Finite Group Databasebeta

← C2×#23778183 #35202114

Subgroups — C2×#23778183 #35202114

Order 20224.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099399C211yesmaximal, characteristic, complemented
2C22×#14579209C211yesmaximal, characteristic, complemented
3#23778183C2132yesmaximal, direct product factor
4C2×#19099379C214yesmaximal, complemented
5C2×#19099376C214yesmaximal, complemented
6C2×#19099372C214yesmaximal, complemented
7C2×#19099369C214yesmaximal, complemented
8C2×#19099363C211yesmaximal, characteristic, complemented
9C2×#19099362C214yesmaximal, complemented
10C2×#19099361C211yesmaximal, characteristic, complemented
11C22×#14579192C211yesmaximal, characteristic, complemented
12C2×#137×D79C214yesmaximal, complemented
13C2×#19099329C211yesmaximal, characteristic, complemented
14C22×#137×C79C211yesmaximal, characteristic, complemented
15#19099399—28no—
16#19099399C22116yescomplemented
17C2×#14579209—28no—
18C2×#14579209—22no—
19C2×#14579209—22no—
20C2×#14579209C2214yescomplemented
21C2×#14579209C2214yescomplemented
22C2×#14579209C2212yescomplemented
23C2×#14579209C22116yescomplemented
24C2×#14579208—21no—
25C2×#14579208C2212yescomplemented
26C2×#14579207—21no—
27C2×#14579207C2212yescomplemented
28C2×#14579206—22no—
29C2×#14579206C2212yescomplemented
30C22×#11929625—21no—
31C22×#11929625C2212yescomplemented
32C22×#11929624—22no—
33C22×#11929624—22no—
34C22×#11929624C2211yescharacteristic
35C22×#11929624C2211yescharacteristic
36C22×#11929624C2211yescharacteristic, complemented
37C2×#41×D79—22no—
38C2×#41×D79C2214yes—
39C22×Q8×D79—21no—
40C22×Q8×D79C2212yescomplemented
41#19099379C22164yescomplemented
42#19099376C22164yescomplemented
43#19099372C22164yescomplemented
44#19099369C22164yescomplemented
45#19099363C22116yescomplemented
46#19099362C22164yescomplemented
47#19099361C22116yescomplemented
48C2×#14579194C2212yescomplemented
49C2×#14579194C2212yescomplemented
50C2×#14579193C2218yescomplemented
51C2×#14579193C2218yescomplemented
52C2×#14579192C2214yescomplemented
53C2×#14579192C2214yescomplemented
54C2×#14579192C2212yescomplemented
55C2×#14579192C22116yescomplemented
56C2×#14579191C2212yescomplemented
57C2×#14579190C2218yescomplemented
58#137×D79C22164yescomplemented
59C2×#14579189C2212yescomplemented
60C2×#14579189C2212yescomplemented
61C2×#14579188C2218yescomplemented
62C2×#14579187C2212yescomplemented
63C2×#14579186C2212yescomplemented
64C2×#14579184C2218yescomplemented
65C2×#14579183C2214yescomplemented
66C2×#14579182C2218yescomplemented
67C2×#14579181C2214yescomplemented
68C22×#11929614C2212yescomplemented
69C2×Q16×D79C2218yescomplemented
70C22×#11929611C2212yescomplemented
71C2×SD16×D79C2218yescomplemented
72#19099329C22116yescomplemented
73C2×#14579169C2214yescomplemented
74C2×#14579167C2214yescomplemented
75C22×#11929608C2211yescharacteristic, complemented
76C2×M16×D79C2214yescomplemented
77C22×#41×C79C2211yescharacteristic
78C23×Q8×C79C2211yescharacteristic, complemented
79C2×#137×C79C2214yescomplemented
80C2×#137×C79C2214yescomplemented
81C2×#137×C79C22116yescomplemented
82C22×Q16×C79C2212yescomplemented
83C22×SD16×C79C2212yescomplemented
84C22×M16×C79C2211yescharacteristic, complemented
85#14579209—216no—
86#14579209—216no—
87#14579209—232no—
88#14579209—232no—
89#14579209—28no—
90#14579209C23132yescomplemented
91#14579209C23132yescomplemented
92#14579209C23116yescomplemented
93#14579208—28no—
94#14579208—216no—
95#14579208C23116yescomplemented
96#14579207—28no—
97#14579207—216no—
98#14579207C23116yescomplemented
99#14579206—28no—
100#14579206—232no—
101#14579206C23116yescomplemented
102C2×#11929625—22no—
103C2×#11929625—24no—
