Finite Group Databasebeta

← C2×#22620158 #33954261

Subgroups — C2×#22620158 #33954261

Order 18688.

2058 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×#17989202C211yesmaximal, characteristic
2C2×#17989063C211yesmaximal, characteristic, complemented
3#22620158C2116yesmaximal, direct product factor
4C2×#17988930C211yesmaximal, characteristic, complemented
5C2×#17988910C211yesmaximal, characteristic
6C2×#17988881C211yesmaximal, characteristic, complemented
7C2×#17988870C211yesmaximal, characteristic, complemented
8C2×#17988808C211yesmaximal, characteristic, complemented
9C2×#17988807C211yesmaximal, characteristic, complemented
10C2×#17988744C211yesmaximal, characteristic, complemented
11C2×#17988724C211yesmaximal, characteristic
12C2×#17988695C211yesmaximal, characteristic, complemented
13C2×C4×#11924018C211yesmaximal, characteristic, complemented
14C2×C4×#11924016C211yesmaximal, characteristic, complemented
15C2×#17988649C211yesmaximal, characteristic, complemented
16C2×#440×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×Dic292C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924016C2211yescharacteristic
21#17989202—24no—
22#17989202C2218yes—
23C2×#14556590C2211yescharacteristic
24C2×#14556584—21no—
25C2×#14556578C2211yescharacteristic
26C2×#14556577—21no—
27C2×#14556574—21no—
28C2×#14556571C2211yescharacteristic
29C2×#14556570—21no—
30C2×#14556562C2211yescharacteristic
31#17989063—24no—
32#17989063C2218yescomplemented
33C2×Q8×Dic73C2211yescharacteristic
34C2×C4×Dic146—21no—
35C2×C4×Dic146C2211yescharacteristic
36C2×C4×Dic146C2211yescharacteristic
37C2×#14556556—21no—
38C2×#14556556C2211yescharacteristic
39C2×#14556549—21no—
40C2×#14556549C2211yescharacteristic
41C2×#14556548—21no—
42C2×#14556548C2211yescharacteristic
43#17988930C2218yescomplemented
44#17988910C2218yes—
45#17988881C2218yescomplemented
46#17988870C2218yescomplemented
47#17988808C2218yescomplemented
48#17988807C2218yescomplemented
49#17988744C2218yescomplemented
50#17988724C2218yes—
51#17988695C2218yescomplemented
52C4×#11924018C2218yescomplemented
53C4×#11924016C2218yescomplemented
54#17988649C2218yescomplemented
55C2×#14556524C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556512C2211yescharacteristic
66C2×#14556503C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C4×#10596831C2211yescharacteristic
69C22×SD16×C73C2211yescharacteristic
70C2×C4×Q8×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72#440×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#102×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146C2311yescharacteristic
80C22×Dic146C2311yescharacteristic
81C2×Q8×D73—24no—
82C2×Q8×D73—22no—
83C2×Q8×D73—24no—
84C2×Q8×D73C2314yes—
85C22×C22⋊D73—21no—
86C22×C4×D73—21no—
87C22×C4×D73C2311yescharacteristic
88C2×Dic292—24no—
89C2×Dic292C2314yes—
90C2×#11924018—24no—
91C2×#11924018C2314yes—
92C2×#11924016—24no—
93C2×#11924016C2314yes—
94C22×#10596831C2311yescharacteristic
95C22×#10596831C2311yescharacteristic
96#14556590—22no—
97#14556590C2314yes—
98#14556584—28no—
99#14556578—22no—
100#14556578C2314yes—
101#14556577—28no—
102#14556574—28no—
103#14556571—22no—
104#14556571C2314yes—
105#14556570—28no—
106#14556562—22no—
107#14556562C2314yes—
108Q8×Dic73—22no—
109Q8×Dic73C2314yes—
