Finite Group Databasebeta

← C2×C3×#4246⋊C3 #72246521

Subgroups — C2×C3×#4246⋊C3 #72246521

Order 3024.

904 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C3⋊AGL(1,𝔽7)C211yesmaximal, characteristic, complemented
2C22×C32×AGL(1,𝔽7)C211yesmaximal, characteristic, complemented
3C2×C3×Dic3×ΓL(1,𝔽8)C211yesmaximal, characteristic, complemented
4C3×#4246⋊C3C214yesmaximal, direct product factor
5C2×C3×#4246C311yesmaximal, characteristic, complemented
6C2×C3×C4⋊AGL(1,𝔽7)—31nomaximal
7C2×#4246⋊C3C311yesmaximal, characteristic, direct product factor
8C2×#4246⋊C3C311yesmaximal, characteristic, direct product factor
9C2×#4246⋊C3C311yesmaximal, characteristic, direct product factor
10C22×C32×ΓL(1,𝔽8)C2211yescharacteristic
11C2×C3×C3⋊AGL(1,𝔽7)—22no—
12C2×C3×C3⋊AGL(1,𝔽7)C2212yescomplemented
13C2×C32×AGL(1,𝔽7)—22no—
14C2×C32×AGL(1,𝔽7)C2212yescomplemented
15C3×Dic3×ΓL(1,𝔽8)C2212yescomplemented
16C22×C3×D21C2×C311yescharacteristic, complemented
17C22×C32×D7C2×C311yescharacteristic, complemented
18C22×C3⋊AGL(1,𝔽7)C2×C311yescharacteristic, complemented
19C22×C3⋊AGL(1,𝔽7)C2×C311yescharacteristic, complemented
20C22×C3⋊AGL(1,𝔽7)C2×C311yescharacteristic, complemented
21C22×C3×AGL(1,𝔽7)—21no—
22C22×C3×AGL(1,𝔽7)—21no—
23C22×C3×AGL(1,𝔽7)—21no—
24C22×C3×AGL(1,𝔽7)—21no—
25C22×C3×AGL(1,𝔽7)—31no—
26C22×C3×AGL(1,𝔽7)D311yescharacteristic, complemented
27C22×C3×AGL(1,𝔽7)C2×C311yescharacteristic, complemented
28C22×C3×AGL(1,𝔽7)C2×C311yescharacteristic, complemented
29C22×C3×AGL(1,𝔽7)C2×C311yescharacteristic, complemented
30C2×C3×C7×Dic3C2×C311yescharacteristic, complemented
31C2×C3×C4×ΓL(1,𝔽8)—31no—
32C3×#4246C2×C314yescomplemented
33C2×Dic3×ΓL(1,𝔽8)C2×C311yescharacteristic, complemented
34C2×Dic3×ΓL(1,𝔽8)C2×C311yescharacteristic, complemented
35C2×Dic3×ΓL(1,𝔽8)C2×C311yescharacteristic, complemented
36C3×C4⋊AGL(1,𝔽7)—34no—
37#4246⋊C3C2×C314yesdirect product factor
38#4246⋊C3C2×C314yesdirect product factor
39#4246⋊C3C2×C314yesdirect product factor
40C2×C32×#67—71nomaximal, Hall
41C2×C32×ΓL(1,𝔽8)D412yescomplemented
42C2×C32×ΓL(1,𝔽8)C2311yescharacteristic
43C3×C3⋊AGL(1,𝔽7)—22no—
44C32×AGL(1,𝔽7)—22no—
45C2×C3×D28—31no—