104C2×#11929625—24no—
105C2×#11929625—216no—
106C2×#11929625—24no—
107C2×#11929625—28no—
108C2×#11929625C2314yes—
109C2×#11929625C2318yes—
110C2×#11929625C23116yescomplemented
111C2×#11929624—21no—
112C2×#11929624—21no—
113C2×#11929624—21no—
114C2×#11929624—24no—
115C2×#11929624—24no—
116C2×#11929624—21no—
117C2×#11929624—232no—
118C2×#11929624—22no—
119C2×#11929624—22no—
120C2×#11929624—24no—
121C2×#11929624—28no—
122C2×#11929624—28no—
123C2×#11929624—232no—
124C2×#11929624—24no—
125C2×#11929624D418yes—
126C2×#11929624D412yes—
127C2×#11929624D412yes—
128C2×#11929624C2312yes—
129C2×#11929624C2312yes—
130C2×#11929624C2312yes—
131C2×#11929624C2318yes—
132C2×#11929624C2312yes—
133C2×#11929624C2312yes—
134C2×#11929624C2312yes—
135C2×#11929624C2318yes—
136C2×#11929624C2318yescomplemented
137C2×#11929623—22no—
138C2×#11929623—24no—
139C2×#11929623—24no—
140C2×#11929623C2314yes—
141#41×D79—232no—
142#41×D79—216no—
143#41×D79C23132yes—
144C22×Dic158—22no—
145C22×Dic158—22no—
146C22×Dic158D411yescharacteristic
147C22×Dic158C2311yescharacteristic
148C22×Dic158C2311yescharacteristic
149C2×Q8×D79—22no—
150C2×Q8×D79—24no—
151C2×Q8×D79—24no—
152C2×Q8×D79—216no—
153C2×Q8×D79—24no—
154C2×Q8×D79—28no—
155C2×Q8×D79C2314yes—
156C2×Q8×D79C2318yes—
157C2×Q8×D79C23116yescomplemented
158C22×D316—22no—
159C22×D316—22no—
160C22×D316D411yescharacteristic
161C22×D316C2311yescharacteristic
162C22×D316C2311yescharacteristic
163C22×C22⋊D79—21no—
164C22×C22⋊D79—21no—
165C22×C22⋊D79—24no—
166C22×C22⋊D79D412yes—
167C2×D4×D79—24no—
168C2×D4×D79—22no—
169C2×D4×D79—24no—
170C2×D4×D79C2314yes—
171C22×C4×D79—21no—
172C22×C4×D79—21no—
173C22×C4×D79—22no—
174C22×C4×D79—22no—
175C22×C4×D79—24no—
176C22×C4×D79C2312yes—
177#14579194C23116yescomplemented
178#14579194C23116yescomplemented
179#14579193C23164yescomplemented
180#14579193C23164yescomplemented
181#14579192C23132yescomplemented
182#14579192C23132yescomplemented
183#14579192C23116yescomplemented
184#14579191C23116yescomplemented
185#14579190C23164yescomplemented
186#14579189C23116yescomplemented
187#14579189C23116yescomplemented
188#14579188C23164yescomplemented
189#14579187C23116yescomplemented
190#14579186C23116yescomplemented
191#14579184C23164yescomplemented
192#14579183C23132yescomplemented
193#14579182C23164yescomplemented
194#14579181C23132yescomplemented
195C2×Dic316C2314yes—
196C2×#11929614C2314yes—
197C2×#11929614C2318yes—
198C2×#11929614C23116yescomplemented
199Q16×D79C23164yescomplemented
200C2×#11929613C2314yes—
201C2×#11929613C2314yes—
202C2×#11929612C2314yes—
203C2×#11929611C2318yes—
204C2×#11929611C2314yes—
205C2×#11929611C23116yescomplemented
206SD16×D79C23164yescomplemented
207C2×D632C2314yes—
208C2×#11929609C2314yes—
209#14579169C23132yescomplemented
210#14579167C23132yescomplemented
211C2×#11929608C2312yes—
212C2×#11929608C2312yes—
213C2×#11929608C2318yescomplemented
214C2×#11929607C2318yes—
215M16×D79C23132yescomplemented
216C22×C79⋊C8C2312yes—
217C2×C8×D79C2318yes—
218C2×#41×C79—21no—
219C2×#41×C79—24no—
220C2×#41×C79—21no—
221C2×#41×C79C2312yes—
222C2×#41×C79C2318yes—
223C2×#41×C79C2312yes—
224C22×Q8×C79—21no—
225C22×Q8×C79—21no—
226C22×Q8×C79—24no—
227C22×Q8×C79—21no—
228C22×Q8×C79C2312yes—
229C22×Q8×C79C2311yescharacteristic
230C22×Q8×C79C2312yes—
231C22×Q8×C79C2312yes—
232C22×Q8×C79C2318yescomplemented
233C22×D4×C79—21no—
234C22×D4×C79C2311yescharacteristic
235C23×C4×C79—21no—
236C23×C4×C79—21no—
237C23×C4×C79C2311yescharacteristic
238#137×C79C23132yescomplemented
239#137×C79C23132yescomplemented
240C2×Q16×C79C2318yes—
241C2×Q16×C79C23116yescomplemented
242C2×SD16×C79C2318yes—
243C2×SD16×C79C23116yescomplemented
