Finite Group Databasebeta

← C2×#22622534 #33964709

Subgroups — C2×#22622534 #33964709

Order 18688.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989290C211yesmaximal, characteristic, complemented
2C2×#17989287C211yesmaximal, characteristic, complemented
3#22622534C2116yesmaximal, direct product factor
4C2×#17988986C211yesmaximal, characteristic, complemented
5C2×#17988913C211yesmaximal, characteristic, complemented
6C2×#17988910C211yesmaximal, characteristic, complemented
7C2×#17988902C211yesmaximal, characteristic, complemented
8C2×#17988899C211yesmaximal, characteristic, complemented
9C2×#17988888C211yesmaximal, characteristic, complemented
10C2×#17988839C211yesmaximal, characteristic, complemented
11C2×#17988839C211yesmaximal, characteristic, complemented
12C2×C4×#11924013C211yesmaximal, characteristic, complemented
13C2×#17988664C211yesmaximal, characteristic, complemented
14C2×#17988628C211yesmaximal, characteristic, complemented
15C2×#17988626C211yesmaximal, characteristic, complemented
16C2×#478×C73C211yesmaximal, characteristic, complemented
17C22×#11924013C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20#17989290—24no—
21#17989290C2218yescomplemented
22#17989287—24no—
23#17989287C2218yescomplemented
24C2×#14556586—21no—
25C2×#14556584—21no—
26C2×#14556583C2211yescharacteristic
27C2×#14556576—21no—
28C2×#14556574—21no—
29C2×#14556566—21no—
30C2×#14556566C2211yescharacteristic
31C2×#14556566C2211yescharacteristic
32C2×#14556564—21no—
33C2×#14556562C2211yescharacteristic
34C2×#14556562C2211yescharacteristic
35C2×C4×D292C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C2×#14556553—21no—
38C2×C4×C22⋊D73—21no—
39C2×#14556549C2211yescharacteristic
40C2×#14556549C2211yescharacteristic
41C2×C4⋊C4×D73C2211yescharacteristic
42C2×C4⋊C4×D73C2211yescharacteristic
43#17988986C2218yescomplemented
44#17988913C2218yescomplemented
45#17988910C2218yescomplemented
46#17988902C2218yescomplemented
47#17988899C2218yescomplemented
48#17988888C2218yescomplemented
49#17988839C2218yescomplemented
50#17988839C2218yescomplemented
51C4×#11924013C2218yescomplemented
52#17988664C2218yescomplemented
53#17988628C2218yescomplemented
54#17988626C2218yescomplemented
55C2×#14556525C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556524C2211yescharacteristic
59C2×#14556523C2211yescharacteristic
60C2×#14556522C2211yescharacteristic
61C2×#14556522C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556512C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C4×#10596831C2211yescharacteristic
69C2×#125×C73C2211yescharacteristic
70C2×C4×D4×C73C2211yescharacteristic
71#478×C73C2218yescomplemented
72C2×#107×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#102×C73C2211yescharacteristic
77C22×D292—21no—
78C22×D292—21no—
79C22×D292D411yescharacteristic
80C22×D292C2311yescharacteristic
81C22×C22⋊D73—21no—
82C22×C22⋊D73—21no—
83C22×C4×D73—21no—
84C22×C4×D73—21no—
85C22×C4×D73—21no—
86C22×C4×D73C2311yescharacteristic
87C22×C4×D73C2311yescharacteristic
88C2×#11924013—24no—
89C2×#11924013C2314yes—
90C2×#11924011—24no—
91C2×#11924011—24no—
92C2×#11924011C2314yes—
93C2×#11924011C2314yes—
94C22×#10596831C2311yescharacteristic
95C22×#10596831C2311yescharacteristic
96#14556586—28no—
97#14556584—28no—
98#14556583—22no—
99#14556583C2314yes—
100#14556576—28no—
101#14556574—28no—
102#14556566—28no—
103#14556566—22no—
