Finite Group Databasebeta

← C2×#22600826 #32876032

Subgroups — C2×#22600826 #32876032

Order 18176.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986704C211yesmaximal, characteristic, complemented
2C2×#17986693C211yesmaximal, characteristic
3#22600826C2116yesmaximal, direct product factor
4C2×#17986406C211yesmaximal, characteristic, complemented
5C2×#17986336C211yesmaximal, characteristic, complemented
6C2×#17986319C211yesmaximal, characteristic, complemented
7C2×#17986340C211yesmaximal, characteristic, complemented
8C2×#17986312C211yesmaximal, characteristic, complemented
9C2×#17986309C211yesmaximal, characteristic, complemented
10C2×#17986278C211yesmaximal, characteristic, complemented
11C2×#17986245C211yesmaximal, characteristic, complemented
12C2×#17986229C211yesmaximal, characteristic, complemented
13C2×#17986098C211yesmaximal, characteristic, complemented
14C2×#17986068C211yesmaximal, characteristic, complemented
15C2×#107×D71C211yesmaximal, characteristic, complemented
16C2×#428×C71C211yesmaximal, characteristic, complemented
17C22×#11765854C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19#17986704—24no—
20#17986704C2218yescomplemented
21#17986693—24no—
22#17986693C2218yes—
23C2×#14556127C2211yescharacteristic
24C2×#14556122—21no—
25C2×#14556119C2211yescharacteristic
26C2×#14556118—21no—
27C2×#14556110—21no—
28C2×#14556108C2211yescharacteristic
29C2×#14556107—21no—
30C2×#14556107C2211yescharacteristic
31C2×#14556106—21no—
32C2×#14556103C2211yescharacteristic
33C2×#14556102C2211yescharacteristic
34C2×#14556101—21no—
35C2×#14556093C2211yescharacteristic
36C2×C4×D284—21no—
37C2×#14556090C2211yescharacteristic
38C2×C4×C22⋊D71—21no—
39C2×C4×C22⋊D71C2211yescharacteristic
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42#17986406C2218yescomplemented
43#17986340C2218yescomplemented
44#17986336C2218yescomplemented
45#17986319C2218yescomplemented
46#17986312C2218yescomplemented
47#17986309C2218yescomplemented
48#17986278C2218yescomplemented
49#17986245C2218yescomplemented
50#17986229C2218yescomplemented
51#17986098C2218yescomplemented
52#17986068C2218yescomplemented
53C2×#14556062C2211yescharacteristic
54C2×#14556061C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57#107×D71C2218yescomplemented
58C2×#14556059C2211yescharacteristic
59C2×Dic71⋊C8C2211yescharacteristic
60C2×#14556053C2211yescharacteristic
61C2×#14556051C2211yescharacteristic
62C2×#14556051C2211yescharacteristic
63C2×#14556050C2211yescharacteristic
64C2×#14556048C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×#14556038C2211yescharacteristic
69C22×M16×C71C2211yescharacteristic
70C2×#117×C71C2211yescharacteristic
71C22×C4⋊C4×C71C2211yescharacteristic
72#428×C71C2218yescomplemented
73C2×#107×C71C2211yescharacteristic
74C2×#107×C71C2211yescharacteristic
75C2×#106×C71C2211yescharacteristic
76C2×#106×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284—21no—
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C22×C22⋊D71D411yescharacteristic
83C22×C4×D71—21no—
84C22×C4×D71—21no—
85C22×C4×D71—21no—
86C22×C4×D71C2311yescharacteristic
87C2×#11765854—24no—
88C2×#11765854C2314yes—
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91C2×C8×D71—24no—
92C2×C8×D71C2314yes—
93#14556127—22no—
94#14556127C2314yes—
95#14556122—28no—
96#14556119—22no—
97#14556119C2314yes—
98#14556118—28no—