244C2×M16×C79C2312yes—
245C2×M16×C79C2312yes—
246C2×M16×C79C2318yescomplemented
247C22×C8×C79C2312yes—
248C23×D79—21no—
249C23×D79—21no—
250C23×D79—24no—
251C23×D79C2×D412yes—
252#11929625—216no—
253#11929625—232no—
254#11929625—232no—
255#11929625—28no—
256#11929625—216no—
257#11929625—232no—
258#11929625C24116yes—
259#11929625C24132yes—
260#11929624—216no—
261#11929624—232no—
262#11929624—216no—
263#11929624—24no—
264#11929624—28no—
265#11929624—24no—
266#11929624—28no—
267#11929624—24no—
268#11929624—24no—
269#11929624—28no—
270#11929624—28no—
271#11929624—232no—
272#11929624—264no—
273#11929624—264no—
274#11929624C2×D4116yes—
275#11929624C2×D4116yes—
276#11929624C2×D418yes—
277#11929624C2×D418yes—
278#11929624C2418yes—
279#11929624C2418yes—
280#11929624C2418yes—
281#11929624C2418yes—
282#11929624C2418yes—
283#11929624C2418yes—
284#11929623—232no—
285#11929623—28no—
286#11929623—216no—
287#11929623—232no—
288#11929623C24116yes—
289C2×Dic158—28no—
290C2×Dic158—216no—
291C2×Dic158—24no—
292C2×Dic158—216no—
293C2×Dic158—21no—
294C2×Dic158—22no—
295C2×Dic158—21no—
296C2×Dic158—22no—
297C2×Dic158C2×D412yes—
298C2×Dic158C2×D412yes—
299C2×Dic158C2×D418yes—
300C2×Dic158C2412yes—
301C2×Dic158C2412yes—
302C2×Dic158C2414yes—
303C2×Dic158C2414yes—
304Q8×D79—216no—
305Q8×D79—232no—
306Q8×D79—28no—
307Q8×D79—232no—
308Q8×D79—232no—
309Q8×D79—216no—
310Q8×D79C24132yes—
311Q8×D79C24116yes—
312C2×D316—216no—
313C2×D316—28no—
314C2×D316—216no—
315C2×D316—24no—
316C2×D316—21no—
317C2×D316—21no—
318C2×D316—22no—
319C2×D316—22no—
320C2×D316C2×D412yes—
321C2×D316C2×D412yes—
322C2×D316C2×D418yes—
323C2×D316C2412yes—
324C2×D316C2412yes—
325C2×D316C2414yes—
326C2×D316C2414yes—
327C2×C22⋊D79—24no—
328C2×C22⋊D79—22no—
329C2×C22⋊D79—22no—
330C2×C22⋊D79—22no—
331C2×C22⋊D79—28no—
332C2×C22⋊D79—22no—
333C2×C22⋊D79—28no—
334C2×C22⋊D79—24no—
335C2×C22⋊D79—232no—
336C2×C22⋊D79C2×D414yes—
337C2×C22⋊D79C2×D414yes—
338C2×C22⋊D79C2×D4116yes—
339D4×D79—216no—
340D4×D79—28no—
341D4×D79—232no—
342D4×D79—232no—
343D4×D79C24116yes—
344C22×Dic79—24no—
345C22×Dic79—21no—
346C22×Dic79—21no—
347C22×Dic79C2×D412yes—
348C2×C4×D79—28no—
349C2×C4×D79—216no—
350C2×C4×D79—24no—
351C2×C4×D79—232no—
352C2×C4×D79—28no—
353C2×C4×D79—216no—
354C2×C4×D79—24no—
355C2×C4×D79—22no—
356C2×C4×D79—22no—
357C2×C4×D79—28no—
358C2×C4×D79—22no—
359C2×C4×D79—28no—
360C2×C4×D79—22no—
361C2×C4×D79C2×D418yes—
362C2×C4×D79C2×D414yes—
363C2×C4×D79C2414yes—
364C2×C4×D79C2418yes—
365Dic316C24116yes—
366#11929614C24116yes—
367#11929614C24132yes—
368#11929613C24116yes—
369#11929613C24116yes—
370#11929612C24116yes—
371#11929611C24132yes—
372#11929611C24116yes—
373D632C24116yes—
374#11929609C24116yes—
375#11929608C2418yes—
376#11929608C2418yes—
377#11929607C24132yes—
378C2×C79⋊C8C2414yes—
379C2×C79⋊C8C2418yes—
380C8×D79C24132yes—
381C24×C79—21no—
382C24×C79C2×D411yescharacteristic
383#41×C79—28no—
384#41×C79—24no—
385#41×C79—28no—
386#41×C79—24no—
387#41×C79C2418yes—
388#41×C79C2418yes—
389C2×Q8×C79—22no—
390C2×Q8×C79—22no—
391C2×Q8×C79—22no—
392C2×Q8×C79—24no—
393C2×Q8×C79—28no—
394C2×Q8×C79—21no—
395C2×Q8×C79—24no—
396C2×Q8×C79—24no—
397C2×Q8×C79—28no—
398C2×Q8×C79—28no—
399C2×Q8×C79—22no—
400C2×Q8×C79C2414yes—
401C2×Q8×C79C2412yes—
402C2×Q8×C79C2418yes—
403C2×Q8×C79C2418yes—
404C2×Q8×C79C2414yes—
405C2×Q8×C79C2418yes—
406C2×D4×C79—22no—
407C2×D4×C79—22no—
408C2×D4×C79—28no—
409C2×D4×C79—21no—
410C2×D4×C79—22no—
411C2×D4×C79C2412yes—
412C2×D4×C79C2414yes—
413C22×C4×C79—22no—
414C22×C4×C79—21no—
415C22×C4×C79—22no—
416C22×C4×C79—22no—
417C22×C4×C79—28no—
418C22×C4×C79—22no—
419C22×C4×C79—28no—
420C22×C4×C79—22no—
