Finite Group Databasebeta

← C2×C71×#2418 #31855520

Subgroups — C2×C71×#2418 #31855520

Order 18176.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C71C211yesmaximal, characteristic, complemented
2C22×#120×C71C211yesmaximal, characteristic
3C22×C4×D4×C71C211yesmaximal, characteristic, complemented
4C23×C22⋊C4×C71C211yesmaximal, characteristic, complemented
5C71×#2418C2116yesmaximal, direct product factor
6C2×#399×C71C211yesmaximal, characteristic, complemented
7C2×#397×C71C211yesmaximal, characteristic, complemented
8C2×#394×C71C211yesmaximal, characteristic, complemented
9C2×#394×C71C211yesmaximal, characteristic, complemented
10C2×#388×C71C211yesmaximal, characteristic, complemented
11C2×#388×C71C211yesmaximal, characteristic, complemented
12C2×#386×C71C211yesmaximal, characteristic, complemented
13C2×#386×C71C211yesmaximal, characteristic, complemented
14C2×#385×C71C211yesmaximal, characteristic, complemented
15C2×#380×C71C211yesmaximal, characteristic, complemented
16C2×#379×C71C211yesmaximal, characteristic, complemented
17C26×C71C2211yescharacteristic
18C23×D4×C71C2211yescharacteristic
19C23×D4×C71C2211yescharacteristic
20C23×D4×C71C2211yescharacteristic
21C24×C4×C71C2211yescharacteristic
22C24×C4×C71C2211yescharacteristic
23C24×C4×C71C2211yescharacteristic, complemented
24C2×#123×C71—28no—
25C2×#123×C71C2218yescomplemented
26C2×#120×C71—28no—
27C2×#120×C71C2218yes—
28C2×C4×D4×C71—28no—
29C2×C4×D4×C71C2218yescomplemented
30C22×C4⋊C4×C71C2211yescharacteristic, complemented
31C22×C4⋊C4×C71C2211yescharacteristic, complemented
32C22×C4⋊C4×C71C2211yescharacteristic, complemented
33C22×C4⋊C4×C71C2211yescharacteristic, complemented
34C22×C4⋊C4×C71C2211yescharacteristic, complemented
35C22×C22⋊C4×C71—28no—
36C22×C22⋊C4×C71C2211yescharacteristic
37C22×C22⋊C4×C71C2211yescharacteristic
38C22×C22⋊C4×C71C2211yescharacteristic
39C22×C22⋊C4×C71C2211yescharacteristic
40C22×C22⋊C4×C71C2211yescharacteristic
41C22×C22⋊C4×C71C2211yescharacteristic
42C22×C22⋊C4×C71C2211yescharacteristic
43C22×C22⋊C4×C71C2211yescharacteristic
44C22×C22⋊C4×C71C2211yescharacteristic
45C22×C22⋊C4×C71C2211yescharacteristic
46C22×C22⋊C4×C71C2211yescharacteristic
47C22×C22⋊C4×C71C2211yescharacteristic
48C22×C22⋊C4×C71C2211yescharacteristic
49C22×C22⋊C4×C71C2218yescomplemented
50C22×C22⋊C4×C71C2211yescharacteristic, complemented
51C22×C22⋊C4×C71C2211yescharacteristic, complemented
52C22×C22⋊C4×C71C2211yescharacteristic, complemented
53C22×C42×C71C2211yescharacteristic, complemented
54#399×C71C2218yescomplemented
55#397×C71C2218yescomplemented
56#394×C71C2218yescomplemented
57#394×C71C2218yescomplemented
58#388×C71C2218yescomplemented
59#388×C71C2218yescomplemented
60#386×C71C2218yescomplemented
61#386×C71C2218yescomplemented
62#385×C71C2218yescomplemented
63#380×C71C2218yescomplemented
64#379×C71C2218yescomplemented
65C2×#95×C71C2211yescharacteristic, complemented
66C2×#95×C71C2211yescharacteristic, complemented
67C2×#95×C71C2211yescharacteristic, complemented
68C2×#95×C71C2211yescharacteristic, complemented
69C2×#95×C71C2211yescharacteristic, complemented