104#14556566—22no—
105#14556566C2314yes—
106#14556566C2314yes—
107#14556564—28no—
108#14556562—22no—
109#14556562—22no—
110#14556562C2314yes—
111#14556562C2314yes—
112C4×D292—22no—
113C4×D292D414yes—
114C4×D292C2314yes—
115C4×D292C2314yes—
116#14556553—28no—
117C4×C22⋊D73—28no—
118#14556549—22no—
119#14556549—22no—
120#14556549C2314yes—
121#14556549C2314yes—
122C2×C4⋊Dic73D411yescharacteristic
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×C4⋊Dic73C2311yescharacteristic
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007—21no—
130C4⋊C4×D73—22no—
131C4⋊C4×D73—22no—
132C4⋊C4×D73C2314yes—
133C4⋊C4×D73C2314yes—
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005D411yescharacteristic
142C2×#11924005D411yescharacteristic
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145#14556525C2314yes—
146#14556524C2314yes—
147#14556524C2314yes—
148#14556524C2314yes—
149#14556523C2314yes—
150#14556522C2314yes—
151#14556522C2314yes—
152#14556513C2314yes—
153#14556513C2314yes—
154#14556512C2314yes—
155#14556511C2314yes—
156#14556503C2314yes—
157#14556503C2314yes—
158C4×#10596831C2314yes—
159C22×D4×C73C2311yescharacteristic
160C23×C4×C73—21no—
161C22×C8×C73C2311yescharacteristic
162C22×C8×C73C2311yescharacteristic
163#125×C73—22no—
164#125×C73C2314yes—
165C4×D4×C73—22no—
166C4×D4×C73C2314yes—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C22⋊C4×C73—21no—
173C2×C42×C73C2311yescharacteristic
174#107×C73C2314yes—
175#106×C73C2314yes—
176C4⋊C8×C73C2314yes—
177#102×C73C2314yes—
178#102×C73C2314yes—
179C23×D73—21no—
180C23×D73C2×D411yescharacteristic
181C23×D73C2×D411yescharacteristic
182C2×D292—22no—
183C2×D292—22no—
184C2×D292—24no—
185C2×D292—21no—
186C2×D292—24no—
187C2×D292—42no—
188C2×D292—44no—
189C2×D292—82no—
190C2×D292C2×D414yes—
191C2×D292C2412yes—
192C2×C22⋊D73—24no—
193C2×C22⋊D73—24no—
194C2×C22⋊D73—44no—
195C2×C22⋊D73—82no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C2×C4×D73—22no—
202C2×C4×D73—22no—
203C2×C4×D73—22no—
204C2×C4×D73—22no—
205C2×C4×D73—24no—
206C2×C4×D73—24no—
207C2×C4×D73—24no—
208C2×C4×D73—82no—
209C2×C4×D73—82no—
210C2×C4×D73—82no—
211C2×C4×D73C2×D412yes—
212C2×C4×D73C2×D412yes—
213C2×C4×D73C2412yes—
214C2×C4×D73C2412yes—
215#11924013—28no—
216#11924011—28no—
217#11924011—28no—
218C2×#10596831—22no—
219C2×#10596831#4114yes—
220C2×#10596831C2412yes—
221C2×#10596831C2412yes—
222C4⋊Dic73—21no—
223C4⋊Dic73—21no—
224C4⋊Dic73—21no—
225C4⋊Dic73C2×D414yes—
226C4⋊Dic73C2412yes—
227C4⋊Dic73C2412yes—
228C4⋊Dic73C2412yes—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233C22⋊Dic73—24no—
234C22⋊Dic73—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005C2×D414yes—
241#11924005C2×D414yes—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C24×C73—21no—
245C2×D4×C73—21no—
246C2×D4×C73—22no—
247C2×D4×C73—22no—
248C2×D4×C73C2412yes—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—24no—
253C22×C4×C73—82no—
254C22×C4×C73C2×D411yescharacteristic
255C22×C4×C73C2×D411yescharacteristic
256C22×C4×C73C2411yescharacteristic
257C2×C8×C73—22no—
258C2×C8×C73—22no—
259C2×C8×C73C2412yes—
260C2×C8×C73C2412yes—
261C4⋊C4×C73—24no—
262C4⋊C4×C73—24no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73C2412yes—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C22⋊C4×C73—24no—
270C42×C73C2×D412yes—
271C42×C73C2412yes—
272C23×C73—22no—
273C23×C73—42no—
274C23×C73—42no—
