C2×C312yescomplemented
38#89514C2×C314yescomplemented
39#89513C2×C314yescomplemented
40C3×#3025—71nomaximal, Hall
41C23×AGL(1,𝔽7)C2311yescharacteristic
42#41×ΓL(1,𝔽8)—22no—
43#41×ΓL(1,𝔽8)—22no—
44C2×Q8×ΓL(1,𝔽8)D411yescharacteristic, complemented
45C2×D4×ΓL(1,𝔽8)D411yescharacteristic, complemented
46C2×D4×ΓL(1,𝔽8)C2312yes—
47C22×C4×ΓL(1,𝔽8)D412yescomplemented
48C22×C4×ΓL(1,𝔽8)C2311yescharacteristic
49C2×(C22⋊D7)⋊C3—24no—
50C2×(C22⋊D7)⋊C3—22no—
51C2×(C22⋊D7)⋊C3C2314yes—
52C22×ΓL(1,𝔽8)⋊C4C2311yescharacteristic
53#66659—24no—
54Q8×AGL(1,𝔽7)—24no—
55#1159⋊C3—24no—
56#1159⋊C3—28no—
57D4×AGL(1,𝔽7)—24no—
58D4×AGL(1,𝔽7)—28no—
59#1157⋊C3—24no—
60#1157⋊C3—24no—
61#1157⋊C3—22no—
62#1157⋊C3—24no—
63#1157⋊C3—22no—
64#1157⋊C3—22no—
65#1157⋊C3—22no—
66C2×C4⋊AGL(1,𝔽7)—22no—
67C2×C4⋊AGL(1,𝔽7)—24no—
68C2×C4⋊AGL(1,𝔽7)D412yescomplemented
69C2×C4×AGL(1,𝔽7)—24no—
70C2×C4×AGL(1,𝔽7)—22no—
71C2×C4×AGL(1,𝔽7)—22no—
72C2×C4×AGL(1,𝔽7)—21no—
73C2×C4×AGL(1,𝔽7)—21no—
74C2×C4×AGL(1,𝔽7)D414yescomplemented
75C2×ΓL(1,𝔽8)⋊Q8—22no—
76C2×ΓL(1,𝔽8)⋊Q8D412yescomplemented
77C4⋊C4×ΓL(1,𝔽8)—22no—
78C22⋊C4×ΓL(1,𝔽8)C2314yes—
79C42×ΓL(1,𝔽8)—22no—
80(C22⋊Dic7)⋊C3—22no—
81(C22⋊Dic7)⋊C3C2312yes—
82(C2×AGL(1,𝔽7))⋊C4—24no—
83(C2×AGL(1,𝔽7))⋊C4—22no—
84(C2×AGL(1,𝔽7))⋊C4—24no—
85C4⋊(ΓL(1,𝔽8)⋊C4)—21no—
86C4⋊(ΓL(1,𝔽8)⋊C4)—24no—
87(ΓL(1,𝔽8)⋊C4)⋊C4—22no—
88C4×ΓL(1,𝔽8)⋊C4—21no—
89C2×C7×#41C22×C311yescharacteristic
90#6554—22no—
91#6553—22no—
92D7×#41—24no—
93#6551—21no—
94#6548—21no—
95#6548C22×C314yes—
96C2×#1157—22no—
97C2×#1157C22×C312yes—
98C22×C4×D7C22×C311yescharacteristic, complemented
99C7×#117C22×C312yescomplemented
100#6509—21no—
101#6501—21no—
102#6500C22×C312yescomplemented
103#6498C22×C312yescomplemented
104C4×C22⋊D7—22no—
105#6489C22×C311yescharacteristic, complemented
106#6460—22no—
107#6458—22no—
108#6449C22×C314yescomplemented
109#6445C22×C314yescomplemented
110C4×D28—24no—
111C7×#99C22×C314yescomplemented
112#6380C22×C318yescomplemented
113C3×#585—71no—
114C3×#525—71no—
115C3×#525—72no—
116C3×#458—74no—
117C3×B(4,𝔽2)—74no—
118C3×#410—72no—
119C3×#410—71no—
120C23×ΓL(1,𝔽8)C2×D412yes—
121C23×ΓL(1,𝔽8)C2411yescharacteristic
122C22×AGL(1,𝔽7)—22no—
123C22×AGL(1,𝔽7)—21no—
124C22×AGL(1,𝔽7)—24no—
