Finite Group Databasebeta

← #72247202

Subgroups — #72247202

Order 3024.

536 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3⋊(C3⋊AGL(1,𝔽7))C211yesmaximal, characteristic
2C2×ΓL(1,𝔽8)×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C32×ΓL(1,𝔽8)⋊C4C211yesmaximal, characteristic, complemented
4#11759168C311yesmaximal, characteristic, complemented
5#66575⋊C3—31nomaximal
6#66575⋊C3—31nomaximal
7#66575⋊C3—31nomaximal
8#66575⋊C3—31nomaximal
9C22×C32×ΓL(1,𝔽8)C2211yescharacteristic
10C2×C3⋊(C3⋊AGL(1,𝔽7))—21no—
11C2×C3⋊(C3⋊AGL(1,𝔽7))—21no—
12C2×C3⋊(C3⋊AGL(1,𝔽7))C412yescomplemented
13ΓL(1,𝔽8)×C3⋊Dic3—21no—
14C32×ΓL(1,𝔽8)⋊C4—21no—
15C22×C3⋊D21C2×C311yescharacteristic
16C22×C3⋊AGL(1,𝔽7)—31no—
17C22×C3⋊AGL(1,𝔽7)—31no—
18C22×C3⋊AGL(1,𝔽7)—31no—
19C22×C3⋊AGL(1,𝔽7)—31no—
20C2×C7×C3⋊Dic3C2×C311yescharacteristic, complemented
21C2×C32×Dic7C2×C311yescharacteristic, complemented
22C2×Dic3×ΓL(1,𝔽8)—31no—
23C2×Dic3×ΓL(1,𝔽8)—31no—
24C2×Dic3×ΓL(1,𝔽8)—31no—
25C2×Dic3×ΓL(1,𝔽8)—31no—
26C2×C3×ΓL(1,𝔽8)⋊C4—21no—
27C2×C3×ΓL(1,𝔽8)⋊C4—21no—
28C2×C3×ΓL(1,𝔽8)⋊C4—21no—
29C2×C3×ΓL(1,𝔽8)⋊C4—21no—
30C2×C3×ΓL(1,𝔽8)⋊C4D311yescharacteristic, complemented
31C2×C3×ΓL(1,𝔽8)⋊C4D311yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽8)⋊C4D311yescharacteristic, complemented
33C2×C3×ΓL(1,𝔽8)⋊C4D311yescharacteristic, complemented
34C3×#3752—71nomaximal, Hall
35C2×C32×ΓL(1,𝔽8)C2×C411yescharacteristic
36C2×C32×ΓL(1,𝔽8)D411yescharacteristic
37C2×C32×ΓL(1,𝔽8)D411yescharacteristic
38C3⋊(C3⋊AGL(1,𝔽7))—22no—
39#66575—31no—
40#66575—31no—
41#66575—31no—
42#66575—31no—
43(C2×AGL(1,𝔽7))⋊C4—91no—
44C22×C32×C7C22×C311yescharacteristic
45C2×C3⋊D21—21no—
46C2×C3⋊D21—21no—
47C2×C3⋊D21C3×C412yescomplemented
48C22×C3×ΓL(1,𝔽8)—21no—
49C22×C3×ΓL(1,𝔽8)—21no—
50C22×C3×ΓL(1,𝔽8)—21no—
51C22×C3×ΓL(1,𝔽8)—21no—
52C22×C3×ΓL(1,𝔽8)C2×D311yescharacteristic
53C22×C3×ΓL(1,𝔽8)C2×D311yescharacteristic
54C22×C3×ΓL(1,𝔽8)C2×D311yescharacteristic
55C22×C3×ΓL(1,𝔽8)C2×D311yescharacteristic
56C2×C3⋊AGL(1,𝔽7)—32no—
57C2×C3⋊AGL(1,𝔽7)—32no—
58C2×C3⋊AGL(1,𝔽7)—32no—
59C2×C3⋊AGL(1,𝔽7)—32no—
60C2×C3⋊AGL(1,𝔽7)—61no—
61C2×C3⋊AGL(1,𝔽7)—61no—
62C2×C3⋊AGL(1,𝔽7)—61no—
63C2×C3⋊AGL(1,𝔽7)—61no—
64C2×C3⋊AGL(1,𝔽7)—61no—
65C2×C3⋊AGL(1,𝔽7)—61no—
66C2×C3⋊AGL(1,𝔽7)—61no—
67C2×C3⋊AGL(1,𝔽7)—61no—
68C7×C3⋊Dic3—21no—
