Finite Group Databasebeta

← C2×#22622432 #33964580

Subgroups — C2×#22622432 #33964580

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×#17989300C211yesmaximal, characteristic, complemented
2C2×#17989285C211yesmaximal, characteristic, complemented
3#22622432C2116yesmaximal, direct product factor
4C2×#17988995C211yesmaximal, characteristic, complemented
5C2×#17988914C211yesmaximal, characteristic, complemented
6C2×#17988913C211yesmaximal, characteristic, complemented
7C2×#17988911C211yesmaximal, characteristic, complemented
8C2×#17988900C211yesmaximal, characteristic, complemented
9C2×#17988886C211yesmaximal, characteristic, complemented
10C2×#17988866C211yesmaximal, characteristic, complemented
11C2×#17988840C211yesmaximal, characteristic, complemented
12C2×#17988824C211yesmaximal, characteristic, complemented
13C2×#17988698C211yesmaximal, characteristic, complemented
14C2×#17988656C211yesmaximal, characteristic, complemented
15C2×#17988622C211yesmaximal, characteristic, complemented
16C2×#428×C73C211yesmaximal, characteristic, complemented
17C22×D584C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19#17989300—24no—
20#17989300C2218yescomplemented
21#17989285—24no—
22#17989285C2218yescomplemented
23C2×#14556590C2211yescharacteristic
24C2×#14556586—21no—
25C2×#14556582C2211yescharacteristic
26C2×#14556579—21no—
27C2×#14556577—21no—
28C2×#14556576—21no—
29C2×#14556566C2211yescharacteristic
30C2×#14556566C2211yescharacteristic
31C2×#14556565—21no—
32C2×#14556565C2211yescharacteristic
33C2×#14556565C2211yescharacteristic
34C2×#14556564—21no—
35C2×#14556553C2211yescharacteristic
36C2×#14556553C2211yescharacteristic
37C2×C4×C22⋊D73—21no—
38C2×C4×C22⋊D73C2211yescharacteristic
39C2×#14556549C2211yescharacteristic
40C2×#14556549C2211yescharacteristic
41C2×#14556548—21no—
42#17988995C2218yescomplemented
43#17988914C2218yescomplemented
44#17988913C2218yescomplemented
45#17988911C2218yescomplemented
46#17988900C2218yescomplemented
47#17988886C2218yescomplemented
48#17988866C2218yescomplemented
49#17988840C2218yescomplemented
50#17988824C2218yescomplemented
51#17988698C2218yescomplemented
52#17988656C2218yescomplemented
53#17988622C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556523C2211yescharacteristic
58C2×#14556522C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556513C2211yescharacteristic
61C2×#14556513C2211yescharacteristic
62C2×#14556511C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×#14556501C2211yescharacteristic
69C22×M16×C73C2211yescharacteristic
70C2×#117×C73C2211yescharacteristic
71C22×C4⋊C4×C73C2211yescharacteristic
72#428×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#107×C73C2211yescharacteristic
75C2×#106×C73C2211yescharacteristic
76C2×#106×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×D292—21no—
79C22×D292—21no—
80C22×D292C2311yescharacteristic
81C22×D292C2311yescharacteristic
82C22×C22⋊D73—21no—
83C22×C22⋊D73—21no—
84C22×C22⋊D73D411yescharacteristic
85C22×C4×D73—21no—
86C22×C4×D73—21no—
87C22×C4×D73C2311yescharacteristic
88C2×D584—24no—
89C2×D584C2314yes—
90C22×#10596831C2311yescharacteristic
91C22×#10596831C2311yescharacteristic
92C2×C8×D73—24no—
93C2×C8×D73C2314yes—
94#14556590—22no—
95#14556590C2314yes—
96#14556586—28no—
97#14556582—22no—
98#14556582C2314yes—
