Finite Group Databasebeta

← C4×#19099108 #34446793

Subgroups — C4×#19099108 #34446793

Order 20224.

3526 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099108C211yesmaximal, characteristic
2C2×C4×#11929623C212yesmaximal, complemented
3#23765971C211yesmaximal, characteristic, complemented
4C4×#14579160C211yesmaximal, characteristic, complemented
5#23765964C211yesmaximal, characteristic, complemented
6C4×#14579157C211yesmaximal, characteristic, complemented
7#23765941C212yesmaximal, complemented
8C4×#14579147C212yesmaximal, complemented
9#121×Dic79C211yesmaximal, characteristic, complemented
10C4×#14579135C211yesmaximal, characteristic, complemented
11#23765910C212yesmaximal, complemented
12C4×#14579133C212yesmaximal, complemented
13#23765906C211yesmaximal, characteristic, complemented
14#23765885C212yesmaximal, complemented
15#23765862C211yesmaximal, characteristic, complemented
16#23765860C212yesmaximal, complemented
17#23765858C211yesmaximal, characteristic, complemented
18#23765802C211yesmaximal, characteristic, complemented
19C4×D4×Dic79C211yesmaximal, characteristic, complemented
20C4×#14579123C211yesmaximal, characteristic, complemented
21C4×(C22⋊D79)⋊C4C212yesmaximal, complemented
22C2×C42×Dic79C211yesmaximal, characteristic, complemented
23C4×#121×C79C211yesmaximal, characteristic, complemented
24C22×#11929623C2212yes—
25#19099108C4116yesdirect product factor
26C2×#14579160C2211yescharacteristic
27C2×#14579157C2211yescharacteristic
28C2×#14579147C2212yes—
29C2×#14579135C2211yescharacteristic
30C2×#14579133C2212yes—
31C4×#11929623—216no—
32C2×C4×Dic158C2212yes—
33C2×#14579126C2212yes—
34C2×C4×D316C2211yescharacteristic
35C2×D4×Dic79C2212yes—
36C2×D4×Dic79C2211yescharacteristic
37C2×D4×Dic79C2211yescharacteristic
38C2×#14579123C2211yescharacteristic
39C2×#14579123C2211yescharacteristic
40C2×C4×C22⋊D79C2212yes—
41C2×C4×C22⋊D79C2212yes—
42C2×C4×C22⋊D79C2212yes—
43C2×(C22⋊D79)⋊C4C2212yes—
44C2×(C22⋊D79)⋊C4C2212yes—
45C2×(C22⋊D79)⋊C4C2212yes—
46C2×(C22⋊D79)⋊C4C2212yes—
47C2×#14579119C2212yes—
48C2×#14579117C2212yes—
49C2×#14579117C2212yes—
50C22×C4×Dic79C2212yes—
51C22×C4×Dic79C2211yescharacteristic
52C22×C4×Dic79C2211yescharacteristic
53C22×C4×Dic79C2211yescharacteristic
54C22×C4×Dic79C2211yescharacteristic
55C22×C4×Dic79C2211yescharacteristic
56C22×C4×Dic79C2211yescharacteristic
57C2×C42×D79C2212yes—
58#19098467C2212yes—
59#19098467C2212yes—
60#19098466C2211yescharacteristic
61#19098465C2211yescharacteristic
62#19098464C2211yescharacteristic
63#19098463C2212yes—
64#19098463C2212yes—
65#19098463C2212yes—
66#19098463C2212yes—
67#19098462C2211yescharacteristic
68#19098461C2211yescharacteristic
69#19098460C2212yes—
70#19098459C2211yescharacteristic
71#19098458C2212yes—
72#19098457C2212yes—
73#19098456C2212yes—
74#19098455C2212yes—
75#19098454C2212yes—
76#19098453C2212yes—
77#19098452C2212yes—
78#19098451C2212yes—
79#19098443C2212yes—
80#19098442C2212yes—
81#19098440C2212yes—
82#19098432C2211yescharacteristic
83#19098432C2211yescharacteristic
84#19098427C2212yes—
85#19098423C2211yescharacteristic
86#19098421C2212yes—
87C4⋊C4×Dic79C2211yescharacteristic
88C4⋊C4×Dic79C2211yescharacteristic
89C4⋊C4×Dic79C2211yescharacteristic
90C4⋊C4×Dic79C2211yescharacteristic
91C4×Dic79⋊C4C2212yes—
92C4×C4⋊Dic79C2211yescharacteristic
93#19098414C2212yes—
94#19098414C2212yes—
95C22⋊C4×Dic79C2212yes—
96C22⋊C4×Dic79C2212yes—