99#14556110—28no—
100#14556108—22no—
101#14556108C2314yes—
102#14556107—28no—
103#14556107—22no—
104#14556107C2314yes—
105#14556106—28no—
106#14556103—22no—
107#14556103C2314yes—
108#14556102—22no—
109#14556102C2314yes—
110#14556101—28no—
111#14556093—22no—
112#14556093C2314yes—
113C4×D284—28no—
114#14556090—22no—
115#14556090C2314yes—
116C4×C22⋊D71—28no—
117C4×C22⋊D71D414yes—
118C4×C22⋊D71C2314yes—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71C2311yescharacteristic
122C2×C4⋊Dic71C2311yescharacteristic
123C2×Dic71⋊C4—21no—
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4D411yescharacteristic
130C4⋊C4×D71—22no—
131C4⋊C4×D71—22no—
132C4⋊C4×D71C2314yes—
133C4⋊C4×D71C2314yes—
134C2×C22⋊Dic71—21no—
135C2×C22⋊Dic71D411yescharacteristic
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4D411yescharacteristic
141C2×C4×Dic71—21no—
142C2×C4×Dic71C2311yescharacteristic
143#14556062C2314yes—
144#14556061C2314yes—
145#14556061C2314yes—
146#14556061C2314yes—
147#14556059C2314yes—
148Dic71⋊C8C2314yes—
149#14556053C2314yes—
150#14556051C2314yes—
151#14556051C2314yes—
152#14556050C2314yes—
153#14556048C2314yes—
154#14556048C2314yes—
155C22⋊(C71⋊C8)C2314yes—
156(C2×D71)⋊C8C2314yes—
157#14556038C2314yes—
158C23×C4×C71—21no—
159C23×C4×C71C2311yescharacteristic
160C2×M16×C71—24no—
161C2×M16×C71C2314yes—
162C22×C8×C71C2311yescharacteristic
163C22×C8×C71C2311yescharacteristic
164#117×C71—22no—
165#117×C71C2314yes—
166C2×C4⋊C4×C71—22no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71C2314yes—
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C22⋊C4×C71—21no—
174C2×C42×C71—21no—
175#107×C71C2314yes—
176#107×C71C2314yes—
177#106×C71C2314yes—
178#106×C71C2314yes—
179C23×D71—21no—
180C23×D71C2×D411yescharacteristic
181C2×Dic142—22no—
182C2×Dic142—22no—
183C2×Dic142—21no—
184C2×Dic142—24no—
185C2×Dic142—82no—
186C2×Dic142C2412yes—
187C2×D284—22no—
188C2×D284—22no—
189C2×D284—24no—
190C2×D284—21no—
191C2×D284—44no—
192C2×D284C2412yes—
193C2×C22⋊D71—24no—
194C2×C22⋊D71—24no—
195C2×C22⋊D71—82no—
196C2×C22⋊D71C2×D414yes—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C22×Dic71—21no—
200C22×Dic71C2×D411yescharacteristic
201C22×Dic71C2×D411yescharacteristic
202C22×Dic71C2×D411yescharacteristic
203C2×C4×D71—22no—
204C2×C4×D71—22no—
205C2×C4×D71—24no—
206C2×C4×D71—24no—
207C2×C4×D71—24no—
208C2×C4×D71—82no—
209C2×C4×D71—82no—
210C2×C4×D71—82no—
211C2×C4×D71C2×D412yes—
212C2×C4×D71C2412yes—
213#11765854—28no—
214C2×C71⋊C8—22no—
215C2×C71⋊C8—22no—
216C2×C71⋊C8C2412yes—
217C2×C71⋊C8C2412yes—
218C8×D71—28no—
219C4⋊Dic71—21no—
220C4⋊Dic71—21no—
221C4⋊Dic71—24no—
222C4⋊Dic71—24no—
223C4⋊Dic71C2412yes—
224C4⋊Dic71C2412yes—
225Dic71⋊C4—24no—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230Dic71⋊C4—24no—
231Dic71⋊C4C2×D414yes—
232C22⋊Dic71—24no—
233C22⋊Dic71C2×D414yes—
234(C2×D71)⋊C4—24no—
235(C2×D71)⋊C4—24no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4—24no—
238(C2×D71)⋊C4C2×D414yes—
239C4×Dic71—24no—
240C4×Dic71C2×D412yes—
241C4×Dic71C2412yes—
242C24×C71C2×D411yescharacteristic
243C22×C4×C71—22no—
244C22×C4×C71—22no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—24no—
250C22×C4×C71—82no—
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D412yes—
253C22×C4×C71C2412yes—
254C22×C4×C71C2411yescharacteristic
255M16×C71—28no—
256C2×C8×C71—22no—