421C22×C4×C79C2×D411yescharacteristic
422C22×C4×C79C2×D411yescharacteristic
423C22×C4×C79C2×D414yes—
424C22×C4×C79C2×D411yescharacteristic
425C22×C4×C79C2411yescharacteristic
426C22×C4×C79C2411yescharacteristic
427C22×C4×C79C2411yescharacteristic
428C22×C4×C79C2414yes—
429Q16×C79C24132yes—
430SD16×C79C24132yes—
431M16×C79C2418yes—
432M16×C79C2418yes—
433C2×C8×C79C2414yes—
434C2×C8×C79C2418yes—
435C23×C79—22no—
436C23×C79—24no—
437C23×C79—42no—
438C23×C79—82no—
439C23×C79C22×D411yescharacteristic
440C23×C79C22×D411yescharacteristic
441C23×C79C22×D411yescharacteristic
442C23×C79C22×D414yes—
443C22×D79—24no—
444C22×D79—22no—
445C22×D79—22no—
446C22×D79—24no—
447C22×D79—216no—
448C22×D79—44no—
449C22×D79—44no—
450C22×D79—88no—
451C22×D79—82no—
452C22×D79C22×D414yes—
453C22×D79C22×D418yes—
454Q8×C79—28no—
455Q8×C79—28no—
456Q8×C79—24no—
457Q8×C79—28no—
458Q8×C79—22no—
459Q8×C79—24no—
460Q8×C79C2518yes—
461Q8×C79C2514yes—
462D4×C79—28no—
463D4×C79—28no—
464D4×C79—22no—
465D4×C79—24no—
466D4×C79C2514yes—
467C2×C4×C79—22no—
468C2×C4×C79—28no—
469C2×C4×C79—24no—
470C2×C4×C79—24no—
471C2×C4×C79—28no—
472C2×C4×C79—28no—
473C2×C4×C79—28no—
474C2×C4×C79—28no—
475C2×C4×C79C22×D411yescharacteristic
476C2×C4×C79C22×D411yescharacteristic
477C2×C4×C79C22×D411yescharacteristic
478C2×C4×C79C22×D414yes—
479C2×C4×C79C22×D414yes—
480C2×C4×C79C22×D412yes—
481C2×C4×C79C22×D412yes—
482C2×C4×C79C22×D414yes—
483C2×C4×C79C22×D412yes—
484C2×C4×C79C2511yescharacteristic
485C2×C4×C79C2512yes—
486C2×C4×C79C2512yes—
487C2×C4×C79C2512yes—
488C22⋊D79—28no—
489C22⋊D79—28no—
490C22⋊D79—28no—
491C22⋊D79—28no—
492C22⋊D79—216no—
493C22⋊D79—216no—
494C22⋊D79C22×D4116yes—
495C22⋊D79C22×D4116yes—
496C2×Dic79—24no—
497C2×Dic79—22no—
498C2×Dic79—22no—
499C2×Dic79—24no—
500C2×Dic79—216no—
501C2×Dic79C22×D414yes—
502C2×Dic79C22×D418yes—
503D316—216no—
504D316—232no—
505D316—22no—
506D316—24no—
507D316—24no—
508D316—22no—
509D316C22×D418yes—
510D316C22×D418yes—
511D316C2514yes—
512D316C2514yes—
513C4×D79—216no—
514C4×D79—232no—
515C4×D79—28no—
516C4×D79—28no—
517C4×D79—28no—
518C4×D79—28no—
519C4×D79—216no—
520C4×D79—232no—
521C4×D79C22×D4116yes—
522C4×D79C22×D418yes—
523C4×D79C2518yes—
524Dic158—24no—
525Dic158—22no—
526Dic158—22no—
527Dic158—24no—
528Dic158—232no—
529Dic158—216no—
530Dic158C22×D418yes—
531Dic158C22×D418yes—
532Dic158C2514yes—
533Dic158C2514yes—
534C8×C79C2518yes—
535C79⋊C8C2518yes—
536C22×C79—22no—
537C22×C79—22no—
538C22×C79—22no—
539C22×C79—24no—
540C22×C79—44no—
541C22×C79—44no—
542C22×C79—84no—
543C22×C79C23×D412yes—
544C22×C79C23×D412yes—
545C22×C79C23×D412yes—
546C22×C79C23×D411yescharacteristic
547C2×D79—28no—
548C2×D79—24no—
549C2×D79—24no—
550C2×D79—48no—
551C2×D79—48no—
552C2×D79—44no—
553C2×D79—44no—
554C2×D79—816no—
555C2×D79—84no—
556C2×D79C23×D418yes—
557C4×C79—24no—
558C4×C79—28no—
559C4×C79C23×D412yes—
560C4×C79C23×D412yes—
561C4×C79C23×D411yescharacteristic
562C4×C79C23×D412yes—
563C4×C79C2611yescharacteristic
564Dic79—24no—
565Dic79—24no—
566Dic79C23×D418yes—
567C2×#3586—791nomaximal, Sylow
568C2×C79—22no—
569C2×C79—22no—
570C2×C79—22no—
571C2×C79—44no—
572C2×C79#358612yescomplemented
573C2×C79C24×D411yescharacteristic
574D79—28no—
575D79—44no—
576D79—44no—
577C2×#585—791no—
578C22×2−1+4—791no—
579#3586—7932no—
580C2×#578—794no—
581C2×#578—794no—
582C2×#577—794no—
583C2×#577—794no—
584C2×#575—791no—
585C2×#575—794no—
586C2×#575—791no—
587C22×#137—791no—
588C22×#137—794no—
589C22×#137D7911yescharacteristic, complemented
590C2×#568—791no—
591C79C2×#358611yescharacteristic, complemented, Sylow
592#585—7916no—
593#585—1588no—
594C2×2−1+4—792no—