97C22⋊C4×Dic79C2212yes—
98C22⋊C4×Dic79C2212yes—
99C4×(C2×D79)⋊C4C2212yes—
100C4×(C2×D79)⋊C4C2212yes—
101C4×C22⋊Dic79C2212yes—
102#19098410C2212yes—
103#19098410C2212yes—
104#19098410C2212yes—
105#19098410C2212yes—
106C42×Dic79C2211yescharacteristic
107C42×Dic79C2211yescharacteristic
108C42×Dic79C2211yescharacteristic
109C42×Dic79C2211yescharacteristic
110C42×Dic79C2211yescharacteristic
111C42×Dic79C2211yescharacteristic
112C42×Dic79C2211yescharacteristic
113C42×Dic79C2211yescharacteristic
114C2×#121×C79C2211yescharacteristic
115C2×C4×D4×C79C2212yes—
116C2×C4×D4×C79C2211yescharacteristic
117C22×C42×C79C2211yescharacteristic
118#390×C79C2211yescharacteristic
119#389×C79C2211yescharacteristic
120#388×C79C2212yes—
121#386×C79C2212yes—
122#380×C79C2211yescharacteristic
123C4×C4⋊C4×C79C2211yescharacteristic
124C4×C22⋊C4×C79C2212yes—
125C2×#11929623—28no—
126C2×#11929623—28no—
127C2×#11929623C2×C4116yescomplemented
128C22×Dic158C2312yes—
129C22×D316C2311yescharacteristic
130C22×C22⋊D79C2312yes—
131C22×C22⋊D79C2312yes—
132C22×C22⋊D79C2312yes—
133C23×Dic79C2312yes—
134C23×Dic79C2311yescharacteristic
135C23×Dic79C2312yes—
136C23×Dic79C2311yescharacteristic
137C23×Dic79C2311yescharacteristic
138C23×Dic79C2311yescharacteristic
139C22×C4×D79C2312yes—
140C22×C4×D79C2312yes—
141C22×C4×D79C2312yes—
142#14579160C2×C418yescomplemented
143#14579157C2×C418yescomplemented
144#14579147C2×C4116yescomplemented
145#14579135C2×C418yescomplemented
146#14579133C2×C4116yescomplemented
147C4×Dic158—28no—
148#14579126—28no—
149C4×D316—24no—
150D4×Dic79—28no—
151D4×Dic79—24no—
152D4×Dic79C2×C418yescomplemented
153#14579123—24no—
154#14579123C2×C418yescomplemented
155C4×C22⋊D79—28no—
156C4×C22⋊D79—28no—
157C4×C22⋊D79—28no—
158(C22⋊D79)⋊C4—28no—
159(C22⋊D79)⋊C4—28no—
160(C22⋊D79)⋊C4—28no—
161(C22⋊D79)⋊C4C2×C4116yescomplemented
162#14579119—28no—
163#14579117—28no—
164#14579117—28no—
165C2×C4⋊Dic79C2311yescharacteristic
166C2×C4⋊Dic79C2311yescharacteristic
167C2×C4⋊Dic79C2312yes—
168C2×C4⋊Dic79C2311yescharacteristic
169C2×Dic79⋊C4C2312yes—
170C2×Dic79⋊C4C2312yes—
171C2×Dic79⋊C4C2312yes—
172C2×Dic79⋊C4C2312yes—
173C2×Dic79⋊C4C2312yes—
174C2×Dic79⋊C4C2312yes—
175C2×Dic79⋊C4C2312yes—
176C2×C22⋊Dic79C2312yes—
177C2×C22⋊Dic79C2312yes—
178C2×C22⋊Dic79C2312yes—
179C2×C22⋊Dic79C2312yes—
180C2×C22⋊Dic79C2312yes—
181C2×(C2×D79)⋊C4C2312yes—
182C2×(C2×D79)⋊C4C2312yes—
183C2×(C2×D79)⋊C4C2312yes—
184C2×(C2×D79)⋊C4C2312yes—
185C2×(C2×D79)⋊C4C2312yes—
186C2×(C2×D79)⋊C4C2312yes—
187C2×(C2×D79)⋊C4C2312yes—
188C2×(C2×D79)⋊C4C2312yes—
189C2×C4×Dic79—24no—
190C2×C4×Dic79—28no—
191C2×C4×Dic79—24no—
192C2×C4×Dic79—24no—
193C2×C4×Dic79—24no—
194C2×C4×Dic79C2×C418yescomplemented
195C2×C4×Dic79D418yescomplemented
196C2×C4×Dic79C2311yescharacteristic
197C2×C4×Dic79C2311yescharacteristic
198C2×C4×Dic79C2311yescharacteristic
199C2×C4×Dic79C2311yescharacteristic
200C2×C4×Dic79C2311yescharacteristic
201C2×C4×Dic79C2311yescharacteristic
202C2×C4×Dic79C2311yescharacteristic
203C2×C4×Dic79C2311yescharacteristic
204C2×C4×Dic79C2311yescharacteristic
205C2×C4×Dic79C2311yescharacteristic
206C2×C4×Dic79C2311yescharacteristic
207C2×C4×Dic79C2311yescharacteristic
208C2×C4×Dic79C2311yescharacteristic
209C2×C4×Dic79C2312yes—
210C2×C4×Dic79C2312yes—
211C2×C4×Dic79C2312yes—
212C2×C4×Dic79C2312yes—
213C2×C4×Dic79C2312yes—
214C2×C4×Dic79C2311yescharacteristic
215C2×C4×Dic79C2311yescharacteristic
