Finite Group Databasebeta

← C2×#22620535 #33955759

Subgroups — C2×#22620535 #33955759

Order 18688.

1986 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989141C211yesmaximal, characteristic, complemented
2C2×#17989124C211yesmaximal, characteristic
3#22620535C2116yesmaximal, direct product factor
4C2×#17988995C211yesmaximal, characteristic, complemented
5C2×#17988980C211yesmaximal, characteristic, complemented
6C2×#17988954C211yesmaximal, characteristic, complemented
7C2×#17988948C211yesmaximal, characteristic, complemented
8C2×#17988844C211yesmaximal, characteristic, complemented
9C2×#17988842C211yesmaximal, characteristic, complemented
10C2×#17988836C211yesmaximal, characteristic
11C2×#17988834C211yesmaximal, characteristic
12C2×C4×#11924018C211yesmaximal, characteristic, complemented
13C2×C4×#11924017C211yesmaximal, characteristic, complemented
14C2×C4×#11924015C211yesmaximal, characteristic, complemented
15C2×C4×#11924011C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C73C211yesmaximal, characteristic, complemented
17C22×#11924018C2211yescharacteristic
18C22×#11924017C2211yescharacteristic
19C22×#11924015C2211yescharacteristic
20C22×#11924011C2211yescharacteristic
21C22×#11924011C2211yescharacteristic
22#17989141—24no—
23#17989141C2218yescomplemented
24C2×#14556590C2211yescharacteristic
25C2×#14556589C2211yescharacteristic
26#17989124—24no—
27#17989124C2218yes—
28C2×#14556586—21no—
29C2×#14556582C2211yescharacteristic
30C2×#14556581—21no—
31C2×#14556580C2211yescharacteristic
32C2×#14556576—21no—
33C2×#14556571C2211yescharacteristic
34C2×#14556569—21no—
35C2×#14556567C2211yescharacteristic
36C2×#14556567C2211yescharacteristic
37C2×#14556566C2211yescharacteristic
38C2×C4×Dic146—21no—
39C2×C4×Dic146C2211yescharacteristic
40C2×C4×D292—21no—
41C2×C4×D292C2211yescharacteristic
42C2×#14556548—21no—
43C2×#14556548—21no—
44C2×C42×D73C2211yescharacteristic
45#17988995C2218yescomplemented
46#17988980C2218yescomplemented
47#17988954C2218yescomplemented
48#17988948C2218yescomplemented
49#17988844C2218yescomplemented
50#17988842C2218yescomplemented
51#17988836C2218yes—
52#17988834C2218yes—
53C4×#11924018C2218yescomplemented
54C4×#11924017C2218yescomplemented
55C4×#11924015C2218yescomplemented
56C2×#14556524C2211yescharacteristic
57C2×#14556523C2211yescharacteristic
58C2×#14556522C2211yescharacteristic
59C2×#14556516C2211yescharacteristic
60C2×#14556515C2211yescharacteristic
61C2×#14556515C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C4×#11924011C2218yescomplemented
66C2×#14556501C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C4×#10596831C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×Q8×C73C2211yescharacteristic
72C4×Q16×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×C4×C8×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146C2311yescharacteristic
79C22×D292—21no—
80C22×D292C2311yescharacteristic
81C22×C4×D73—21no—
82C22×C4×D73D411yescharacteristic
83C22×C4×D73D411yescharacteristic
84C22×C4×D73C2311yescharacteristic
85C2×#11924018—24no—
86C2×#11924018C2314yes—
87C2×#11924017—24no—
88C2×#11924017C2314yes—
89C2×#11924015—24no—
90C2×#11924015C2314yes—
91C2×#11924011—24no—
92C2×#11924011—24no—
93C2×#11924011C2314yes—
94C2×#11924011C2314yes—
95C22×#10596831C2311yescharacteristic