110C4×Dic146—28no—
111C4×Dic146—22no—
112C4×Dic146—22no—
113C4×Dic146C2314yes—
114C4×Dic146C2314yes—
115#14556556—28no—
116#14556556—22no—
117#14556556C2314yes—
118#14556549—22no—
119#14556549—28no—
120#14556549C2314yes—
121#14556548—28no—
122#14556548D414yes—
123#14556548C2314yes—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×#11924007—21no—
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007D411yescharacteristic
133C2×#11924007D411yescharacteristic
134C2×C22⋊Dic73—21no—
135C2×C22⋊Dic73—21no—
136C2×C22⋊Dic73—21no—
137C2×#11924005—21no—
138C2×#11924005—21no—
139C2×#11924005D411yescharacteristic
140C2×#11924005D411yescharacteristic
141C2×C4×Dic73—21no—
142C2×C4×Dic73—21no—
143C2×C4×Dic73—21no—
144C2×C4×Dic73—21no—
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556524C2314yes—
148#14556523C2314yes—
149#14556522C2314yes—
150#14556520C2314yes—
151#14556520C2314yes—
152#14556516C2314yes—
153#14556516C2314yes—
154#14556515C2314yes—
155#14556514C2314yes—
156#14556514C2314yes—
157#14556512C2314yes—
158#14556503C2314yes—
159#14556503C2314yes—
160C4×#10596831C2314yes—
161C22×Q8×C73C2311yescharacteristic
162C22×D4×C73C2311yescharacteristic
163C23×C4×C73—21no—
164C2×SD16×C73—24no—
165C2×SD16×C73C2314yes—
166C22×C8×C73C2311yescharacteristic
167C22×C8×C73C2311yescharacteristic
168C4×Q8×C73—22no—
169C4×Q8×C73C2314yes—
170C4×D4×C73—22no—
171C4×D4×C73C2314yes—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73C2311yescharacteristic
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C22⋊C4×C73—21no—
176C2×C42×C73—21no—
177C2×C42×C73C2311yescharacteristic
178#107×C73C2314yes—
179#103×C73C2314yes—
180#102×C73C2314yes—
181#97×C73C2314yes—
182C23×D73C2×D411yescharacteristic
183C2×Dic146—28no—
184C2×Dic146—21no—
185C2×Dic146—22no—
186C2×Dic146—24no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—21no—
190C2×Dic146—24no—
191C2×Dic146—82no—
192C2×Dic146#4114yes—
193C2×Dic146C2412yes—
194C2×Dic146C2412yes—
195Q8×D73—216no—
196Q8×D73—28no—
197Q8×D73—28no—
198C2×C22⋊D73—24no—
199C2×C22⋊D73—82no—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C2×C4×D73—28no—
208C2×C4×D73—24no—
209C2×C4×D73—22no—
210C2×C4×D73—22no—
211C2×C4×D73C2×D412yes—
212C2×C4×D73C2412yes—
213Dic292—28no—
214#11924018—28no—
215#11924016—28no—
216C2×#10596831—22no—
217C2×#10596831—22no—
218C2×#10596831C2412yes—
219C2×#10596831C2412yes—
220C4⋊Dic73—21no—
221C4⋊Dic73—21no—
222C4⋊Dic73—24no—
223C4⋊Dic73—24no—
224C4⋊Dic73C2412yes—
225C4⋊Dic73C2412yes—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007C2×D414yes—
231#11924007C2×D414yes—
232C22⋊Dic73—24no—
233C22⋊Dic73—24no—
234C22⋊Dic73—24no—
235#11924005—24no—
236#11924005—24no—
237#11924005C2×D414yes—
238#11924005C2×D414yes—
239C4×Dic73—24no—
240C4×Dic73—24no—
241C4×Dic73—24no—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C4×Dic73C2×D412yes—
245C4×Dic73C2412yes—
246C24×C73—21no—
247C2×Q8×C73—21no—
248C2×Q8×C73—22no—
249C2×Q8×C73#4114yes—
250C2×Q8×C73C2412yes—
251C2×D4×C73—21no—
252C2×D4×C73—22no—
253C2×D4×C73—22no—
254C2×D4×C73C2412yes—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—24no—
259C22×C4×C73—82no—
260C22×C4×C73C2×D411yescharacteristic
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2411yescharacteristic
263SD16×C73—28no—