275C23×C73—42no—
276C23×C73C22×D411yescharacteristic
277C22×D73—22no—
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—22no—
281C22×D73—22no—
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—42no—
285C22×D73—42no—
286C22×D73—42no—
287C22×D73C22×D412yes—
288C22×D73C22×D412yes—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—42no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—42no—
298C2×C4×C73—42no—
299C2×C4×C73—42no—
300C2×C4×C73—84no—
301C2×C4×C73C22×D412yes—
302C2×C4×C73C22×D412yes—
303C2×C4×C73C22×D411yescharacteristic
304C2×C4×C73C2×#4112yes—
305C2×C4×C732−1+412yes—
306C2×C4×C73C2511yescharacteristic
307C22⋊D73—48no—
308C22⋊D73—84no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73C22×D412yes—
318C2×Dic73C22×D412yes—
319D292—22no—
320D292—22no—
321D292—44no—
322D292—48no—
323D292—42no—
324D292—84no—
325C4×D73—24no—
326C4×D73—24no—
327C4×D73—22no—
328C4×D73—22no—
329C4×D73—22no—
330C4×D73—22no—
331C4×D73—84no—
332C4×D73—84no—
333C4×D73—84no—
334C8×C73—22no—
335C8×C73—22no—
336#10596831—22no—
337#10596831C2×#4114yes—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—84no—
342C22×C73#54712yes—
343C22×C73#57512yes—
344C22×C73#57612yes—
345C22×C73C23×D411yescharacteristic
346C2×D73—22no—
347C2×D73—22no—
348C2×D73—22no—
349C2×D73—22no—
350C2×D73—22no—
351C2×D73—22no—
352C2×D73—44no—
353C2×D73—44no—
354C2×D73—42no—
355C2×D73—42no—
356C2×D73—42no—
357C2×D73—84no—
358C4×C73—22no—
359C4×C73—22no—
360C4×C73—42no—
361C4×C73—42no—
362C4×C73—42no—
363C4×C73#54712yes—
364C4×C73C22×#4111yescharacteristic
365C4×C73C2×2−1+411yescharacteristic
366Dic73—22no—
367Dic73—22no—
368Dic73—42no—
369Dic73—42no—
370Dic73—42no—
371C2×#3355—731nomaximal, Sylow
372C2×C73—82no—
373C2×C73#335514yescomplemented
374C2×C73C2×#54711yescharacteristic
375C2×C73C2×#57511yescharacteristic
376C2×C73C2×#57611yescharacteristic
377D73—42no—
378D73—42no—
379D73—82no—
380C2×#553—731no—
381C2×#553—731no—
382#3355—7316no—
383C2×#499—731no—
384C2×#482—731no—
385C2×#482—731no—
386C2×#480—731no—
387C2×#480—731no—
388C2×#478—731no—
389C2×#478D7311yescharacteristic, complemented
390C2×#469—731no—
391C2×#469—731no—
392C2×C4×D8—731no—
393C2×#436—731no—
394C2×#428—731no—
395C2×#428—731no—
396C73C2×#335511yescharacteristic, complemented, Sylow
397C22×D8—731no—
398C22×M16—731no—
399C22×M16—731no—
400#553—738no—
401#553—738no—
402#553—1464no—
403#553—1464no—
404C2×#126—1461no—
405C2×#126—1461no—
406C2×#125—731no—
407C2×#125C2×D7311yescharacteristic
408C2×#123—1461no—
409C2×#123—1461no—
410C2×#121—731no—
411C2×#121—731no—
412C2×#121—731no—
413C2×#121—731no—
414C2×#121—1461no—
415C2×#121—1461no—
416C2×C4×D4—731no—
417C2×C4×D4—731no—
418C2×C4×D4—1461no—
419C2×C4×D4—1461no—
420C2×C4×D4C2×D7311yescharacteristic
421C2×#117—731no—
422C2×#117—731no—
423C22×C4⋊C4—731no—
424C22×C4⋊C4—731no—
425#499—738no—
426#482—738no—
427#482—738no—
428#480—738no—
429#480—738no—
430#478—738no—
431#478C2×D7318yescomplemented
432#469—738no—
433#469—738no—
434C4×D8—738no—
435#436—738no—
436#428—738no—
437#428—738no—
438C2×#107—731no—
439C2×#107—731no—
440C2×#107—731no—
441C2×#107—731no—
442C2×#107C2×D7311yescharacteristic
443C2×#106—731no—
444C2×#106—731no—
445C2×#106—731no—
446C2×#106C2×D7311yescharacteristic
447C2×C4⋊C8C2×D7311yescharacteristic
448C2×#102—731no—
449C2×#102—731no—
450C2×#102—731no—
451C2×#102—731no—
452C2×#102C2×D7311yescharacteristic