70C2×#95×C71C2211yescharacteristic, complemented
71C25×C71—24no—
72C25×C71—24no—
73C25×C71—24no—
74C25×C71—24no—
75C25×C71—24no—
76C25×C71—42no—
77C25×C71—42no—
78C25×C71C2311yescharacteristic
79C25×C71C2311yescharacteristic
80C25×C71C2311yescharacteristic
81C25×C71C2314yes—
82C25×C71C2311yescharacteristic
83C22×D4×C71—24no—
84C22×D4×C71—24no—
85C22×D4×C71—24no—
86C22×D4×C71—24no—
87C22×D4×C71—24no—
88C22×D4×C71—24no—
89C22×D4×C71—42no—
90C22×D4×C71—42no—
91C22×D4×C71D418yes—
92C22×D4×C71C2314yes—
93C22×D4×C71C2314yes—
94C22×D4×C71C2314yes—
95C23×C4×C71—24no—
96C23×C4×C71—24no—
97C23×C4×C71—24no—
98C23×C4×C71—24no—
99C23×C4×C71—24no—
100C23×C4×C71—24no—
101C23×C4×C71—42no—
102C23×C4×C71—42no—
103C23×C4×C71—42no—
104C23×C4×C71C2311yescharacteristic
105C23×C4×C71C2311yescharacteristic
106C23×C4×C71C2311yescharacteristic
107C23×C4×C71C2311yescharacteristic
108C23×C4×C71C2311yescharacteristic
109C23×C4×C71C2311yescharacteristic
110C23×C4×C71C2311yescharacteristic
111C23×C4×C71C2311yescharacteristic
112C23×C4×C71C2314yes—
113C23×C4×C71C2314yes—
114C23×C4×C71C2311yescharacteristic
115C23×C4×C71C2311yescharacteristic
116C23×C4×C71C2311yescharacteristic
117C23×C4×C71C2314yescomplemented
118#123×C71—232no—
119#120×C71—232no—
120C4×D4×C71—232no—
121C2×C4⋊C4×C71—24no—
122C2×C4⋊C4×C71—24no—
123C2×C4⋊C4×C71—24no—
124C2×C4⋊C4×C71—42no—
125C2×C4⋊C4×C71—42no—
126C2×C4⋊C4×C71C2314yescomplemented
127C2×C4⋊C4×C71C2314yescomplemented
128C2×C4⋊C4×C71C2314yescomplemented
129C2×C4⋊C4×C71C2314yescomplemented
130C2×C4⋊C4×C71C2314yescomplemented
131C2×C22⋊C4×C71—24no—
132C2×C22⋊C4×C71—24no—
133C2×C22⋊C4×C71—24no—
134C2×C22⋊C4×C71—24no—
135C2×C22⋊C4×C71—24no—
136C2×C22⋊C4×C71—24no—
137C2×C22⋊C4×C71—24no—
138C2×C22⋊C4×C71—24no—
139C2×C22⋊C4×C71—24no—
140C2×C22⋊C4×C71—24no—
141C2×C22⋊C4×C71—24no—
142C2×C22⋊C4×C71—24no—
143C2×C22⋊C4×C71—232no—
144C2×C22⋊C4×C71—42no—
145C2×C22⋊C4×C71—42no—
146C2×C22⋊C4×C71—42no—
147C2×C22⋊C4×C71D418yescomplemented
148C2×C22⋊C4×C71C2314yes—
149C2×C22⋊C4×C71C2314yes—
150C2×C22⋊C4×C71C2314yes—
151C2×C22⋊C4×C71C2314yes—
152C2×C22⋊C4×C71C2314yes—
153C2×C22⋊C4×C71C2314yes—
154C2×C22⋊C4×C71C2314yes—
155C2×C22⋊C4×C71C2314yes—
156C2×C22⋊C4×C71C2314yes—
157C2×C22⋊C4×C71C2314yes—
158C2×C22⋊C4×C71C2314yes—
159C2×C22⋊C4×C71C2314yes—
160C2×C22⋊C4×C71C2314yes—
161C2×C22⋊C4×C71C2314yescomplemented
162C2×C22⋊C4×C71C2314yescomplemented
163C2×C22⋊C4×C71C2314yescomplemented
164C2×C42×C71—24no—
165C2×C42×C71C2314yescomplemented
166#95×C71C2314yescomplemented
167#95×C71C2314yescomplemented
168#95×C71C2314yescomplemented
169#95×C71C2314yescomplemented
170#95×C71C2314yescomplemented
171#95×C71C2314yescomplemented
172C24×C71—22no—
173C24×C71—22no—
174C24×C71—22no—
175C24×C71—22no—
176C24×C71—232no—
177C24×C71—28no—
178C24×C71—22no—
179C24×C71—22no—
180C24×C71—22no—
181C24×C71—22no—
182C24×C71—22no—
183C24×C71—22no—
184C24×C71—22no—
185C24×C71—28no—
186C24×C71—28no—
187C24×C71—22no—
188C24×C71—22no—
189C24×C71—22no—
190C24×C71—22no—
191C24×C71—22no—
192C24×C71—22no—
193C24×C71—22no—
194C24×C71—22no—
195C24×C71—22no—
196C24×C71—22no—
197C24×C71—22no—
198C24×C71—28no—
199C24×C71—28no—