257C2×C8×C71#4114yes—
258C2×C8×C71C2412yes—
259C2×C8×C71C2412yes—
260C4⋊C4×C71—21no—
261C4⋊C4×C71—24no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71C2412yes—
266C4⋊C4×C71C2412yes—
267C4⋊C4×C71C2412yes—
268C4⋊C4×C71C2412yes—
269C22⋊C4×C71—24no—
270C42×C71—24no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71C22×D412yes—
275C23×C71C22×D411yescharacteristic
276C22×D71—22no—
277C22×D71—22no—
278C22×D71—22no—
279C22×D71—42no—
280C22×D71—42no—
281C22×D71—42no—
282C22×D71#13714yes—
283C22×D71C22×D412yes—
284C2×C4×C71—22no—
285C2×C4×C71—24no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—42no—
293C2×C4×C71—42no—
294C2×C4×C71—42no—
295C2×C4×C71—42no—
296C2×C4×C71—84no—
297C2×C4×C71C22×D412yes—
298C2×C4×C71C22×D411yescharacteristic
299C2×C4×C71C2×#4112yes—
300C2×C4×C712−1+412yes—
301C2×C4×C71C2511yescharacteristic
302C22⋊D71—28no—
303C22⋊D71—84no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—42no—
311C2×Dic71—42no—
312C2×Dic71—42no—
313C2×Dic71C22×D412yes—
314C2×Dic71C22×D412yes—
315C2×Dic71C22×D412yes—
316D284—22no—
317D284—22no—
318D284—48no—
319D284—42no—
320C4×D71—24no—
321C4×D71—22no—
322C4×D71—22no—
323C4×D71—84no—
324C4×D71—84no—
325C4×D71—84no—
326Dic142—22no—
327Dic142—22no—
328Dic142—42no—
329Dic142—84no—
330C8×C71—22no—
331C8×C71C2×#4114yes—
332C71⋊C8—22no—
333C71⋊C8—22no—
334C22×C71—22no—
335C22×C71—22no—
336C22×C71—22no—
337C22×C71—44no—
338C22×C71#54712yes—
339C22×C71C2×#13712yes—
340C22×C71#57612yes—
341C22×C71C23×D411yescharacteristic
342C2×D71—28no—
343C2×D71—22no—
344C2×D71—22no—
345C2×D71—42no—
346C2×D71—42no—
347C2×D71—42no—
348C2×D71—84no—
349C2×D71C2×#13714yes—
350C4×C71—22no—
351C4×C71—42no—
352C4×C71—42no—
353C4×C71—42no—
354C4×C71—42no—
355C4×C71#54712yes—
356C4×C71C22×#4111yescharacteristic
357C4×C71C2×2−1+411yescharacteristic
358Dic71—22no—
359Dic71—22no—
360Dic71—22no—
361Dic71—42no—
362Dic71—42no—
363Dic71—42no—
364C2×#3346—711nomaximal, Sylow
365C2×C71—42no—
366C2×C71#334614yescomplemented
367C2×C71C2×#54711yescharacteristic
368C2×C71C22×#13711yescharacteristic
369C2×C71C2×#57611yescharacteristic
370D71—24no—
371D71—82no—
372C2×#554—711no—
373C2×#553—711no—
374#3346—7116no—
375C2×#501—711no—
376C2×#484—711no—
377C2×#481—711no—
378C2×#485—711no—
379C2×#480—711no—
380C2×#479—711no—
381C2×#474—711no—
382C2×#468—711no—
383C2×#465—711no—
384C2×#440—711no—
385C2×#435—711no—
386C2×#428D7111yescharacteristic, complemented
387C22×#107—711no—
388C71C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—711no—
390C22×M16C2×D7111yescharacteristic
391C23×C8—711no—
392#554—718no—
393#554—1424no—
394#553—718no—
395#553—1424no—
396C2×C4⋊Q8—711no—
397C2×#126—1421no—
398C2×#125—711no—
399C2×#125—1421no—
400C2×#123—1421no—
401C2×C22⋊Q8—711no—
402C2×C22⋊Q8—711no—
403C2×C22⋊Q8—1421no—
404C2×C22⋊Q8—1421no—
405C2×#121—711no—
406C2×#121—711no—
407C2×#121—1421no—
408C2×C4×Q8—711no—
409C2×C4×D4—711no—
410C2×C4×D4—711no—
411C2×C4×D4—1421no—
412C2×C4×D4—1421no—
413C2×#117C2×D7111yescharacteristic
414C22×C4⋊C4—711no—
415C22×C4⋊C4—711no—
416C22×C4⋊C4C2×D7111yescharacteristic
417#501—718no—
418#485—718no—
419#484—718no—
420#481—718no—
421#480—718no—
422#479—718no—
423#474—718no—
424#468—718no—
425#465—718no—
426#440—718no—
427#435—718no—
428#428C2×D7118yescomplemented
429C2×#107—711no—
430C2×#107—711no—
431C2×#107—711no—
432C2×#107—711no—
433C2×#107—718no—