216C2×C4×Dic79C2311yescharacteristic
217C2×C4×Dic79C2311yescharacteristic
218C2×C4×Dic79C2311yescharacteristic
219C2×C4×Dic79C2311yescharacteristic
220C2×C4×Dic79C2311yescharacteristic
221C2×C4×Dic79C2311yescharacteristic
222C2×C4×Dic79C2311yescharacteristic
223C2×C4×Dic79C2311yescharacteristic
224C2×C4×Dic79C2311yescharacteristic
225C42×D79—28no—
226C79⋊#95C2312yes—
227C79⋊#95C2312yes—
228C79⋊#95C2312yes—
229C79⋊#95C2312yes—
230C79⋊#95C2312yes—
231C79⋊#95C2312yes—
232C79⋊#95C2312yes—
233C79⋊#95C2312yes—
234C79⋊#95C2312yes—
235C22×D4×C79C2312yes—
236C22×D4×C79C2311yescharacteristic
237C23×C4×C79C2312yes—
238C23×C4×C79C2311yescharacteristic
239C23×C4×C79C2311yescharacteristic
240C23×C4×C79C2311yescharacteristic
241#121×C79C2×C418yescomplemented
242C4×D4×C79—28no—
243C4×D4×C79—24no—
244C2×C4⋊C4×C79C2311yescharacteristic
245C2×C4⋊C4×C79C2311yescharacteristic
246C2×C4⋊C4×C79C2312yes—
247C2×C4⋊C4×C79C2311yescharacteristic
248C2×C22⋊C4×C79C2312yes—
249C2×C22⋊C4×C79C2312yes—
250C2×C22⋊C4×C79C2312yes—
251C2×C22⋊C4×C79C2312yes—
252C2×C22⋊C4×C79C2312yes—
253C2×C42×C79—24no—
254C2×C42×C79C2311yescharacteristic
255C2×C42×C79C2311yescharacteristic
256C2×C42×C79C2311yescharacteristic
257C2×C42×C79C2312yes—
258C2×C42×C79C2311yescharacteristic
259#95×C79C2312yes—
260#95×C79C2312yes—
261#95×C79C2312yes—
262C23×D79C2412yes—
263#11929623—264no—
264C2×Dic158—24no—
265C2×Dic158—24no—
266C2×Dic158C22×C418yes—
267C2×D316—22no—
268C2×D316—22no—
269C2×D316C22×C414yes—
270C2×C22⋊D79—24no—
271C2×C22⋊D79—24no—
272C2×C22⋊D79—24no—
273C2×C22⋊D79—24no—
274C2×C22⋊D79—24no—
275C2×C22⋊D79—24no—
276C2×C22⋊D79C22×C418yes—
277C2×C22⋊D79C22×C418yes—
278C2×C22⋊D79C22×C418yes—
279C22×Dic79—24no—
280C22×Dic79—24no—
281C22×Dic79—22no—
282C22×Dic79—22no—
283C22×Dic79—22no—
284C22×Dic79—22no—
285C22×Dic79—22no—
286C22×Dic79—22no—
287C22×Dic79—24no—
288C22×Dic79—24no—
289C22×Dic79—24no—
290C22×Dic79—22no—
291C22×Dic79C22×C418yes—
292C22×Dic79C22×C414yes—
293C22×Dic79C22×C414yes—
294C22×Dic79C2×D414yes—
295C22×Dic79C2×D414yes—
296C22×Dic79#4114yes—
297C22×Dic79C2412yes—
298C22×Dic79C2412yes—
299C22×Dic79C2412yes—
300C22×Dic79C2411yescharacteristic
301C22×Dic79C2411yescharacteristic
302C22×Dic79C2411yescharacteristic
303C22×Dic79C2411yescharacteristic
304C22×Dic79C2411yescharacteristic
305C22×Dic79C2411yescharacteristic
306C22×Dic79C2411yescharacteristic
307C22×Dic79C2411yescharacteristic
308C2×C4×D79—24no—
309C2×C4×D79—24no—
310C2×C4×D79—24no—
311C2×C4×D79—24no—
312C2×C4×D79—24no—
313C2×C4×D79—24no—
314C2×C4×D79—24no—
315C2×C4×D79—24no—
316C2×C4×D79C22×C418yes—
317C4⋊Dic79—24no—
318C4⋊Dic79—22no—
319C4⋊Dic79—22no—
320C4⋊Dic79C22×C414yes—
321Dic79⋊C4—24no—
322Dic79⋊C4—24no—
323Dic79⋊C4—24no—
324Dic79⋊C4—24no—
325Dic79⋊C4—24no—
326Dic79⋊C4—24no—
327Dic79⋊C4C22×C418yes—
328C22⋊Dic79—24no—
329C22⋊Dic79—24no—
330C22⋊Dic79—24no—
331C22⋊Dic79—24no—
332C22⋊Dic79C22×C418yes—
333(C2×D79)⋊C4—24no—
334(C2×D79)⋊C4—24no—
335(C2×D79)⋊C4—24no—
336(C2×D79)⋊C4—24no—
337(C2×D79)⋊C4—24no—
338(C2×D79)⋊C4—24no—
339(C2×D79)⋊C4C22×C418yes—
340(C2×D79)⋊C4C22×C418yes—
341C4×Dic79—24no—
342C4×Dic79—24no—
343C4×Dic79—24no—
344C4×Dic79—24no—
345C4×Dic79—22no—
346C4×Dic79—22no—
347C4×Dic79—22no—
348C4×Dic79—22no—
349C4×Dic79—22no—
350C4×Dic79—22no—
351C4×Dic79—22no—
352C4×Dic79—22no—
353C4×Dic79—22no—
354C4×Dic79—22no—
355C4×Dic79—24no—
356C4×Dic79—22no—
357C4×Dic79—22no—
