Finite Group Databasebeta

← C2×C107×#2418 #41060612

Subgroups — C2×C107×#2418 #41060612

Order 27392.

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×C107C211yesmaximal, characteristic, complemented
2C22×#120×C107C211yesmaximal, characteristic
3C22×C4×D4×C107C211yesmaximal, characteristic, complemented
4C23×C22⋊C4×C107C211yesmaximal, characteristic, complemented
5C107×#2418C2116yesmaximal, direct product factor
6C2×#399×C107C211yesmaximal, characteristic, complemented
7C2×#397×C107C211yesmaximal, characteristic, complemented
8C2×#394×C107C211yesmaximal, characteristic, complemented
9C2×#394×C107C211yesmaximal, characteristic, complemented
10C2×#388×C107C211yesmaximal, characteristic, complemented
11C2×#388×C107C211yesmaximal, characteristic, complemented
12C2×#386×C107C211yesmaximal, characteristic, complemented
13C2×#386×C107C211yesmaximal, characteristic, complemented
14C2×#385×C107C211yesmaximal, characteristic, complemented
15C2×#380×C107C211yesmaximal, characteristic, complemented
16C2×#379×C107C211yesmaximal, characteristic, complemented
17C26×C107C2211yescharacteristic
18C23×D4×C107C2211yescharacteristic
19C23×D4×C107C2211yescharacteristic
20C23×D4×C107C2211yescharacteristic
21C24×C4×C107C2211yescharacteristic
22C24×C4×C107C2211yescharacteristic
23C24×C4×C107C2211yescharacteristic, complemented
24C2×#123×C107—28no—
25C2×#123×C107C2218yescomplemented
26C2×#120×C107—28no—
27C2×#120×C107C2218yes—
28C2×C4×D4×C107—28no—
29C2×C4×D4×C107C2218yescomplemented
30C22×C4⋊C4×C107C2211yescharacteristic, complemented
31C22×C4⋊C4×C107C2211yescharacteristic, complemented
32C22×C4⋊C4×C107C2211yescharacteristic, complemented
33C22×C4⋊C4×C107C2211yescharacteristic, complemented
34C22×C4⋊C4×C107C2211yescharacteristic, complemented
35C22×C22⋊C4×C107—28no—
36C22×C22⋊C4×C107C2211yescharacteristic
37C22×C22⋊C4×C107C2211yescharacteristic
38C22×C22⋊C4×C107C2211yescharacteristic
39C22×C22⋊C4×C107C2211yescharacteristic
40C22×C22⋊C4×C107C2211yescharacteristic
41C22×C22⋊C4×C107C2211yescharacteristic
42C22×C22⋊C4×C107C2211yescharacteristic
43C22×C22⋊C4×C107C2211yescharacteristic
44C22×C22⋊C4×C107C2211yescharacteristic
45C22×C22⋊C4×C107C2211yescharacteristic
46C22×C22⋊C4×C107C2211yescharacteristic
47C22×C22⋊C4×C107C2211yescharacteristic
48C22×C22⋊C4×C107C2211yescharacteristic
49C22×C22⋊C4×C107C2218yescomplemented
50C22×C22⋊C4×C107C2211yescharacteristic, complemented
51C22×C22⋊C4×C107C2211yescharacteristic, complemented
52C22×C22⋊C4×C107C2211yescharacteristic, complemented
53C22×C42×C107C2211yescharacteristic, complemented
54#399×C107C2218yescomplemented
55#397×C107C2218yescomplemented
56#394×C107C2218yescomplemented
57#394×C107C2218yescomplemented
58#388×C107C2218yescomplemented
59#388×C107C2218yescomplemented
60#386×C107C2218yescomplemented
61#386×C107C2218yescomplemented
62#385×C107C2218yescomplemented
63#380×C107C2218yescomplemented
64#379×C107C2218yescomplemented
65C2×#95×C107C2211yescharacteristic, complemented
66C2×#95×C107C2211yescharacteristic, complemented
67C2×#95×C107C2211yescharacteristic, complemented