264C2×C8×C73—22no—
265C2×C8×C73—22no—
266C2×C8×C73C2412yes—
267C2×C8×C73C2412yes—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73C2412yes—
272C4⋊C4×C73C2412yes—
273C22⋊C4×C73—24no—
274C42×C73—24no—
275C42×C73C2×D412yes—
276C42×C73C2412yes—
277C23×C73—22no—
278C23×C73—42no—
279C23×C73—42no—
280C23×C73—42no—
281C23×C73C22×D411yescharacteristic
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—22no—
285C22×D73C22×D412yes—
286Q8×C73—24no—
287Q8×C73—22no—
288Q8×C73C2×#4114yes—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—42no—
292C2×C4×C73—24no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
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×C73C2×#4112yes—
306C2×C4×C73C2511yescharacteristic
307C22⋊D73—84no—
308C2×Dic73—24no—
309C2×Dic73—22no—
310C2×Dic73—22no—
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—42no—
317C2×Dic73—42no—
318C2×Dic73—42no—
319C2×Dic73C22×D412yes—
320C2×Dic73C22×D412yes—
321C2×Dic73C22×D412yes—
322C4×D73—216no—
323C4×D73—24no—
324C4×D73—22no—
325C4×D73—22no—
326Dic146—216no—
327Dic146—24no—
328Dic146—22no—
329Dic146—22no—
330Dic146—22no—
331Dic146—42no—
332Dic146—84no—
333Dic146C2×#4114yes—
334C8×C73—22no—
335C8×C73—22no—
336#10596831—22no—
337#10596831—22no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—84no—
342C22×C73#52512yes—
343C22×C73#57712yes—
344C22×C73#57812yes—
345C22×C73C23×D411yescharacteristic
346C2×D73—22no—
347C2×D73—22no—
348C2×D73—22no—
349C2×D73—44no—
350C4×C73—24no—
351C4×C73—22no—
352C4×C73—22no—
353C4×C73—42no—
354C4×C73—42no—
355C4×C73#52512yes—
356C4×C73C22×#4111yescharacteristic
357C4×C73C22×#4111yescharacteristic
358Dic73—22no—
359Dic73—24no—
360Dic73—22no—
361Dic73—22no—
362Dic73—42no—
363Dic73—42no—
364Dic73—42no—
365C2×#3121—731nomaximal, Sylow
366C2×C73—82no—
367C2×C73#312114yescomplemented
368C2×C73C2×#52511yescharacteristic
369C2×C73C2×#57711yescharacteristic
370C2×C73C2×#57811yescharacteristic
371D73—42no—
372C2×#542—731no—
373C2×#519—731no—
374#3121—7316no—
375C2×#485—731no—
376C2×#482—731no—
377C2×#477—731no—
378C2×#475—731no—
379C2×#464—731no—
380C2×#464—731no—
381C2×#451—731no—
382C2×#448—731no—
383C2×#441—731no—
384C2×#440D7311yescharacteristic, complemented
385C2×C4×Q16—731no—
386C2×C4×SD16—731no—
387C2×#433—731no—
388C73C2×#312111yescharacteristic, complemented, Sylow
389C23×Q8—731no—
390C22×Q16—731no—
391C22×Q16—731no—
392C22×SD16—731no—
393C22×SD16C2×D7311yescharacteristic
394#542—738no—
395#542—1464no—
396C2×C4⋊Q8—731no—
397C2×#126—1461no—
398C2×#124—731no—
399C2×#124—1461no—
400C2×#123—1461no—
401C2×C22⋊Q8—731no—
402C2×C22⋊Q8—1461no—
403C2×#121—731no—
404#519—738no—
405#519—1464no—
406C2×C4×Q8—731no—
407C2×C4×Q8—731no—
408C2×C4×Q8—731no—
409C2×C4×Q8—731no—
410C2×C4×Q8—1461no—
411C2×C4×Q8—1461no—
412C2×C4×Q8C2×D7311yescharacteristic
413C2×C4×D4C2×D7311yescharacteristic
414C2×#117—731no—
415C2×#117—731no—
416C2×#117—1461no—
417C2×#117—1461no—
418#485—738no—
419#482—738no—
420#477—738no—
421#475—738no—
422#464—738no—
423#464—738no—
424#451—738no—
425#448—738no—
426#441—738no—
427#440C2×D7318yescomplemented
428C4×Q16—738no—
429C4×SD16—738no—
430#433—738no—
431C2×#107—731no—
432C2×#107C2×D7311yescharacteristic
433C2×#106—731no—
434C2×#106—731no—
435C2×C4⋊C8—731no—