434C2×#107C2×D7111yescharacteristic
435C2×#107C2×D7111yescharacteristic
436C2×#106—711no—
437C2×#106C2×D7111yescharacteristic
438C2×#106C2×D7111yescharacteristic
439C2×C4⋊C8—711no—
440C2×#103—711no—
441C2×#103—711no—
442C2×#103—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×#102—711no—
446C2×C22⋊C8—711no—
447C2×C22⋊C8—711no—
448C2×#97—711no—
449C22×Q8—711no—
450C22×Q8—1421no—
451C22×D4—711no—
452C22×D4—711no—
453C22×D4—1421no—
454C22×D4—1421no—
455C23×C4—21no—
456C23×C4—711no—
457C23×C4—1421no—
458C23×C4—1421no—
459C23×C4—1421no—
460C23×C4C22×D7111yescharacteristic
461C2×SD16—714no—
462C2×SD16—1424no—
463C2×M16—24no—
464C2×M16C22×D7114yes—
465C22×C8—711no—
466C22×C8—711no—
467C22×C8—714no—
468C22×C8—1424no—
469C22×C8C22×D7111yescharacteristic
470C22×C8C22×D7111yescharacteristic
471C4⋊Q8—714no—
472C4⋊Q8—1422no—
473#126—1428no—
474#125—714no—
475#125—1422no—
476#125—1428no—
477#123—1428no—
478C22⋊Q8—714no—
479C22⋊Q8—714no—
480C22⋊Q8—1428no—
481C22⋊Q8—1428no—
482C22⋊Q8—1422no—
483C22⋊Q8—1422no—
484#121—714no—
485#121—714no—
486#121—1428no—
487#121—1422no—
488#121—1422no—
489C4×Q8—714no—
490C4×Q8—1422no—
491C4×D4—714no—
492C4×D4—714no—
493C4×D4—714no—
494C4×D4—1428no—
495C4×D4—1422no—
496C4×D4—1428no—
497#117—22no—
498#117C22×D7114yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—711no—
502C2×C4⋊C4—711no—
503C2×C4⋊C4—711no—
504C2×C4⋊C4—714no—
505C2×C4⋊C4—714no—
506C2×C4⋊C4—1422no—
507C2×C4⋊C4—1422no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4—1421no—
510C2×C4⋊C4—1421no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4C22×D7111yescharacteristic
517C2×C4⋊C4C22×D7111yescharacteristic
518C2×C4⋊C4C22×D7111yescharacteristic
519C2×C4⋊C4C22×D7114yes—
520C2×C4⋊C4C22×D7111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—711no—
523C2×C22⋊C4—711no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4—1421no—
529C2×C42—21no—
530C2×C42—711no—
531C2×C42—1421no—
532#107—714no—
533#107—714no—
534#107—714no—
535#107—714no—
536#107C22×D7114yes—
537#107C22×D7114yes—
538#106—714no—
539#106C22×D7114yes—
540#106C22×D7114yes—
541C4⋊C8—714no—
542#103—714no—
543#103—714no—
544#103—714no—
545#102—714no—
546#102—714no—
547#102—714no—
548C22⋊C8—714no—
549C22⋊C8—714no—
550#97—714no—
551C24—711no—
552C24—1421no—
553C24D4×D7111yescharacteristic
554C2×Q8—5682no—
555C2×Q8—712no—
556C2×Q8—1424no—
557C2×Q8—1422no—
558C2×Q8—1422no—
559C2×Q8—1421no—
560C2×D4—2844no—
561C2×D4—5682no—
562C2×D4—714no—
563C2×D4—712no—
564C2×D4—1424no—
565C2×D4—1424no—
566C2×D4—1424no—
567C2×D4—1421no—
568C2×D4—1422no—
569C2×D4—1422no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—82no—
578C22×C4—5682no—
579C22×C4—5682no—
580C22×C4—5682no—
581C22×C4—711no—
582C22×C4—711no—
583C22×C4—711no—
584C22×C4—712no—
585C22×C4—712no—
586C22×C4—1424no—
587C22×C4—1424no—
588C22×C4—1424no—
589C22×C4—1421no—
590C22×C4—1421no—
591C22×C4—1421no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4D4×D7112yes—
595C22×C4D4×D7111yescharacteristic
596C22×C4C23×D7112yes—
597C22×C4C23×D7111yescharacteristic
598SD16—1428no—
599M16—28no—
600C2×C8—22no—
601C2×C8—712no—
602C2×C8—712no—
603C2×C8—1422no—
604C2×C8—1422no—
605C2×C8—1428no—
606C2×C8#1176586514yes—
607C2×C8C23×D7112yes—
608C2×C8C23×D7112yes—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—714no—
615C4⋊C4—712no—
616C4⋊C4—712no—
617C4⋊C4—1424no—