68C2×#95×C107C2211yescharacteristic, complemented
69C2×#95×C107C2211yescharacteristic, complemented
70C2×#95×C107C2211yescharacteristic, complemented
71C25×C107—24no—
72C25×C107—24no—
73C25×C107—24no—
74C25×C107—24no—
75C25×C107—24no—
76C25×C107—42no—
77C25×C107—42no—
78C25×C107C2311yescharacteristic
79C25×C107C2311yescharacteristic
80C25×C107C2311yescharacteristic
81C25×C107C2314yes—
82C25×C107C2311yescharacteristic
83C22×D4×C107—24no—
84C22×D4×C107—24no—
85C22×D4×C107—24no—
86C22×D4×C107—24no—
87C22×D4×C107—24no—
88C22×D4×C107—24no—
89C22×D4×C107—42no—
90C22×D4×C107—42no—
91C22×D4×C107D418yes—
92C22×D4×C107C2314yes—
93C22×D4×C107C2314yes—
94C22×D4×C107C2314yes—
95C23×C4×C107—24no—
96C23×C4×C107—24no—
97C23×C4×C107—24no—
98C23×C4×C107—24no—
99C23×C4×C107—24no—
100C23×C4×C107—24no—
101C23×C4×C107—42no—
102C23×C4×C107—42no—
103C23×C4×C107—42no—
104C23×C4×C107C2311yescharacteristic
105C23×C4×C107C2311yescharacteristic
106C23×C4×C107C2311yescharacteristic
107C23×C4×C107C2311yescharacteristic
108C23×C4×C107C2311yescharacteristic
109C23×C4×C107C2311yescharacteristic
110C23×C4×C107C2311yescharacteristic
111C23×C4×C107C2311yescharacteristic
112C23×C4×C107C2314yes—
113C23×C4×C107C2314yes—
114C23×C4×C107C2311yescharacteristic
115C23×C4×C107C2311yescharacteristic
116C23×C4×C107C2311yescharacteristic
117C23×C4×C107C2314yescomplemented
118#123×C107—232no—
119#120×C107—232no—
120C4×D4×C107—232no—
121C2×C4⋊C4×C107—24no—
122C2×C4⋊C4×C107—24no—
123C2×C4⋊C4×C107—24no—
124C2×C4⋊C4×C107—42no—
125C2×C4⋊C4×C107—42no—
126C2×C4⋊C4×C107C2314yescomplemented
127C2×C4⋊C4×C107C2314yescomplemented
128C2×C4⋊C4×C107C2314yescomplemented
129C2×C4⋊C4×C107C2314yescomplemented
130C2×C4⋊C4×C107C2314yescomplemented
131C2×C22⋊C4×C107—24no—
132C2×C22⋊C4×C107—24no—
133C2×C22⋊C4×C107—24no—
134C2×C22⋊C4×C107—24no—
135C2×C22⋊C4×C107—24no—
136C2×C22⋊C4×C107—24no—
137C2×C22⋊C4×C107—24no—
138C2×C22⋊C4×C107—24no—
139C2×C22⋊C4×C107—24no—
140C2×C22⋊C4×C107—24no—
141C2×C22⋊C4×C107—24no—
142C2×C22⋊C4×C107—24no—
143C2×C22⋊C4×C107—232no—
144C2×C22⋊C4×C107—42no—
145C2×C22⋊C4×C107—42no—
146C2×C22⋊C4×C107—42no—
147C2×C22⋊C4×C107D418yescomplemented
148C2×C22⋊C4×C107C2314yes—
149C2×C22⋊C4×C107C2314yes—
150C2×C22⋊C4×C107C2314yes—
151C2×C22⋊C4×C107C2314yes—
152C2×C22⋊C4×C107C2314yes—
153C2×C22⋊C4×C107C2314yes—
154C2×C22⋊C4×C107C2314yes—
155C2×C22⋊C4×C107C2314yes—
156C2×C22⋊C4×C107C2314yes—
157C2×C22⋊C4×C107C2314yes—
158C2×C22⋊C4×C107C2314yes—
159C2×C22⋊C4×C107C2314yes—
160C2×C22⋊C4×C107C2314yes—
161C2×C22⋊C4×C107C2314yescomplemented
162C2×C22⋊C4×C107C2314yescomplemented
163C2×C22⋊C4×C107C2314yescomplemented
164C2×C42×C107—24no—
165C2×C42×C107C2314yescomplemented
166#95×C107C2314yescomplemented
167#95×C107C2314yescomplemented
168#95×C107C2314yescomplemented
169#95×C107C2314yescomplemented
170#95×C107C2314yescomplemented
171#95×C107C2314yescomplemented
172C24×C107—22no—
173C24×C107—22no—
174C24×C107—22no—
175C24×C107—22no—
176C24×C107—232no—
177C24×C107—28no—
178C24×C107—22no—
179C24×C107—22no—
180C24×C107—22no—
181C24×C107—22no—
182C24×C107—22no—
183C24×C107—22no—