200C24×C71—44no—
201C24×C71—44no—
202C24×C71—416no—
203C24×C71—416no—
204C24×C71—416no—
205C24×C71—416no—
206C24×C71—416no—
207C24×C71—416no—
208C24×C71C2×D414yes—
209C24×C71C2×D414yes—
210C24×C71C2×D414yes—
211C24×C71#4114yes—
212C24×C71#4114yes—
213C24×C71#4114yes—
214C24×C71C2412yes—
215C24×C71C2412yes—
216C24×C71C2412yes—
217C24×C71C2412yes—
218C24×C71C2411yescharacteristic
219C2×D4×C71—232no—
220C2×D4×C71—28no—
221C2×D4×C71—28no—
222C2×D4×C71—28no—
223C2×D4×C71—28no—
224C2×D4×C71—28no—
225C2×D4×C71—28no—
226C2×D4×C71—44no—
227C2×D4×C71—44no—
228C2×D4×C71—416no—
229C2×D4×C71—416no—
230C2×D4×C71C2×D4116yes—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71—22no—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71—28no—
248C22×C4×C71—28no—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—28no—
254C22×C4×C71—22no—
255C22×C4×C71—22no—
256C22×C4×C71—22no—
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—22no—
262C22×C4×C71—22no—
263C22×C4×C71—22no—
264C22×C4×C71—28no—
265C22×C4×C71—28no—
266C22×C4×C71—28no—
267C22×C4×C71—44no—
268C22×C4×C71—44no—
269C22×C4×C71—44no—
270C22×C4×C71—416no—
271C22×C4×C71—416no—
272C22×C4×C71—416no—
273C22×C4×C71C2×D414yes—
274C22×C4×C71C2×D414yes—
275C22×C4×C71C2×D414yes—
276C22×C4×C71C2412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2412yes—
279C22×C4×C71C2412yes—
280C22×C4×C71C2412yes—
281C22×C4×C71C2412yes—
282C22×C4×C71C2412yes—
283C22×C4×C71C2412yes—
284C22×C4×C71C2412yes—
285C22×C4×C71C2412yes—
286C22×C4×C71C2412yes—
287C4⋊C4×C71—28no—
288C4⋊C4×C71—28no—
289C4⋊C4×C71—28no—
290C4⋊C4×C71—44no—
291C4⋊C4×C71—44no—
292C22⋊C4×C71—28no—
293C22⋊C4×C71—28no—
294C22⋊C4×C71—28no—
295C22⋊C4×C71—28no—
296C22⋊C4×C71—28no—
297C22⋊C4×C71—28no—
298C22⋊C4×C71—28no—
299C22⋊C4×C71—28no—
300C22⋊C4×C71—28no—
301C22⋊C4×C71—28no—
302C22⋊C4×C71—28no—
303C22⋊C4×C71—28no—
304C22⋊C4×C71—44no—
305C22⋊C4×C71—44no—
306C22⋊C4×C71—44no—
307C22⋊C4×C71C2×D4116yescomplemented
308C42×C71—28no—
309C23×C71—28no—
310C23×C71—28no—
311C23×C71—28no—
312C23×C71—28no—
313C23×C71—28no—
314C23×C71—28no—
315C23×C71—22no—
316C23×C71—22no—
317C23×C71—22no—
318C23×C71—22no—
319C23×C71—232no—
320C23×C71—28no—
321C23×C71—28no—
322C23×C71—28no—
323C23×C71—28no—
324C23×C71—28no—
325C23×C71—28no—
326C23×C71—28no—
327C23×C71—28no—
328C23×C71—28no—
329C23×C71—22no—
330C23×C71—22no—
331C23×C71—22no—
332C23×C71—22no—
333C23×C71—22no—
334C23×C71—22no—
335C23×C71—22no—
336C23×C71—22no—
337C23×C71—22no—
338C23×C71—22no—
339C23×C71—22no—
340C23×C71—22no—
341C23×C71—22no—
342C23×C71—22no—
343C23×C71—22no—
344C23×C71—22no—
345C23×C71—22no—
346C23×C71—22no—
347C23×C71—416no—
348C23×C71—416no—
349C23×C71—416no—
350C23×C71—416no—
351C23×C71—4128no—
352C23×C71—416no—
353C23×C71—44no—
354C23×C71—44no—
355C23×C71—416no—
356C23×C71—44no—
357C23×C71—44no—
358C23×C71—44no—
359C23×C71—44no—
360C23×C71—44no—
361C23×C71—44no—
362C23×C71—44no—
363C23×C71—44no—
364C23×C71—44no—
365C23×C71—44no—
366C23×C71#123116yescomplemented
367C23×C71C22×D414yes—
368C23×C71C22×D414yes—
369C23×C71C22×D414yes—
370C23×C71C22×D412yes—
371C23×C71C22×D412yes—
372C23×C71C2×#4114yes—