453C2×#102C2×D7311yescharacteristic
454C2×C22⋊C8—731no—
455C2×C22⋊C8—731no—
456C2×C4×C8—731no—
457C22×D4—731no—
458C22×D4—731no—
459C22×D4—1461no—
460C22×D4—1461no—
461C22×D4—1461no—
462C22×D4—1461no—
463C22×D4C22×D7311yescharacteristic
464C23×C4—21no—
465C23×C4—731no—
466C23×C4—731no—
467C23×C4—1461no—
468C23×C4—1461no—
469C23×C4—1461no—
470C2×D8—734no—
471C2×D8—1464no—
472C2×M16—734no—
473C2×M16—734no—
474C2×M16—1464no—
475C2×M16—1464no—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8C22×D7311yescharacteristic
479C22×C8C22×D7311yescharacteristic
480#126—1468no—
481#126—1468no—
482#125—22no—
483#125—734no—
484#125—1462no—
485#125C22×D7314yes—
486#123—1468no—
487#123—1468no—
488#121—734no—
489#121—734no—
490#121—734no—
491#121—734no—
492#121—1468no—
493#121—1462no—
494#121—1462no—
495#121—1468no—
496#121—1462no—
497#121—1462no—
498C4×D4—22no—
499C4×D4—734no—
500C4×D4—734no—
501C4×D4—734no—
502C4×D4—1468no—
503C4×D4—1468no—
504C4×D4—1462no—
505C4×D4C22×D7314yes—
506#117—734no—
507#117—734no—
508#117—1462no—
509#117—1462no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4—731no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—734no—
517C2×C4⋊C4—734no—
518C2×C4⋊C4—1462no—
519C2×C4⋊C4—1462no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4—1461no—
522C2×C4⋊C4—1461no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4C22×D7311yescharacteristic
525C2×C4⋊C4C22×D7311yescharacteristic
526C2×C4⋊C4C22×D7311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—731no—
529C2×C22⋊C4—731no—
530C2×C22⋊C4—1461no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C22⋊C4—1461no—
537C2×C42—1461no—
538C2×C42—1461no—
539C2×C42C22×D7311yescharacteristic
540#107—734no—
541#107—734no—
542#107—734no—
543#107—734no—
544#107C22×D7314yes—
545#106—734no—
546#106—734no—
547#106—734no—
548#106C22×D7314yes—
549C4⋊C8C22×D7314yes—
550#102—734no—
551#102—734no—
552#102—734no—
553#102—734no—
554#102C22×D7314yes—
555#102C22×D7314yes—
556C22⋊C8—734no—
557C22⋊C8—734no—
558C4×C8—734no—
559C24—21no—
560C24—731no—
561C24—731no—
562C24—1461no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—2922no—
567C2×D4—2924no—
568C2×D4—2924no—
569C2×D4—5842no—
570C2×D4—5842no—
571C2×D4—734no—
572C2×D4—732no—
573C2×D4—1464no—
574C2×D4—1464no—
575C2×D4—1464no—
576C2×D4—1464no—
577C2×D4—1461no—
578C2×D4—1462no—
579C2×D4—1462no—
580C2×D4C23×D7312yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—5842no—
587C22×C4—5842no—
588C22×C4—5842no—
589C22×C4—731no—
590C22×C4—731no—
591C22×C4—732no—
592C22×C4—732no—
593C22×C4—732no—
594C22×C4—732no—
595C22×C4—1464no—
596C22×C4—1464no—
597C22×C4—1461no—
598C22×C4—1461no—
599C22×C4—1461no—
600C22×C4—1464no—
601C22×C4—1462no—
602C22×C4—1462no—
603C22×C4—1462no—
604C22×C4—1462no—
605C22×C4D4×D7311yescharacteristic
606C22×C4D4×D7311yescharacteristic
607C22×C4C23×D7311yescharacteristic
608D8—1468no—
609M16—1468no—
610M16—1468no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—734no—
614C2×C8—732no—
615C2×C8—732no—
616C2×C8—1462no—
617C2×C8C23×D7312yes—
618C2×C8C23×D7312yes—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—734no—
625C4⋊C4—732no—
626C4⋊C4—732no—
627C4⋊C4—732no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1464no—
632C4⋊C4—1461no—
633C4⋊C4—1461no—
634C4⋊C4—1461no—
635C4⋊C4C23×D7312yes—
636C4⋊C4C23×D7312yes—
637C4⋊C4C23×D7312yes—
638C22⋊C4—24no—