184C24×C107—22no—
185C24×C107—28no—
186C24×C107—28no—
187C24×C107—22no—
188C24×C107—22no—
189C24×C107—22no—
190C24×C107—22no—
191C24×C107—22no—
192C24×C107—22no—
193C24×C107—22no—
194C24×C107—22no—
195C24×C107—22no—
196C24×C107—22no—
197C24×C107—22no—
198C24×C107—28no—
199C24×C107—28no—
200C24×C107—44no—
201C24×C107—44no—
202C24×C107—416no—
203C24×C107—416no—
204C24×C107—416no—
205C24×C107—416no—
206C24×C107—416no—
207C24×C107—416no—
208C24×C107C2×D414yes—
209C24×C107C2×D414yes—
210C24×C107C2×D414yes—
211C24×C107#4114yes—
212C24×C107#4114yes—
213C24×C107#4114yes—
214C24×C107C2412yes—
215C24×C107C2412yes—
216C24×C107C2412yes—
217C24×C107C2412yes—
218C24×C107C2411yescharacteristic
219C2×D4×C107—232no—
220C2×D4×C107—28no—
221C2×D4×C107—28no—
222C2×D4×C107—28no—
223C2×D4×C107—28no—
224C2×D4×C107—28no—
225C2×D4×C107—28no—
226C2×D4×C107—44no—
227C2×D4×C107—44no—
228C2×D4×C107—416no—
229C2×D4×C107—416no—
230C2×D4×C107C2×D4116yes—
231C22×C4×C107—22no—
232C22×C4×C107—22no—
233C22×C4×C107—22no—
234C22×C4×C107—22no—
235C22×C4×C107—22no—
236C22×C4×C107—22no—
237C22×C4×C107—22no—
238C22×C4×C107—22no—
239C22×C4×C107—22no—
240C22×C4×C107—22no—
241C22×C4×C107—22no—
242C22×C4×C107—22no—
243C22×C4×C107—22no—
244C22×C4×C107—22no—
245C22×C4×C107—22no—
246C22×C4×C107—22no—
247C22×C4×C107—28no—
248C22×C4×C107—28no—
249C22×C4×C107—22no—
250C22×C4×C107—22no—
251C22×C4×C107—22no—
252C22×C4×C107—22no—
253C22×C4×C107—28no—
254C22×C4×C107—22no—
255C22×C4×C107—22no—
256C22×C4×C107—22no—
257C22×C4×C107—22no—
258C22×C4×C107—22no—
259C22×C4×C107—22no—
260C22×C4×C107—22no—
261C22×C4×C107—22no—
262C22×C4×C107—22no—
263C22×C4×C107—22no—
264C22×C4×C107—28no—
265C22×C4×C107—28no—
266C22×C4×C107—28no—
267C22×C4×C107—44no—
268C22×C4×C107—44no—
269C22×C4×C107—44no—
270C22×C4×C107—416no—
271C22×C4×C107—416no—
272C22×C4×C107—416no—
273C22×C4×C107C2×D414yes—
274C22×C4×C107C2×D414yes—
275C22×C4×C107C2×D414yes—
276C22×C4×C107C2412yes—
277C22×C4×C107C2412yes—
278C22×C4×C107C2412yes—
279C22×C4×C107C2412yes—
280C22×C4×C107C2412yes—
281C22×C4×C107C2412yes—
282C22×C4×C107C2412yes—
283C22×C4×C107C2412yes—
284C22×C4×C107C2412yes—
285C22×C4×C107C2412yes—
286C22×C4×C107C2412yes—
287C4⋊C4×C107—28no—
288C4⋊C4×C107—28no—
289C4⋊C4×C107—28no—
290C4⋊C4×C107—44no—
291C4⋊C4×C107—44no—
292C22⋊C4×C107—28no—
293C22⋊C4×C107—28no—
294C22⋊C4×C107—28no—
295C22⋊C4×C107—28no—
296C22⋊C4×C107—28no—
297C22⋊C4×C107—28no—
298C22⋊C4×C107—28no—
299C22⋊C4×C107—28no—
300C22⋊C4×C107—28no—
301C22⋊C4×C107—28no—
302C22⋊C4×C107—28no—
303C22⋊C4×C107—28no—
304C22⋊C4×C107—44no—
305C22⋊C4×C107—44no—
306C22⋊C4×C107—44no—
307C22⋊C4×C107C2×D4116yescomplemented
308C42×C107—28no—
309C23×C107—28no—
310C23×C107—28no—
311C23×C107—28no—
312C23×C107—28no—
313C23×C107—28no—
314C23×C107—28no—
315C23×C107—22no—
316C23×C107—22no—
317C23×C107—22no—
318C23×C107—22no—
319C23×C107—232no—
320C23×C107—28no—
321C23×C107—28no—
322C23×C107—28no—
323C23×C107—28no—
324C23×C107—28no—
325C23×C107—28no—
326C23×C107—28no—
327C23×C107—28no—
328C23×C107—28no—
329C23×C107—22no—
330C23×C107—22no—
331C23×C107—22no—