125C22×AGL(1,𝔽7)—42no—
126C22×AGL(1,𝔽7)C2×D414yes—
127Q8×ΓL(1,𝔽8)—22no—
128D4×ΓL(1,𝔽8)—24no—
129D4×ΓL(1,𝔽8)—22no—
130C2×C4×ΓL(1,𝔽8)—22no—
131C2×C4×ΓL(1,𝔽8)—22no—
132C2×C4×ΓL(1,𝔽8)—24no—
133C2×C4×ΓL(1,𝔽8)C2×D412yes—
134C2×C4×ΓL(1,𝔽8)C2×D412yes—
135C2×C4×ΓL(1,𝔽8)C2×D412yes—
136C2×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
137C2×C4×ΓL(1,𝔽8)C2×D411yescharacteristic
138(C22⋊D7)⋊C3—28no—
139(C22⋊D7)⋊C3—24no—
140(C22⋊D7)⋊C3—24no—
141(C22⋊D7)⋊C3—44no—
142C2×ΓL(1,𝔽8)⋊C4—24no—
143C2×ΓL(1,𝔽8)⋊C4—21no—
144C2×ΓL(1,𝔽8)⋊C4—22no—
145C2×ΓL(1,𝔽8)⋊C4—22no—
146C2×ΓL(1,𝔽8)⋊C4C2×D414yes—
147C4⋊AGL(1,𝔽7)—24no—
148C4⋊AGL(1,𝔽7)—22no—
149C4⋊AGL(1,𝔽7)—22no—
150C4⋊AGL(1,𝔽7)—48no—
151C4×AGL(1,𝔽7)—28no—
152C4×AGL(1,𝔽7)—24no—
153C4×AGL(1,𝔽7)—24no—
154C4×AGL(1,𝔽7)—41no—
155C4×AGL(1,𝔽7)—42no—
156C4×AGL(1,𝔽7)—41no—
157ΓL(1,𝔽8)⋊Q8—24no—
158ΓL(1,𝔽8)⋊Q8—22no—
159ΓL(1,𝔽8)⋊Q8—22no—
160#3025—71noSylow
161C23×D7C23×C311yescharacteristic
162C7×#41—22no—
163C7×#41—22no—
164C2×C7×Q8C3×D411yescharacteristic, complemented
165C2×C7×D4C3×D411yescharacteristic, complemented
166C2×C7×D4C23×C312yes—
167C22×C4×C7C3×D412yescomplemented
168C22×C4×C7C23×C311yescharacteristic
169C2×C22⋊D7—24no—
170C2×C22⋊D7—22no—
171C2×C22⋊D7C23×C314yes—
172C22×Dic7C23×C311yescharacteristic
173#1161—24no—
174Q8×D7—24no—
175#1159—24no—
176#1159—28no—
177D4×D7—24no—
178D4×D7—28no—
179#1157—24no—
180#1157—24no—
181#1157—22no—
182#1157—24no—
183#1157—22no—
184#1157—22no—
185#1157—22no—
186C2×D28—22no—
187C2×D28—24no—
188C2×D28C3×D412yescomplemented
189C2×C4×D7—24no—
190C2×C4×D7—22no—
191C2×C4×D7—22no—
192C2×C4×D7—21no—
193C2×C4×D7—21no—
194C2×C4×D7C3×D414yescomplemented
195C2×Dic14—22no—
196C2×Dic14C3×D412yescomplemented
197C7×C4⋊C4—22no—
198C7×C22⋊C4C23×C314yes—
199C42×C7—22no—
200C22⋊Dic7—22no—
201C22⋊Dic7C23×C312yes—
202(C2×D7)⋊C4—24no—
203(C2×D7)⋊C4—22no—
204(C2×D7)⋊C4—24no—
205C4⋊Dic7—21no—
206C4⋊Dic7—24no—
207Dic7⋊C4—22no—
208C4×Dic7—21no—
209C3×2−1+4—141no—
210C3×2−1+4—142no—
211C3×H(5,𝔽2)—74no—
212C3×H(5,𝔽2)—141no—
213C3×H(5,𝔽2)—142no—
214C2×C3×#41—72no—
215C2×C3×#41—71no—
216C2×C3×#41—142no—
217C2×C3×#41—144no—
218C23×C3×C4—71no—
219C3×#123—74no—
220C3×#123—72no—
221C3×C22⋊Q8—142no—
222C3×C22⋊Q8—141no—
223C3×#121—142no—
