Finite Group Databasebeta

← C2×#22599186 #32868099

Subgroups — C2×#22599186 #32868099

Order 18176.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986563C211yesmaximal, characteristic, complemented
2#22599186C2116yesmaximal, direct product factor
3C2×#17986317C211yesmaximal, characteristic, complemented
4C2×#17986337C211yesmaximal, characteristic, complemented
5C2×#17986320C211yesmaximal, characteristic, complemented
6C2×#17986312C211yesmaximal, characteristic, complemented
7C2×#17986250C211yesmaximal, characteristic, complemented
8C2×#17986247C211yesmaximal, characteristic, complemented
9C2×#17986233C211yesmaximal, characteristic, complemented
10C2×#17986230C211yesmaximal, characteristic, complemented
11C2×#17986144C211yesmaximal, characteristic, complemented
12C2×#17986144C211yesmaximal, characteristic, complemented
13C2×#17986149C211yesmaximal, characteristic, complemented
14C2×#17986132C211yesmaximal, characteristic, complemented
15C2×#17985966C211yesmaximal, characteristic, complemented
16C2×#537×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C22×#11765852C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765850C2211yescharacteristic
22C22×#11765849C2211yescharacteristic, complemented
23C23×C71⋊C8C2211yescharacteristic, complemented
24#17986563—24no—
25#17986563C2218yescomplemented
26C2×#14556124—21no—
27C2×#14556117—21no—
28C2×#14556102C2211yescharacteristic
29C2×#14556102C2211yescharacteristic
30C2×#14556102C2211yescharacteristic
31C2×#14556102C2211yescharacteristic
32C2×#14556096—21no—
33C2×#14556096—21no—
34C2×#14556087C2211yescharacteristic
35#17986337C2218yescomplemented
36#17986320C2218yescomplemented
37#17986317C2218yescomplemented
38#17986312C2218yescomplemented
39#17986250C2218yescomplemented
40#17986247C2218yescomplemented
41#17986233C2218yescomplemented
42#17986230C2218yescomplemented
43#17986149C2218yescomplemented
44#17986144C2218yescomplemented
45#17986144C2218yescomplemented
46#17986132C2218yescomplemented
47C2×#14556061C2211yescharacteristic, complemented
48C2×#14556061C2211yescharacteristic, complemented
49C2×#14556059C2211yescharacteristic, complemented
50C2×#14556059C2211yescharacteristic, complemented
51C2×#14556052C2211yescharacteristic, complemented
52C2×#14556052C2211yescharacteristic, complemented
53C2×#14556049C2211yescharacteristic, complemented
54C2×#14556049C2211yescharacteristic, complemented
55C2×#14556048C2211yescharacteristic
56C2×#14556048C2211yescharacteristic
57C2×#14556048C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59#17985966C2218yescomplemented
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
63C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
64C22×#41×C71C2211yescharacteristic
65C22×#41×C71C2211yescharacteristic, complemented
66#537×C71—24no—
67#537×C71C2218yescomplemented
68C2×C22⋊Q8×C71—21no—
69C2×C22⋊Q8×C71C2211yescharacteristic
70C2×C22⋊Q8×C71C2211yescharacteristic, complemented
71C2×#121×C71—21no—
72C2×#121×C71—21no—
73C2×#121×C71—21no—