69C32×Dic7—21no—
70Dic3×ΓL(1,𝔽8)—61no—
71Dic3×ΓL(1,𝔽8)—61no—
72Dic3×ΓL(1,𝔽8)—61no—
73Dic3×ΓL(1,𝔽8)—61no—
74C3×ΓL(1,𝔽8)⋊C4—21no—
75C3×ΓL(1,𝔽8)⋊C4—21no—
76C3×ΓL(1,𝔽8)⋊C4—21no—
77C3×ΓL(1,𝔽8)⋊C4—21no—
78C3×ΓL(1,𝔽8)⋊C4—21no—
79C3×ΓL(1,𝔽8)⋊C4—21no—
80C3×ΓL(1,𝔽8)⋊C4—21no—
81C3×ΓL(1,𝔽8)⋊C4—21no—
82C3×ΓL(1,𝔽8)⋊C4—21no—
83C3×ΓL(1,𝔽8)⋊C4—21no—
84C3×ΓL(1,𝔽8)⋊C4—21no—
85C3×ΓL(1,𝔽8)⋊C4—21no—
86C22×C3×C3⋊D3—71no—
87C2×C33×C4—71no—
88C2×C3×C3⋊Dic3—141no—
89C32×ΓL(1,𝔽8)C22⋊C411yescharacteristic, complemented, Hall
90C22×D21—31no—
91C22×D21—31no—
92C22×D21—31no—
93C22×D21—31no—
94C22×AGL(1,𝔽7)—91no—
95C2×C7×Dic3—31no—
96C2×C7×Dic3—31no—
97C2×C7×Dic3—31no—
98C2×C7×Dic3—31no—
99C2×C3×Dic7C3×D311yescharacteristic, complemented
100C2×C3×Dic7C3×D311yescharacteristic, complemented
101C2×C3×Dic7C3×D311yescharacteristic, complemented
102C2×C3×Dic7C3×D311yescharacteristic, complemented
103C2×C4×ΓL(1,𝔽8)—91no—
104C2×ΓL(1,𝔽8)⋊C4—21no—
105C2×ΓL(1,𝔽8)⋊C4—21no—
106C2×ΓL(1,𝔽8)⋊C4—21no—
107C2×ΓL(1,𝔽8)⋊C4—21no—
108C2×ΓL(1,𝔽8)⋊C4C3⋊D311yescharacteristic, complemented
109#3752—71no—
110C3×(C2×D3)⋊C4—211no—
111C3×(C2×D3)⋊C4—211no—
112C3×(C2×D3)⋊C4—211no—
113C3×(C2×D3)⋊C4—211no—
114C2×C32×C7C2×C3×C411yescharacteristic
115C2×C32×C7C3×D411yescharacteristic
116C2×C32×C7C3×D411yescharacteristic
117C3⋊D21—22no—
118C2×C3×ΓL(1,𝔽8)—21no—
119C2×C3×ΓL(1,𝔽8)—21no—
120C2×C3×ΓL(1,𝔽8)—21no—
121C2×C3×ΓL(1,𝔽8)—21no—
122C2×C3×ΓL(1,𝔽8)—21no—
123C2×C3×ΓL(1,𝔽8)—21no—
124C2×C3×ΓL(1,𝔽8)—21no—
125C2×C3×ΓL(1,𝔽8)—21no—
126C2×C3×ΓL(1,𝔽8)—21no—
127C2×C3×ΓL(1,𝔽8)—21no—
128C2×C3×ΓL(1,𝔽8)—21no—
129C2×C3×ΓL(1,𝔽8)—21no—
130C2×C3×ΓL(1,𝔽8)C4×D311yescharacteristic
131C2×C3×ΓL(1,𝔽8)C4×D311yescharacteristic
132C2×C3×ΓL(1,𝔽8)C4×D311yescharacteristic
133C2×C3×ΓL(1,𝔽8)C4×D311yescharacteristic
134C2×C3×ΓL(1,𝔽8)D1211yescharacteristic
135C2×C3×ΓL(1,𝔽8)D1211yescharacteristic
136C2×C3×ΓL(1,𝔽8)D1211yescharacteristic
137C2×C3×ΓL(1,𝔽8)D1211yescharacteristic
138C2×C3×ΓL(1,𝔽8)#6711yescharacteristic
139C2×C3×ΓL(1,𝔽8)#6711yescharacteristic
140C2×C3×ΓL(1,𝔽8)#6711yescharacteristic
141C2×C3×ΓL(1,𝔽8)#6711yescharacteristic
142C3⋊AGL(1,𝔽7)—62no—
143C3⋊AGL(1,𝔽7)—62no—
144C3⋊AGL(1,𝔽7)—62no—
145C3⋊AGL(1,𝔽7)—62no—
146(C2×D7)⋊C4—91noHall
147C22×C33—141no—
148C2×C3×C3⋊D3—72no—
149C2×C3×C3⋊D3—141no—
150C2×C3×C3⋊D3—141no—