373C23×C71C2×#4114yes—
374C23×C71C2×#4114yes—
375C23×C71C2×#4112yes—
376C23×C71C2×#4112yes—
377C23×C71C2×#4112yes—
378C23×C71H(5,𝔽2)12yes—
379C23×C71H(5,𝔽2)12yes—
380C23×C71C2511yescharacteristic
381D4×C71—232no—
382D4×C71—416no—
383D4×C71—416no—
384C2×C4×C71—28no—
385C2×C4×C71—28no—
386C2×C4×C71—28no—
387C2×C4×C71—22no—
388C2×C4×C71—22no—
389C2×C4×C71—22no—
390C2×C4×C71—22no—
391C2×C4×C71—22no—
392C2×C4×C71—22no—
393C2×C4×C71—22no—
394C2×C4×C71—22no—
395C2×C4×C71—22no—
396C2×C4×C71—22no—
397C2×C4×C71—22no—
398C2×C4×C71—22no—
399C2×C4×C71—22no—
400C2×C4×C71—22no—
401C2×C4×C71—22no—
402C2×C4×C71—22no—
403C2×C4×C71—22no—
404C2×C4×C71—22no—
405C2×C4×C71—22no—
406C2×C4×C71—22no—
407C2×C4×C71—22no—
408C2×C4×C71—22no—
409C2×C4×C71—22no—
410C2×C4×C71—22no—
411C2×C4×C71—22no—
412C2×C4×C71—22no—
413C2×C4×C71—22no—
414C2×C4×C71—22no—
415C2×C4×C71—22no—
416C2×C4×C71—22no—
417C2×C4×C71—416no—
418C2×C4×C71—416no—
419C2×C4×C71—416no—
420C2×C4×C71—44no—
421C2×C4×C71—44no—
422C2×C4×C71—44no—
423C2×C4×C71—44no—
424C2×C4×C71—44no—
425C2×C4×C71—44no—
426C2×C4×C71—44no—
427C2×C4×C71—44no—
428C2×C4×C71C22×D414yes—
429C2×C4×C71C22×D414yes—
430C2×C4×C71C22×D414yes—
431C22×C71—24no—
432C22×C71—232no—
433C22×C71—24no—
434C22×C71—24no—
435C22×C71—24no—
436C22×C71—24no—
437C22×C71—24no—
438C22×C71—24no—
439C22×C71—24no—
440C22×C71—24no—
441C22×C71—24no—
442C22×C71—24no—
443C22×C71—24no—
444C22×C71—24no—
445C22×C71—24no—
446C22×C71—24no—
447C22×C71—464no—
448C22×C71—42no—
449C22×C71—42no—
450C22×C71—42no—
451C22×C71—416no—
452C22×C71—416no—
453C22×C71—416no—
454C22×C71—42no—
455C22×C71—42no—
456C22×C71—42no—
457C22×C71—42no—
458C22×C71—42no—
459C22×C71—42no—
460C22×C71—42no—
461C22×C71—42no—
462C22×C71—42no—
463C22×C71C2×#12314yes—
464C22×C71C2×#12318yescomplemented
465C22×C71#52514yes—
466C22×C71#53814yes—
467C22×C71D4214yes—
468C22×C71#54614yes—
469C22×C71#54614yes—
470C22×C71#55114yes—
471C22×C71C23×D411yescharacteristic
472C22×C71C23×D411yescharacteristic
473C22×C71C22×#4111yescharacteristic
474C22×C71C22×#4111yescharacteristic
475C22×C71C22×#4111yescharacteristic
476C22×C71C2×H(5,𝔽2)11yescharacteristic
477C22×C71C2×H(5,𝔽2)11yescharacteristic
478C4×C71—24no—
479C4×C71—24no—
480C4×C71—24no—
481C4×C71—42no—
482C4×C71—42no—
483C4×C71—42no—
484C4×C71—42no—
485C4×C71—42no—
486C4×C71—42no—
487C4×C71—42no—
488C4×C71—42no—
489C2×#2418C7111yesmaximal, characteristic, direct product factor, Sylow
490C2×C71—28no—
491C2×C71—44no—
492C2×C71—44no—
493C2×C71—44no—
494C2×C71#241818yesdirect product factor
495C2×C71C22×#12311yescharacteristic
496C2×C71C2×#52511yescharacteristic
497C2×C71C2×#53811yescharacteristic
498C2×C71C2×D4211yescharacteristic
499C2×C71C2×#54611yescharacteristic
500C2×C71C2×#54611yescharacteristic
501C2×C71C2×#55111yescharacteristic
502C22×#123C2×C7111yescharacteristic, complemented
503C22×#120C2×C7111yescharacteristic
504C22×C4×D4C2×C7111yescharacteristic, complemented
505C23×C22⋊C4C2×C7111yescharacteristic, complemented
506#2418C2×C71116yesdirect product factor
507C2×#399C2×C7111yescharacteristic, complemented
508C2×#397C2×C7111yescharacteristic, complemented