74C2×#121×C71C2211yescharacteristic
75C2×#121×C71C2211yescharacteristic, complemented
76C22×C4⋊C4×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C22×D284—22no—
79C22×D284—21no—
80C22×D284—42no—
81C22×D284—42no—
82C22×D284C2311yescharacteristic
83C22×D284C2311yescharacteristic
84C22×D284C2314yes—
85C22×C22⋊D71—21no—
86C22×C22⋊D71—21no—
87C22×C22⋊D71—21no—
88C22×C22⋊D71—21no—
89C2×#11765852—42no—
90C2×#11765852—42no—
91C2×#11765852C2314yes—
92C2×#11765852C2314yes—
93C2×#11765850—42no—
94C2×#11765850—42no—
95C2×#11765850C2314yes—
96C2×#11765850C2314yes—
97C2×#11765849—42no—
98C2×#11765849C2314yescomplemented
99C22×C71⋊C8—42no—
100C22×C71⋊C8C2311yescharacteristic
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2311yescharacteristic
103C22×C71⋊C8C2311yescharacteristic
104C22×C71⋊C8C2314yescomplemented
105#14556124—28no—
106#14556117—28no—
107#14556102—22no—
108#14556102—22no—
109#14556102—22no—
110#14556102—22no—
111#14556102C2314yes—
112#14556102C2314yes—
113#14556102C2314yes—
114#14556102C2314yes—
115#14556096—28no—
116#14556096—28no—
117#14556087—22no—
118#14556087C2314yes—
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×C22⋊Dic71—21no—
122C2×(C2×D71)⋊C4—21no—
123C2×(C2×D71)⋊C4—21no—
124C2×(C2×D71)⋊C4—21no—
125C2×(C2×D71)⋊C4—21no—
126C2×C4×Dic71—21no—
127#14556061C2314yescomplemented
128#14556061C2314yescomplemented
129#14556059C2314yescomplemented
130#14556059C2314yescomplemented
131#14556052C2314yescomplemented
132#14556052C2314yescomplemented
133#14556049C2314yescomplemented
134#14556049C2314yescomplemented
135#14556048C2314yes—
136#14556048C2314yes—
137#14556048C2314yes—
138#14556048C2314yes—
139C22⋊(C71⋊C8)C2314yes—
140C22⋊(C71⋊C8)C2314yes—
141C22⋊(C71⋊C8)C2314yescomplemented
142C22⋊(C71⋊C8)C2314yescomplemented
143C2×#41×C71—22no—
144C2×#41×C71—42no—
145C2×#41×C71—42no—
146C2×#41×C71—42no—
147C2×#41×C71—42no—
148C2×#41×C71D414yes—
149C2×#41×C71C2314yes—
150C2×#41×C71C2314yescomplemented
151C22×Q8×C71D411yescharacteristic
152C22×Q8×C71C2311yescharacteristic
153C22×D4×C71—21no—
154C22×D4×C71—21no—
155C22×D4×C71—21no—
156C22×D4×C71D411yescharacteristic
157C22×D4×C71D411yescharacteristic
158C22×D4×C71D411yescharacteristic
159C22×D4×C71C2311yescharacteristic
160C23×C4×C71—21no—
161C23×C4×C71—21no—
162C23×C4×C71C2311yescharacteristic
163C23×C4×C71C2311yescharacteristic
164C23×C4×C71C2311yescharacteristic
165C22⋊Q8×C71—28no—
166C22⋊Q8×C71—22no—
167C22⋊Q8×C71—22no—
168C22⋊Q8×C71C2314yes—
169C22⋊Q8×C71C2314yescomplemented
170#121×C71—28no—
171#121×C71—28no—
172#121×C71—28no—
173#121×C71—22no—
174#121×C71—22no—
175#121×C71C2314yes—
176#121×C71C2314yescomplemented
177C2×C4⋊C4×C71—21no—
178C2×C4⋊C4×C71—22no—
179C2×C4⋊C4×C71—21no—
180C2×C4⋊C4×C71—21no—
181C2×C4⋊C4×C71C2311yescharacteristic
182C2×C4⋊C4×C71C2311yescharacteristic
183C2×C4⋊C4×C71C2314yescomplemented
184C2×C22⋊C4×C71—21no—
185C2×C22⋊C4×C71—21no—
186C2×C22⋊C4×C71—21no—
187C2×C22⋊C4×C71—21no—
188C23×D71—21no—
189C23×D71—21no—
190C23×D71—24no—