99#14556579—28no—
100#14556577—28no—
101#14556576—28no—
102#14556566—22no—
103#14556566—22no—
104#14556566C2314yes—
105#14556566C2314yes—
106#14556565—28no—
107#14556565—22no—
108#14556565—22no—
109#14556565C2314yes—
110#14556565C2314yes—
111#14556564—28no—
112#14556553—22no—
113#14556553—22no—
114#14556553C2314yes—
115#14556553C2314yes—
116C4×C22⋊D73—28no—
117C4×C22⋊D73D414yes—
118C4×C22⋊D73C2314yes—
119#14556549—22no—
120#14556549—22no—
121#14556549C2314yes—
122#14556549C2314yes—
123#14556548—28no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73C2311yescharacteristic
126C2×C4⋊Dic73C2311yescharacteristic
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007D411yescharacteristic
130C2×C22⋊Dic73D411yescharacteristic
131C2×#11924005—21no—
132C2×#11924005—21no—
133C2×#11924005—21no—
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005D411yescharacteristic
140C2×C4×Dic73—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73C2311yescharacteristic
143#14556524C2314yes—
144#14556524C2314yes—
145#14556524C2314yes—
146#14556523C2314yes—
147#14556522C2314yes—
148#14556520C2314yes—
149#14556513C2314yes—
150#14556513C2314yes—
151#14556511C2314yes—
152#14556511C2314yes—
153#14556511C2314yes—
154#14556511C2314yes—
155C22⋊#10596831C2314yes—
156#14556503C2314yes—
157#14556501C2314yes—
158C23×C4×C73—21no—
159C23×C4×C73C2311yescharacteristic
160C2×M16×C73—24no—
161C2×M16×C73C2314yes—
162C22×C8×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164#117×C73—22no—
165#117×C73C2314yes—
166C2×C4⋊C4×C73—22no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2314yes—
173C2×C22⋊C4×C73—21no—
174C2×C42×C73—21no—
175#107×C73C2314yes—
176#107×C73C2314yes—
177#106×C73C2314yes—
178#106×C73C2314yes—
179C23×D73—21no—
180C23×D73—21no—
181C23×D73C2×D411yescharacteristic
182C2×Dic146—24no—
183C2×Dic146—82no—
184C2×D292—22no—
185C2×D292—22no—
186C2×D292—22no—
187C2×D292—22no—
188C2×D292—21no—
189C2×D292—21no—
190C2×D292—24no—
191C2×D292—24no—
192C2×D292—82no—
193C2×D292—82no—
194C2×D292C2412yes—
195C2×D292C2412yes—
196C2×C22⋊D73—24no—
197C2×C22⋊D73—24no—
198C2×C22⋊D73—42no—
199C2×C22⋊D73—44no—
200C2×C22⋊D73—82no—
201C2×C22⋊D73C2×D414yes—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C2×C4×D73—22no—
208C2×C4×D73—22no—
209C2×C4×D73—24no—
210C2×C4×D73—24no—
211C2×C4×D73—44no—
212C2×C4×D73—82no—
213C2×C4×D73C2×D412yes—
214C2×C4×D73C2412yes—
215D584—28no—
216C2×#10596831—22no—
217C2×#10596831—22no—
218C2×#10596831C2412yes—
219C2×#10596831C2412yes—
220C8×D73—28no—
221C4⋊Dic73—21no—
222C4⋊Dic73—21no—
223C4⋊Dic73—24no—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226#11924007—24no—
227#11924007—24no—
228#11924007C2×D414yes—
229C22⋊Dic73C2×D414yes—
230#11924005—24no—
231#11924005—24no—
232#11924005—24no—
233#11924005—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005C2×D414yes—
239C4×Dic73—24no—
240C4×Dic73—24no—
241C4×Dic73C2×D412yes—
242C4×Dic73C2412yes—
243C24×C73C2×D411yescharacteristic
244C22×C4×C73—22no—
245C22×C4×C73—22no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—24no—
251C22×C4×C73—82no—
252C22×C4×C73C2×D411yescharacteristic
253C22×C4×C73C2×D412yes—
254C22×C4×C73C2412yes—
255C22×C4×C73C2411yescharacteristic
256M16×C73—28no—
257C2×C8×C73—22no—
258C2×C8×C73#4114yes—
259C2×C8×C73C2412yes—