332C23×C107—22no—
333C23×C107—22no—
334C23×C107—22no—
335C23×C107—22no—
336C23×C107—22no—
337C23×C107—22no—
338C23×C107—22no—
339C23×C107—22no—
340C23×C107—22no—
341C23×C107—22no—
342C23×C107—22no—
343C23×C107—22no—
344C23×C107—22no—
345C23×C107—22no—
346C23×C107—22no—
347C23×C107—416no—
348C23×C107—416no—
349C23×C107—416no—
350C23×C107—416no—
351C23×C107—4128no—
352C23×C107—416no—
353C23×C107—44no—
354C23×C107—44no—
355C23×C107—416no—
356C23×C107—44no—
357C23×C107—44no—
358C23×C107—44no—
359C23×C107—44no—
360C23×C107—44no—
361C23×C107—44no—
362C23×C107—44no—
363C23×C107—44no—
364C23×C107—44no—
365C23×C107—44no—
366C23×C107#123116yescomplemented
367C23×C107C22×D414yes—
368C23×C107C22×D414yes—
369C23×C107C22×D414yes—
370C23×C107C22×D412yes—
371C23×C107C22×D412yes—
372C23×C107C2×#4114yes—
373C23×C107C2×#4114yes—
374C23×C107C2×#4114yes—
375C23×C107C2×#4112yes—
376C23×C107C2×#4112yes—
377C23×C107C2×#4112yes—
378C23×C107H(5,𝔽2)12yes—
379C23×C107H(5,𝔽2)12yes—
380C23×C107C2511yescharacteristic
381D4×C107—232no—
382D4×C107—416no—
383D4×C107—416no—
384C2×C4×C107—28no—
385C2×C4×C107—28no—
386C2×C4×C107—28no—
387C2×C4×C107—22no—
388C2×C4×C107—22no—
389C2×C4×C107—22no—
390C2×C4×C107—22no—
391C2×C4×C107—22no—
392C2×C4×C107—22no—
393C2×C4×C107—22no—
394C2×C4×C107—22no—
395C2×C4×C107—22no—
396C2×C4×C107—22no—
397C2×C4×C107—22no—
398C2×C4×C107—22no—
399C2×C4×C107—22no—
400C2×C4×C107—22no—
401C2×C4×C107—22no—
402C2×C4×C107—22no—
403C2×C4×C107—22no—
404C2×C4×C107—22no—
405C2×C4×C107—22no—
406C2×C4×C107—22no—
407C2×C4×C107—22no—
408C2×C4×C107—22no—
409C2×C4×C107—22no—
410C2×C4×C107—22no—
411C2×C4×C107—22no—
412C2×C4×C107—22no—
413C2×C4×C107—22no—
414C2×C4×C107—22no—
415C2×C4×C107—22no—
416C2×C4×C107—22no—
417C2×C4×C107—416no—
418C2×C4×C107—416no—
419C2×C4×C107—416no—
420C2×C4×C107—44no—
421C2×C4×C107—44no—
422C2×C4×C107—44no—
423C2×C4×C107—44no—
424C2×C4×C107—44no—
425C2×C4×C107—44no—
426C2×C4×C107—44no—
427C2×C4×C107—44no—
428C2×C4×C107C22×D414yes—
429C2×C4×C107C22×D414yes—
430C2×C4×C107C22×D414yes—
431C22×C107—24no—
432C22×C107—232no—
433C22×C107—24no—
434C22×C107—24no—
435C22×C107—24no—
436C22×C107—24no—
437C22×C107—24no—
438C22×C107—24no—
439C22×C107—24no—
440C22×C107—24no—
441C22×C107—24no—
442C22×C107—24no—
443C22×C107—24no—
444C22×C107—24no—
445C22×C107—24no—
446C22×C107—24no—
447C22×C107—464no—
448C22×C107—42no—
449C22×C107—42no—
450C22×C107—42no—
451C22×C107—416no—
452C22×C107—416no—
453C22×C107—416no—
454C22×C107—42no—
455C22×C107—42no—
456C22×C107—42no—
457C22×C107—42no—
458C22×C107—42no—
459C22×C107—42no—
460C22×C107—42no—
461C22×C107—42no—
462C22×C107—42no—
463C22×C107C2×#12314yes—
464C22×C107C2×#12318yescomplemented
465C22×C107#52514yes—
466C22×C107#53814yes—
467C22×C107D4214yes—
468C22×C107#54614yes—
469C22×C107#54614yes—
470C22×C107#55114yes—
471C22×C107C23×D411yescharacteristic
472C22×C107C23×D411yescharacteristic
473C22×C107C22×#4111yescharacteristic
474C22×C107C22×#4111yescharacteristic
475C22×C107C22×#4111yescharacteristic
476C22×C107C2×H(5,𝔽2)11yescharacteristic
477C22×C107C2×H(5,𝔽2)11yescharacteristic