358C4×Dic79—22no—
359C4×Dic79C22×C414yes—
360C4×Dic79C22×C414yes—
361C4×Dic79C22×C414yes—
362C4×Dic79C22×C414yes—
363C4×Dic79C2×D414yes—
364C4×Dic79C2×D414yes—
365C4×Dic79C2×D414yes—
366C4×Dic79C2×D414yes—
367C4×Dic79#4114yescomplemented
368C4×Dic79#4114yescomplemented
369C4×Dic79#4114yescomplemented
370C24×C79C2412yes—
371C24×C79C2411yescharacteristic
372C2×D4×C79—24no—
373C2×D4×C79—24no—
374C2×D4×C79—22no—
375C2×D4×C79—22no—
376C2×D4×C79C22×C418yes—
377C2×D4×C79C22×C414yes—
378C22×C4×C79—22no—
379C22×C4×C79—22no—
380C22×C4×C79—22no—
381C22×C4×C79—22no—
382C22×C4×C79—22no—
383C22×C4×C79—22no—
384C22×C4×C79—22no—
385C22×C4×C79—24no—
386C22×C4×C79—24no—
387C22×C4×C79—24no—
388C22×C4×C79C22×C414yes—
389C22×C4×C79C2×D414yes—
390C22×C4×C79C2412yes—
391C22×C4×C79C2412yes—
392C22×C4×C79C2412yes—
393C22×C4×C79C2411yescharacteristic
394C22×C4×C79C2411yescharacteristic
395C22×C4×C79C2411yescharacteristic
396C22×C4×C79C2411yescharacteristic
397C22×C4×C79C2411yescharacteristic
398C22×C4×C79C2411yescharacteristic
399C4⋊C4×C79—24no—
400C4⋊C4×C79—22no—
401C4⋊C4×C79—22no—
402C4⋊C4×C79C22×C414yes—
403C22⋊C4×C79—24no—
404C22⋊C4×C79—24no—
405C22⋊C4×C79—24no—
406C22⋊C4×C79—24no—
407C22⋊C4×C79C22×C418yes—
408C42×C79—24no—
409C42×C79—22no—
410C42×C79—22no—
411C42×C79—22no—
412C42×C79#4114yescomplemented
413C23×C79—21no—
414C23×C79—21no—
415C23×C79—21no—
416C23×C79—21no—
417C23×C79—22no—
418C23×C79—22no—
419C23×C79—22no—
420C23×C79—22no—
421C23×C79—22no—
422C23×C79—22no—
423C23×C79C23×C414yes—
424C23×C79C23×C412yes—
425C23×C79C22×D412yes—
426C23×C79C2×#4112yes—
427C23×C79C2511yescharacteristic
428C22×D79—22no—
429C22×D79—22no—
430C22×D79—22no—
431C22×D79—22no—
432C22×D79—22no—
433C22×D79—22no—
434C22×D79C23×C414yes—
435D4×C79—216no—
436D4×C79—28no—
437C2×C4×C79—28no—
438C2×C4×C79—22no—
439C2×C4×C79—21no—
440C2×C4×C79—21no—
441C2×C4×C79—21no—
442C2×C4×C79—21no—
443C2×C4×C79—21no—
444C2×C4×C79—22no—
445C2×C4×C79—21no—
446C2×C4×C79—21no—
447C2×C4×C79—21no—
448C2×C4×C79—28no—
449C2×C4×C79—28no—
450C2×C4×C79—22no—
451C2×C4×C79—22no—
452C2×C4×C79—22no—
453C2×C4×C79—22no—
454C2×C4×C79—22no—
455C2×C4×C79—22no—
456C2×C4×C79—48no—
457C2×C4×C79C23×C412yes—
458C2×C4×C79C23×C414yes—
459C2×C4×C79C23×C412yes—
460C2×C4×C79C22×D412yes—
461C2×C4×C79C22×D412yes—
462C2×C4×C79C2×#4112yes—
463C2×C4×C79C2×#4112yes—
464C2×C4×C79C2×#4112yes—
465C2×C4×C79C2×#4112yes—
466C2×C4×C79C2×#4112yes—
467C2×C4×C79C2×#4112yes—
468C22⋊D79—216no—
469C22⋊D79—216no—
470C22⋊D79—216no—
471C2×Dic79—28no—
472C2×Dic79—22no—
473C2×Dic79—21no—
474C2×Dic79—21no—
475C2×Dic79—21no—
476C2×Dic79—21no—
477C2×Dic79—21no—
478C2×Dic79—21no—
479C2×Dic79—21no—
480C2×Dic79—21no—
481C2×Dic79—22no—
482C2×Dic79—216no—
483C2×Dic79—28no—
484C2×Dic79—28no—
485C2×Dic79—22no—
486C2×Dic79—22no—
487C2×Dic79—22no—
488C2×Dic79—22no—
489C2×Dic79—22no—
490C2×Dic79—22no—
491C2×Dic79—48no—
492C2×Dic79C4×D4116yescomplemented
493C2×Dic79C23×C412yes—
494C2×Dic79C23×C414yes—
495C2×Dic79C23×C412yes—
496C2×Dic79C23×C412yes—
497C2×Dic79C23×C412yes—
498C2×Dic79C22×D412yes—
499C2×Dic79C22×D412yes—
500C2×Dic79C22×D412yes—
501C2×Dic79C22×D412yes—
502C2×Dic79C2×#4112yes—
503C2×Dic79C2×#4112yes—
504C2×Dic79C2×#4112yes—
505C2×Dic79C2×#4112yes—
506C2×Dic79C2×#4112yes—
507C2×Dic79C2×#4112yes—
508C2×Dic79C2×#4112yes—
509C2×Dic79C2×#4112yes—
510D316—28no—
511C4×D79—216no—
512C4×D79—48no—
513C4×D79—48no—
514Dic158—216no—