436C2×C4⋊C8—731no—
437C2×#103—731no—
438C2×#103—731no—
439C2×#103—731no—
440C2×#103—731no—
441C2×#103—731no—
442C2×#103C2×D7311yescharacteristic
443C2×#102—731no—
444C2×#102C2×D7311yescharacteristic
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×#97C2×D7311yescharacteristic
448C2×C4×C8—731no—
449C22×Q8—734no—
450C22×Q8—731no—
451C22×Q8—731no—
452C22×Q8—1461no—
453C22×Q8—1461no—
454C22×Q8—1462no—
455C22×Q8—1464no—
456C22×Q8—1464no—
457C22×Q8C22×D7311yescharacteristic
458C22×D4—1461no—
459C22×D4C22×D7311yescharacteristic
460C23×C4—21no—
461C23×C4—731no—
462C23×C4—1461no—
463C2×Q16—734no—
464C2×Q16—734no—
465C2×Q16—1464no—
466C2×Q16—1464no—
467C2×SD16—24no—
468C2×SD16—734no—
469C2×SD16—1464no—
470C2×SD16C22×D7314yes—
471C22×C8—731no—
472C22×C8—731no—
473C22×C8C22×D7311yescharacteristic
474C22×C8C22×D7311yescharacteristic
475C4⋊Q8—734no—
476C4⋊Q8—1462no—
477#126—1468no—
478#124—734no—
479#124—1462no—
480#124—1468no—
481#123—1468no—
482C22⋊Q8—734no—
483C22⋊Q8—1462no—
484C22⋊Q8—1468no—
485#121—734no—
486#121—1462no—
487C4×Q8—22no—
488C4×Q8—734no—
489C4×Q8—734no—
490C4×Q8—734no—
491C4×Q8—734no—
492C4×Q8—1468no—
493C4×Q8—1462no—
494C4×Q8—1462no—
495C4×Q8—1468no—
496C4×Q8—1462no—
497C4×Q8—1462no—
498C4×Q8C22×D7314yes—
499C4×D4—22no—
500C4×D4C22×D7314yes—
501#117—734no—
502#117—734no—
503#117—734no—
504#117—1468no—
505#117—1468no—
506#117—1462no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—731no—
509C2×C4⋊C4—731no—
510C2×C4⋊C4—731no—
511C2×C4⋊C4—731no—
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⋊C4C22×D7311yescharacteristic
519C2×C4⋊C4C22×D7311yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—731no—
522C2×C22⋊C4—731no—
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—731no—
530C2×C42—1461no—
531C2×C42—1461no—
532C2×C42—1461no—
533C2×C42—1461no—
534C2×C42—1461no—
535C2×C42C22×D7311yescharacteristic
536#107—734no—
537#107C22×D7314yes—
538#106—734no—
539#106—734no—
540C4⋊C8—734no—
541C4⋊C8—734no—
542#103—734no—
543#103—734no—
544#103—734no—
545#103—734no—
546#103—734no—
547#103C22×D7314yes—
548#102—734no—
549#102C22×D7314yes—
550C22⋊C8—734no—
551C22⋊C8—734no—
552#97C22×D7314yes—
553C4×C8—734no—
554C24—21no—
555C24—731no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—5842no—
559C2×Q8—734no—
560C2×Q8—732no—
561C2×Q8—732no—
562C2×Q8—1464no—
563C2×Q8—1464no—
564C2×Q8—1468no—
565C2×Q8—1462no—
566C2×Q8—1462no—
567C2×Q8—1468no—
568C2×Q8—14616no—
569C2×Q8—1468no—
570C2×Q8—1461no—
571C2×Q8—1461no—
572C2×Q8—1462no—
573C2×Q8#1192402814yes—
574C2×Q8C23×D7312yes—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—5842no—
579C2×D4—1464no—
580C2×D4C23×D7312yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—82no—
586C22×C4—731no—
587C22×C4—731no—
588C22×C4—731no—
589C22×C4—732no—
590C22×C4—732no—
591C22×C4—1464no—
592C22×C4—1468no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4—1462no—
598C22×C4—1462no—
599C22×C4D4×D7311yescharacteristic
600C22×C4D4×D7311yescharacteristic
601C22×C4C23×D7311yescharacteristic
602Q16—1468no—
603Q16—1468no—
604SD16—28no—
605SD16—1468no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—732no—
609C2×C8—732no—
610C2×C8—1462no—
611C2×C8—1462no—
612C2×C8C23×D7312yes—
613C2×C8C23×D7312yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—734no—