191C23×D71—44no—
192C23×D71—82no—
193C23×D71—82no—
194C2×D284—22no—
195C2×D284—22no—
196C2×D284—22no—
197C2×D284—22no—
198C2×D284—21no—
199C2×D284—21no—
200C2×D284—24no—
201C2×D284—44no—
202C2×D284—44no—
203C2×D284—44no—
204C2×D284—48no—
205C2×D284C2412yes—
206C2×D284C2412yes—
207C2×C22⋊D71—24no—
208C2×C22⋊D71—24no—
209C2×C22⋊D71—24no—
210C2×C22⋊D71—24no—
211C2×C22⋊D71—82no—
212C2×C22⋊D71—82no—
213C2×C22⋊D71—82no—
214C2×C22⋊D71—82no—
215C22×Dic71—21no—
216C22×Dic71—21no—
217#11765852—44no—
218#11765852—44no—
219#11765850—44no—
220#11765850—44no—
221#11765849—44no—
222C2×C71⋊C8—22no—
223C2×C71⋊C8—22no—
224C2×C71⋊C8—22no—
225C2×C71⋊C8—22no—
226C2×C71⋊C8—44no—
227C2×C71⋊C8C2412yes—
228C2×C71⋊C8C2412yes—
229C2×C71⋊C8C2412yes—
230C2×C71⋊C8C2412yes—
231C4⋊Dic71—21no—
232C4⋊Dic71—21no—
233C4⋊Dic71C2412yes—
234C4⋊Dic71C2412yes—
235C22⋊Dic71—24no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4—24no—
238(C2×D71)⋊C4—24no—
239(C2×D71)⋊C4—24no—
240C4×Dic71—24no—
241C24×C71—21no—
242C24×C71C2×D411yescharacteristic
243C24×C71C2×D411yescharacteristic
244C24×C71C2×D411yescharacteristic
245#41×C71—48no—
246#41×C71—44no—
247#41×C71—44no—
248#41×C71—44no—
249#41×C71—44no—
250#41×C71—48no—
251C2×Q8×C71—21no—
252C2×Q8×C71—22no—
253C2×Q8×C71—22no—
254C2×Q8×C71—42no—
255C2×Q8×C71C2×D414yes—
256C2×Q8×C71C2412yes—
257C2×D4×C71—24no—
258C2×D4×C71—24no—
259C2×D4×C71—24no—
260C2×D4×C71—21no—
261C2×D4×C71—22no—
262C2×D4×C71—22no—
263C2×D4×C71—42no—
264C2×D4×C71—42no—
265C2×D4×C71—42no—
266C2×D4×C71—44no—
267C2×D4×C71—82no—
268C2×D4×C71—82no—
269C2×D4×C71C2×D414yes—
270C2×D4×C71C2×D414yes—
271C2×D4×C71C2×D414yes—
272C2×D4×C71C2412yes—
273C22×C4×C71—22no—
274C22×C4×C71—22no—
275C22×C4×C71—22no—
276C22×C4×C71—22no—
277C22×C4×C71—22no—
278C22×C4×C71—22no—
279C22×C4×C71—21no—
280C22×C4×C71—21no—
281C22×C4×C71—21no—
282C22×C4×C71—24no—
283C22×C4×C71—24no—
284C22×C4×C71—44no—
285C22×C4×C71—82no—
286C22×C4×C71C2×D411yescharacteristic
287C22×C4×C71C2×D412yes—
288C22×C4×C71C2×D411yescharacteristic
289C22×C4×C71C2×D411yescharacteristic
290C22×C4×C71C2×D412yes—
291C22×C4×C71C2×D412yes—
292C22×C4×C71C2412yes—
293C22×C4×C71C2412yes—
294C22×C4×C71C2412yes—
295C22×C4×C71C2411yescharacteristic
296C4⋊C4×C71—21no—
297C4⋊C4×C71—21no—
298C4⋊C4×C71—24no—
299C4⋊C4×C71—24no—
300C4⋊C4×C71—24no—
301C4⋊C4×C71C2412yes—
302C4⋊C4×C71C2412yes—
303C22⋊C4×C71—24no—
304C22⋊C4×C71—24no—
305C22⋊C4×C71—24no—
306C22⋊C4×C71—24no—
307C23×C71—22no—
308C23×C71—22no—
309C23×C71—22no—
310C23×C71—22no—
311C23×C71—22no—
312C23×C71—22no—
313C23×C71—22no—
314C23×C71—22no—
315C23×C71—22no—
316C23×C71—22no—
317C23×C71—42no—
318C23×C71—42no—
319C23×C71—42no—
320C23×C71C22×D412yes—
321C23×C71C22×D412yes—
322C23×C71C22×D412yes—
323C23×C71C22×D411yescharacteristic
324C22×D71—22no—
325C22×D71—22no—
326C22×D71—48no—
327C22×D71—42no—
328C22×D71—42no—
329C22×D71—42no—
330C22×D71—42no—
331C22×D71—42no—
332C22×D71—42no—
333C22×D71—84no—
334C22×D71—84no—
335C22×D71—816no—
336Q8×C71—22no—
337Q8×C71—22no—