515C22×C79—22no—
516C22×C79—22no—
517C22×C79—22no—
518C22×C79—22no—
519C22×C79—22no—
520C22×C79—22no—
521C22×C79—24no—
522C22×C79—24no—
523C22×C79—24no—
524C22×C79—42no—
525C22×C79—42no—
526C22×C79—42no—
527C22×C79—42no—
528C22×C79C2×C4×D414yes—
529C22×C79C24×C411yescharacteristic
530C22×C79C23×D411yescharacteristic
531C22×C79C22×#4111yescharacteristic
532C22×C79C22×#4111yescharacteristic
533C22×C79C22×#4111yescharacteristic
534C22×C79C22×#4111yescharacteristic
535C22×C79C22×#4111yescharacteristic
536C2×D79—24no—
537C2×D79—24no—
538C2×D79—24no—
539C2×D79—42no—
540C2×D79—42no—
541C2×D79—42no—
542C2×D79—42no—
543C4×C79—24no—
544C4×C79—22no—
545C4×C79—22no—
546C4×C79—22no—
547C4×C79—22no—
548C4×C79—42no—
549C4×C79—42no—
550C4×C79C4×#4114yescomplemented
551C4×C79#53214yescomplemented
552Dic79—24no—
553Dic79—22no—
554Dic79—22no—
555Dic79—22no—
556Dic79—22no—
557Dic79—42no—
558Dic79—42no—
559Dic79C2×C4×D414yes—
560Dic79C2×C4×D414yes—
561Dic79C4×#4114yescomplemented
562Dic79#53214yescomplemented
563C4×#532—791nomaximal, Sylow
564C2×C79—24no—
565C2×C79—44no—
566C2×C79C22×C4×D411yescharacteristic
567C2×C79C2×C4×#4111yescharacteristic
568C2×C79C2×C4×#4111yescharacteristic
569C2×C79C2×#53211yescharacteristic
570C2×C79C2×#53211yescharacteristic
571C2×C79#344411yescharacteristic
572C2×C79#344411yescharacteristic
573D79—44no—
574C2×#532—791no—
575C2×C4×#41—792no—
576C4×C4⋊Q8—791no—
577C4×C4⋊Q8—791no—
578C4×#127—791no—
579C4×#127—791no—
580C4×#124—792no—
581C4×#124—792no—
582C4×#121—791no—
583C4×#121—792no—
584C4×#121—791no—
585C4×#121—791no—
586C4×#121—792no—
587C4×#121D7911yescharacteristic, complemented
588#2297—792no—
589#2293—791no—
590#2293—791no—
591#2293—792no—
592#2285—791no—
593C42×D4—791no—
594C42×D4—792no—
595C42×D4—791no—
596C2×C43—791no—
597C79C4×#53211yescharacteristic, complemented, Sylow
598C22×#41—792no—
599#532—7916no—
600C2×C4⋊Q8—791no—
601C2×#127—791no—
602C2×#124—792no—
603C2×#121—792no—
604C2×#121—791no—
605C2×#121C2×D7911yescharacteristic
606C4×#41—15816no—
607C2×C4×Q8—792no—
608C2×C4×Q8—792no—
609C2×C4×D4—791no—
610C2×C4×D4—791no—
611C2×C4×D4—792no—
612C2×C4×D4—792no—
613C2×C4×D4—792no—
614C2×C4×D4—792no—
615C2×C4×D4—791no—
616C2×C4×D4—791no—
617C2×C4×D4—792no—
618C2×C4×D4—792no—
619C2×C4×D4—792no—
620C2×C4×D4—792no—
621C2×C4×D4—791no—
622C2×C4×D4C2×D7911yescharacteristic
623C2×C4×D4C2×D7912yes—
624C2×#117—792no—
625C2×#117—792no—
626C2×#117—792no—
627C22×C42—791no—
628C22×C42—791no—
629C22×C42—792no—
630C22×C42—791no—
631C22×C42—791no—
632C22×C42—791no—
633C22×C42—791no—
634C22×C42—792no—
635C22×C42C2×D7911yescharacteristic
636#391—792no—
637#391—792no—
638#390—791no—
639#390—791no—
640#390—792no—
641#390—792no—
642#390—792no—
643#390—792no—
644#390—791no—
645#390C2×D7911yescharacteristic
646#389—792no—
647#389—791no—
648#389—791no—
649#389—791no—
650#389—792no—
651#389C2×D7911yescharacteristic
652#388—792no—
653#388—792no—
654#388—792no—
655#388—792no—
656#388—792no—
657#388—792no—
658#388—792no—
659#388C2×D7912yes—
660#386—792no—
661#386—792no—
662#386—792no—
663#386C2×D7912yes—
664#384—791no—
665#384—791no—
666#382—792no—
667#380—791no—
668#380—792no—
669#380C2×D7911yescharacteristic
670C4×C4⋊C4—791no—
671C4×C4⋊C4—791no—
672C4×C4⋊C4—791no—
673C4×C4⋊C4—791no—
674C4×C4⋊C4—791no—
675C4×C4⋊C4—792no—
676C4×C4⋊C4—792no—
677C4×C4⋊C4—792no—
678C4×C4⋊C4C2×D7911yescharacteristic
679C4×C22⋊C4—792no—