151C33×C4—141no—
152C3×C3⋊Dic3—141no—
153C22×C3×C7C2×C3×D311yescharacteristic
154C22×C3×C7C2×C3×D311yescharacteristic
155C22×C3×C7C2×C3×D311yescharacteristic
156C22×C3×C7C2×C3×D311yescharacteristic
157C2×D21—32no—
158C2×D21—32no—
159C2×D21—32no—
160C2×D21—32no—
161C2×D21—61no—
162C2×D21—61no—
163C2×D21—61no—
164C2×D21—61no—
165C2×D21—61no—
166C2×D21—61no—
167C2×D21—61no—
168C2×D21—61no—
169C22×ΓL(1,𝔽8)—21no—
170C22×ΓL(1,𝔽8)—21no—
171C22×ΓL(1,𝔽8)—21no—
172C22×ΓL(1,𝔽8)—21no—
173C22×ΓL(1,𝔽8)C2×C3⋊D311yescharacteristic
174C2×AGL(1,𝔽7)—92no—
175C2×AGL(1,𝔽7)—181no—
176C2×AGL(1,𝔽7)—181no—
177C3×Dic7—21no—
178C3×Dic7—21no—
179C3×Dic7—21no—
180C3×Dic7—21no—
181C7×Dic3—61no—
182C7×Dic3—61no—
183C7×Dic3—61no—
184C7×Dic3—61no—
185C4×ΓL(1,𝔽8)—181no—
186ΓL(1,𝔽8)⋊C4—21no—
187ΓL(1,𝔽8)⋊C4—21no—
188ΓL(1,𝔽8)⋊C4—21no—
189ΓL(1,𝔽8)⋊C4—21no—
190ΓL(1,𝔽8)⋊C4—21no—
191ΓL(1,𝔽8)⋊C4—21no—
192ΓL(1,𝔽8)⋊C4—21no—
193ΓL(1,𝔽8)⋊C4—21no—
194ΓL(1,𝔽8)⋊C4—21no—
195C22×C3⋊D3—71no—
196C22×C3×D3—211no—
197C22×C3×D3—211no—
198C22×C3×D3—211no—
199C22×C3×D3—211no—
200C2×C32×C4—71no—
201C2×C32×C4—71no—
202C2×C32×C4—71no—
203C2×C32×C4—71no—
204C2×C32×C4—71no—
205C2×C32×C4—141no—
206C2×C32×C4—141no—
207C2×C32×C4—141no—
208C2×C32×C4—141no—
209C2×C3⋊Dic3AGL(1,𝔽7)11yescharacteristic, complemented
210C2×C3×Dic3—421no—
211C2×C3×Dic3—421no—
212C2×C3×Dic3—421no—
213C2×C3×Dic3—421no—
214C32×C7C3×C22⋊C411yescharacteristic, complemented
215C3×ΓL(1,𝔽8)—21no—
216C3×ΓL(1,𝔽8)—21no—
217C3×ΓL(1,𝔽8)—21no—
218C3×ΓL(1,𝔽8)—21no—
219C3×ΓL(1,𝔽8)(C2×D3)⋊C411yescharacteristic, complemented
220C3×ΓL(1,𝔽8)(C2×D3)⋊C411yescharacteristic, complemented
221C3×ΓL(1,𝔽8)(C2×D3)⋊C411yescharacteristic, complemented
222C3×ΓL(1,𝔽8)(C2×D3)⋊C411yescharacteristic, complemented
223C22×D7—91no—
224C2×C4×C7—91no—
225C2×Dic7C3×C3⋊D311yescharacteristic, complemented
226C2×C33—141no—
227C2×C33—141no—
228C2×C33—141no—
229C3×C3⋊D3—142no—
230C3×C22⋊C4—631no—
231(C2×D3)⋊C4—211no—
232(C2×D3)⋊C4—211no—
233(C2×D3)⋊C4—211no—
234(C2×D3)⋊C4—211no—
235C2×C3×C7C3×C4×D311yescharacteristic
236C2×C3×C7C3×C4×D311yescharacteristic
237C2×C3×C7C3×C4×D311yescharacteristic
238C2×C3×C7C3×C4×D311yescharacteristic
239C2×C3×C7C3×D1211yescharacteristic
240C2×C3×C7C3×D1211yescharacteristic
241C2×C3×C7C3×D1211yescharacteristic