338Q8×C71—44no—
339Q8×C71—42no—
340D4×C71—22no—
341D4×C71—22no—
342D4×C71—44no—
343D4×C71—44no—
344D4×C71—44no—
345D4×C71—48no—
346D4×C71—42no—
347D4×C71—84no—
348D4×C71—84no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—24no—
353C2×C4×C71—24no—
354C2×C4×C71—24no—
355C2×C4×C71—22no—
356C2×C4×C71—22no—
357C2×C4×C71—22no—
358C2×C4×C71—22no—
359C2×C4×C71—22no—
360C2×C4×C71—22no—
361C2×C4×C71—22no—
362C2×C4×C71—22no—
363C2×C4×C71—22no—
364C2×C4×C71—48no—
365C2×C4×C71—42no—
366C2×C4×C71—42no—
367C2×C4×C71—42no—
368C2×C4×C71—84no—
369C2×C4×C71C22×D412yes—
370C2×C4×C71C22×D412yes—
371C2×C4×C71C22×D412yes—
372C2×C4×C71C22×D411yescharacteristic
373C2×C4×C71H(5,𝔽2)12yes—
374C2×C4×C71H(5,𝔽2)12yes—
375C2×C4×C71C2511yescharacteristic
376C22⋊D71—84no—
377C22⋊D71—84no—
378C22⋊D71—84no—
379C22⋊D71—84no—
380C2×Dic71—22no—
381C2×Dic71—22no—
382C2×Dic71—42no—
383C2×Dic71—42no—
384D284—22no—
385D284—22no—
386D284—22no—
387D284—22no—
388D284—48no—
389D284—42no—
390D284—42no—
391C71⋊C8—22no—
392C71⋊C8—22no—
393C71⋊C8—22no—
394C71⋊C8—22no—
395C22×C71—22no—
396C22×C71—22no—
397C22×C71—22no—
398C22×C71—22no—
399C22×C71—22no—
400C22×C71—22no—
401C22×C71—22no—
402C22×C71—22no—
403C22×C71—22no—
404C22×C71—44no—
405C22×C71—44no—
406C22×C71—44no—
407C22×C71—42no—
408C22×C71—42no—
409C22×C71—42no—
410C22×C71—84no—
411C22×C71#53412yes—
412C22×C71#57612yes—
413C22×C71#57712yes—
414C22×C71C23×D411yescharacteristic
415C2×D71—42no—
416C2×D71—42no—
417C2×D71—42no—
418C2×D71—42no—
419C2×D71—42no—
420C2×D71—42no—
421C2×D71—816no—
422C2×D71—84no—
423C2×D71—84no—
424C4×C71—22no—
425C4×C71—22no—
426C4×C71—22no—
427C4×C71—42no—
428C4×C71—42no—
429C4×C71—42no—
430C4×C71#53412yes—
431C4×C71C2×H(5,𝔽2)11yescharacteristic
432C4×C71C2×H(5,𝔽2)11yescharacteristic
433Dic71—42no—
434Dic71—42no—
435C2×#3198—711nomaximal, Sylow
436C2×C71—42no—
437C2×C71—42no—
438C2×C71—42no—
439C2×C71—82no—
440C2×C71#319814yescomplemented
441C2×C71C2×#53411yescharacteristic
442C2×C71C2×#57611yescharacteristic
443C2×C71C2×#57711yescharacteristic
444D71—82no—
445D71—82no—
446C2×#537D7111yescharacteristic, complemented
447C2×#535—711no—
448#3198—7116no—
449C2×#481—711no—
450C2×#485—711no—
451C2×#482—711no—
452C2×#480—711no—
453C2×#469—711no—
454C2×#468—711no—
455C2×#466—711no—
456C2×#465—711no—
457C2×#449—711no—
458C2×#449—711no—
459C2×#450—711no—
460C2×#447—711no—
461C2×#408—711no—
462C71C2×#319811yescharacteristic, complemented, Sylow
463C22×#41C2×D7111yescharacteristic
464C22×#41C2×D7111yescharacteristic, complemented
465C23×D4—711no—
466C22×SD16—711no—
467C22×SD16—711no—
468C22×D8—711no—
469C22×D8—711no—
470C22×M16—711no—
471C23×C8—711no—
472#537—24no—
473#537C2×D7118yescomplemented
474#535—718no—
475#535—1424no—
476C2×#127—1421no—
477C2×#124—1421no—
478C2×C22⋊Q8—21no—
479C2×C22⋊Q8C2×D7111yescharacteristic
480C2×C22⋊Q8C2×D7111yescharacteristic, complemented
481C2×#121—21no—
482C2×#121—21no—
483C2×#121—21no—
484C2×#121—711no—
485C2×#121—711no—
486C2×#121—711no—
487C2×#121—711no—