680C4×C22⋊C4—792no—
681C4×C22⋊C4—792no—
682C4×C22⋊C4—792no—
683C4×C22⋊C4—792no—
684C4×C22⋊C4—792no—
685C4×C22⋊C4—792no—
686C4×C22⋊C4—792no—
687C4×C22⋊C4—792no—
688C4×C22⋊C4—792no—
689C4×C22⋊C4—792no—
690C4×C22⋊C4C2×D7912yes—
691C43—791no—
692C43—791no—
693C43—791no—
694C43—791no—
695C43—791no—
696C43—791no—
697C43—791no—
698C43—791no—
699C2×#41—7916no—
700C2×#41—1588no—
701C2×#41—1588no—
702C22×Q8—792no—
703C22×D4—792no—
704C22×D4—792no—
705C22×D4—792no—
706C22×D4—791no—
707C22×D4C22×D7911yescharacteristic
708C22×D4C22×D7912yes—
709C23×C4—791no—
710C23×C4—792no—
711C23×C4—791no—
712C23×C4—791no—
713C23×C4—792no—
714C23×C4—792no—
715C23×C4—791no—
716C23×C4—792no—
717C23×C4—792no—
718C23×C4C22×D7911yescharacteristic
719C23×C4C22×D7912yes—
720C23×C4C22×D7911yescharacteristic
721C23×C4C22×D7911yescharacteristic
722C4⋊Q8—798no—
723#127—798no—
724#124—7916no—
725#121—7916no—
726#121—798no—
727#121C4×D7918yescomplemented
728C4×Q8—1588no—
729C4×Q8—1588no—
730C4×D4—28no—
731C4×D4—24no—
732C4×D4—798no—
733C4×D4—798no—
734C4×D4—7916no—
735C4×D4—1588no—
736C4×D4—1588no—
737C4×D4—1584no—
738C4×D4—1588no—
739C4×D4—1588no—
740C4×D4—1584no—
741C4×D4—1588no—
742C4×D4—1588no—
743C4×D4—1588no—
744C4×D4—1584no—
745#117—1588no—
746#117—1588no—
747#117—1588no—
748C2×C4⋊C4—792no—
749C2×C4⋊C4—791no—
750C2×C4⋊C4—792no—
751C2×C4⋊C4—792no—
752C2×C4⋊C4—792no—
753C2×C4⋊C4—792no—
754C2×C4⋊C4—792no—
755C2×C4⋊C4—792no—
756C2×C4⋊C4—792no—
757C2×C4⋊C4—791no—
758C2×C4⋊C4—791no—
759C2×C4⋊C4C22×D7912yes—
760C2×C4⋊C4C22×D7911yescharacteristic
761C2×C4⋊C4C22×D7911yescharacteristic
762C2×C4⋊C4C22×D7911yescharacteristic
763C2×C22⋊C4—792no—
764C2×C22⋊C4—792no—
765C2×C22⋊C4—792no—
766C2×C22⋊C4—792no—
767C2×C22⋊C4—792no—
768C2×C22⋊C4—792no—
769C2×C22⋊C4—792no—
770C2×C22⋊C4—792no—
771C2×C22⋊C4—792no—
772C2×C22⋊C4—792no—
773C2×C22⋊C4—792no—
774C2×C22⋊C4—792no—
775C2×C22⋊C4—792no—
776C2×C22⋊C4C22×D7912yes—
777C2×C22⋊C4C22×D7912yes—
778C2×C22⋊C4C22×D7912yes—
779C2×C22⋊C4C22×D7912yes—
780C2×C22⋊C4C22×D7912yes—
781C2×C42—24no—
782C2×C42—798no—
783C2×C42—798no—
784C2×C42—791no—
785C2×C42—791no—
786C2×C42—791no—
787C2×C42—791no—
788C2×C42—791no—
789C2×C42—791no—
790C2×C42—791no—
791C2×C42—791no—
792C2×C42—791no—
793C2×C42—791no—
794C2×C42—791no—
795C2×C42—792no—
796C2×C42—792no—
797C2×C42—792no—
798C2×C42—792no—
799C2×C42—791no—
800C2×C42—791no—
801C2×C42—791no—
802C2×C42—791no—
803C2×C42—791no—
804C2×C42—791no—
805C2×C42—791no—
806C2×C42—791no—
807C2×C42—791no—
808C2×C42—791no—
809C2×C42—791no—
810C2×C42—791no—
811C2×C42—792no—
812C2×C42—791no—
813C2×C42—1588no—
814C2×C42—1588no—
815C2×C42—1584no—
816C2×C42—1584no—
817C2×C42—1584no—
818C2×C42—1584no—
819C2×C42C22×D7911yescharacteristic
820C2×C42C22×D7911yescharacteristic
821C2×C42C22×D7912yes—
822C2×C42C22×D7911yescharacteristic
823C2×C42C22×D7911yescharacteristic
824#95—792no—
825#95—792no—
826#95—792no—
827#95—792no—
828#95—792no—
829#95—792no—
830#95—792no—
831#95—792no—
832#95—792no—
833#95C22×D7912yes—
834#95C22×D7912yes—
835#95C22×D7912yes—
836C24—792no—
837C24C23×D7912yes—
838C24C23×D7911yescharacteristic
839#41—15864no—
840C2×Q8—798no—
841C2×Q8—1584no—
842C2×Q8—1584no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—798no—
848C2×D4—798no—
849C2×D4—798no—
850C2×D4—794no—
851C2×D4—1584no—
852C2×D4—1584no—
853C2×D4—1584no—
854C2×D4—1584no—
855C2×D4—1584no—
856C2×D4—1584no—
857C2×D4—1582no—
858C2×D4—1582no—