260C2×C8×C73C2412yes—
261C4⋊C4×C73—21no—
262C4⋊C4×C73—21no—
263C4⋊C4×C73—24no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73C2412yes—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C4⋊C4×C73C2412yes—
270C22⋊C4×C73—24no—
271C42×C73—24no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73C22×D412yes—
276C23×C73C22×D411yescharacteristic
277C22×D73—22no—
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—22no—
281C22×D73—22no—
282C22×D73—42no—
283C22×D73—42no—
284C22×D73—42no—
285C22×D73—42no—
286C22×D73—42no—
287C22×D73—42no—
288C22×D73C22×D412yes—
289C2×C4×C73—22no—
290C2×C4×C73—24no—
291C2×C4×C73—22no—
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—42no—
301C2×C4×C73—84no—
302C2×C4×C73C22×D412yes—
303C2×C4×C73C22×D411yescharacteristic
304C2×C4×C73C2×#4112yes—
305C2×C4×C732−1+412yes—
306C2×C4×C73C2511yescharacteristic
307C22⋊D73—44no—
308C22⋊D73—48no—
309C22⋊D73—84no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—42no—
316C2×Dic73—42no—
317C2×Dic73C22×D412yes—
318C2×Dic73C22×D412yes—
319C2×Dic73C22×D412yes—
320D292—22no—
321D292—22no—
322D292—22no—
323D292—22no—
324D292—42no—
325D292—42no—
326D292—84no—
327D292—84no—
328C4×D73—24no—
329C4×D73—22no—
330C4×D73—22no—
331C4×D73—48no—
332C4×D73—84no—
333Dic146—84no—
334C8×C73—22no—
335C8×C73C2×#4114yes—
336#10596831—22no—
337#10596831—22no—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—22no—
341C22×C73—44no—
342C22×C73#54712yes—
343C22×C73#57512yes—
344C22×C73#57612yes—
345C22×C73C23×D411yescharacteristic
346C2×D73—22no—
347C2×D73—22no—
348C2×D73—22no—
349C2×D73—44no—
350C2×D73—42no—
351C2×D73—42no—
352C2×D73—42no—
353C2×D73—42no—
354C2×D73—42no—
355C2×D73—42no—
356C2×D73—84no—
357C2×D73—84no—
358C4×C73—22no—
359C4×C73—42no—
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—22no—
369Dic73—42no—
370Dic73—42no—
371C2×#3347—731nomaximal, Sylow
372C2×C73—42no—
373C2×C73#334714yescomplemented
374C2×C73C2×#54711yescharacteristic
375C2×C73C2×#57511yescharacteristic
376C2×C73C2×#57611yescharacteristic
377D73—42no—
378D73—82no—
379D73—82no—
380C2×#555—731no—
381C2×#553—731no—
382#3347—7316no—
383C2×#501—731no—
384C2×#482—731no—
385C2×#482—731no—
386C2×#482—731no—
387C2×#480—731no—
388C2×#478—731no—
389C2×#474—731no—
390C2×#469—731no—
391C2×#466—731no—
392C2×#442—731no—
393C2×#435—731no—
394C2×#428D7311yescharacteristic, complemented
395C2×#427—731no—
396C73C2×#334711yescharacteristic, complemented, Sylow
397C22×D8—731no—
398C22×M16C2×D7311yescharacteristic
399C23×C8—731no—
400#555—738no—
401#555—1464no—
402#553—738no—
403#553—1464no—
404C2×C4⋊Q8—731no—
405C2×#126—1461no—
406C2×#125—731no—
407C2×#124—1461no—
408C2×#124—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—731no—
419C2×C4×D4—1461no—
420C2×#117—731no—
421C2×#117—731no—
422C2×#117—1461no—
423C2×#117C2×D7311yescharacteristic
424C22×C4⋊C4C2×D7311yescharacteristic
425#501—738no—
426#482—738no—
427#482—738no—
428#482—738no—
429#480—738no—
430#478—738no—
431#474—738no—
432#469—738no—
433#466—738no—
434#442—738no—
435#435—738no—
436#428C2×D7318yescomplemented
437#427—738no—
438C2×#107—731no—
439C2×#107—731no—
440C2×#107—731no—
441C2×#107C2×D7311yescharacteristic
442C2×#107C2×D7311yescharacteristic
443C2×#106—731no—
444C2×#106—731no—
445C2×#106C2×D7311yescharacteristic