46C2×#4246C3211yescharacteristic, complemented
47C2×C4⋊AGL(1,𝔽7)—31no—
48C2×C4⋊AGL(1,𝔽7)—31no—
49C2×C4⋊AGL(1,𝔽7)—31no—
50C22×C32×C7C22×C311yescharacteristic
51C2×C3×D21—22no—
52C2×C3×D21C22×C312yescomplemented
53C2×C32×D7—22no—
54C2×C32×D7C22×C312yescomplemented
55C22×C3×ΓL(1,𝔽8)—21no—
56C22×C3×ΓL(1,𝔽8)—21no—
57C22×C3×ΓL(1,𝔽8)—21no—
58C22×C3×ΓL(1,𝔽8)—21no—
59C22×C3×ΓL(1,𝔽8)C2×D311yescharacteristic
60C22×C3×ΓL(1,𝔽8)C22×C311yescharacteristic
61C22×C3×ΓL(1,𝔽8)C22×C311yescharacteristic
62C22×C3×ΓL(1,𝔽8)C22×C311yescharacteristic
63C2×C3⋊AGL(1,𝔽7)—22no—
64C2×C3⋊AGL(1,𝔽7)—22no—
65C2×C3⋊AGL(1,𝔽7)—22no—
66C2×C3⋊AGL(1,𝔽7)C22×C312yescomplemented
67C2×C3⋊AGL(1,𝔽7)C22×C312yescomplemented
68C2×C3⋊AGL(1,𝔽7)C22×C312yescomplemented
69C2×C3×AGL(1,𝔽7)—22no—
70C2×C3×AGL(1,𝔽7)—22no—
71C2×C3×AGL(1,𝔽7)—22no—
72C2×C3×AGL(1,𝔽7)—22no—
73C2×C3×AGL(1,𝔽7)—22no—
74C2×C3×AGL(1,𝔽7)—22no—
75C2×C3×AGL(1,𝔽7)—22no—
76C2×C3×AGL(1,𝔽7)—22no—
77C2×C3×AGL(1,𝔽7)—22no—
78C2×C3×AGL(1,𝔽7)—22no—
79C2×C3×AGL(1,𝔽7)—22no—
80C2×C3×AGL(1,𝔽7)—22no—
81C2×C3×AGL(1,𝔽7)—22no—
82C2×C3×AGL(1,𝔽7)—22no—
83C2×C3×AGL(1,𝔽7)—22no—
84C2×C3×AGL(1,𝔽7)—22no—
85C2×C3×AGL(1,𝔽7)—32no—
86C2×C3×AGL(1,𝔽7)—62no—
87C2×C3×AGL(1,𝔽7)C2×D312yescomplemented
88C2×C3×AGL(1,𝔽7)C22×C312yescomplemented
89C2×C3×AGL(1,𝔽7)C22×C312yescomplemented
90C2×C3×AGL(1,𝔽7)C22×C312yescomplemented
91C3×C7×Dic3C22×C312yescomplemented
92C3×C4×ΓL(1,𝔽8)—32no—
93Dic3×ΓL(1,𝔽8)C22×C312yescomplemented
94Dic3×ΓL(1,𝔽8)C22×C312yescomplemented
95Dic3×ΓL(1,𝔽8)C22×C312yescomplemented
96C23×C33—71no—
97C22×C32×D3—71no—
98C32×#67—74no—
99C2×C32×Dic3—141no—
100C32×ΓL(1,𝔽8)C2×D411yescharacteristic, complemented, Hall
101C22×D21C2×C3211yescharacteristic, complemented
102C22×C3×D7—21no—
103C22×C3×D7—31no—
104C22×C3×D7C3×D311yescharacteristic, complemented
105C22×C3×D7C2×C3211yescharacteristic, complemented
106C22×AGL(1,𝔽7)—21no—
107C22×AGL(1,𝔽7)—21no—
108C22×AGL(1,𝔽7)—21no—
109C22×AGL(1,𝔽7)—31no—
110C22×AGL(1,𝔽7)—31no—
111C22×AGL(1,𝔽7)—31no—
112C22×AGL(1,𝔽7)C3×D311yescharacteristic, complemented
113C22×AGL(1,𝔽7)C3×D311yescharacteristic, complemented
114C22×AGL(1,𝔽7)C3×D311yescharacteristic, complemented
115C2×C3×C4×C7—31no—