224C3×#121—141no—
225C3×#120—74no—
226C3×#120—72no—
227C3×C4×D4—144no—
228C3×C4×D4—142no—
229C3×#117—71no—
230C3×#117—72no—
231C3×#99—78no—
232C3×#99—74no—
233C22×ΓL(1,𝔽8)—22no—
234C22×ΓL(1,𝔽8)—41no—
235C22×ΓL(1,𝔽8)—42no—
236C22×ΓL(1,𝔽8)C22×D411yescharacteristic
237C22×ΓL(1,𝔽8)C22×D412yes—
238C2×AGL(1,𝔽7)—24no—
239C2×AGL(1,𝔽7)—22no—
240C2×AGL(1,𝔽7)—24no—
241C2×AGL(1,𝔽7)—41no—
242C2×AGL(1,𝔽7)—42no—
243C2×AGL(1,𝔽7)—41no—
244C2×AGL(1,𝔽7)—44no—
245C2×AGL(1,𝔽7)—84no—
246C4×ΓL(1,𝔽8)—22no—
247C4×ΓL(1,𝔽8)—44no—
248C4×ΓL(1,𝔽8)#12011yescharacteristic
249C4×ΓL(1,𝔽8)#12012yes—
250C4×ΓL(1,𝔽8)#12011yescharacteristic
251ΓL(1,𝔽8)⋊C4—24no—
252ΓL(1,𝔽8)⋊C4—42no—
253ΓL(1,𝔽8)⋊C4—41no—
254#585—71no—
255#525—71no—
256#525—72no—
257#458—74no—
258B(4,𝔽2)—74no—
259#410—72no—
260#410AGL(1,𝔽7)11yescharacteristic, complemented
261C23×C7C2×C3×D412yes—
262C23×C7C24×C311yescharacteristic
263C22×D7—22no—
264C22×D7—21no—
265C22×D7—24no—
266C22×D7—42no—
267C22×D7C2×C3×D414yes—
268C7×Q8—22no—
269C7×D4—24no—
270C7×D4—22no—
271C2×C4×C7—22no—
272C2×C4×C7—22no—
273C2×C4×C7—24no—
274C2×C4×C7C2×C3×D412yes—
275C2×C4×C7C2×C3×D411yescharacteristic
276C2×C4×C7C2×C3×D411yescharacteristic
277C2×C4×C7C2×C3×D412yes—
278C2×C4×C7C2×C3×D412yes—
279C22⋊D7—28no—
280C22⋊D7—24no—
281C22⋊D7—24no—
282C22⋊D7—44no—
283C2×Dic7—24no—
284C2×Dic7—22no—
285C2×Dic7—21no—
286C2×Dic7—22no—
287C2×Dic7C2×C3×D414yes—
288D28—24no—
289D28—22no—
290D28—22no—
291D28—48no—
292C4×D7—28no—
293C4×D7—24no—
294C4×D7—24no—
295C4×D7—41no—
296C4×D7—42no—
297C4×D7—41no—
298Dic14—24no—
299Dic14—22no—
300Dic14—22no—
301C24×C3—71no—
302C3×#41—142no—
303C3×#41—142no—
304C3×#41—142no—
305C3×#41—142no—
306C3×#41—142no—
307C3×#41—142no—
308C3×#41—144no—
309C3×#41—148no—
310C3×#41—144no—
311C3×#41—144no—
312C3×#41—144no—
313C3×#41—144no—
314C2×C3×Q8—72no—
315C2×C3×Q8—71no—
316C2×C3×Q8—142no—
317C2×C3×Q8—144no—
318C2×C3×D4—74no—
319C2×C3×D4—72no—
320C2×C3×D4—71no—
321C2×C3×D4—72no—
322C2×C3×D4—148no—
323C2×C3×D4—144no—
324C2×C3×D4—142no—
325C2×C3×D4—144no—
326C2×C3×D4—144no—
327C2×C3×D4—142no—
328C22×C3×C4—74no—
329C22×C3×C4—71no—
330C22×C3×C4—72no—
331C22×C3×C4—71no—
332C22×C3×C4—141no—
333C22×C3×C4—142no—
334C22×C3×C4—141no—
335C22×C3×C4—142no—