618C4⋊C4—1424no—
619C4⋊C4—1424no—
620C4⋊C4—1424no—
621C4⋊C4—1424no—
622C4⋊C4—1424no—
623C4⋊C4—1424no—
624C4⋊C4—1424no—
625C4⋊C4—1421no—
626C4⋊C4—1421no—
627C4⋊C4C23×D7112yes—
628C4⋊C4C23×D7112yes—
629C4⋊C4C23×D7112yes—
630C4⋊C4C23×D7112yes—
631C22⋊C4—24no—
632C22⋊C4—714no—
633C22⋊C4—714no—
634C22⋊C4—1424no—
635C22⋊C4—1424no—
636C22⋊C4—1424no—
637C22⋊C4—1424no—
638C22⋊C4—1424no—
639C42—24no—
640C42—712no—
641C42—712no—
642C42—1424no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—2842no—
647C23—2842no—
648C23—2842no—
649C23—712no—
650C23—714no—
651C23—1422no—
652C23—1422no—
653C23—1422no—
654C23C2×D4×D7112yes—
655C23C2×D4×D7111yescharacteristic
656Q8—2842no—
657Q8—5684no—
658Q8—1422no—
659Q8—1422no—
660D4—2848no—
661D4—2842no—
662D4—5684no—
663D4—1428no—
664D4—1422no—
665D4—1422no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—84no—
679C2×C4—2842no—
680C2×C4—2842no—
681C2×C4—2842no—
682C2×C4—5684no—
683C2×C4—5684no—
684C2×C4—5684no—
685C2×C4—712no—
686C2×C4—712no—
687C2×C4—712no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1424no—
697C2×C4C2×D4×D7112yes—
698C2×C4C2×D4×D7111yescharacteristic
699C2×C4C2×#1176586512yes—
700C2×C4#1455617612yes—
701C2×C4C24×D7111yescharacteristic
702C8—22no—
703C8—1422no—
704C8—1422no—
705C8C2×#1176586514yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—2842no—
711C22—2842no—
712C22—2842no—
713C22—5684no—
714C22—714no—
715C22—1422no—
716C22—1422no—
717C22—1428no—
718C22#1798665012yes—
719C22#137×D7112yes—
720C22#1798680312yes—
721C22C22×D4×D7111yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—2842no—
728C4—2842no—
729C4—2842no—
730C4—1422no—
731C4—1422no—
732C4—1422no—
733C4#1798665012yes—
734C4C22×#1176586511yescharacteristic
735C4C2×#1455617611yescharacteristic
736C2—42no—
737C2—5682no—
738C2—1424no—
739C2#2260082614yesdirect product factor
740C2C2×#1798665011yescharacteristic
741C2C2×#137×D7111yescharacteristic
742C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#428×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986693C2
hypercenterC2×#428D71
hypocenterC71C2×#3346
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#17986704C2semidirect
3. #22600826C2direct (N × H)
4. C2×#17986406C2semidirect
5. C2×#17986336C2semidirect
6. C2×#17986319C2semidirect
7. C2×#17986340C2semidirect
8. C2×#17986312C2semidirect
9. C2×#17986309C2semidirect
10. C2×#17986278C2semidirect
11. C2×#17986245C2semidirect
12. C2×#17986229C2semidirect
13. C2×#17986098C2semidirect
14. C2×#17986068C2semidirect
15. C2×#107×D71C2semidirect
16. C2×#428×C71C2semidirect
20. #17986704C22semidirect
42. #17986406C22semidirect
43. #17986340C22semidirect
44. #17986336C22semidirect
45. #17986319C22semidirect
46. #17986312C22semidirect
47. #17986309C22semidirect
48. #17986278C22semidirect
49. #17986245C22semidirect
50. #17986229C22semidirect
51. #17986098C22semidirect
52. #17986068C22semidirect
57. #107×D71C22semidirect
72. #428×C71C22semidirect
366. C2×C71#3346semidirect
386. C2×#428D71semidirect
388. C71C2×#3346semidirect
428. #428C2×D71semidirect
739. C2#22600826direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867042
C2×#179866932
#226008262
C2×#179864062
C2×#179863362
C2×#179863192
C2×#179863402
C2×#179863122
C2×#179863092
C2×#179862782
C2×#179862452
C2×#179862292
C2×#179860982
C2×#179860682
C2×#107×D712
C2×#428×C712
C2×#334671