116C2×C7×Dic3C2×C3211yescharacteristic, complemented
117C3×D28—34no—
118C2×C4×ΓL(1,𝔽8)—31no—
119C2×C4×ΓL(1,𝔽8)—31no—
120C2×C4×ΓL(1,𝔽8)—31no—
121#4246C2×C3214yescomplemented
122C4⋊AGL(1,𝔽7)—34no—
123C4⋊AGL(1,𝔽7)—34no—
124C4⋊AGL(1,𝔽7)—34no—
125C2×C32×D4—211no—
126C2×C3×#67—71no—
127C2×C3×#67—71no—
128C2×C3×#67—71no—
129C2×C3×#67—71no—
130C2×C32×C7C3×D412yescomplemented
131C2×C32×C7C23×C311yescharacteristic
132C3×D21—22no—
133C32×D7—22no—
134C2×C3×ΓL(1,𝔽8)—22no—
135C2×C3×ΓL(1,𝔽8)—22no—
136C2×C3×ΓL(1,𝔽8)—21no—
137C2×C3×ΓL(1,𝔽8)—21no—
138C2×C3×ΓL(1,𝔽8)—22no—
139C2×C3×ΓL(1,𝔽8)—21no—
140C2×C3×ΓL(1,𝔽8)—22no—
141C2×C3×ΓL(1,𝔽8)—21no—
142C2×C3×ΓL(1,𝔽8)#6712yescomplemented
143C2×C3×ΓL(1,𝔽8)C3×D412yescomplemented
144C2×C3×ΓL(1,𝔽8)C3×D412yescomplemented
145C2×C3×ΓL(1,𝔽8)C3×D412yescomplemented
146C2×C3×ΓL(1,𝔽8)C22×D311yescharacteristic
147C2×C3×ΓL(1,𝔽8)C23×C311yescharacteristic
148C2×C3×ΓL(1,𝔽8)C23×C311yescharacteristic
149C2×C3×ΓL(1,𝔽8)C23×C311yescharacteristic
150C3⋊AGL(1,𝔽7)—22no—
151C3⋊AGL(1,𝔽7)—22no—
152C3⋊AGL(1,𝔽7)—22no—
153C3×AGL(1,𝔽7)—22no—
154C3×AGL(1,𝔽7)—22no—
155C3×AGL(1,𝔽7)—22no—
156C3×AGL(1,𝔽7)—22no—
157C3×AGL(1,𝔽7)—22no—
158C3×AGL(1,𝔽7)—22no—
159C3×AGL(1,𝔽7)—22no—
160C3×AGL(1,𝔽7)—22no—
161C3×AGL(1,𝔽7)—22no—
162C3×AGL(1,𝔽7)—22no—
163C3×AGL(1,𝔽7)—22no—
164C3×AGL(1,𝔽7)—22no—
165C3×AGL(1,𝔽7)—62no—
166C2×D28—31noHall
167C22×C33—72no—
168C22×C33—142no—
169C22×C33—141no—
170C2×C32×D3—72no—
171C2×C32×D3—142no—
172C32×Dic3—142no—
173C22×C3×C7—21no—
174C22×C3×C7C2×C3×D311yescharacteristic
175C22×C3×C7C22×C3211yescharacteristic
176C2×D21—22no—
177C2×D21C22×C3212yescomplemented
178C2×C3×D7—22no—
179C2×C3×D7—22no—
180C2×C3×D7—22no—
181C2×C3×D7—22no—
182C2×C3×D7—22no—
183C2×C3×D7—32no—
184C2×C3×D7—62no—
185C2×C3×D7C2×C3×D312yescomplemented
186C2×C3×D7C22×C3212yescomplemented
187C22×ΓL(1,𝔽8)—21no—
188C22×ΓL(1,𝔽8)—21no—
189C22×ΓL(1,𝔽8)—21no—
190C22×ΓL(1,𝔽8)C2×C3×D311yescharacteristic
191C22×ΓL(1,𝔽8)C2×C3×D311yescharacteristic
192C22×ΓL(1,𝔽8)C2×C3×D311yescharacteristic
193C2×AGL(1,𝔽7)—22no—
194C2×AGL(1,𝔽7)—22no—
195C2×AGL(1,𝔽7)—22no—
196C2×AGL(1,𝔽7)—22no—
197C2×AGL(1,𝔽7)—22no—
198C2×AGL(1,𝔽7)—22no—
199C2×AGL(1,𝔽7)—22no—