242C2×C3×C7C3×D1211yescharacteristic
243C2×C3×C7C3×#6711yescharacteristic
244C2×C3×C7C3×#6711yescharacteristic
245C2×C3×C7C3×#6711yescharacteristic
246C2×C3×C7C3×#6711yescharacteristic
247D21—62no—
248D21—62no—
249D21—62no—
250D21—62no—
251C2×ΓL(1,𝔽8)—21no—
252C2×ΓL(1,𝔽8)—21no—
253C2×ΓL(1,𝔽8)—21no—
254C2×ΓL(1,𝔽8)—21no—
255C2×ΓL(1,𝔽8)—21no—
256C2×ΓL(1,𝔽8)—21no—
257C2×ΓL(1,𝔽8)—21no—
258C2×ΓL(1,𝔽8)—21no—
259C2×ΓL(1,𝔽8)—21no—
260C2×ΓL(1,𝔽8)—21no—
261C2×ΓL(1,𝔽8)—21no—
262C2×ΓL(1,𝔽8)—21no—
263C2×ΓL(1,𝔽8)C4×C3⋊D311yescharacteristic
264C2×ΓL(1,𝔽8)C4⋊(C3⋊D3)11yescharacteristic
265C2×ΓL(1,𝔽8)#63811yescharacteristic
266AGL(1,𝔽7)—182no—
267C22×C32—141no—
268C22×C32—141no—
269C22×C32—141no—
270C22×C32—141no—
271C22×C32—281no—
272C22×C32—281no—
273C22×C32—281no—
274C22×C32—281no—
275C22×C32C2×AGL(1,𝔽7)11yescharacteristic
276C2×C3⋊D3—72no—
277C2×C3⋊D3—141no—
278C2×C3⋊D3—141no—
279C2×C3×D3—212no—
280C2×C3×D3—212no—
281C2×C3×D3—212no—
282C2×C3×D3—212no—
283C2×C3×D3—421no—
284C2×C3×D3—421no—
285C2×C3×D3—421no—
286C2×C3×D3—421no—
287C2×C3×D3—421no—
288C2×C3×D3—421no—
289C2×C3×D3—421no—
290C2×C3×D3—421no—
291C32×C4—141no—
292C32×C4—141no—
293C32×C4—141no—
294C32×C4—141no—
295C32×C4—141no—
296C32×C4—141no—
297C32×C4—141no—
298C32×C4—141no—
299C32×C4—141no—
300C32×C4—141no—
301C32×C4—141no—
302C32×C4—141no—
303C32×C4—141no—
304C3⋊Dic3—21no—
305C3×Dic3—421no—
306C3×Dic3—421no—
307C3×Dic3—421no—
308C3×Dic3—421no—
309C22×C7C2×C3×C3⋊D311yescharacteristic
310C2×D7—92no—
311C2×D7—181no—
312C2×D7—181no—
313C4×C7—181no—
314Dic7—21no—
315C33—141noSylow
316C23×C3—631no—
317C22×D3—211no—
318C22×D3—211no—
319C22×D3—211no—
320C22×D3—211no—
321C2×C3×C4—71no—
322C2×C3×C4—71no—
323C2×C3×C4—71no—
324C2×C3×C4—71no—
325C2×C3×C4—71no—
326C2×C3×C4—141no—
327C2×C3×C4—141no—
328C2×C3×C4—141no—
329C2×C3×C4—141no—
330C2×C3×C4—1261no—
331C2×Dic3—31no—
332C2×Dic3—31no—
333C2×Dic3—31no—
334C2×Dic3—31no—
335C3×C7C3×(C2×D3)⋊C411yescharacteristic, complemented
336C3×C7C3×(C2×D3)⋊C411yescharacteristic, complemented
337C3×C7C3×(C2×D3)⋊C411yescharacteristic, complemented
338C3×C7C3×(C2×D3)⋊C411yescharacteristic, complemented
339ΓL(1,𝔽8)—21no—
340ΓL(1,𝔽8)—21no—
341ΓL(1,𝔽8)—21no—
342ΓL(1,𝔽8)—21no—
343ΓL(1,𝔽8)#375211yescharacteristic, complemented
344C2×C32—141no—
345C2×C32—141no—