639C22⋊C4—734no—
640C22⋊C4—734no—
641C22⋊C4—1464no—
642C22⋊C4—1464no—
643C22⋊C4—1464no—
644C22⋊C4—1464no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C22⋊C4—1464no—
648C42—1464no—
649C42—1464no—
650C42D4×D7312yes—
651C42C23×D7312yes—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—2922no—
657C23—2922no—
658C23—2922no—
659C23—732no—
660C23—732no—
661C23—1462no—
662C23—1462no—
663C23—1462no—
664C23—1462no—
665C23—1462no—
666C23—1462no—
667C23—1462no—
668C23C2×D4×D7311yescharacteristic
669D4—22no—
670D4—22no—
671D4—42no—
672D4—2924no—
673D4—2928no—
674D4—2928no—
675D4—2922no—
676D4—5844no—
677D4—5844no—
678D4—1462no—
679D4—1462no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—2922no—
690C2×C4—2922no—
691C2×C4—2922no—
692C2×C4—5844no—
693C2×C4—5844no—
694C2×C4—5844no—
695C2×C4—732no—
696C2×C4—732no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1462no—
700C2×C4—1462no—
701C2×C4—1462no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C2×C4—1462no—
706C2×C4—1464no—
707C2×C4—1464no—
708C2×C4C2×D4×D7312yes—
709C2×C4C2×D4×D7312yes—
710C2×C4C2×D4×D7311yescharacteristic
711C2×C4#41×D7312yes—
712C2×C4#1455663912yes—
713C2×C4C24×D7311yescharacteristic
714C8—22no—
715C8—22no—
716C8—734no—
717C8—1462no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—2924no—
723C22—2924no—
724C22—2922no—
725C22—2922no—
726C22—2922no—
727C22—5844no—
728C22—1462no—
729C22—1462no—
730C22—1462no—
731C22—1462no—
732C22—1462no—
733C22—1462no—
734C22#1798923912yes—
735C22#1798938412yes—
736C22#1798939112yes—
737C22C22×D4×D7311yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—2922no—
744C4—2922no—
745C4—2922no—
746C4—1462no—
747C4—1462no—
748C4#1798923912yes—
749C4C2×#41×D7311yescharacteristic
750C4C2×#1455663911yescharacteristic
751C2—82no—
752C2—2922no—
753C2—2922no—
754C2—5842no—
755C2#2262253414yesdirect product factor
756C2C2×#1798923911yescharacteristic
757C2C2×#1798938411yescharacteristic
758C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#478×C73C2
socleC23×C73C22×D4
hypercenterC2×#478D73
hypocenterC73C2×#3355
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#17989290C2semidirect
2. C2×#17989287C2semidirect
3. #22622534C2direct (N × H)
4. C2×#17988986C2semidirect
5. C2×#17988913C2semidirect
6. C2×#17988910C2semidirect
7. C2×#17988902C2semidirect
8. C2×#17988899C2semidirect
9. C2×#17988888C2semidirect
10. C2×#17988839C2semidirect
11. C2×#17988839C2semidirect
12. C2×C4×#11924013C2semidirect
13. C2×#17988664C2semidirect
14. C2×#17988628C2semidirect
15. C2×#17988626C2semidirect
16. C2×#478×C73C2semidirect
21. #17989290C22semidirect
23. #17989287C22semidirect
43. #17988986C22semidirect
44. #17988913C22semidirect
45. #17988910C22semidirect
46. #17988902C22semidirect
47. #17988899C22semidirect
48. #17988888C22semidirect
49. #17988839C22semidirect
50. #17988839C22semidirect
51. C4×#11924013C22semidirect
52. #17988664C22semidirect
53. #17988628C22semidirect
54. #17988626C22semidirect
71. #478×C73C22semidirect
373. C2×C73#3355semidirect
389. C2×#478D73semidirect
396. C73C2×#3355semidirect
431. #478C2×D73semidirect
755. C2#22622534direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892902
C2×#179892872
#226225342
C2×#179889862
C2×#179889132
C2×#179889102
C2×#179889022
C2×#179888992
C2×#179888882
C2×#179888392
C2×C4×#119240132
C2×#179886642
C2×#179886282
C2×#179886262
C2×#478×C732
C2×#335573