478C4×C107—24no—
479C4×C107—24no—
480C4×C107—24no—
481C4×C107—42no—
482C4×C107—42no—
483C4×C107—42no—
484C4×C107—42no—
485C4×C107—42no—
486C4×C107—42no—
487C4×C107—42no—
488C4×C107—42no—
489C2×#2418C10711yesmaximal, characteristic, direct product factor, Sylow
490C2×C107—28no—
491C2×C107—44no—
492C2×C107—44no—
493C2×C107—44no—
494C2×C107#241818yesdirect product factor
495C2×C107C22×#12311yescharacteristic
496C2×C107C2×#52511yescharacteristic
497C2×C107C2×#53811yescharacteristic
498C2×C107C2×D4211yescharacteristic
499C2×C107C2×#54611yescharacteristic
500C2×C107C2×#54611yescharacteristic
501C2×C107C2×#55111yescharacteristic
502C22×#123C2×C10711yescharacteristic, complemented
503C22×#120C2×C10711yescharacteristic
504C22×C4×D4C2×C10711yescharacteristic, complemented
505C23×C22⋊C4C2×C10711yescharacteristic, complemented
506#2418C2×C107116yesdirect product factor
507C2×#399C2×C10711yescharacteristic, complemented
508C2×#397C2×C10711yescharacteristic, complemented
509C2×#394C2×C10711yescharacteristic, complemented
510C2×#394C2×C10711yescharacteristic, complemented
511C2×#388C2×C10711yescharacteristic, complemented
512C2×#388C2×C10711yescharacteristic, complemented
513C2×#386C2×C10711yescharacteristic, complemented
514C2×#386C2×C10711yescharacteristic, complemented
515C2×#385C2×C10711yescharacteristic, complemented
516C2×#380C2×C10711yescharacteristic, complemented
517C2×#379C2×C10711yescharacteristic, complemented
518C107C2×#241811yescharacteristic, direct product factor, Sylow
519C26C22×C10711yescharacteristic
520C23×D4C22×C10711yescharacteristic
521C23×D4C22×C10711yescharacteristic
522C23×D4C22×C10711yescharacteristic
523C24×C4C22×C10711yescharacteristic
524C24×C4C22×C10711yescharacteristic
525C24×C4C22×C10711yescharacteristic, complemented
526C2×#123—28no—
527C2×#123C22×C10718yescomplemented
528C2×#120—28no—
529C2×#120C22×C10718yes—
530C2×C4×D4—28no—
531C2×C4×D4C22×C10718yescomplemented
532C22×C4⋊C4C22×C10711yescharacteristic, complemented
533C22×C4⋊C4C22×C10711yescharacteristic, complemented
534C22×C4⋊C4C22×C10711yescharacteristic, complemented
535C22×C4⋊C4C22×C10711yescharacteristic, complemented
536C22×C4⋊C4C22×C10711yescharacteristic, complemented
537C22×C22⋊C4—28no—
538C22×C22⋊C4C22×C10711yescharacteristic
539C22×C22⋊C4C22×C10711yescharacteristic
540C22×C22⋊C4C22×C10711yescharacteristic
541C22×C22⋊C4C22×C10711yescharacteristic
542C22×C22⋊C4C22×C10711yescharacteristic
543C22×C22⋊C4C22×C10711yescharacteristic
544C22×C22⋊C4C22×C10711yescharacteristic
545C22×C22⋊C4C22×C10711yescharacteristic
546C22×C22⋊C4C22×C10711yescharacteristic
547C22×C22⋊C4C22×C10711yescharacteristic
548C22×C22⋊C4C22×C10711yescharacteristic
549C22×C22⋊C4C22×C10711yescharacteristic
550C22×C22⋊C4C22×C10711yescharacteristic
551C22×C22⋊C4C22×C10718yescomplemented
552C22×C22⋊C4C22×C10711yescharacteristic, complemented
553C22×C22⋊C4C22×C10711yescharacteristic, complemented
554C22×C22⋊C4C22×C10711yescharacteristic, complemented
555C22×C42C22×C10711yescharacteristic, complemented
556#399C22×C10718yescomplemented
557#397C22×C10718yescomplemented