859C2×D4C2×C4×D7914yes—
860C2×D4C2×C4×D7918yes—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—794no—
872C22×C4—791no—
873C22×C4—791no—
874C22×C4—791no—
875C22×C4—791no—
876C22×C4—794no—
877C22×C4—794no—
878C22×C4—791no—
879C22×C4—791no—
880C22×C4—791no—
881C22×C4—792no—
882C22×C4—791no—
883C22×C4—794no—
884C22×C4—798no—
885C22×C4—794no—
886C22×C4—798no—
887C22×C4—792no—
888C22×C4—792no—
889C22×C4—1584no—
890C22×C4—1584no—
891C22×C4—1584no—
892C22×C4—1584no—
893C22×C4—1584no—
894C22×C4—1584no—
895C22×C4—1584no—
896C22×C4—1584no—
897C22×C4—1584no—
898C22×C4—1584no—
899C22×C4—1584no—
900C22×C4—1584no—
901C22×C4—1582no—
902C22×C4—1582no—
903C22×C4—1582no—
904C22×C4—1582no—
905C22×C4—1582no—
906C22×C4—1582no—
907C22×C4—1584no—
908C22×C4—1582no—
909C22×C4C2×C4×D7914yes—
910C22×C4D4×D7914yes—
911C22×C4C23×D7912yes—
912C22×C4C23×D7912yes—
913C22×C4C23×D7911yescharacteristic
914C22×C4C23×D7911yescharacteristic
915C22×C4C23×D7911yescharacteristic
916C22×C4C23×D7912yes—
917C22×C4C23×D7911yescharacteristic
918C22×C4C23×D7911yescharacteristic
919C22×C4C23×D7911yescharacteristic
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—24no—
923C4⋊C4—798no—
924C4⋊C4—794no—
925C4⋊C4—1584no—
926C4⋊C4—1584no—
927C4⋊C4—1584no—
928C4⋊C4—1584no—
929C4⋊C4—1584no—
930C4⋊C4—1584no—
931C4⋊C4—1582no—
932C4⋊C4—1582no—
933C4⋊C4—1584no—
934C4⋊C4C2×C4×D7914yes—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—798no—
940C22⋊C4—798no—
941C22⋊C4—798no—
942C22⋊C4—1584no—
943C22⋊C4—1584no—
944C22⋊C4—1584no—
945C22⋊C4—1584no—
946C22⋊C4—1584no—
947C22⋊C4—1584no—
948C22⋊C4—1584no—
949C22⋊C4—1584no—
950C22⋊C4—1584no—
951C22⋊C4—1584no—
952C22⋊C4C2×C4×D7918yes—
953C42—22no—
954C42—22no—
955C42—22no—
956C42—24no—
957C42—794no—
958C42—794no—
959C42—794no—
960C42—794no—
961C42—794no—
962C42—794no—
963C42—794no—
964C42—794no—
965C42—794no—
966C42—794no—
967C42—794no—
968C42—1582no—
969C42—1582no—
970C42—1582no—
971C42—1582no—
972C42—1582no—
973C42—1582no—
974C42—1582no—
975C42—1582no—
976C42—1582no—
977C42—1582no—
978C42—1584no—
979C42—1584no—
980C42—1584no—
981C42—1584no—
982C42—1582no—
983C42—1582no—
984C42—1582no—
985C42—1584no—
986C42#1192962314yescomplemented
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—794no—
998C23—1582no—
999C23—1582no—
1000C23—1582no—
1001C23—1582no—
1002C23—1582no—
1003C23—1582no—
1004C23C22×C4×D7914yes—
1005C23C22×C4×D7912yes—
1006C23C2×D4×D7912yes—
1007C23#41×D7912yes—
1008C23C24×D7911yescharacteristic
1009Q8—15816no—
1010D4—216no—
1011D4—28no—
1012D4—15816no—
1013D4—15816no—
1014D4—15816no—
1015D4—1588no—
1016C2×C4—28no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—48no—
1036C2×C4—3168no—
1037C2×C4—3168no—
1038C2×C4—3168no—
1039C2×C4—7916no—
1040C2×C4—792no—
1041C2×C4—792no—
1042C2×C4—792no—
1043C2×C4—792no—
1044C2×C4—792no—
1045C2×C4—792no—
1046C2×C4—792no—
1047C2×C4—792no—
1048C2×C4—792no—
1049C2×C4—792no—
1050C2×C4—792no—
1051C2×C4—792no—
1052C2×C4—792no—
1053C2×C4—794no—
1054C2×C4—792no—
1055C2×C4—792no—
1056C2×C4—792no—
1057C2×C4—15816no—
1058C2×C4—1582no—
1059C2×C4—1582no—
1060C2×C4—1582no—
1061C2×C4—1582no—
1062C2×C4—1582no—
1063C2×C4—1582no—
1064C2×C4—15816no—
1065C2×C4—1588no—
1066C2×C4—1588no—
1067C2×C4—1588no—
1068C2×C4—1582no—
1069C2×C4—1581no—
1070C2×C4—1581no—
1071C2×C4—1581no—
1072C2×C4—1581no—
1073C2×C4—1581no—
1074C2×C4—1581no—
1075C2×C4—1581no—
1076C2×C4—1581no—
1077C2×C4—1582no—