446C2×#106C2×D7311yescharacteristic
447C2×C4⋊C8—731no—
448C2×#102—731no—
449C2×#102—731no—
450C2×#102—731no—
451C2×#102—731no—
452C2×#102—731no—
453C2×#102—731no—
454C2×C22⋊C8—731no—
455C2×C22⋊C8—731no—
456C2×#97—731no—
457C22×Q8—1461no—
458C22×D4—731no—
459C22×D4—731no—
460C22×D4—731no—
461C22×D4—1461no—
462C22×D4—1461no—
463C22×D4—1461no—
464C22×D4—1461no—
465C23×C4—21no—
466C23×C4—731no—
467C23×C4—1461no—
468C23×C4—1461no—
469C23×C4C22×D7311yescharacteristic
470C2×D8—734no—
471C2×D8—1464no—
472C2×M16—24no—
473C2×M16C22×D7314yes—
474C22×C8—731no—
475C22×C8—731no—
476C22×C8—734no—
477C22×C8—1464no—
478C22×C8C22×D7311yescharacteristic
479C22×C8C22×D7311yescharacteristic
480C4⋊Q8—734no—
481C4⋊Q8—1462no—
482#126—1468no—
483#125—734no—
484#125—1462no—
485#124—1468no—
486#124—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—734no—
499C4×D4—734no—
500C4×D4—734no—
501C4×D4—734no—
502C4×D4—1462no—
503C4×D4—1462no—
504C4×D4—1468no—
505#117—22no—
506#117—734no—
507#117—734no—
508#117—1468no—
509#117—1462no—
510#117—1462no—
511#117C22×D7314yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—731no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4C22×D7311yescharacteristic
521C2×C4⋊C4C22×D7311yescharacteristic
522C2×C4⋊C4C22×D7314yes—
523C2×C4⋊C4C22×D7311yescharacteristic
524C2×C4⋊C4C22×D7311yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—731no—
527C2×C22⋊C4—731no—
528C2×C22⋊C4—1461no—
529C2×C22⋊C4—1461no—
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×C42—21no—
537C2×C42—731no—
538C2×C42—1461no—
539C2×C42—1461no—
540#107—734no—
541#107—734no—
542#107—734no—
543#107C22×D7314yes—
544#107C22×D7314yes—
545#106—734no—
546#106—734no—
547#106C22×D7314yes—
548#106C22×D7314yes—
549C4⋊C8—734no—
550#102—734no—
551#102—734no—
552#102—734no—
553#102—734no—
554#102—734no—
555#102—734no—
556C22⋊C8—734no—
557C22⋊C8—734no—
558#97—734no—
559C24—731no—
560C24—1461no—
561C24—1461no—
562C24D4×D7311yescharacteristic
563C2×Q8—5842no—
564C2×Q8—1464no—
565C2×D4—2924no—
566C2×D4—2922no—
567C2×D4—5842no—
568C2×D4—5842no—
569C2×D4—5842no—
570C2×D4—734no—
571C2×D4—732no—
572C2×D4—732no—
573C2×D4—1464no—
574C2×D4—1464no—
575C2×D4—1464no—
576C2×D4—1464no—
577C2×D4—1461no—
578C2×D4—1461no—
579C2×D4—1462no—
580C2×D4—1462no—
581C2×D4—1462no—
582C2×D4—1462no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—82no—
591C22×C4—2924no—
592C22×C4—5842no—
593C22×C4—731no—
594C22×C4—731no—
595C22×C4—731no—
596C22×C4—732no—
597C22×C4—732no—
598C22×C4—1464no—
599C22×C4—1464no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1462no—
603C22×C4—1462no—
604C22×C4D4×D7312yes—
605C22×C4D4×D7311yescharacteristic
606C22×C4C23×D7312yes—
607C22×C4C23×D7311yescharacteristic
608D8—1468no—
609M16—28no—
610C2×C8—22no—
611C2×C8—732no—
612C2×C8—732no—
613C2×C8—1462no—
614C2×C8—1462no—
615C2×C8—1468no—
616C2×C8#1192402814yes—
617C2×C8C23×D7312yes—
618C2×C8C23×D7312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—734no—
625C4⋊C4—732no—
626C4⋊C4—732no—
627C4⋊C4—1464no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1461no—
631C4⋊C4—1461no—
632C4⋊C4C23×D7312yes—
633C4⋊C4C23×D7312yes—
634C4⋊C4C23×D7312yes—
635C4⋊C4C23×D7312yes—
636C22⋊C4—24no—
637C22⋊C4—734no—
638C22⋊C4—734no—
639C22⋊C4—1464no—
640C22⋊C4—1464no—
641C22⋊C4—1464no—
642C22⋊C4—1464no—