595C2×2−1+4—794no—
596C2×2−1+4—794no—
597C2×2−1+4—792no—
598C2×2−1+4—7916no—
599C2×2−1+4—1582no—
600C2×2−1+4—1582no—
601C2×2−1+4—1588no—
602C2×2−1+4—1581no—
603C2×H(5,𝔽2)—792no—
604C2×H(5,𝔽2)—792no—
605C2×H(5,𝔽2)—1582no—
606C2×H(5,𝔽2)—1581no—
607C22×#41—791no—
608C22×#41—794no—
609C22×#41—792no—
610C22×#41—791no—
611C22×#41—791no—
612C22×#41—1582no—
613C22×#41—1582no—
614C22×#41—1581no—
615C22×#41—1582no—
616C22×#41C2×D7911yescharacteristic
617C23×Q8—792no—
618C23×Q8—1581no—
619C23×Q8C2×D7911yescharacteristic, complemented
620#578—7964no—
621#578—7964no—
622#577—7964no—
623#577—7964no—
624#575—7916no—
625#575—7964no—
626#575—7916no—
627C2×#137—792no—
628C2×#137—794no—
629C2×#137—794no—
630C2×#137—792no—
631C2×#137—7916no—
632C2×#137—7964no—
633C2×#137—798no—
634C2×#137—798no—
635C2×#137—798no—
636C2×#137—792no—
637C2×#137—792no—
638C2×#137C2×D7914yescomplemented
639C2×#137C2×D7914yescomplemented
640C2×#137C2×D79116yescomplemented
641C2×AGL(1,ℤ/8)—792no—
642C2×AGL(1,ℤ/8)—792no—
643C2×AGL(1,ℤ/8)—798no—
644C2×AGL(1,ℤ/8)—792no—
645C2×AGL(1,ℤ/8)—792no—
646C2×#135—794no—
647C2×#135—798no—
648C2×#135—798no—
649C2×#135—794no—
650C22×Q16—792no—
651C22×Q16—798no—
652C22×Q16C2×D7912yescomplemented
653C22×SD16—792no—
654C22×SD16—798no—
655C22×SD16C2×D7912yescomplemented
656#568—7916no—
657C2×#131—794no—
658C2×#131—794no—
659C22×M16—791no—
660C22×M16—794no—
661C22×M16C2×D7911yescharacteristic, complemented
6622−1+4—7916no—
6632−1+4—7932no—
6642−1+4—7932no—
6652−1+4—7916no—
6662−1+4—15816no—
6672−1+4—15816no—
6682−1+4—15832no—
6692−1+4—15832no—
6702−1+4—1588no—
6712−1+4—15816no—
6722−1+4—1588no—
673H(5,𝔽2)—7916no—
674H(5,𝔽2)—7916no—
675H(5,𝔽2)—15832no—
676H(5,𝔽2)—1588no—
677H(5,𝔽2)—15816no—
678H(5,𝔽2)—1588no—
679C2×#41—21no—
680C2×#41—21no—
681C2×#41—24no—
682C2×#41—792no—
683C2×#41—792no—
684C2×#41—798no—
685C2×#41—792no—
686C2×#41—792no—
687C2×#41—798no—
688C2×#41—7932no—
689C2×#41—798no—
690C2×#41—794no—
691C2×#41—7916no—
692C2×#41—794no—
693C2×#41—792no—
694C2×#41—792no—
695C2×#41—792no—
696C2×#41—792no—
697C2×#41—798no—
698C2×#41—798no—
699C2×#41—1584no—
700C2×#41—1584no—
701C2×#41—1582no—
702C2×#41—1588no—
703C2×#41—1588no—
704C2×#41—15832no—
705C2×#41—1582no—
706C2×#41—15832no—
707C2×#41—1584no—
708C2×#41—1584no—
709C2×#41—1588no—
710C2×#41—15816no—
711C2×#41—1584no—
712C2×#41—1582no—
713C2×#41—1582no—
714C2×#41—1584no—
715C2×#41—1584no—
716C2×#41—15816no—
717C2×#41—15832no—
718C2×#41—1581no—
719C2×#41—1581no—
720C2×#41—1581no—
721C2×#41—1581no—
722C2×#41—1584no—
723C2×#41—1584no—
724C2×#41C22×D7912yes—
725C2×#41C22×D7912yes—
726C2×#41C22×D7918yes—
727C22×Q8—21no—
728C22×Q8—21no—
729C22×Q8—21no—
730C22×Q8—24no—
731C22×Q8—791no—
732C22×Q8—798no—
733C22×Q8—794no—
734C22×Q8—7916no—
735C22×Q8—791no—
736C22×Q8—791no—
737C22×Q8—1582no—
738C22×Q8—1582no—
739C22×Q8—1584no—
740C22×Q8—1588no—
741C22×Q8—1584no—
742C22×Q8—1584no—
743C22×Q8—15816no—
744C22×Q8—1582no—
745C22×Q8C22×D7912yes—
746C22×Q8C22×D7912yes—
747C22×Q8C22×D7911yescharacteristic
748C22×Q8C22×D7912yes—
749C22×Q8C22×D7918yescomplemented
750C22×D4—21no—
751C22×D4—792no—
752C22×D4—794no—
753C22×D4—791no—
754C22×D4—791no—
755C22×D4—791no—
756C22×D4—1582no—
757C22×D4—1582no—
758C22×D4—1584no—
759C22×D4—1582no—
760C22×D4—1584no—
761C22×D4—1584no—
762C22×D4—1581no—
763C22×D4—1581no—
764C22×D4C22×D7911yescharacteristic
765C23×C4—21no—
766C23×C4—21no—
767C23×C4—792no—
768C23×C4—1582no—
769C23×C4—1584no—
770C23×C4—1582no—
771C23×C4—1581no—
772C23×C4—1581no—
773C23×C4C22×D7911yescharacteristic
774#137—7916no—
775#137—7932no—
776#137—7932no—
777#137—7916no—
778#137—7964no—
779#137—7964no—
780#137—7964no—
781#137—7916no—