200C2×AGL(1,𝔽7)—22no—
201C2×AGL(1,𝔽7)—22no—
202C2×AGL(1,𝔽7)—22no—
203C2×AGL(1,𝔽7)—22no—
204C2×AGL(1,𝔽7)—22no—
205C2×AGL(1,𝔽7)—32no—
206C2×AGL(1,𝔽7)—32no—
207C2×AGL(1,𝔽7)—32no—
208C2×AGL(1,𝔽7)—62no—
209C2×AGL(1,𝔽7)—62no—
210C2×AGL(1,𝔽7)—62no—
211C2×AGL(1,𝔽7)C2×C3×D312yescomplemented
212C2×AGL(1,𝔽7)C2×C3×D312yescomplemented
213C2×AGL(1,𝔽7)C2×C3×D312yescomplemented
214C3×C4×C7—32no—
215C7×Dic3C22×C3212yescomplemented
216C4×ΓL(1,𝔽8)—32no—
217C4×ΓL(1,𝔽8)—32no—
218C4×ΓL(1,𝔽8)—32no—
219C23×C32—71no—
220C23×C32—71no—
221C23×C32—71no—
222C23×C32—71no—
223C23×C32—71no—
224C23×C32—141no—
225C23×C32—141no—
226C23×C32—141no—
227C23×C32—141no—
228C23×C32—211no—
229C22×C3×D3—71no—
230C22×C3×D3—71no—
231C22×C3×D3—71no—
232C22×C3×D3—71no—
233C32×D4—214no—
234C2×C32×C4—421no—
235C3×#67—74no—
236C3×#67—74no—
237C3×#67—74no—
238C3×#67—74no—
239C2×C3×Dic3—141no—
240C2×C3×Dic3—141no—
241C2×C3×Dic3—141no—
242C2×C3×Dic3AGL(1,𝔽7)11yescharacteristic, complemented
243C32×C7C2×C3×D411yescharacteristic, complemented
244C3×ΓL(1,𝔽8)—21no—
245C3×ΓL(1,𝔽8)—21no—
246C3×ΓL(1,𝔽8)—21no—
247C3×ΓL(1,𝔽8)—21no—
248C3×ΓL(1,𝔽8)C2×#6711yescharacteristic, complemented
249C3×ΓL(1,𝔽8)C2×C3×D411yescharacteristic, complemented
250C3×ΓL(1,𝔽8)C2×C3×D411yescharacteristic, complemented
251C3×ΓL(1,𝔽8)C2×C3×D411yescharacteristic, complemented
252C22×D7—31no—
253C22×D7C32×D311yescharacteristic, complemented
254C2×C4×C7—31no—
255D28—34no—
256C2×C33—142no—
257C2×C33—142no—
258C2×C33—141no—
259C32×D3—142no—
260C2×C3×D4—211no—
261C2×C3×D4—211no—
262C2×C3×D4—211no—
263C2×C3×D4—211no—
264C2×#67—71no—
265C2×C3×C7—22no—
266C2×C3×C7—21no—
267C2×C3×C7C3×#6712yescomplemented
268C2×C3×C7C32×D412yescomplemented
269C2×C3×C7C22×C3×D311yescharacteristic
270C2×C3×C7C23×C3211yescharacteristic
271D21—22no—
272C3×D7—22no—
273C3×D7—22no—
274C3×D7—22no—
275C3×D7—22no—
276C3×D7—62no—
277C2×ΓL(1,𝔽8)—22no—
278C2×ΓL(1,𝔽8)—21no—
279C2×ΓL(1,𝔽8)—22no—
280C2×ΓL(1,𝔽8)—22no—
281C2×ΓL(1,𝔽8)—21no—
282C2×ΓL(1,𝔽8)—21no—
283C2×ΓL(1,𝔽8)C3×#6712yescomplemented
284C2×ΓL(1,𝔽8)C3×#6712yescomplemented
285C2×ΓL(1,𝔽8)C3×#6712yescomplemented
286C2×ΓL(1,𝔽8)C22×C3×D311yescharacteristic
287C2×ΓL(1,𝔽8)C22×C3×D311yescharacteristic