509C2×#394C2×C7111yescharacteristic, complemented
510C2×#394C2×C7111yescharacteristic, complemented
511C2×#388C2×C7111yescharacteristic, complemented
512C2×#388C2×C7111yescharacteristic, complemented
513C2×#386C2×C7111yescharacteristic, complemented
514C2×#386C2×C7111yescharacteristic, complemented
515C2×#385C2×C7111yescharacteristic, complemented
516C2×#380C2×C7111yescharacteristic, complemented
517C2×#379C2×C7111yescharacteristic, complemented
518C71C2×#241811yescharacteristic, direct product factor, Sylow
519C26C22×C7111yescharacteristic
520C23×D4C22×C7111yescharacteristic
521C23×D4C22×C7111yescharacteristic
522C23×D4C22×C7111yescharacteristic
523C24×C4C22×C7111yescharacteristic
524C24×C4C22×C7111yescharacteristic
525C24×C4C22×C7111yescharacteristic, complemented
526C2×#123—28no—
527C2×#123C22×C7118yescomplemented
528C2×#120—28no—
529C2×#120C22×C7118yes—
530C2×C4×D4—28no—
531C2×C4×D4C22×C7118yescomplemented
532C22×C4⋊C4C22×C7111yescharacteristic, complemented
533C22×C4⋊C4C22×C7111yescharacteristic, complemented
534C22×C4⋊C4C22×C7111yescharacteristic, complemented
535C22×C4⋊C4C22×C7111yescharacteristic, complemented
536C22×C4⋊C4C22×C7111yescharacteristic, complemented
537C22×C22⋊C4—28no—
538C22×C22⋊C4C22×C7111yescharacteristic
539C22×C22⋊C4C22×C7111yescharacteristic
540C22×C22⋊C4C22×C7111yescharacteristic
541C22×C22⋊C4C22×C7111yescharacteristic
542C22×C22⋊C4C22×C7111yescharacteristic
543C22×C22⋊C4C22×C7111yescharacteristic
544C22×C22⋊C4C22×C7111yescharacteristic
545C22×C22⋊C4C22×C7111yescharacteristic
546C22×C22⋊C4C22×C7111yescharacteristic
547C22×C22⋊C4C22×C7111yescharacteristic
548C22×C22⋊C4C22×C7111yescharacteristic
549C22×C22⋊C4C22×C7111yescharacteristic
550C22×C22⋊C4C22×C7111yescharacteristic
551C22×C22⋊C4C22×C7118yescomplemented
552C22×C22⋊C4C22×C7111yescharacteristic, complemented
553C22×C22⋊C4C22×C7111yescharacteristic, complemented
554C22×C22⋊C4C22×C7111yescharacteristic, complemented
555C22×C42C22×C7111yescharacteristic, complemented
556#399C22×C7118yescomplemented
557#397C22×C7118yescomplemented
558#394C22×C7118yescomplemented
559#394C22×C7118yescomplemented
560#388C22×C7118yescomplemented
561#388C22×C7118yescomplemented
562#386C22×C7118yescomplemented
563#386C22×C7118yescomplemented
564#385C22×C7118yescomplemented
565#380C22×C7118yescomplemented
566#379C22×C7118yescomplemented
567C2×#95C22×C7111yescharacteristic, complemented
568C2×#95C22×C7111yescharacteristic, complemented
569C2×#95C22×C7111yescharacteristic, complemented
570C2×#95C22×C7111yescharacteristic, complemented
571C2×#95C22×C7111yescharacteristic, complemented
572C2×#95C22×C7111yescharacteristic, complemented
573C25—24no—
574C25—24no—
575C25—24no—
576C25—24no—
577C25—24no—
578C25—42no—
579C25—42no—
580C25C23×C7111yescharacteristic
581C25C23×C7111yescharacteristic
582C25C23×C7111yescharacteristic
583C25C23×C7114yes—
584C25C23×C7111yescharacteristic
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—24no—
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4D4×C7118yes—
594C22×D4C23×C7114yes—
595C22×D4C23×C7114yes—
596C22×D4C23×C7114yes—
597C23×C4—24no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—24no—