782#137—7916no—
783#137C22×D79132yescomplemented
784#137C22×D79132yescomplemented
785AGL(1,ℤ/8)—7916no—
786AGL(1,ℤ/8)—7916no—
787AGL(1,ℤ/8)—7964no—
788AGL(1,ℤ/8)—7916no—
789AGL(1,ℤ/8)—7916no—
790#135—7932no—
791#135—7964no—
792#135—7964no—
793#135—7932no—
794C2×Q16—794no—
795C2×Q16—798no—
796C2×Q16—7916no—
797C2×Q16—7964no—
798C2×Q16—794no—
799C2×Q16C22×D7918yes—
800C2×Q16C22×D79116yescomplemented
801C2×SD16—798no—
802C2×SD16—7916no—
803C2×SD16—794no—
804C2×SD16—794no—
805C2×SD16—7964no—
806C2×SD16—794no—
807C2×SD16—794no—
808C2×SD16C22×D7918yes—
809C2×SD16C22×D79116yescomplemented
810C2×D8—794no—
811C2×D8—794no—
812#131—7932no—
813#131—7932no—
814C2×M16—792no—
815C2×M16—792no—
816C2×M16—798no—
817C2×M16—7932no—
818C2×M16—798no—
819C2×M16C22×D7912yes—
820C2×M16C22×D7912yes—
821C2×M16C22×D7918yescomplemented
822C22×C8—792no—
823C22×C8—798no—
824C22×C8C22×D7912yes—
825C24—21no—
826C24—792no—
827C24—1584no—
828C24—1581no—
829C24—1581no—
830C24D4×D7911yescharacteristic
831#41—24no—
832#41—28no—
833#41—28no—
834#41—24no—
835#41—798no—
836#41—798no—
837#41—7916no—
838#41—7916no—
839#41—798no—
840#41—798no—
841#41—7932no—
842#41—7916no—
843#41—7916no—
844#41—798no—
845#41—798no—
846#41—798no—
847#41—798no—
848#41—15832no—
849#41—15832no—
850#41—15816no—
851#41—15864no—
852#41—15864no—
853#41—15816no—
854#41—15832no—
855#41—1588no—
856#41—1588no—
857#41—15832no—
858#41—15816no—
859#41—15832no—
860#41—15816no—
861#41—15816no—
862#41—15832no—
863#41—15832no—
864#41—1588no—
865#41—1584no—
866#41—1588no—
867#41—1584no—
868#41—1588no—
869#41—1588no—
870#41—1584no—
871#41—1584no—
872#41C23×D7918yes—
873#41C23×D7918yes—
874C2×Q8—24no—
875C2×Q8—22no—
876C2×Q8—22no—
877C2×Q8—22no—
878C2×Q8—28no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—28no—
882C2×Q8—28no—
883C2×Q8—21no—
884C2×Q8—22no—
885C2×Q8—792no—
886C2×Q8—792no—
887C2×Q8—798no—
888C2×Q8—7932no—
889C2×Q8—7916no—
890C2×Q8—792no—
891C2×Q8—792no—
892C2×Q8—794no—
893C2×Q8—794no—
894C2×Q8—15816no—
895C2×Q8—1588no—
896C2×Q8—1584no—
897C2×Q8—15816no—
898C2×Q8—15832no—
899C2×Q8—15816no—
900C2×Q8—1588no—
901C2×Q8—15832no—
902C2×Q8—15832no—
903C2×Q8—15816no—
904C2×Q8—1582no—
905C2×Q8—1581no—
906C2×Q8—1581no—
907C2×Q8—1582no—
908C2×Q8C23×D7914yes—
909C2×Q8C23×D7912yes—
910C2×Q8C23×D7918yes—
911C2×Q8C23×D7918yes—
912C2×Q8C23×D7914yes—
913C2×Q8C23×D7918yes—
914C2×D4—22no—
915C2×D4—22no—
916C2×D4—28no—
917C2×D4—21no—
918C2×D4—22no—
919C2×D4—794no—
920C2×D4—794no—
921C2×D4—7916no—
922C2×D4—7916no—
923C2×D4—792no—
924C2×D4—792no—
925C2×D4—794no—
926C2×D4—794no—
927C2×D4—792no—
928C2×D4—792no—
929C2×D4—798no—
930C2×D4—15816no—
931C2×D4—1584no—
932C2×D4—15816no—
933C2×D4—1588no—
934C2×D4—1588no—
935C2×D4—1584no—
936C2×D4—15832no—
937C2×D4—15816no—
938C2×D4—15832no—
939C2×D4—15832no—
940C2×D4—1584no—
941C2×D4—1582no—
942C2×D4—1582no—
943C2×D4—1588no—
944C2×D4—1582no—
945C2×D4—1582no—
946C2×D4—1588no—
947C2×D4—1581no—
948C2×D4—1582no—
949C2×D4—1581no—
950C2×D4—1582no—
951C2×D4C23×D7912yes—
952C2×D4C23×D7914yes—
953C22×C4—22no—
954C22×C4—21no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—28no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—28no—
961C22×C4—792no—
962C22×C4—794no—
963C22×C4—798no—
964C22×C4—794no—
965C22×C4—798no—
966C22×C4—1584no—
967C22×C4—15816no—
968C22×C4—1588no—
969C22×C4—15832no—
970C22×C4—1584no—
971C22×C4—15816no—
972C22×C4—1588no—
973C22×C4—1584no—
974C22×C4—1581no—
975C22×C4—1581no—
976C22×C4—1582no—
977C22×C4—1582no—
978C22×C4—1588no—
979C22×C4—1582no—
980C22×C4—1582no—
981C22×C4—1588no—
982C22×C4D4×D7911yescharacteristic
983C22×C4D4×D7911yescharacteristic
984C22×C4D4×D7911yescharacteristic