346C2×C32—141no—
347C2×C32—141no—
348C2×C32—141no—
349C2×C32—141no—
350C2×C32—141no—
351C2×C32—141no—
352C2×C32—141no—
353C2×C32—141no—
354C2×C32—141no—
355C2×C32—141no—
356C2×C32—281no—
357C2×C32—281no—
358C2×C32—281no—
359C2×C32—281no—
360C2×C32—281no—
361C2×C32—281no—
362C2×C32—281no—
363C2×C32—281no—
364C2×C32—281no—
365C2×C32—281no—
366C2×C32—281no—
367C2×C32—281no—
368C2×C32C4×AGL(1,𝔽7)11yescharacteristic
369C2×C32C4⋊AGL(1,𝔽7)11yescharacteristic
370C2×C32(C22⋊D7)⋊C311yescharacteristic
371C3⋊D3—142no—
372C3×D3—422no—
373C3×D3—422no—
374C3×D3—422no—
375C3×D3—422no—
376C22⋊C4—631noSylow
377C2×C7C3×C4×C3⋊D311yescharacteristic
378C2×C7C3×C4⋊(C3⋊D3)11yescharacteristic
379C2×C7C3×#63811yescharacteristic
380D7—182no—
381C22×C3—141no—
382C22×C3—141no—
383C22×C3—141no—
384C22×C3—281no—
385C22×C3—281no—
386C22×C3—632no—
387C22×C3—1261no—
388C22×C3—1261no—
389C22×C3D3×AGL(1,𝔽7)11yescharacteristic
390C22×C3D3×AGL(1,𝔽7)11yescharacteristic
391C22×C3D3×AGL(1,𝔽7)11yescharacteristic
392C22×C3D3×AGL(1,𝔽7)11yescharacteristic
393C2×D3—212no—
394C2×D3—212no—
395C2×D3—212no—
396C2×D3—212no—
397C2×D3—421no—
398C2×D3—421no—
399C2×D3—421no—
400C2×D3—421no—
401C2×D3—421no—
402C2×D3—421no—
403C2×D3—421no—
404C2×D3—421no—
405C3×C4—141no—
406C3×C4—141no—
407C3×C4—141no—
408C3×C4—141no—
409C3×C4—141no—
410C3×C4—141no—
411C3×C4—141no—
412C3×C4—141no—
413C3×C4—141no—
414C3×C4—141no—
415C3×C4—141no—
416C3×C4—141no—
417C3×C4—141no—
418C3×C4—1261no—
419Dic3—61no—
420Dic3—61no—
421Dic3—61no—
422Dic3—61no—
423C32—141no—
424C32—141no—
425C32—141no—
426C32—141no—
427C32—281no—
428C32—281no—
429C32—281no—
430C32—281no—
431C32(C2×AGL(1,𝔽7))⋊C411yescharacteristic, complemented
432C23—631no—
433C2×C4—71no—
434C2×C4—91no—
435C7C3×#375211yescharacteristic, complemented, Sylow
436C2×C3—141no—
437C2×C3—141no—
438C2×C3—141no—
439C2×C3—141no—
440C2×C3—141no—
441C2×C3—141no—
442C2×C3—141no—
443C2×C3—141no—
444C2×C3—141no—
445C2×C3—281no—
446C2×C3—281no—
447C2×C3—281no—
448C2×C3—281no—
449C2×C3—281no—
450C2×C3—281no—
451C2×C3—1262no—
452C2×C3(C3⋊AGL(1,𝔽7))⋊C411yescharacteristic
453C2×C3(C3⋊AGL(1,𝔽7))⋊C411yescharacteristic
454C2×C3(C3⋊AGL(1,𝔽7))⋊C411yescharacteristic
455C2×C3(C3⋊AGL(1,𝔽7))⋊C411yescharacteristic
456C2×C3#4246⋊C311yescharacteristic
457C2×C3#4246⋊C311yescharacteristic