643C22⋊C4—1464no—
644C22⋊C4—1464no—
645C22⋊C4—1464no—
646C22⋊C4—1464no—
647C42—24no—
648C42—732no—
649C42—732no—
650C42—1464no—
651C42—1464no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—2922no—
656C23—2922no—
657C23—2922no—
658C23—2922no—
659C23—2922no—
660C23—2922no—
661C23—732no—
662C23—1462no—
663C23—1462no—
664C23—1462no—
665C23—1462no—
666C23—1462no—
667C23C2×D4×D7312yes—
668C23C2×D4×D7311yescharacteristic
669Q8—5844no—
670D4—2928no—
671D4—2924no—
672D4—2922no—
673D4—2922no—
674D4—5844no—
675D4—5844no—
676D4—5844no—
677D4—1462no—
678D4—1462no—
679D4—1462no—
680D4—1462no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—84no—
694C2×C4—2928no—
695C2×C4—2922no—
696C2×C4—2922no—
697C2×C4—5844no—
698C2×C4—732no—
699C2×C4—732no—
700C2×C4—732no—
701C2×C4—1462no—
702C2×C4—1462no—
703C2×C4—1462no—
704C2×C4—1462no—
705C2×C4—1462no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4—1464no—
709C2×C4C2×D4×D7312yes—
710C2×C4C2×D4×D7311yescharacteristic
711C2×C4C2×#1192402812yes—
712C2×C4#1455663912yes—
713C2×C4C24×D7311yescharacteristic
714C8—22no—
715C8—1462no—
716C8—1462no—
717C8C2×#1192402814yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—2924no—
723C22—2922no—
724C22—2922no—
725C22—2922no—
726C22—2922no—
727C22—2922no—
728C22—2922no—
729C22—5844no—
730C22—5844no—
731C22—1462no—
732C22—1462no—
733C22—1462no—
734C22#1798923812yes—
735C22#1798938612yes—
736C22#1798939112yes—
737C22C22×D4×D7311yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—2922no—
744C4—2922no—
745C4—1462no—
746C4—1462no—
747C4—1462no—
748C4#1798923812yes—
749C4C22×#1192402811yescharacteristic
750C4C2×#1455663911yescharacteristic
751C2—42no—
752C2—2922no—
753C2—5842no—
754C2—5842no—
755C2#2262243214yesdirect product factor
756C2C2×#1798923811yescharacteristic
757C2C2×#1798938611yescharacteristic
758C2C2×#1798939111yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#428×C73C2
socleC23×C73C22×D4
hypercenterC2×#428D73
hypocenterC73C2×#3347
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#17989300C2semidirect
2. C2×#17989285C2semidirect
3. #22622432C2direct (N × H)
4. C2×#17988995C2semidirect
5. C2×#17988914C2semidirect
6. C2×#17988913C2semidirect
7. C2×#17988911C2semidirect
8. C2×#17988900C2semidirect
9. C2×#17988886C2semidirect
10. C2×#17988866C2semidirect
11. C2×#17988840C2semidirect
12. C2×#17988824C2semidirect
13. C2×#17988698C2semidirect
14. C2×#17988656C2semidirect
15. C2×#17988622C2semidirect
16. C2×#428×C73C2semidirect
20. #17989300C22semidirect
22. #17989285C22semidirect
42. #17988995C22semidirect
43. #17988914C22semidirect
44. #17988913C22semidirect
45. #17988911C22semidirect
46. #17988900C22semidirect
47. #17988886C22semidirect
48. #17988866C22semidirect
49. #17988840C22semidirect
50. #17988824C22semidirect
51. #17988698C22semidirect
52. #17988656C22semidirect
53. #17988622C22semidirect
72. #428×C73C22semidirect
373. C2×C73#3347semidirect
394. C2×#428D73semidirect
396. C73C2×#3347semidirect
436. #428C2×D73semidirect
755. C2#22622432direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893002
C2×#179892852
#226224322
C2×#179889952
C2×#179889142
C2×#179889132
C2×#179889112
C2×#179889002
C2×#179888862
C2×#179888662
C2×#179888402
C2×#179888242
C2×#179886982
C2×#179886562
C2×#179886222
C2×#428×C732
C2×#334773