558#394C22×C10718yescomplemented
559#394C22×C10718yescomplemented
560#388C22×C10718yescomplemented
561#388C22×C10718yescomplemented
562#386C22×C10718yescomplemented
563#386C22×C10718yescomplemented
564#385C22×C10718yescomplemented
565#380C22×C10718yescomplemented
566#379C22×C10718yescomplemented
567C2×#95C22×C10711yescharacteristic, complemented
568C2×#95C22×C10711yescharacteristic, complemented
569C2×#95C22×C10711yescharacteristic, complemented
570C2×#95C22×C10711yescharacteristic, complemented
571C2×#95C22×C10711yescharacteristic, complemented
572C2×#95C22×C10711yescharacteristic, complemented
573C25—24no—
574C25—24no—
575C25—24no—
576C25—24no—
577C25—24no—
578C25—42no—
579C25—42no—
580C25C23×C10711yescharacteristic
581C25C23×C10711yescharacteristic
582C25C23×C10711yescharacteristic
583C25C23×C10714yes—
584C25C23×C10711yescharacteristic
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×C10718yes—
594C22×D4C23×C10714yes—
595C22×D4C23×C10714yes—
596C22×D4C23×C10714yes—
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×C10711yescharacteristic
607C23×C4C23×C10711yescharacteristic
608C23×C4C23×C10711yescharacteristic
609C23×C4C23×C10711yescharacteristic
610C23×C4C23×C10711yescharacteristic
611C23×C4C23×C10711yescharacteristic
612C23×C4C23×C10711yescharacteristic
613C23×C4C23×C10711yescharacteristic
614C23×C4C23×C10714yes—
615C23×C4C23×C10714yes—
616C23×C4C23×C10711yescharacteristic
617C23×C4C23×C10711yescharacteristic
618C23×C4C23×C10711yescharacteristic
619C23×C4C23×C10714yescomplemented
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×C10714yescomplemented
629C2×C4⋊C4C23×C10714yescomplemented
630C2×C4⋊C4C23×C10714yescomplemented
631C2×C4⋊C4C23×C10714yescomplemented
632C2×C4⋊C4C23×C10714yescomplemented
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×C10718yescomplemented
650C2×C22⋊C4C23×C10714yes—
651C2×C22⋊C4C23×C10714yes—
652C2×C22⋊C4C23×C10714yes—
653C2×C22⋊C4C23×C10714yes—
654C2×C22⋊C4C23×C10714yes—
655C2×C22⋊C4C23×C10714yes—
656C2×C22⋊C4C23×C10714yes—
657C2×C22⋊C4C23×C10714yes—
658C2×C22⋊C4C23×C10714yes—
659C2×C22⋊C4C23×C10714yes—
660C2×C22⋊C4C23×C10714yes—
661C2×C22⋊C4C23×C10714yes—
662C2×C22⋊C4C23×C10714yes—
663C2×C22⋊C4C23×C10714yescomplemented
664C2×C22⋊C4C23×C10714yescomplemented
665C2×C22⋊C4C23×C10714yescomplemented
666C2×C42—24no—
667C2×C42C23×C10714yescomplemented
668#95C23×C10714yescomplemented
669#95C23×C10714yescomplemented
670#95C23×C10714yescomplemented
671#95C23×C10714yescomplemented
672#95C23×C10714yescomplemented
673#95C23×C10714yescomplemented
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×C10714yes—
711C24C2×D4×C10714yes—
712C24C2×D4×C10714yes—
713C24#41×C10714yes—
714C24#41×C10714yes—
715C24#41×C10714yes—
716C24C24×C10712yes—
717C24C24×C10712yes—
718C24C24×C10712yes—
719C24C24×C10712yes—
720C24C24×C10711yescharacteristic
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×C107116yes—
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×C10714yes—
776C22×C4C2×D4×C10714yes—
777C22×C4C2×D4×C10714yes—
778C22×C4C24×C10712yes—
779C22×C4C24×C10712yes—