985C22×C4D4×D7914yes—
986C22×C4C23×D7911yescharacteristic
987C22×C4C23×D7911yescharacteristic
988C22×C4C23×D7911yescharacteristic
989C22×C4C23×D7914yes—
990Q16—7916no—
991Q16—7932no—
992Q16—7916no—
993Q16C23×D79132yes—
994SD16—7932no—
995SD16—7916no—
996SD16—7916no—
997SD16—7916no—
998SD16—7916no—
999SD16C23×D79132yes—
1000D8—7916no—
1001D8—7916no—
1002M16—798no—
1003M16—798no—
1004M16—7932no—
1005M16C23×D7918yes—
1006M16C23×D7918yes—
1007C2×C8—794no—
1008C2×C8—798no—
1009C2×C8—7932no—
1010C2×C8C23×D7914yes—
1011C2×C8C23×D7918yes—
1012C23—22no—
1013C23—24no—
1014C23—42no—
1015C23—82no—
1016C23—3164no—
1017C23—3164no—
1018C23—798no—
1019C23—794no—
1020C23—6322no—
1021C23—6328no—
1022C23—15816no—
1023C23—1584no—
1024C23—1582no—
1025C23—1582no—
1026C23—1584no—
1027C23C2×D4×D7911yescharacteristic
1028C23C2×D4×D7911yescharacteristic
1029C23C2×D4×D7911yescharacteristic
1030C23C2×D4×D7914yes—
1031Q8—28no—
1032Q8—28no—
1033Q8—24no—
1034Q8—28no—
1035Q8—22no—
1036Q8—24no—
1037Q8—798no—
1038Q8—798no—
1039Q8—794no—
1040Q8—794no—
1041Q8—15832no—
1042Q8—15816no—
1043Q8—1584no—
1044Q8—1582no—
1045Q8—1584no—
1046Q8—1582no—
1047Q8C24×D7918yes—
1048Q8C24×D7914yes—
1049D4—28no—
1050D4—28no—
1051D4—22no—
1052D4—24no—
1053D4—7916no—
1054D4—7916no—
1055D4—794no—
1056D4—794no—
1057D4—798no—
1058D4—798no—
1059D4—15816no—
1060D4—15832no—
1061D4—15816no—
1062D4—15816no—
1063D4—1588no—
1064D4—1588no—
1065D4—1588no—
1066D4—1588no—
1067D4—1584no—
1068D4—1582no—
1069D4—1584no—
1070D4—1582no—
1071D4C24×D7914yes—
1072C2×C4—28no—
1073C2×C4—24no—
1074C2×C4—28no—
1075C2×C4—28no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—28no—
1079C2×C4—28no—
1080C2×C4—798no—
1081C2×C4—794no—
1082C2×C4—798no—
1083C2×C4—7916no—
1084C2×C4—798no—
1085C2×C4—15816no—
1086C2×C4—15832no—
1087C2×C4—15816no—
1088C2×C4—15832no—
1089C2×C4—15816no—
1090C2×C4—1584no—
1091C2×C4—1584no—
1092C2×C4—1582no—
1093C2×C4—1582no—
1094C2×C4—1588no—
1095C2×C4—1588no—
1096C2×C4—1588no—
1097C2×C4—1588no—
1098C2×C4C2×D4×D7914yes—
1099C2×C4C2×D4×D7912yes—
1100C2×C4C2×D4×D7914yes—
1101C2×C4C2×D4×D7914yes—
1102C2×C4C2×D4×D7912yes—
1103C2×C4C2×D4×D7912yes—
1104C2×C4C2×D4×D7911yescharacteristic
1105C2×C4C2×D4×D7911yescharacteristic
1106C2×C4C2×D4×D7911yescharacteristic
1107C2×C4C24×D7912yes—
1108C2×C4C24×D7912yes—
1109C2×C4C24×D7912yes—
1110C2×C4C24×D7911yescharacteristic
1111C8—798no—
1112C8C24×D7918yes—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—24no—
1117C22—44no—
1118C22—44no—
1119C22—84no—
1120C22—3168no—
1121C22—3168no—
1122C22—3164no—
1123C22—3164no—
1124C22—798no—
1125C22—6324no—
1126C22—63216no—
1127C22—1584no—
1128C22—1584no—
1129C22—1588no—
1130C22C22×D4×D7912yes—
1131C22C22×D4×D7912yes—
1132C22C22×D4×D7912yes—
1133C22C22×D4×D7911yescharacteristic
1134C4—24no—
1135C4—28no—
1136C4—798no—
1137C4—1584no—
1138C4—1584no—
1139C4C22×D4×D7912yes—
1140C4C22×D4×D7912yes—
1141C4C22×D4×D7911yescharacteristic
1142C4C22×D4×D7912yes—
1143C4C25×D7911yescharacteristic
1144C2—22no—
1145C2—22no—
1146C2—22no—
1147C2—44no—
1148C2—3164no—
1149C2—3164no—
1150C2—1588no—
1151C2#2377818312yesdirect product factor
1152C2C23×D4×D7911yescharacteristic
subgroupG/H
centerC22C22×D4×D79
commutator, cosocleC4×C79C26
FrattiniC4C25×D79
FittingC22×#137×C79C2
socleC22×C79C23×D4
hypercenterC22×#137D79
hypocenterC79C2×#3586
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C2×#19099399C2semidirect
2. C22×#14579209C2semidirect
3. #23778183C2direct (N × H)
4. C2×#19099379C2semidirect
5. C2×#19099376C2semidirect
6. C2×#19099372C2semidirect
7. C2×#19099369C2semidirect
8. C2×#19099363C2semidirect
9. C2×#19099362C2semidirect