96C22×#10596831C2311yescharacteristic
97#14556590—22no—
98#14556590C2314yes—
99#14556589—22no—
100#14556589C2314yes—
101#14556586—28no—
102#14556582—22no—
103#14556582C2314yes—
104#14556581—28no—
105#14556580—22no—
106#14556580C2314yes—
107#14556576—28no—
108#14556571—22no—
109#14556571C2314yes—
110#14556569—28no—
111#14556567—22no—
112#14556567—22no—
113#14556567C2314yes—
114#14556567C2314yes—
115#14556566—22no—
116#14556566C2314yes—
117C4×Dic146—28no—
118C4×Dic146—22no—
119C4×Dic146C2314yes—
120C4×D292—28no—
121C4×D292—22no—
122C4×D292C2314yes—
123#14556548—28no—
124#14556548—28no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73D411yescharacteristic
145C2×C4×Dic73D411yescharacteristic
146C2×C4×Dic73C2311yescharacteristic
147C42×D73D414yes—
148C42×D73C2314yes—
149#14556524C2314yes—
150#14556523C2314yes—
151#14556522C2314yes—
152#14556516C2314yes—
153#14556515C2314yes—
154#14556515C2314yes—
155#14556514C2314yes—
156#14556513C2314yes—
157#14556511C2314yes—
158#14556501C2314yes—
159#14556501C2314yes—
160C4×#10596831C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×Q8×C73C2311yescharacteristic
163C2×Q16×C73—24no—
164C2×Q16×C73C2314yes—
165C22×C8×C73C2311yescharacteristic
166C22×C8×C73C2311yescharacteristic
167C4×Q8×C73—22no—
168C4×Q8×C73—22no—
169C4×Q8×C73C2314yes—
170C4×Q8×C73C2314yes—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C42×C73—21no—
176C2×C42×C73—21no—
177C2×C42×C73C2311yescharacteristic
178#107×C73C2314yes—
179#103×C73C2314yes—
180#103×C73C2314yes—
181C4×C8×C73C2314yes—
182C23×D73—21no—
183C23×D73C2×D411yescharacteristic
184C2×Dic146—22no—
185C2×Dic146—22no—
186C2×Dic146—21no—
187C2×Dic146—24no—
188C2×Dic146—44no—
189C2×Dic146C2412yes—
190C2×D292—22no—
191C2×D292—22no—
192C2×D292—24no—
193C2×D292—21no—
194C2×D292—44no—
195C2×D292C2412yes—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C22×Dic73C2×D411yescharacteristic
202C2×C4×D73—24no—
203C2×C4×D73—22no—
204C2×C4×D73—22no—
205C2×C4×D73—24no—
206C2×C4×D73—42no—
207C2×C4×D73—44no—
208C2×C4×D73C2×D412yes—
209C2×C4×D73C2×D414yes—
210C2×C4×D73C2×D414yes—
211C2×C4×D73C2412yes—
212#11924018—28no—
213#11924017—28no—
214#11924015—28no—
215#11924011—28no—
216#11924011—28no—
217C2×#10596831—22no—
218C2×#10596831#4114yes—
219C2×#10596831C2412yes—
220C2×#10596831C2412yes—
221C4⋊Dic73—21no—
222C4⋊Dic73—21no—
223C4⋊Dic73—24no—
224C4⋊Dic73—24no—
225C4⋊Dic73C2412yes—
226C4⋊Dic73C2412yes—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924005—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240#11924005—24no—
241C4×Dic73—24no—
242C4×Dic73C2×D412yes—
243C4×Dic73C2×D414yes—
244C4×Dic73C2×D414yes—
245C4×Dic73C2412yes—
246C2×Q8×C73—21no—
247C2×Q8×C73—21no—
248C2×Q8×C73—22no—
249C2×Q8×C73—22no—
250C2×Q8×C73—22no—
251C2×Q8×C73—22no—
252C2×Q8×C73C2412yes—
253C2×Q8×C73C2412yes—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73C2×D411yescharacteristic
259C22×C4×C73C2×D411yescharacteristic
260C22×C4×C73C2411yescharacteristic
261Q16×C73—28no—
262C2×C8×C73—22no—
263C2×C8×C73#4114yes—
264C2×C8×C73C2412yes—
265C2×C8×C73C2412yes—
266C4⋊C4×C73—24no—
267C4⋊C4×C73—24no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73C2412yes—
271C4⋊C4×C73C2412yes—
272C42×C73—24no—
273C42×C73—24no—
274C42×C73C2×D412yes—
275C42×C73C2412yes—