488C2×#121C2×D7111yescharacteristic
489C2×#121C2×D7111yescharacteristic, complemented
490C2×#120—1421no—
491C2×#120—1421no—
492C2×#117—711no—
493C22×C4⋊C4C2×D7111yescharacteristic, complemented
494#485—718no—
495#482—718no—
496#481—718no—
497#480—718no—
498#469—718no—
499#468—718no—
500#466—718no—
501#465—718no—
502#450—718no—
503#449—718no—
504#449—718no—
505#447—718no—
506C2×#107—711no—
507C2×#107—711no—
508C2×#106—711no—
509C2×#106—711no—
510C2×#103—711no—
511C2×#103—711no—
512C2×#102—711no—
513C2×#102—711no—
514C2×#102—711no—
515C2×#102—711no—
516C2×#102—711no—
517C2×#102—711no—
518#408—718no—
519C2×C22⋊C8—711no—
520C2×C22⋊C8—711no—
521C2×C22⋊C8—711no—
522C2×C22⋊C8—711no—
523C25—1421no—
524C2×#41—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41C22⋊D7114yes—
530C2×#41C22×D7114yes—
531C2×#41C22×D7114yescomplemented
532C22×Q8C22⋊D7111yescharacteristic
533C22×Q8C22×D7111yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—2842no—
538C22×D4—2842no—
539C22×D4—714no—
540C22×D4—711no—
541C22×D4—711no—
542C22×D4—1421no—
543C22×D4—1421no—
544C22×D4—1421no—
545C22×D4—1421no—
546C22×D4—1421no—
547C22×D4—1422no—
548C22×D4C22⋊D7111yescharacteristic
549C22×D4C22⋊D7111yescharacteristic
550C22×D4C22⋊D7111yescharacteristic
551C22×D4C22×D7111yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C22×D7111yescharacteristic
555C23×C4C22×D7111yescharacteristic
556C23×C4C22×D7111yescharacteristic
557C2×SD16—2842no—
558C2×SD16—2842no—
559C2×SD16—714no—
560C2×SD16—714no—
561C2×D8—2842no—
562C2×D8—2842no—
563C2×D8—714no—
564C2×D8—714no—
565C2×M16—2842no—
566C2×M16—714no—
567C22×C8—2842no—
568C22×C8—714no—
569C22×C8—711no—
570C22×C8—711no—
571C22×C8—711no—
572C22×C8—711no—
573#127—1428no—
574#124—1428no—
575C22⋊Q8—28no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8C22×D7114yes—
579C22⋊Q8C22×D7114yescomplemented
580#121—28no—
581#121—28no—
582#121—28no—
583#121—22no—
584#121—22no—
585#121—714no—
586#121—714no—
587#121—714no—
588#121—714no—
589#121—1422no—
590#121—1422no—
591#121—1422no—
592#121—1422no—
593#121C22×D7114yes—
594#121C22×D7114yescomplemented
595#120—1428no—
596#120—1428no—
597#117—714no—
598#117—1422no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—711no—
604C2×C4⋊C4—711no—
605C2×C4⋊C4C22×D7111yescharacteristic
606C2×C4⋊C4C22×D7111yescharacteristic
607C2×C4⋊C4C22×D7114yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—1421no—
613C2×C22⋊C4—1421no—
614C2×C22⋊C4—1421no—
615C2×C22⋊C4—1421no—
616C2×C22⋊C4—1421no—
617C2×C42—1421no—
618#107—714no—
619#107—714no—
620#106—714no—
621#106—714no—
622#103—714no—
623#103—714no—
624#102—714no—
625#102—714no—
626#102—714no—
627#102—714no—
628#102—714no—
629#102—714no—
630C22⋊C8—714no—
631C22⋊C8—714no—
632C22⋊C8—714no—
633C22⋊C8—714no—
634C24—21no—
635C24—2844no—
636C24—5682no—
637C24—5682no—
638C24—1421no—
639C24—1421no—
640C24—1424no—
641C24C2×C22⋊D7111yescharacteristic
642C24C2×C22⋊D7111yescharacteristic
643C24C2×C22⋊D7111yescharacteristic
644#41—48no—
645#41—44no—