336C22×C3×C4—144no—
337C3×C4⋊C4—142no—
338C3×C4⋊C4—141no—
339C3×C4⋊C4—142no—
340C3×C4⋊C4—144no—
341C3×C22⋊C4—72no—
342C3×C22⋊C4—74no—
343C3×C22⋊C4—144no—
344C3×C22⋊C4—142no—
345C3×C22⋊C4—144no—
346C3×C22⋊C4—142no—
347C3×C42—142no—
348C3×C42—141no—
349C2×ΓL(1,𝔽8)—21no—
350C2×ΓL(1,𝔽8)—22no—
351C2×ΓL(1,𝔽8)—42no—
352C2×ΓL(1,𝔽8)C2×#12011yescharacteristic
353AGL(1,𝔽7)—42no—
354AGL(1,𝔽7)—44no—
3552−1+4—142no—
3562−1+4—141no—
357H(5,𝔽2)—74no—
358H(5,𝔽2)—142no—
359H(5,𝔽2)—141no—
360C2×#41—72no—
361C2×#41—144no—
362C2×#41—142no—
363C2×#41C2×AGL(1,𝔽7)11yescharacteristic
364C23×C4—71no—
365#123—72no—
366#123—74no—
367C22⋊Q8—142no—
368C22⋊Q8—141no—
369#121—142no—
370#121—141no—
371#120—72no—
372#120—74no—
373C4×D4—144no—
374C4×D4—142no—
375#117—71no—
376#117C2×AGL(1,𝔽7)12yescomplemented
377#99—78no—
378#99C2×AGL(1,𝔽7)14yescomplemented
379C22×C7—22no—
380C22×C7—41no—
381C22×C7—42no—
382C22×C7C22×C3×D411yescharacteristic
383C22×C7C22×C3×D412yes—
384C2×D7—24no—
385C2×D7—22no—
386C2×D7—24no—
387C2×D7—41no—
388C2×D7—42no—
389C2×D7—41no—
390C2×D7—44no—
391C2×D7—84no—
392C4×C7—22no—
393C4×C7—44no—
394C4×C7C3×#12011yescharacteristic
395C4×C7C3×#12012yes—
396C4×C7C3×#12011yescharacteristic
397Dic7—24no—
398Dic7—42no—
399Dic7—41no—
400C23×C3—74no—
401C23×C3—72no—
402C23×C3—71no—
403C23×C3—141no—
404C23×C3—142no—
405C23×C3—144no—
406C23×C3—282no—
407C3×Q8—142no—
408C3×Q8—142no—
409C3×Q8—142no—
410C3×Q8—144no—
411C3×D4—142no—
412C3×D4—144no—
413C3×D4—142no—
414C3×D4—142no—
415C3×D4—144no—
416C3×D4—144no—
417C3×D4—144no—
418C3×D4—148no—
419C3×D4—288no—
420C3×D4—284no—
421C2×C3×C4—74no—
422C2×C3×C4—71no—
423C2×C3×C4—71no—
424C2×C3×C4—72no—
425C2×C3×C4—72no—
426C2×C3×C4—72no—
427C2×C3×C4—142no—
428C2×C3×C4—142no—
429C2×C3×C4—144no—
430C2×C3×C4—144no—
431C2×C3×C4—144no—
432C2×C3×C4—148no—
433C2×C3×C4—144no—
434C2×C3×C4—142no—
435C2×C3×C4—141no—
436C2×C3×C4—142no—
437C2×C3×C4—281no—
438C2×C3×C4—282no—
439C2×C3×C4—281no—
440ΓL(1,𝔽8)#302511yescharacteristic, complemented, Hall
441C24—71no—
442#41—22no—
443#41—22no—
444#41—144no—
445#41—144no—
446#41—148no—
447#41—144no—
448#41—144no—
449#41—142no—
450#41—142no—
451#41—144no—
452#41—142no—
453#41—142no—
454C2×Q8—72no—
455C2×Q8—142no—