276C23×C73C22×D411yescharacteristic
277C22×D73—22no—
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—22no—
281C22×D73—42no—
282C22×D73—42no—
283C22×D73—42no—
284C22×D73C22×D412yes—
285Q8×C73—22no—
286Q8×C73—22no—
287Q8×C73—22no—
288Q8×C73—22no—
289Q8×C73—42no—
290Q8×C73—42no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—42no—
297C2×C4×C73—42no—
298C2×C4×C73—42no—
299C2×C4×C73—42no—
300C2×C4×C73#13714yes—
301C2×C4×C73C22×D412yes—
302C2×C4×C73C22×D411yescharacteristic
303C2×C4×C73C22×D412yes—
304C2×C4×C73C2×#4112yes—
305C2×C4×C73C2×#4112yes—
306C2×C4×C73C2511yescharacteristic
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—42no—
314C2×Dic73—42no—
315C2×Dic73—42no—
316C2×Dic73C22×D412yes—
317C2×Dic73C22×D412yes—
318C2×Dic73C22×D412yes—
319D292—22no—
320D292—22no—
321D292—48no—
322D292—42no—
323C4×D73—24no—
324C4×D73—28no—
325C4×D73—22no—
326C4×D73—22no—
327C4×D73—44no—
328C4×D73—48no—
329Dic146—22no—
330Dic146—22no—
331Dic146—48no—
332Dic146—42no—
333C8×C73—22no—
334C8×C73C2×#4114yes—
335#10596831—22no—
336#10596831C2×#4114yes—
337C22×C73#53212yes—
338C22×C73C2×#13712yes—
339C22×C73#57512yes—
340C22×C73C23×D411yescharacteristic
341C2×D73—22no—
342C2×D73—22no—
343C2×D73—22no—
344C2×D73—44no—
345C2×D73—42no—
346C2×D73—42no—
347C2×D73—42no—
348C2×D73—84no—
349C4×C73—22no—
350C4×C73—42no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73—42no—
354C4×C73#53212yes—
355C4×C73C2×#13714yes—
356C4×C73C22×#4111yescharacteristic
357C4×C73C22×#4111yescharacteristic
358Dic73—22no—
359Dic73—22no—
360Dic73—22no—
361Dic73—42no—
362Dic73—42no—
363Dic73—42no—
364C2×#3172—731nomaximal, Sylow
365C2×C73#317214yescomplemented
366C2×C73C2×#53211yescharacteristic
367C2×C73C22×#13711yescharacteristic
368C2×C73C2×#57511yescharacteristic
369D73—42no—
370D73—82no—
371C2×#533—731no—
372C2×#529—731no—
373#3172—7316no—
374C2×#501—731no—
375C2×#497—731no—
376C2×#491—731no—
377C2×#489—731no—
378C2×#470—731no—
379C2×#470—731no—
380C2×#468—731no—
381C2×#468—731no—
382C2×C4×Q16—731no—
383C2×C4×Q16D7311yescharacteristic, complemented
384C2×C4×SD16—731no—
385C2×C4×SD16—731no—
386C2×C4×M16—731no—
387C73C2×#317211yescharacteristic, complemented, Sylow
388C22×Q16—731no—
389C22×Q16C2×D7311yescharacteristic
390C22×SD16—731no—
391C22×SD16—731no—
392C22×M16—731no—
393C22×M16—731no—
394#533—738no—
395#533—1464no—
396C2×C4⋊Q8—731no—
397C2×C4⋊Q8—731no—
398#529—738no—
399#529—1464no—
400C2×#126—1461no—
401C2×#125—731no—
402C2×#125—1461no—
403C2×#124—731no—
404C2×#123—1461no—
405C2×C22⋊Q8—731no—
406C2×C22⋊Q8—731no—
407C2×C22⋊Q8—731no—
408C2×C22⋊Q8—1461no—
409C2×#121—731no—
410C2×C4×Q8—731no—
411C2×C4×Q8—1461no—
412C2×C4×Q8C2×D7311yescharacteristic
413C2×C4×Q8C2×D7311yescharacteristic
414C2×C4×D4—731no—
415C2×C4×D4—1461no—
416C2×#117—1461no—
417C2×#117—1461no—
418C22×C42—731no—
419#501—738no—
420#497—738no—
421#491—738no—
422#489—738no—
423#470—738no—
424#470—738no—
425#468—738no—
426#468—738no—
427C4×Q16—738no—
428C4×Q16C2×D7318yescomplemented
429C4×SD16—738no—
430C4×SD16—738no—
431C2×#107—731no—
432C2×#107C2×D7311yescharacteristic
433C2×#106—731no—
434C2×#106—731no—
435C2×#103—731no—
436C2×#103—731no—
437C2×#103—731no—
438C2×#103—731no—
439C2×#103C2×D7311yescharacteristic
440C2×#103C2×D7311yescharacteristic
441C2×#102—731no—
442C2×#102—731no—