288C2×ΓL(1,𝔽8)C22×C3×D311yescharacteristic
289AGL(1,𝔽7)—22no—
290AGL(1,𝔽7)—22no—
291AGL(1,𝔽7)—22no—
292AGL(1,𝔽7)—22no—
293AGL(1,𝔽7)—22no—
294AGL(1,𝔽7)—22no—
295AGL(1,𝔽7)—22no—
296AGL(1,𝔽7)—22no—
297AGL(1,𝔽7)—22no—
298AGL(1,𝔽7)—62no—
299AGL(1,𝔽7)—62no—
300AGL(1,𝔽7)—62no—
301C22×C32—72no—
302C22×C32—72no—
303C22×C32—72no—
304C22×C32—72no—
305C22×C32—72no—
306C22×C32—141no—
307C22×C32—141no—
308C22×C32—142no—
309C22×C32—142no—
310C22×C32—142no—
311C22×C32—142no—
312C22×C32—142no—
313C22×C32—142no—
314C22×C32—142no—
315C22×C32—142no—
316C22×C32—142no—
317C22×C32—142no—
318C22×C32—142no—
319C22×C32—142no—
320C22×C32—142no—
321C22×C32—142no—
322C22×C32—142no—
323C22×C32—142no—
324C22×C32—142no—
325C22×C32—141no—
326C22×C32—141no—
327C22×C32—141no—
328C22×C32—141no—
329C22×C32—212no—
330C22×C32—281no—
331C22×C32—281no—
332C22×C32—422no—
333C22×C32C2×AGL(1,𝔽7)11yescharacteristic
334C2×C3×D3—72no—
335C2×C3×D3—72no—
336C2×C3×D3—72no—
337C2×C3×D3—72no—
338C2×C3×D3—142no—
339C2×C3×D3—142no—
340C2×C3×D3—142no—
341C2×C3×D3—142no—
342C32×C4—422no—
343C3×Dic3—142no—
344C3×Dic3—142no—
345C3×Dic3—142no—
346C3×Dic3C2×AGL(1,𝔽7)12yescomplemented
347C22×C7C2×C32×D311yescharacteristic
348C2×D7—22no—
349C2×D7—32no—
350C2×D7—62no—
351C2×D7C2×C32×D312yescomplemented
352C4×C7—32no—
353C33—141noSylow
354C23×C3—71no—
355C23×C3—71no—
356C23×C3—71no—
357C23×C3—71no—
358C23×C3—71no—
359C23×C3—141no—
360C23×C3—141no—
361C23×C3—141no—
362C23×C3—141no—
363C23×C3—211no—
364C23×C3—211no—
365C23×C3—211no—
366C23×C3—211no—
367C22×D3—71no—
368C3×D4—214no—
369C3×D4—214no—
370C3×D4—214no—
371C3×D4—214no—
372C2×C3×C4—31no—
373C2×C3×C4—421no—
374C2×C3×C4—421no—
375C2×C3×C4—421no—
376#67—74no—
377C2×Dic3C3×AGL(1,𝔽7)11yescharacteristic, complemented
378C3×C7—21no—
379C3×C7C2×C3×#6711yescharacteristic, complemented
380C3×C7C2×C32×D411yescharacteristic, complemented
381ΓL(1,𝔽8)—21no—
382ΓL(1,𝔽8)—21no—
383ΓL(1,𝔽8)—21no—
384ΓL(1,𝔽8)C2×C3×#6711yescharacteristic, complemented
385ΓL(1,𝔽8)C2×C3×#6711yescharacteristic, complemented
386ΓL(1,𝔽8)C2×C3×#6711yescharacteristic, complemented
387C2×C32—142no—
388C2×C32—142no—
389C2×C32—141no—