780C22×C4C24×C10712yes—
781C22×C4C24×C10712yes—
782C22×C4C24×C10712yes—
783C22×C4C24×C10712yes—
784C22×C4C24×C10712yes—
785C22×C4C24×C10712yes—
786C22×C4C24×C10712yes—
787C22×C4C24×C10712yes—
788C22×C4C24×C10712yes—
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×C107116yescomplemented
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×C107116yescomplemented
869C23C22×D4×C10714yes—
870C23C22×D4×C10714yes—
871C23C22×D4×C10714yes—
872C23C22×D4×C10712yes—
873C23C22×D4×C10712yes—
874C23C2×#41×C10714yes—
875C23C2×#41×C10714yes—
876C23C2×#41×C10714yes—
877C23C2×#41×C10712yes—
878C23C2×#41×C10712yes—
879C23C2×#41×C10712yes—
880C23H(5,𝔽2)×C10712yes—
881C23H(5,𝔽2)×C10712yes—
882C23C25×C10711yescharacteristic
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×C10714yes—
931C2×C4C22×D4×C10714yes—
932C2×C4C22×D4×C10714yes—
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×C10714yes—
966C22C2×#123×C10718yescomplemented
967C22#525×C10714yes—
968C22#538×C10714yes—
969C22D42×C10714yes—
970C22#546×C10714yes—
971C22#546×C10714yes—
972C22#551×C10714yes—
973C22C23×D4×C10711yescharacteristic
974C22C23×D4×C10711yescharacteristic
975C22C22×#41×C10711yescharacteristic
976C22C22×#41×C10711yescharacteristic
977C22C22×#41×C10711yescharacteristic
978C22C2×H(5,𝔽2)×C10711yescharacteristic
979C22C2×H(5,𝔽2)×C10711yescharacteristic
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—
995C2C107×#241818yesdirect product factor
996C2C22×#123×C10711yescharacteristic
997C2C2×#525×C10711yescharacteristic
998C2C2×#538×C10711yescharacteristic
999C2C2×D42×C10711yescharacteristic
1000C2C2×#546×C10711yescharacteristic
1001C2C2×#546×C10711yescharacteristic
1002C2C2×#551×C10711yescharacteristic
subgroupG/H
center, socleC24×C107C24
commutator, Frattini, cosocleC23C25×C107
prime radicalC22×#120×C107C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#123×C107C2semidirect
3. C22×C4×D4×C107C2semidirect
4. C23×C22⋊C4×C107C2semidirect
5. C107×#2418C2direct (N × H)
6. C2×#399×C107C2semidirect
7. C2×#397×C107C2semidirect
8. C2×#394×C107C2semidirect
9. C2×#394×C107C2semidirect
10. C2×#388×C107C2semidirect
11. C2×#388×C107C2semidirect
12. C2×#386×C107C2semidirect
13. C2×#386×C107C2semidirect
14. C2×#385×C107C2semidirect
15. C2×#380×C107C2semidirect
16. C2×#379×C107C2semidirect
23. C24×C4×C107C22semidirect
25. C2×#123×C107C22semidirect
29. C2×C4×D4×C107C22semidirect
30. C22×C4⋊C4×C107C22semidirect
31. C22×C4⋊C4×C107C22semidirect
32. C22×C4⋊C4×C107C22semidirect
33. C22×C4⋊C4×C107C22semidirect
34. C22×C4⋊C4×C107C22semidirect
49. C22×C22⋊C4×C107C22semidirect
50. C22×C22⋊C4×C107C22semidirect
51. C22×C22⋊C4×C107C22semidirect
52. C22×C22⋊C4×C107C22semidirect
53. C22×C42×C107C22semidirect
54. #399×C107C22semidirect
55. #397×C107C22semidirect
56. #394×C107C22semidirect
57. #394×C107C22semidirect
58. #388×C107C22semidirect
59. #388×C107C22semidirect
60. #386×C107C22semidirect
61. #386×C107C22semidirect
62. #385×C107C22semidirect
63. #380×C107C22semidirect
64. #379×C107C22semidirect
65. C2×#95×C107C22semidirect
66. C2×#95×C107C22semidirect