456C2×Q8—144no—
457C2×Q8C4⋊AGL(1,𝔽7)11yescharacteristic, complemented
458C2×D4—74no—
459C2×D4—72no—
460C2×D4—142no—
461C2×D4—144no—
462C2×D4—148no—
463C2×D4—144no—
464C2×D4—144no—
465C2×D4—142no—
466C2×D4C4⋊AGL(1,𝔽7)11yescharacteristic, complemented
467C2×D4C22×AGL(1,𝔽7)12yes—
468C22×C4—74no—
469C22×C4—71no—
470C22×C4—144no—
471C22×C4—141no—
472C22×C4—141no—
473C22×C4—142no—
474C22×C4—142no—
475C22×C4C4⋊AGL(1,𝔽7)12yescomplemented
476C22×C4C22×AGL(1,𝔽7)11yescharacteristic
477C4⋊C4—22no—
478C4⋊C4—144no—
479C4⋊C4—142no—
480C4⋊C4—141no—
481C22⋊C4—72no—
482C22⋊C4—144no—
483C22⋊C4—144no—
484C22⋊C4—142no—
485C22⋊C4—142no—
486C22⋊C4C22×AGL(1,𝔽7)14yes—
487C42—22no—
488C42—141no—
489C2×C7—21no—
490C2×C7—22no—
491C2×C7—42no—
492C2×C7C2×C3×#12011yescharacteristic
493D7—42no—
494D7—44no—
495C22×C3—71no—
496C22×C3—72no—
497C22×C3—142no—
498C22×C3—144no—
499C22×C3—144no—
500C22×C3—142no—
501C22×C3—281no—
502C22×C3—282no—
503C22×C3—281no—
504C22×C3—284no—
505C22×C3—282no—
506C22×C3—281no—
507C22×C3—564no—
508C3×C4—71no—
509C3×C4—72no—
510C3×C4—71no—
511C3×C4—142no—
512C3×C4—144no—
513C3×C4—284no—
514C3×C4—281no—
515C3×C4—282no—
516C23—74no—
517C23—144no—
518C23—141no—
519C23—142no—
520C23—282no—
521C23C2×C4⋊AGL(1,𝔽7)12yes—
522C23C23×AGL(1,𝔽7)11yescharacteristic
523Q8—22no—
524Q8—144no—
525Q8—142no—
526Q8—142no—
527D4—24no—
528D4—22no—
529D4—144no—
530D4—148no—
531D4—144no—
532D4—144no—
533D4—142no—
534D4—142no—
535D4—288no—
536D4—284no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—74no—
541C2×C4—148no—
542C2×C4—144no—
543C2×C4—144no—
544C2×C4—144no—
545C2×C4—142no—
546C2×C4—141no—
547C2×C4—142no—
548C2×C4—281no—
549C2×C4—282no—
550C2×C4—281no—
551C2×C4C2×C4⋊AGL(1,𝔽7)12yes—
552C2×C4C2×C4⋊AGL(1,𝔽7)11yescharacteristic
553C2×C4C2×C4⋊AGL(1,𝔽7)11yescharacteristic
554C2×C4D4×AGL(1,𝔽7)12yes—
555C2×C4D4×AGL(1,𝔽7)12yes—
556C7C3×#302511yescharacteristic, complemented, Sylow
557C2×C3—71no—
558C2×C3—142no—
559C2×C3—141no—
560C2×C3—282no—
561C2×C3—282no—
562C2×C3—284no—
563C22—22no—
564C22—41no—
565C22—42no—
566C22—144no—
567C22—142no—
568C22—144no—
569C22—284no—
570C22—282no—
571C22—281no—
572C22—281no—
573C22—564no—
574C22C22×C4⋊AGL(1,𝔽7)11yescharacteristic