390C2×C32—141no—
391C2×C32—142no—
392C2×C32—142no—
393C2×C32—142no—
394C2×C32—142no—
395C2×C32—142no—
396C2×C32—142no—
397C2×C32—142no—
398C2×C32—142no—
399C2×C32—142no—
400C2×C32—142no—
401C2×C32—142no—
402C2×C32—142no—
403C2×C32—142no—
404C2×C32—141no—
405C2×C32—142no—
406C2×C32—141no—
407C2×C32—142no—
408C2×C32—141no—
409C2×C32—141no—
410C2×C32—142no—
411C2×C32—142no—
412C2×C32—282no—
413C2×C32—281no—
414C2×C32—281no—
415C2×C32—282no—
416C2×C32—422no—
417C2×C32C4⋊AGL(1,𝔽7)12yescomplemented
418C2×C32C22×AGL(1,𝔽7)11yescharacteristic
419C3×D3—142no—
420C3×D3—142no—
421C3×D3—142no—
422C3×D3—142no—
423C2×D4—211noSylow
424C2×C7C32×#6712yescomplemented
425C2×C7C22×C32×D311yescharacteristic
426D7—22no—
427D7—62no—
428C22×C3—21no—
429C22×C3—72no—
430C22×C3—72no—
431C22×C3—72no—
432C22×C3—72no—
433C22×C3—72no—
434C22×C3—142no—
435C22×C3—142no—
436C22×C3—142no—
437C22×C3—142no—
438C22×C3—142no—
439C22×C3—142no—
440C22×C3—142no—
441C22×C3—142no—
442C22×C3—142no—
443C22×C3—142no—
444C22×C3—142no—
445C22×C3—142no—
446C22×C3—142no—
447C22×C3—142no—
448C22×C3—142no—
449C22×C3—142no—
450C22×C3—142no—
451C22×C3—141no—
452C22×C3—141no—
453C22×C3—141no—
454C22×C3—141no—
455C22×C3—212no—
456C22×C3—212no—
457C22×C3—212no—
458C22×C3—212no—
459C22×C3—281no—
460C22×C3—281no—
461C22×C3—422no—
462C22×C3—422no—
463C22×C3—422no—
464C22×C3—422no—
465C22×C3D3×AGL(1,𝔽7)11yescharacteristic
466C22×C3C2×C3×AGL(1,𝔽7)11yescharacteristic
467C2×D3—72no—
468C2×D3—142no—
469C3×C4—32no—
470C3×C4—422no—
471C3×C4—422no—
472C3×C4—422no—
473Dic3C2×C3×AGL(1,𝔽7)12yescomplemented
474C32—141no—
475C32—141no—
476C32—141no—
477C32—141no—
478C32—141no—
479C32—141no—
480C32—281no—
481C32—281no—
482C32C2×C4⋊AGL(1,𝔽7)11yescharacteristic, complemented
483C23—71no—
484C23—211no—
485D4—214no—
486C2×C4—31no—
487C7C2×C32×#6711yescharacteristic, complemented, Sylow
488C2×C3—22no—
489C2×C3—21no—
490C2×C3—142no—
491C2×C3—142no—
492C2×C3—142no—
493C2×C3—142no—
494C2×C3—142no—
495C2×C3—142no—
496C2×C3—142no—
497C2×C3—142no—
498C2×C3—142no—
499C2×C3—142no—
500C2×C3—142no—
501C2×C3—142no—
502C2×C3—142no—
503C2×C3—142no—
504C2×C3—142no—
505C2×C3—142no—
506C2×C3—142no—