67. C2×#95×C107C22semidirect
68. C2×#95×C107C22semidirect
69. C2×#95×C107C22semidirect
70. C2×#95×C107C22semidirect
117. C23×C4×C107C23semidirect
126. C2×C4⋊C4×C107C23semidirect
127. C2×C4⋊C4×C107C23semidirect
128. C2×C4⋊C4×C107C23semidirect
129. C2×C4⋊C4×C107C23semidirect
130. C2×C4⋊C4×C107C23semidirect
147. C2×C22⋊C4×C107D4semidirect
161. C2×C22⋊C4×C107C23semidirect
162. C2×C22⋊C4×C107C23semidirect
163. C2×C22⋊C4×C107C23semidirect
165. C2×C42×C107C23semidirect
166. #95×C107C23semidirect
167. #95×C107C23semidirect
168. #95×C107C23semidirect
169. #95×C107C23semidirect
170. #95×C107C23semidirect
171. #95×C107C23semidirect
307. C22⋊C4×C107C2×D4semidirect
366. C23×C107#123semidirect
464. C22×C107C2×#123semidirect
489. C2×#2418C107direct (N × H)
494. C2×C107#2418direct (N × H)
502. C22×#123C2×C107semidirect
504. C22×C4×D4C2×C107semidirect
505. C23×C22⋊C4C2×C107semidirect
506. #2418C2×C107direct (N × H)
507. C2×#399C2×C107semidirect
508. C2×#397C2×C107semidirect
509. C2×#394C2×C107semidirect
510. C2×#394C2×C107semidirect
511. C2×#388C2×C107semidirect
512. C2×#388C2×C107semidirect
513. C2×#386C2×C107semidirect
514. C2×#386C2×C107semidirect
515. C2×#385C2×C107semidirect
516. C2×#380C2×C107semidirect
517. C2×#379C2×C107semidirect
518. C107C2×#2418direct (N × H)
525. C24×C4C22×C107semidirect
527. C2×#123C22×C107semidirect
531. C2×C4×D4C22×C107semidirect
532. C22×C4⋊C4C22×C107semidirect
533. C22×C4⋊C4C22×C107semidirect
534. C22×C4⋊C4C22×C107semidirect
535. C22×C4⋊C4C22×C107semidirect
536. C22×C4⋊C4C22×C107semidirect
551. C22×C22⋊C4C22×C107semidirect
552. C22×C22⋊C4C22×C107semidirect
553. C22×C22⋊C4C22×C107semidirect
554. C22×C22⋊C4C22×C107semidirect
555. C22×C42C22×C107semidirect
556. #399C22×C107semidirect
557. #397C22×C107semidirect
558. #394C22×C107semidirect
559. #394C22×C107semidirect
560. #388C22×C107semidirect
561. #388C22×C107semidirect
562. #386C22×C107semidirect
563. #386C22×C107semidirect
564. #385C22×C107semidirect
565. #380C22×C107semidirect
566. #379C22×C107semidirect
567. C2×#95C22×C107semidirect
568. C2×#95C22×C107semidirect
569. C2×#95C22×C107semidirect
570. C2×#95C22×C107semidirect
571. C2×#95C22×C107semidirect
572. C2×#95C22×C107semidirect
619. C23×C4C23×C107semidirect
628. C2×C4⋊C4C23×C107semidirect
629. C2×C4⋊C4C23×C107semidirect
630. C2×C4⋊C4C23×C107semidirect
631. C2×C4⋊C4C23×C107semidirect
632. C2×C4⋊C4C23×C107semidirect
649. C2×C22⋊C4D4×C107semidirect
663. C2×C22⋊C4C23×C107semidirect
664. C2×C22⋊C4C23×C107semidirect
665. C2×C22⋊C4C23×C107semidirect
667. C2×C42C23×C107semidirect
668. #95C23×C107semidirect
669. #95C23×C107semidirect
670. #95C23×C107semidirect
671. #95C23×C107semidirect
672. #95C23×C107semidirect
673. #95C23×C107semidirect
809. C22⋊C4C2×D4×C107semidirect
868. C23#123×C107semidirect
966. C22C2×#123×C107semidirect
995. C2C107×#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×C1072
C22×#120×C1072
C22×C4×D4×C1072
C23×C22⋊C4×C1072
C107×#24182
C2×#399×C1072
C2×#397×C1072
C2×#394×C1072
C2×#388×C1072
C2×#386×C1072
C2×#385×C1072
C2×#380×C1072
C2×#379×C1072
C2×#2418107