458C2×C3#4246⋊C311yescharacteristic
459C2×C3#4246⋊C311yescharacteristic
460C2×C3#4247⋊C311yescharacteristic
461C2×C3#4247⋊C311yescharacteristic
462C2×C3#4247⋊C311yescharacteristic
463C2×C3#4247⋊C311yescharacteristic
464D3—422no—
465D3—422no—
466D3—422no—
467D3—422no—
468C22—632no—
469C22—1261no—
470C22—1261no—
471C22C3⋊D3×AGL(1,𝔽7)11yescharacteristic
472C4—141no—
473C4—181no—
474C3—141no—
475C3—141no—
476C3—141no—
477C3—281no—
478C3—281no—
479C3#66575⋊C311yescharacteristic, complemented
480C3#66575⋊C311yescharacteristic, complemented
481C3#66575⋊C311yescharacteristic, complemented
482C3#66575⋊C311yescharacteristic, complemented
483C2—1262no—
484C2#1309471311yescharacteristic
485C2#1309471511yescharacteristic
486C2#1309471611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22C3⋊D3×AGL(1,𝔽7)
commutatorC2×C32×C7C2×C3×C4
Fitting, socle, cosocleC22×C32×C7C22×C3
prime radicalC22×C3⋊(C3⋊AGL(1,𝔽7))C2
hypocenterC32×C7C3×C22⋊C4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×ΓL(1,𝔽8)×C3⋊Dic3C2semidirect
3. C2×C32×ΓL(1,𝔽8)⋊C4C2semidirect
4. #11759168C3semidirect
12. C2×C3⋊(C3⋊AGL(1,𝔽7))C4semidirect
20. C2×C7×C3⋊Dic3C2×C3semidirect
21. C2×C32×Dic7C2×C3semidirect
30. C2×C3×ΓL(1,𝔽8)⋊C4D3semidirect
31. C2×C3×ΓL(1,𝔽8)⋊C4D3semidirect
32. C2×C3×ΓL(1,𝔽8)⋊C4D3semidirect
33. C2×C3×ΓL(1,𝔽8)⋊C4D3semidirect
47. C2×C3⋊D21C3×C4semidirect
89. C32×ΓL(1,𝔽8)C22⋊C4semidirect
99. C2×C3×Dic7C3×D3semidirect
100. C2×C3×Dic7C3×D3semidirect
101. C2×C3×Dic7C3×D3semidirect
102. C2×C3×Dic7C3×D3semidirect
108. C2×ΓL(1,𝔽8)⋊C4C3⋊D3semidirect
209. C2×C3⋊Dic3AGL(1,𝔽7)semidirect
214. C32×C7C3×C22⋊C4semidirect
219. C3×ΓL(1,𝔽8)(C2×D3)⋊C4semidirect
220. C3×ΓL(1,𝔽8)(C2×D3)⋊C4semidirect
221. C3×ΓL(1,𝔽8)(C2×D3)⋊C4semidirect
222. C3×ΓL(1,𝔽8)(C2×D3)⋊C4semidirect
225. C2×Dic7C3×C3⋊D3semidirect
335. C3×C7C3×(C2×D3)⋊C4semidirect
336. C3×C7C3×(C2×D3)⋊C4semidirect
337. C3×C7C3×(C2×D3)⋊C4semidirect
338. C3×C7C3×(C2×D3)⋊C4semidirect
343. ΓL(1,𝔽8)#3752semidirect
431. C32(C2×AGL(1,𝔽7))⋊C4semidirect
435. C7C3×#3752semidirect
479. C3#66575⋊C3semidirect
480. C3#66575⋊C3semidirect
481. C3#66575⋊C3semidirect
482. C3#66575⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C3⋊(C3⋊AGL(1,𝔽7))2
C2×ΓL(1,𝔽8)×C3⋊Dic32
C2×C32×ΓL(1,𝔽8)⋊C42
#117591683
#66575⋊C33
C3×#37527