507C2×C3—141no—
508C2×C3—141no—
509C2×C3—141no—
510C2×C3—141no—
511C2×C3—282no—
512C2×C3—282no—
513C2×C3—281no—
514C2×C3—281no—
515C2×C3—422no—
516C2×C3—422no—
517C2×C3—422no—
518C2×C3—422no—
519C2×C3#4246⋊C312yesdirect product factor
520C2×C3C3×C4⋊AGL(1,𝔽7)12yescomplemented
521C2×C3C2×D3×AGL(1,𝔽7)11yescharacteristic
522C2×C3C22×C3×AGL(1,𝔽7)11yescharacteristic
523D3—142no—
524C22—72no—
525C22—142no—
526C22—212no—
527C22—422no—
528C22C3×D3×AGL(1,𝔽7)11yescharacteristic
529C4—32no—
530C3—21no—
531C3—141no—
532C3—141no—
533C3—141no—
534C3—141no—
535C3—281no—
536C3—281no—
537C3C2×#4246⋊C311yescharacteristic, direct product factor
538C3C2×C3×C4⋊AGL(1,𝔽7)11yescharacteristic, complemented
539C2—142no—
540C2—422no—
541C2C3×#4246⋊C312yesdirect product factor
542C2C2×C3×D3×AGL(1,𝔽7)11yescharacteristic
subgroupG/H
center, hypercenterC22×C3D3×AGL(1,𝔽7)
commutator, cosocleC2×C3×C7C23×C32
FrattiniC2C2×C3×D3×AGL(1,𝔽7)
Fitting, socleC22×C32×C7C22×C3
hypocenterC3×C7C2×C32×D4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×C3⋊AGL(1,𝔽7)C2semidirect
2. C22×C32×AGL(1,𝔽7)C2semidirect
3. C2×C3×Dic3×ΓL(1,𝔽8)C2semidirect
4. C3×#4246⋊C3C2direct (N × H)
5. C2×C3×#4246C3semidirect
7. C2×#4246⋊C3C3direct (N × H)
8. C2×#4246⋊C3C3direct (N × H)
9. C2×#4246⋊C3C3direct (N × H)
12. C2×C3×C3⋊AGL(1,𝔽7)C22semidirect
14. C2×C32×AGL(1,𝔽7)C22semidirect
15. C3×Dic3×ΓL(1,𝔽8)C22semidirect
16. C22×C3×D21C2×C3semidirect
17. C22×C32×D7C2×C3semidirect
18. C22×C3⋊AGL(1,𝔽7)C2×C3semidirect
19. C22×C3⋊AGL(1,𝔽7)C2×C3semidirect
20. C22×C3⋊AGL(1,𝔽7)C2×C3semidirect
26. C22×C3×AGL(1,𝔽7)D3semidirect
27. C22×C3×AGL(1,𝔽7)C2×C3semidirect
28. C22×C3×AGL(1,𝔽7)C2×C3semidirect
29. C22×C3×AGL(1,𝔽7)C2×C3semidirect
30. C2×C3×C7×Dic3C2×C3semidirect
32. C3×#4246C2×C3semidirect
33. C2×Dic3×ΓL(1,𝔽8)C2×C3semidirect
34. C2×Dic3×ΓL(1,𝔽8)C2×C3semidirect
35. C2×Dic3×ΓL(1,𝔽8)C2×C3semidirect
37. #4246⋊C3C2×C3direct (N × H)
38. #4246⋊C3C2×C3direct (N × H)
39. #4246⋊C3C2×C3direct (N × H)
41. C2×C32×ΓL(1,𝔽8)D4semidirect
46. C2×#4246C32semidirect
52. C2×C3×D21C22×C3semidirect
54. C2×C32×D7C22×C3semidirect
66. C2×C3⋊AGL(1,𝔽7)C22×C3semidirect
67. C2×C3⋊AGL(1,𝔽7)C22×C3semidirect