10. C2×#19099361C2semidirect
11. C22×#14579192C2semidirect
12. C2×#137×D79C2semidirect
13. C2×#19099329C2semidirect
14. C22×#137×C79C2semidirect
16. #19099399C22semidirect
20. C2×#14579209C22semidirect
21. C2×#14579209C22semidirect
22. C2×#14579209C22semidirect
23. C2×#14579209C22semidirect
25. C2×#14579208C22semidirect
27. C2×#14579207C22semidirect
29. C2×#14579206C22semidirect
31. C22×#11929625C22semidirect
36. C22×#11929624C22semidirect
40. C22×Q8×D79C22semidirect
41. #19099379C22semidirect
42. #19099376C22semidirect
43. #19099372C22semidirect
44. #19099369C22semidirect
45. #19099363C22semidirect
46. #19099362C22semidirect
47. #19099361C22semidirect
48. C2×#14579194C22semidirect
49. C2×#14579194C22semidirect
50. C2×#14579193C22semidirect
51. C2×#14579193C22semidirect
52. C2×#14579192C22semidirect
53. C2×#14579192C22semidirect
54. C2×#14579192C22semidirect
55. C2×#14579192C22semidirect
56. C2×#14579191C22semidirect
57. C2×#14579190C22semidirect
58. #137×D79C22semidirect
59. C2×#14579189C22semidirect
60. C2×#14579189C22semidirect
61. C2×#14579188C22semidirect
62. C2×#14579187C22semidirect
63. C2×#14579186C22semidirect
64. C2×#14579184C22semidirect
65. C2×#14579183C22semidirect
66. C2×#14579182C22semidirect
67. C2×#14579181C22semidirect
68. C22×#11929614C22semidirect
69. C2×Q16×D79C22semidirect
70. C22×#11929611C22semidirect
71. C2×SD16×D79C22semidirect
72. #19099329C22semidirect
73. C2×#14579169C22semidirect
74. C2×#14579167C22semidirect
75. C22×#11929608C22semidirect
76. C2×M16×D79C22semidirect
78. C23×Q8×C79C22semidirect
79. C2×#137×C79C22semidirect
80. C2×#137×C79C22semidirect
81. C2×#137×C79C22semidirect
82. C22×Q16×C79C22semidirect
83. C22×SD16×C79C22semidirect
84. C22×M16×C79C22semidirect
90. #14579209C23semidirect
91. #14579209C23semidirect
92. #14579209C23semidirect
95. #14579208C23semidirect
98. #14579207C23semidirect
101. #14579206C23semidirect
110. C2×#11929625C23semidirect
136. C2×#11929624C23semidirect
157. C2×Q8×D79C23semidirect
177. #14579194C23semidirect
178. #14579194C23semidirect
179. #14579193C23semidirect
180. #14579193C23semidirect
181. #14579192C23semidirect
182. #14579192C23semidirect
183. #14579192C23semidirect
184. #14579191C23semidirect
185. #14579190C23semidirect
186. #14579189C23semidirect
187. #14579189C23semidirect
188. #14579188C23semidirect
189. #14579187C23semidirect
190. #14579186C23semidirect
191. #14579184C23semidirect
192. #14579183C23semidirect
193. #14579182C23semidirect
194. #14579181C23semidirect
198. C2×#11929614C23semidirect
199. Q16×D79C23semidirect
205. C2×#11929611C23semidirect
206. SD16×D79C23semidirect
209. #14579169C23semidirect
210. #14579167C23semidirect
213. C2×#11929608C23semidirect
215. M16×D79C23semidirect
232. C22×Q8×C79C23semidirect
238. #137×C79C23semidirect
239. #137×C79C23semidirect
241. C2×Q16×C79C23semidirect
243. C2×SD16×C79C23semidirect
246. C2×M16×C79C23semidirect
572. C2×C79#3586semidirect
589. C22×#137D79semidirect
591. C79C2×#3586semidirect
619. C23×Q8C2×D79semidirect
638. C2×#137C2×D79semidirect
639. C2×#137C2×D79semidirect
640. C2×#137C2×D79semidirect
652. C22×Q16C2×D79semidirect
655. C22×SD16C2×D79semidirect
661. C22×M16C2×D79semidirect
749. C22×Q8C22×D79semidirect
783. #137C22×D79semidirect
784. #137C22×D79semidirect
800. C2×Q16C22×D79semidirect
809. C2×SD16C22×D79semidirect
821. C2×M16C22×D79semidirect
1151. C2#23778183direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190993992
C22×#145792092
#237781832
C2×#190993792
C2×#190993762
C2×#190993722
C2×#190993692
C2×#190993632
C2×#190993622
C2×#190993612
C22×#145791922
C2×#137×D792
C2×#190993292
C22×#137×C792
C2×#358679