443C4×M16—738no—
444C2×#97—731no—
445C2×#97—731no—
446C2×C4×C8—731no—
447C2×C4×C8C2×D7311yescharacteristic
448C22×Q8—731no—
449C22×Q8—1461no—
450C22×Q8C22×D7311yescharacteristic
451C22×Q8C22×D7311yescharacteristic
452C22×D4—731no—
453C22×D4—1461no—
454C23×C4—731no—
455C23×C4—731no—
456C23×C4—731no—
457C23×C4—1461no—
458C2×Q16—24no—
459C2×Q16—734no—
460C2×Q16—1464no—
461C2×Q16C22×D7314yes—
462C2×SD16—734no—
463C2×SD16—734no—
464C2×SD16—1464no—
465C2×SD16—1464no—
466C2×M16—734no—
467C2×M16—734no—
468C2×M16—1464no—
469C2×M16—1464no—
470C22×C8—731no—
471C22×C8—731no—
472C22×C8C22×D7311yescharacteristic
473C22×C8C22×D7311yescharacteristic
474C4⋊Q8—734no—
475C4⋊Q8—734no—
476C4⋊Q8—1462no—
477C4⋊Q8—1462no—
478#126—1468no—
479#125—734no—
480#125—1462no—
481#125—1468no—
482#124—734no—
483#124—1462no—
484#123—1468no—
485C22⋊Q8—734no—
486C22⋊Q8—734no—
487C22⋊Q8—734no—
488C22⋊Q8—1462no—
489C22⋊Q8—1468no—
490C22⋊Q8—1462no—
491C22⋊Q8—1462no—
492#121—734no—
493#121—1462no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—734no—
497C4×Q8—1468no—
498C4×Q8—1462no—
499C4×Q8C22×D7314yes—
500C4×Q8C22×D7314yes—
501C4×D4—734no—
502C4×D4—1468no—
503C4×D4—1462no—
504#117—1468no—
505#117—1468no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—731no—
510C2×C4⋊C4—1461no—
511C2×C4⋊C4—1461no—
512C2×C4⋊C4—1461no—
513C2×C4⋊C4—1461no—
514C2×C4⋊C4—1461no—
515C2×C4⋊C4—1461no—
516C2×C4⋊C4—1461no—
517C2×C4⋊C4—1461no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4C22×D7311yescharacteristic
520C2×C4⋊C4C22×D7311yescharacteristic
521C2×C22⋊C4—1461no—
522C2×C22⋊C4—1461no—
523C2×C22⋊C4—1461no—
524C2×C22⋊C4—1461no—
525C2×C22⋊C4—1461no—
526C2×C22⋊C4—1461no—
527C2×C22⋊C4—1461no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—731no—
531C2×C42—731no—
532C2×C42—731no—
533C2×C42—734no—
534C2×C42—734no—
535C2×C42—1461no—
536C2×C42C22×D7311yescharacteristic
537#107—734no—
538#107C22×D7314yes—
539#106—734no—
540#106—734no—
541#103—734no—
542#103—734no—
543#103—734no—
544#103—734no—
545#103C22×D7314yes—
546#103C22×D7314yes—
547#102—734no—
548#102—734no—
549#97—734no—
550#97—734no—
551C4×C8—734no—
552C4×C8C22×D7314yes—
553C24—731no—
554C24—1461no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—2924no—
562C2×Q8—732no—
563C2×Q8—1464no—
564C2×Q8—1462no—
565C2×Q8—1462no—
566C2×Q8—1461no—
567C2×Q8C23×D7312yes—
568C2×Q8C23×D7312yes—
569C2×D4—2924no—
570C2×D4—732no—
571C2×D4—1464no—
572C2×D4—1461no—
573C2×D4—1462no—
574C2×D4—1462no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—2922no—
580C22×C4—2924no—
581C22×C4—734no—
582C22×C4—731no—
583C22×C4—731no—
584C22×C4—731no—
585C22×C4—734no—
586C22×C4—732no—
587C22×C4—732no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1464no—
592C22×C4—1464no—
593C22×C4—1462no—
594C22×C4—1462no—
595C22×C4D4×D7311yescharacteristic
596C22×C4D4×D7311yescharacteristic
597C22×C4C23×D7311yescharacteristic
598Q16—28no—
599Q16—1468no—
600SD16—1468no—
601SD16—1468no—
602M16—1468no—
603M16—1468no—
604C2×C8—22no—
605C2×C8—734no—
606C2×C8—732no—
607C2×C8—732no—
608C2×C8—1462no—
609C2×C8#1192402814yes—
610C2×C8C23×D7312yes—
611C2×C8C23×D7312yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—732no—
617C4⋊C4—732no—
618C4⋊C4—1464no—
619C4⋊C4—1464no—
620C4⋊C4—1464no—
621C4⋊C4—1464no—