601C23×C4—24no—
602C23×C4—24no—
603C23×C4—42no—
604C23×C4—42no—
605C23×C4—42no—
606C23×C4C23×C7111yescharacteristic
607C23×C4C23×C7111yescharacteristic
608C23×C4C23×C7111yescharacteristic
609C23×C4C23×C7111yescharacteristic
610C23×C4C23×C7111yescharacteristic
611C23×C4C23×C7111yescharacteristic
612C23×C4C23×C7111yescharacteristic
613C23×C4C23×C7111yescharacteristic
614C23×C4C23×C7114yes—
615C23×C4C23×C7114yes—
616C23×C4C23×C7111yescharacteristic
617C23×C4C23×C7111yescharacteristic
618C23×C4C23×C7111yescharacteristic
619C23×C4C23×C7114yescomplemented
620#123—232no—
621#120—232no—
622C4×D4—232no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—42no—
627C2×C4⋊C4—42no—
628C2×C4⋊C4C23×C7114yescomplemented
629C2×C4⋊C4C23×C7114yescomplemented
630C2×C4⋊C4C23×C7114yescomplemented
631C2×C4⋊C4C23×C7114yescomplemented
632C2×C4⋊C4C23×C7114yescomplemented
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—232no—
646C2×C22⋊C4—42no—
647C2×C22⋊C4—42no—
648C2×C22⋊C4—42no—
649C2×C22⋊C4D4×C7118yescomplemented
650C2×C22⋊C4C23×C7114yes—
651C2×C22⋊C4C23×C7114yes—
652C2×C22⋊C4C23×C7114yes—
653C2×C22⋊C4C23×C7114yes—
654C2×C22⋊C4C23×C7114yes—
655C2×C22⋊C4C23×C7114yes—
656C2×C22⋊C4C23×C7114yes—
657C2×C22⋊C4C23×C7114yes—
658C2×C22⋊C4C23×C7114yes—
659C2×C22⋊C4C23×C7114yes—
660C2×C22⋊C4C23×C7114yes—
661C2×C22⋊C4C23×C7114yes—
662C2×C22⋊C4C23×C7114yes—
663C2×C22⋊C4C23×C7114yescomplemented
664C2×C22⋊C4C23×C7114yescomplemented
665C2×C22⋊C4C23×C7114yescomplemented
666C2×C42—24no—
667C2×C42C23×C7114yescomplemented
668#95C23×C7114yescomplemented
669#95C23×C7114yescomplemented
670#95C23×C7114yescomplemented
671#95C23×C7114yescomplemented
672#95C23×C7114yescomplemented
673#95C23×C7114yescomplemented
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—232no—
679C24—28no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—28no—
688C24—28no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—28no—
701C24—28no—
702C24—44no—
703C24—44no—
704C24—416no—
705C24—416no—
706C24—416no—
707C24—416no—
708C24—416no—
709C24—416no—
710C24C2×D4×C7114yes—
711C24C2×D4×C7114yes—
712C24C2×D4×C7114yes—
713C24#41×C7114yes—
714C24#41×C7114yes—
715C24#41×C7114yes—
716C24C24×C7112yes—
717C24C24×C7112yes—
718C24C24×C7112yes—
719C24C24×C7112yes—
720C24C24×C7111yescharacteristic
721C2×D4—232no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—416no—
731C2×D4—416no—
732C2×D4C2×D4×C71116yes—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—28no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—416no—
773C22×C4—416no—
774C22×C4—416no—
775C22×C4C2×D4×C7114yes—
776C22×C4C2×D4×C7114yes—
777C22×C4C2×D4×C7114yes—
778C22×C4C24×C7112yes—
779C22×C4C24×C7112yes—
780C22×C4C24×C7112yes—
781C22×C4C24×C7112yes—
782C22×C4C24×C7112yes—
783C22×C4C24×C7112yes—
784C22×C4C24×C7112yes—
785C22×C4C24×C7112yes—
786C22×C4C24×C7112yes—
787C22×C4C24×C7112yes—
788C22×C4C24×C7112yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4C2×D4×C71116yescomplemented
810C42—28no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—232no—
822C23—28no—
823C23—28no—