575C22C2×D4×AGL(1,𝔽7)12yes—
576C4—22no—
577C4—44no—
578C4—144no—
579C4—282no—
580C4—281no—
581C4#6445⋊C311yescharacteristic
582C4#6445⋊C312yes—
583C4#6445⋊C311yescharacteristic
584C3—71noSylow
585C2—22no—
586C2—21no—
587C2—42no—
588C2—282no—
589C2—284no—
590C2C2×#6445⋊C311yescharacteristic
subgroupG/H
centerC4#6445⋊C3
commutator, cosocleC23×C7C24×C3
FrattiniC23C23×AGL(1,𝔽7)
FittingC7×#410C2×C3
socleC2×C7C2×C3×#120
hypercenter#410AGL(1,𝔽7)
hypocenterC7C3×#3025
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #13062154C2semidirect
2. #90519⋊C3C2semidirect
3. #90215⋊C3C2semidirect
4. ΓL(1,𝔽8)×#410C2semidirect
5. #89778⋊C3C2semidirect
6. #89514⋊C3C2semidirect
7. #89513⋊C3C2semidirect
8. #11736135C3semidirect
18. C22×C4×AGL(1,𝔽7)C22semidirect
19. ΓL(1,𝔽8)×#117C22semidirect
22. #6500⋊C3C22semidirect
23. #6498⋊C3C22semidirect
25. #6489⋊C3C22semidirect
28. #6449⋊C3C22semidirect
29. #6445⋊C3C22semidirect
31. ΓL(1,𝔽8)×#99C22semidirect
32. #6380⋊C3C22semidirect
33. #90616C2×C3semidirect
34. #90519C2×C3semidirect
35. #90215C2×C3semidirect
36. C7×#410C2×C3semidirect
37. #89778C2×C3semidirect
38. #89514C2×C3semidirect
39. #89513C2×C3semidirect
44. C2×Q8×ΓL(1,𝔽8)D4semidirect
45. C2×D4×ΓL(1,𝔽8)D4semidirect
47. C22×C4×ΓL(1,𝔽8)D4semidirect
68. C2×C4⋊AGL(1,𝔽7)D4semidirect
74. C2×C4×AGL(1,𝔽7)D4semidirect
76. C2×ΓL(1,𝔽8)⋊Q8D4semidirect
98. C22×C4×D7C22×C3semidirect
99. C7×#117C22×C3semidirect
102. #6500C22×C3semidirect
103. #6498C22×C3semidirect
105. #6489C22×C3semidirect
108. #6449C22×C3semidirect
109. #6445C22×C3semidirect
111. C7×#99C22×C3semidirect
112. #6380C22×C3semidirect
164. C2×C7×Q8C3×D4semidirect
165. C2×C7×D4C3×D4semidirect
167. C22×C4×C7C3×D4semidirect
188. C2×D28C3×D4semidirect
194. C2×C4×D7C3×D4semidirect
196. C2×Dic14C3×D4semidirect
260. #410AGL(1,𝔽7)semidirect
376. #117C2×AGL(1,𝔽7)semidirect
378. #99C2×AGL(1,𝔽7)semidirect
440. ΓL(1,𝔽8)#3025semidirect
457. C2×Q8C4⋊AGL(1,𝔽7)semidirect
466. C2×D4C4⋊AGL(1,𝔽7)semidirect
475. C22×C4C4⋊AGL(1,𝔽7)semidirect
556. C7C3×#3025semidirect

Maximal subgroups

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

subgroupindex
#130621542
#90519⋊C32
#90215⋊C32
ΓL(1,𝔽8)×#4102
#89778⋊C32
#89514⋊C32
#89513⋊C32
#117361353
C3×#30257