68. C2×C3⋊AGL(1,𝔽7)C22×C3semidirect
87. C2×C3×AGL(1,𝔽7)C2×D3semidirect
88. C2×C3×AGL(1,𝔽7)C22×C3semidirect
89. C2×C3×AGL(1,𝔽7)C22×C3semidirect
90. C2×C3×AGL(1,𝔽7)C22×C3semidirect
91. C3×C7×Dic3C22×C3semidirect
93. Dic3×ΓL(1,𝔽8)C22×C3semidirect
94. Dic3×ΓL(1,𝔽8)C22×C3semidirect
95. Dic3×ΓL(1,𝔽8)C22×C3semidirect
100. C32×ΓL(1,𝔽8)C2×D4semidirect
101. C22×D21C2×C32semidirect
104. C22×C3×D7C3×D3semidirect
105. C22×C3×D7C2×C32semidirect
112. C22×AGL(1,𝔽7)C3×D3semidirect
113. C22×AGL(1,𝔽7)C3×D3semidirect
114. C22×AGL(1,𝔽7)C3×D3semidirect
116. C2×C7×Dic3C2×C32semidirect
121. #4246C2×C32semidirect
130. C2×C32×C7C3×D4semidirect
142. C2×C3×ΓL(1,𝔽8)#67semidirect
143. C2×C3×ΓL(1,𝔽8)C3×D4semidirect
144. C2×C3×ΓL(1,𝔽8)C3×D4semidirect
145. C2×C3×ΓL(1,𝔽8)C3×D4semidirect
177. C2×D21C22×C32semidirect
185. C2×C3×D7C2×C3×D3semidirect
186. C2×C3×D7C22×C32semidirect
211. C2×AGL(1,𝔽7)C2×C3×D3semidirect
212. C2×AGL(1,𝔽7)C2×C3×D3semidirect
213. C2×AGL(1,𝔽7)C2×C3×D3semidirect
215. C7×Dic3C22×C32semidirect
242. C2×C3×Dic3AGL(1,𝔽7)semidirect
243. C32×C7C2×C3×D4semidirect
248. C3×ΓL(1,𝔽8)C2×#67semidirect
249. C3×ΓL(1,𝔽8)C2×C3×D4semidirect
250. C3×ΓL(1,𝔽8)C2×C3×D4semidirect
251. C3×ΓL(1,𝔽8)C2×C3×D4semidirect
253. C22×D7C32×D3semidirect
267. C2×C3×C7C3×#67semidirect
268. C2×C3×C7C32×D4semidirect
283. C2×ΓL(1,𝔽8)C3×#67semidirect
284. C2×ΓL(1,𝔽8)C3×#67semidirect
285. C2×ΓL(1,𝔽8)C3×#67semidirect
346. C3×Dic3C2×AGL(1,𝔽7)semidirect
351. C2×D7C2×C32×D3semidirect
377. C2×Dic3C3×AGL(1,𝔽7)semidirect
379. C3×C7C2×C3×#67semidirect
380. C3×C7C2×C32×D4semidirect
384. ΓL(1,𝔽8)C2×C3×#67semidirect
385. ΓL(1,𝔽8)C2×C3×#67semidirect
386. ΓL(1,𝔽8)C2×C3×#67semidirect
417. C2×C32C4⋊AGL(1,𝔽7)semidirect
424. C2×C7C32×#67semidirect
473. Dic3C2×C3×AGL(1,𝔽7)semidirect
482. C32C2×C4⋊AGL(1,𝔽7)semidirect
487. C7C2×C32×#67semidirect
519. C2×C3#4246⋊C3direct (N × H)
520. C2×C3C3×C4⋊AGL(1,𝔽7)semidirect
537. C3C2×#4246⋊C3direct (N × H)
538. C3C2×C3×C4⋊AGL(1,𝔽7)semidirect
541. C2C3×#4246⋊C3direct (N × H)

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
C22×C32×AGL(1,𝔽7)2
C2×C3×Dic3×ΓL(1,𝔽8)2
C3×#4246⋊C32
C2×C3×#42463
C2×C3×C4⋊AGL(1,𝔽7)3
C2×#4246⋊C33
C2×C32×#677