646#41—44no—
647#41—44no—
648#41—44no—
649#41—48no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—42no—
654C2×Q8C2×C22⋊D7114yes—
655C2×Q8C23×D7112yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—82no—
667C2×D4—82no—
668C2×D4—2844no—
669C2×D4—2848no—
670C2×D4—2844no—
671C2×D4—2844no—
672C2×D4—5682no—
673C2×D4—5682no—
674C2×D4—5682no—
675C2×D4—5682no—
676C2×D4—712no—
677C2×D4—712no—
678C2×D4—1424no—
679C2×D4—1424no—
680C2×D4—1424no—
681C2×D4—1424no—
682C2×D4—1421no—
683C2×D4—1421no—
684C2×D4—1424no—
685C2×D4—1422no—
686C2×D4—1422no—
687C2×D4—1422no—
688C2×D4—1422no—
689C2×D4C2×C22⋊D7114yes—
690C2×D4C2×C22⋊D7114yes—
691C2×D4C2×C22⋊D7114yes—
692C2×D4C23×D7112yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—44no—
705C22×C4—82no—
706C22×C4—1421no—
707C22×C4—1421no—
708C22×C4C2×C22⋊D7112yes—
709C22×C4C2×C22⋊D7112yes—
710C22×C4C2×C22⋊D7112yes—
711C22×C4C2×C22⋊D7111yescharacteristic
712C22×C4C2×C22⋊D7111yescharacteristic
713C22×C4C2×C22⋊D7111yescharacteristic
714C22×C4C23×D7112yes—
715C22×C4C23×D7112yes—
716C22×C4C23×D7112yes—
717C22×C4C23×D7111yescharacteristic
718SD16—2844no—
719SD16—2844no—
720D8—2844no—
721D8—2844no—
722M16—2844no—
723C2×C8—2844no—
724C2×C8—712no—
725C2×C8—712no—
726C2×C8—712no—
727C2×C8—712no—
728C2×C8—1422no—
729C2×C8—1422no—
730C2×C8—1422no—
731C2×C8—1422no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—712no—
738C4⋊C4—712no—
739C4⋊C4—1421no—
740C4⋊C4—1421no—
741C4⋊C4C23×D7112yes—
742C4⋊C4C23×D7112yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—1424no—
748C22⋊C4—1424no—
749C22⋊C4—1424no—
750C22⋊C4—1424no—
751C22⋊C4—1424no—
752C42—1424no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—2848no—
767C23—2842no—
768C23—2842no—
769C23—2842no—
770C23—2842no—
771C23—2842no—
772C23—2842no—
773C23—5684no—
774C23—5684no—
775C23—56816no—
776C23—1422no—
777C23—1422no—
778C23C22×C22⋊D7112yes—
779C23C22×C22⋊D7112yes—
780C23C22×C22⋊D7112yes—
781C23C22×C22⋊D7111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—42no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—44no—
790D4—44no—
791D4—48no—
792D4—42no—
793D4—84no—
794D4—84no—
795D4—2848no—
796D4—2842no—
797D4—2842no—
798D4—5684no—
799D4—5684no—
800D4—5684no—
801D4—5684no—
802D4—1422no—
803D4—1422no—
804D4—1422no—
805D4—1422no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—48no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—84no—
826C2×C4—2842no—
827C2×C4—2842no—
828C2×C4—1422no—
829C2×C4—1422no—
830C2×C4C22×C22⋊D7112yes—
831C2×C4C22×C22⋊D7112yes—
832C2×C4C22×C22⋊D7112yes—
833C2×C4C22×C22⋊D7111yescharacteristic
834C2×C4#1455617312yes—
835C2×C4#1455617312yes—
836C2×C4C24×D7111yescharacteristic
837C8—1422no—
838C8—1422no—
839C8—1422no—
840C8—1422no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—84no—
857C22—2842no—
858C22—2842no—
859C22—2842no—
860C22—2842no—
861C22—2842no—
862C22—2842no—
863C22—56816no—
864C22—5684no—
865C22—5684no—
866C22#1798655812yes—
867C22#1798680212yes—
868C22#1798680712yes—