1078C2×C4C22×C4×D7912yes—
1079C2×C4C22×C4×D7914yes—
1080C2×C4C22×C4×D7912yes—
1081C2×C4C2×D4×D7912yes—
1082C2×C4C2×D4×D7912yes—
1083C2×C4#41×D7912yes—
1084C2×C4#41×D7912yes—
1085C2×C4#41×D7912yes—
1086C2×C4C2×#1192962312yes—
1087C2×C4C2×#1192962312yes—
1088C2×C4C2×#1192962312yes—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—24no—
1096C22—24no—
1097C22—24no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—3162no—
1103C22—3162no—
1104C22—3162no—
1105C22—3162no—
1106C22—1584no—
1107C22—1584no—
1108C22—1584no—
1109C22C4×D4×D7914yes—
1110C22C23×C4×D7911yescharacteristic
1111C22C22×D4×D7911yescharacteristic
1112C22C2×#41×D7911yescharacteristic
1113C22C2×#41×D7911yescharacteristic
1114C22C2×#41×D7911yescharacteristic
1115C22C2×#41×D7911yescharacteristic
1116C22C22×#1192962311yescharacteristic
1117C4—24no—
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—42no—
1123C4—42no—
1124C4—3162no—
1125C4—3162no—
1126C4—794no—
1127C4—794no—
1128C4—794no—
1129C4—794no—
1130C4—1584no—
1131C4—1582no—
1132C4—1582no—
1133C4—1582no—
1134C4—1582no—
1135C4C4×#1192962314yescomplemented
1136C4#1909910814yesdirect product factor
1137C2—24no—
1138C2—44no—
1139C2—3164no—
1140C2C2×C4×D4×D7911yescharacteristic
1141C2C4×#41×D7911yescharacteristic
1142C2C2×C4×#1192962311yescharacteristic
1143C2#532×D7911yescharacteristic
1144C2C2×#1909910811yescharacteristic
1145C2#2377669211yescharacteristic
1146C2#2377669411yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC4×#121×C79C2
socle, cosocleC23×C79C25
prime radicalC2×#19099108C2
hypercenterC4×#121D79
hypocenterC79C4×#532
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11929623C2semidirect
3. #23765971C2semidirect
4. C4×#14579160C2semidirect
5. #23765964C2semidirect
6. C4×#14579157C2semidirect
7. #23765941C2semidirect
8. C4×#14579147C2semidirect
9. #121×Dic79C2semidirect
10. C4×#14579135C2semidirect
11. #23765910C2semidirect
12. C4×#14579133C2semidirect
13. #23765906C2semidirect
14. #23765885C2semidirect
15. #23765862C2semidirect
16. #23765860C2semidirect
17. #23765858C2semidirect
18. #23765802C2semidirect
19. C4×D4×Dic79C2semidirect
20. C4×#14579123C2semidirect
21. C4×(C22⋊D79)⋊C4C2semidirect
22. C2×C42×Dic79C2semidirect
23. C4×#121×C79C2semidirect
25. #19099108C4direct (N × H)
127. C2×#11929623C2×C4semidirect
142. #14579160C2×C4semidirect
143. #14579157C2×C4semidirect
144. #14579147C2×C4semidirect
145. #14579135C2×C4semidirect
146. #14579133C2×C4semidirect
152. D4×Dic79C2×C4semidirect
154. #14579123C2×C4semidirect
161. (C22⋊D79)⋊C4C2×C4semidirect
194. C2×C4×Dic79C2×C4semidirect
195. C2×C4×Dic79D4semidirect
241. #121×C79C2×C4semidirect
367. C4×Dic79#41semidirect
368. C4×Dic79#41semidirect
369. C4×Dic79#41semidirect
412. C42×C79#41semidirect
492. C2×Dic79C4×D4semidirect
550. C4×C79C4×#41semidirect
551. C4×C79#532semidirect
561. Dic79C4×#41semidirect
562. Dic79#532semidirect
587. C4×#121D79semidirect
597. C79C4×#532semidirect
727. #121C4×D79semidirect
986. C42#11929623semidirect
1135. C4C4×#11929623semidirect
1136. C4#19099108direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991082
C2×C4×#119296232
#237659712
C4×#145791602
#237659642
C4×#145791572
#237659412
C4×#145791472
#121×Dic792
C4×#145791352
#237659102
C4×#145791332
#237659062
#237658852
#237658622
#237658602
#237658582
#237658022
C4×D4×Dic792
C4×#145791232
C4×(C22⋊D79)⋊C42
C2×C42×Dic792
C4×#121×C792
C4×#53279