824C23—28no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—28no—
829C23—28no—
830C23—28no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—416no—
850C23—416no—
851C23—416no—
852C23—416no—
853C23—4128no—
854C23—416no—
855C23—44no—
856C23—44no—
857C23—416no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23#123×C71116yescomplemented
869C23C22×D4×C7114yes—
870C23C22×D4×C7114yes—
871C23C22×D4×C7114yes—
872C23C22×D4×C7112yes—
873C23C22×D4×C7112yes—
874C23C2×#41×C7114yes—
875C23C2×#41×C7114yes—
876C23C2×#41×C7114yes—
877C23C2×#41×C7112yes—
878C23C2×#41×C7112yes—
879C23C2×#41×C7112yes—
880C23H(5,𝔽2)×C7112yes—
881C23H(5,𝔽2)×C7112yes—
882C23C25×C7111yescharacteristic
883D4—232no—
884D4—416no—
885D4—416no—
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—416no—
920C2×C4—416no—
921C2×C4—416no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4C22×D4×C7114yes—
931C2×C4C22×D4×C7114yes—
932C2×C4C22×D4×C7114yes—
933C22—24no—
934C22—232no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—464no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—416no—
954C22—416no—
955C22—416no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22C2×#123×C7114yes—
966C22C2×#123×C7118yescomplemented
967C22#525×C7114yes—
968C22#538×C7114yes—
969C22D42×C7114yes—
970C22#546×C7114yes—
971C22#546×C7114yes—
972C22#551×C7114yes—
973C22C23×D4×C7111yescharacteristic
974C22C23×D4×C7111yescharacteristic
975C22C22×#41×C7111yescharacteristic
976C22C22×#41×C7111yescharacteristic
977C22C22×#41×C7111yescharacteristic
978C22C2×H(5,𝔽2)×C7111yescharacteristic
979C22C2×H(5,𝔽2)×C7111yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C2—28no—
992C2—44no—
993C2—44no—
994C2—44no—
995C2C71×#241818yesdirect product factor
996C2C22×#123×C7111yescharacteristic
997C2C2×#525×C7111yescharacteristic
998C2C2×#538×C7111yescharacteristic
999C2C2×D42×C7111yescharacteristic
1000C2C2×#546×C7111yescharacteristic
1001C2C2×#546×C7111yescharacteristic
1002C2C2×#551×C7111yescharacteristic
subgroupG/H
center, socleC24×C71C24
commutator, Frattini, cosocleC23C25×C71
prime radicalC22×#120×C71C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#123×C71C2semidirect
3. C22×C4×D4×C71C2semidirect
4. C23×C22⋊C4×C71C2semidirect
5. C71×#2418C2direct (N × H)
6. C2×#399×C71C2semidirect
7. C2×#397×C71C2semidirect
8. C2×#394×C71C2semidirect
9. C2×#394×C71C2semidirect
10. C2×#388×C71C2semidirect
11. C2×#388×C71C2semidirect
12. C2×#386×C71C2semidirect
13. C2×#386×C71C2semidirect
14. C2×#385×C71C2semidirect
15. C2×#380×C71C2semidirect
16. C2×#379×C71C2semidirect
23. C24×C4×C71C22semidirect
25. C2×#123×C71C22semidirect
29. C2×C4×D4×C71C22semidirect
30. C22×C4⋊C4×C71C22semidirect
31. C22×C4⋊C4×C71C22semidirect
32. C22×C4⋊C4×C71C22semidirect
33. C22×C4⋊C4×C71C22semidirect
34. C22×C4⋊C4×C71C22semidirect
49. C22×C22⋊C4×C71C22semidirect
50. C22×C22⋊C4×C71C22semidirect
51. C22×C22⋊C4×C71C22semidirect
52. C22×C22⋊C4×C71C22semidirect
53. C22×C42×C71C22semidirect
54. #399×C71C22semidirect
55. #397×C71C22semidirect
56. #394×C71C22semidirect
57. #394×C71C22semidirect
58. #388×C71C22semidirect
59. #388×C71C22semidirect
60. #386×C71C22semidirect