622C4⋊C4—1464no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1464no—
627C4⋊C4—1461no—
628C4⋊C4—1461no—
629C4⋊C4C23×D7312yes—
630C4⋊C4C23×D7312yes—
631C22⋊C4—1464no—
632C22⋊C4—1464no—
633C22⋊C4—1464no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C42—24no—
639C42—24no—
640C42—734no—
641C42—732no—
642C42—734no—
643C42—732no—
644C42—1464no—
645C42D4×D7312yes—
646C42C23×D7312yes—
647C23—2922no—
648C23—2922no—
649C23—2922no—
650C23—732no—
651C23—1462no—
652C23—1462no—
653C23—1462no—
654C23—1462no—
655C23C2×D4×D7311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—2928no—
663Q8—2922no—
664Q8—1462no—
665Q8—1462no—
666D4—2928no—
667D4—2922no—
668D4—1462no—
669D4—1462no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—2924no—
680C2×C4—2922no—
681C2×C4—2922no—
682C2×C4—2922no—
683C2×C4—2928no—
684C2×C4—732no—
685C2×C4—732no—
686C2×C4—732no—
687C2×C4—1462no—
688C2×C4—1462no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1468no—
694C2×C4—1464no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4#1455662314yes—
698C2×C4C2×D4×D7312yes—
699C2×C4C2×D4×D7312yes—
700C2×C4C2×D4×D7311yescharacteristic
701C2×C4#41×D7312yes—
702C2×C4C2×#1192402812yes—
703C2×C4C24×D7311yescharacteristic
704C8—22no—
705C8—734no—
706C8—1462no—
707C8C2×#1192402814yes—
708C22—2924no—
709C22—2922no—
710C22—2922no—
711C22—2922no—
712C22—5844no—
713C22—1462no—
714C22—1462no—
715C22—1462no—
716C22#1798913412yes—
717C22C2×#1455662312yes—
718C22#1798938412yes—
719C22C22×D4×D7311yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—2922no—
726C4—2922no—
727C4—2922no—
728C4—1462no—
729C4—1462no—
730C4—1462no—
731C4#1798913412yes—
732C4C2×#1455662314yes—
733C4C2×#41×D7311yescharacteristic
734C4C22×#1192402811yescharacteristic
735C2—2922no—
736C2—5842no—
737C2#2262053514yesdirect product factor
738C2C2×#1798913411yescharacteristic
739C2C22×#1455662311yescharacteristic
740C2C2×#1798938411yescharacteristic
subgroupG/H
centerC22×C4D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×C4×Q16×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556566C22
hypercenterC2×C4×Q16D73
hypocenterC73C2×#3172
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#17989141C2semidirect
3. #22620535C2direct (N × H)
4. C2×#17988995C2semidirect
5. C2×#17988980C2semidirect
6. C2×#17988954C2semidirect
7. C2×#17988948C2semidirect
8. C2×#17988844C2semidirect
9. C2×#17988842C2semidirect
12. C2×C4×#11924018C2semidirect
13. C2×C4×#11924017C2semidirect
14. C2×C4×#11924015C2semidirect
15. C2×C4×#11924011C2semidirect
16. C2×C4×Q16×C73C2semidirect
23. #17989141C22semidirect
45. #17988995C22semidirect
46. #17988980C22semidirect
47. #17988954C22semidirect
48. #17988948C22semidirect
49. #17988844C22semidirect
50. #17988842C22semidirect
53. C4×#11924018C22semidirect
54. C4×#11924017C22semidirect
55. C4×#11924015C22semidirect
65. C4×#11924011C22semidirect
72. C4×Q16×C73C22semidirect
365. C2×C73#3172semidirect
383. C2×C4×Q16D73semidirect
387. C73C2×#3172semidirect
428. C4×Q16C2×D73semidirect
737. C2#22620535direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891412
C2×#179891242
#226205352
C2×#179889952
C2×#179889802
C2×#179889542
C2×#179889482
C2×#179888442
C2×#179888422
C2×#179888362
C2×#179888342
C2×C4×#119240182
C2×C4×#119240172
C2×C4×#119240152
C2×C4×#119240112
C2×C4×Q16×C732
C2×#317273