869C22C23×C22⋊D7111yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—2842no—
877C4—2842no—
878C4#1798655812yes—
879C4C2×#1455617311yescharacteristic
880C4C2×#1455617311yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—5682no—
886C2—5682no—
887C2#2259918614yesdirect product factor
888C2C2×#1798655811yescharacteristic
889C2C2×#1798680211yescharacteristic
890C2C2×#1798680711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#537×C71C2
socleC23×C71C22×D4
hypercenterC2×#537D71
hypocenterC71C2×#3198
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#17986563C2semidirect
2. #22599186C2direct (N × H)
3. C2×#17986317C2semidirect
4. C2×#17986337C2semidirect
5. C2×#17986320C2semidirect
6. C2×#17986312C2semidirect
7. C2×#17986250C2semidirect
8. C2×#17986247C2semidirect
9. C2×#17986233C2semidirect
10. C2×#17986230C2semidirect
11. C2×#17986144C2semidirect
12. C2×#17986144C2semidirect
13. C2×#17986149C2semidirect
14. C2×#17986132C2semidirect
15. C2×#17985966C2semidirect
16. C2×#537×C71C2semidirect
22. C22×#11765849C22semidirect
23. C23×C71⋊C8C22semidirect
25. #17986563C22semidirect
35. #17986337C22semidirect
36. #17986320C22semidirect
37. #17986317C22semidirect
38. #17986312C22semidirect
39. #17986250C22semidirect
40. #17986247C22semidirect
41. #17986233C22semidirect
42. #17986230C22semidirect
43. #17986149C22semidirect
44. #17986144C22semidirect
45. #17986144C22semidirect
46. #17986132C22semidirect
47. C2×#14556061C22semidirect
48. C2×#14556061C22semidirect
49. C2×#14556059C22semidirect
50. C2×#14556059C22semidirect
51. C2×#14556052C22semidirect
52. C2×#14556052C22semidirect
53. C2×#14556049C22semidirect
54. C2×#14556049C22semidirect
59. #17985966C22semidirect
62. C2×C22⋊(C71⋊C8)C22semidirect
63. C2×C22⋊(C71⋊C8)C22semidirect
65. C22×#41×C71C22semidirect
67. #537×C71C22semidirect
70. C2×C22⋊Q8×C71C22semidirect
75. C2×#121×C71C22semidirect
76. C22×C4⋊C4×C71C22semidirect
98. C2×#11765849C23semidirect
104. C22×C71⋊C8C23semidirect
127. #14556061C23semidirect
128. #14556061C23semidirect
129. #14556059C23semidirect
130. #14556059C23semidirect
131. #14556052C23semidirect
132. #14556052C23semidirect
133. #14556049C23semidirect
134. #14556049C23semidirect
141. C22⋊(C71⋊C8)C23semidirect
142. C22⋊(C71⋊C8)C23semidirect
150. C2×#41×C71C23semidirect
169. C22⋊Q8×C71C23semidirect
176. #121×C71C23semidirect
183. C2×C4⋊C4×C71C23semidirect
440. C2×C71#3198semidirect
446. C2×#537D71semidirect
462. C71C2×#3198semidirect
464. C22×#41C2×D71semidirect
473. #537C2×D71semidirect
480. C2×C22⋊Q8C2×D71semidirect
489. C2×#121C2×D71semidirect
493. C22×C4⋊C4C2×D71semidirect
531. C2×#41C22×D71semidirect
579. C22⋊Q8C22×D71semidirect
594. #121C22×D71semidirect
607. C2×C4⋊C4C22×D71semidirect
887. C2#22599186direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865632
#225991862
C2×#179863172
C2×#179863372
C2×#179863202
C2×#179863122
C2×#179862502
C2×#179862472
C2×#179862332
C2×#179862302
C2×#179861442
C2×#179861492
C2×#179861322
C2×#179859662
C2×#537×C712
C2×#319871