61. #386×C71C22semidirect
62. #385×C71C22semidirect
63. #380×C71C22semidirect
64. #379×C71C22semidirect
65. C2×#95×C71C22semidirect
66. C2×#95×C71C22semidirect
67. C2×#95×C71C22semidirect
68. C2×#95×C71C22semidirect
69. C2×#95×C71C22semidirect
70. C2×#95×C71C22semidirect
117. C23×C4×C71C23semidirect
126. C2×C4⋊C4×C71C23semidirect
127. C2×C4⋊C4×C71C23semidirect
128. C2×C4⋊C4×C71C23semidirect
129. C2×C4⋊C4×C71C23semidirect
130. C2×C4⋊C4×C71C23semidirect
147. C2×C22⋊C4×C71D4semidirect
161. C2×C22⋊C4×C71C23semidirect
162. C2×C22⋊C4×C71C23semidirect
163. C2×C22⋊C4×C71C23semidirect
165. C2×C42×C71C23semidirect
166. #95×C71C23semidirect
167. #95×C71C23semidirect
168. #95×C71C23semidirect
169. #95×C71C23semidirect
170. #95×C71C23semidirect
171. #95×C71C23semidirect
307. C22⋊C4×C71C2×D4semidirect
366. C23×C71#123semidirect
464. C22×C71C2×#123semidirect
489. C2×#2418C71direct (N × H)
494. C2×C71#2418direct (N × H)
502. C22×#123C2×C71semidirect
504. C22×C4×D4C2×C71semidirect
505. C23×C22⋊C4C2×C71semidirect
506. #2418C2×C71direct (N × H)
507. C2×#399C2×C71semidirect
508. C2×#397C2×C71semidirect
509. C2×#394C2×C71semidirect
510. C2×#394C2×C71semidirect
511. C2×#388C2×C71semidirect
512. C2×#388C2×C71semidirect
513. C2×#386C2×C71semidirect
514. C2×#386C2×C71semidirect
515. C2×#385C2×C71semidirect
516. C2×#380C2×C71semidirect
517. C2×#379C2×C71semidirect
518. C71C2×#2418direct (N × H)
525. C24×C4C22×C71semidirect
527. C2×#123C22×C71semidirect
531. C2×C4×D4C22×C71semidirect
532. C22×C4⋊C4C22×C71semidirect
533. C22×C4⋊C4C22×C71semidirect
534. C22×C4⋊C4C22×C71semidirect
535. C22×C4⋊C4C22×C71semidirect
536. C22×C4⋊C4C22×C71semidirect
551. C22×C22⋊C4C22×C71semidirect
552. C22×C22⋊C4C22×C71semidirect
553. C22×C22⋊C4C22×C71semidirect
554. C22×C22⋊C4C22×C71semidirect
555. C22×C42C22×C71semidirect
556. #399C22×C71semidirect
557. #397C22×C71semidirect
558. #394C22×C71semidirect
559. #394C22×C71semidirect
560. #388C22×C71semidirect
561. #388C22×C71semidirect
562. #386C22×C71semidirect
563. #386C22×C71semidirect
564. #385C22×C71semidirect
565. #380C22×C71semidirect
566. #379C22×C71semidirect
567. C2×#95C22×C71semidirect
568. C2×#95C22×C71semidirect
569. C2×#95C22×C71semidirect
570. C2×#95C22×C71semidirect
571. C2×#95C22×C71semidirect
572. C2×#95C22×C71semidirect
619. C23×C4C23×C71semidirect
628. C2×C4⋊C4C23×C71semidirect
629. C2×C4⋊C4C23×C71semidirect
630. C2×C4⋊C4C23×C71semidirect
631. C2×C4⋊C4C23×C71semidirect
632. C2×C4⋊C4C23×C71semidirect
649. C2×C22⋊C4D4×C71semidirect
663. C2×C22⋊C4C23×C71semidirect
664. C2×C22⋊C4C23×C71semidirect
665. C2×C22⋊C4C23×C71semidirect
667. C2×C42C23×C71semidirect
668. #95C23×C71semidirect
669. #95C23×C71semidirect
670. #95C23×C71semidirect
671. #95C23×C71semidirect
672. #95C23×C71semidirect
673. #95C23×C71semidirect
809. C22⋊C4C2×D4×C71semidirect
868. C23#123×C71semidirect
966. C22C2×#123×C71semidirect
995. C2C71×#2418direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C712
C22×#120×C712
C22×C4×D4×C712
C23×C22⋊C4×C712
C71×#24182
C2×#399×C712
C2×#397×C712
C2×#394×C712
C2×#388×C712
C2×#386×C712
C2×#385×C712
C2×#380×C712
C2×#379×C712
C2×#241871