618C4⋊C4—734no—
619C4⋊C4—732no—
620C4⋊C4—732no—
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—24no—
632C22⋊C4—734no—
633C22⋊C4—734no—
634C22⋊C4—1464no—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C42—24no—
640C42—732no—
641C42—732no—
642C42—1464no—
643C42—1464no—
644C42—1464no—
645C42—1464no—
646C42—1464no—
647C42D4×D7312yes—
648C42C23×D7312yes—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—732no—
654C23—1462no—
655C23—1462no—
656C23—1462no—
657C23C2×D4×D7311yescharacteristic
658Q8—22no—
659Q8—24no—
660Q8—2922no—
661Q8—5844no—
662Q8—734no—
663Q8—14616no—
664Q8—1462no—
665Q8—1462no—
666Q8—1462no—
667Q8—1464no—
668Q8C2×#1192402814yes—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—5844no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—84no—
682C2×C4—2922no—
683C2×C4—2922no—
684C2×C4—2922no—
685C2×C4—732no—
686C2×C4—732no—
687C2×C4—732no—
688C2×C4—14616no—
689C2×C4—1462no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1462no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1464no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1464no—
700C2×C4C2×D4×D7312yes—
701C2×C4C2×D4×D7312yes—
702C2×C4C2×D4×D7311yescharacteristic
703C2×C4#41×D7312yes—
704C2×C4C2×#1192402812yes—
705C2×C4C24×D7311yescharacteristic
706C8—22no—
707C8—22no—
708C8—1462no—
709C8—1462no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—2924no—
715C22—1462no—
716C22—1462no—
717C22—1462no—
718C22#1798909612yes—
719C22#1798939712yes—
720C22#1798940312yes—
721C22C22×D4×D7311yescharacteristic
722C4—22no—
723C4—22no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—2922no—
728C4—2922no—
729C4—2922no—
730C4—1462no—
731C4—1462no—
732C4—1462no—
733C4—1464no—
734C4#1798909612yes—
735C4C2×#41×D7311yescharacteristic
736C4C22×#1192402811yescharacteristic
737C2—82no—
738C2—2922no—
739C2#2262015814yesdirect product factor
740C2C2×#1798909611yescharacteristic
741C2C2×#1798939711yescharacteristic
742C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#440×C73C2
socleC23×C73C22×D4
prime radicalC2×#14556562C22
hypercenterC2×#440D73
hypocenterC73C2×#3121
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#17989063C2semidirect
3. #22620158C2direct (N × H)
4. C2×#17988930C2semidirect
6. C2×#17988881C2semidirect
7. C2×#17988870C2semidirect
8. C2×#17988808C2semidirect
9. C2×#17988807C2semidirect
10. C2×#17988744C2semidirect
12. C2×#17988695C2semidirect
13. C2×C4×#11924018C2semidirect
14. C2×C4×#11924016C2semidirect
15. C2×#17988649C2semidirect
16. C2×#440×C73C2semidirect
32. #17989063C22semidirect
43. #17988930C22semidirect
45. #17988881C22semidirect
46. #17988870C22semidirect
47. #17988808C22semidirect
48. #17988807C22semidirect
49. #17988744C22semidirect
51. #17988695C22semidirect
52. C4×#11924018C22semidirect
53. C4×#11924016C22semidirect
54. #17988649C22semidirect
72. #440×C73C22semidirect
367. C2×C73#3121semidirect
384. C2×#440D73semidirect
388. C73C2×#3121semidirect
427. #440C2×D73semidirect
739. C2#22620158direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892022
C2×#179890632
#226201582
C2×#179889302
C2×#179889102
C2×#179888812
C2×#179888702
C2×#179888082
C2×#179888072
C2×#179887442
C2×#179887242
C2×#179886952
C2×C4×#119240182
C2×C4×#119240162
C2×#179886492
C2×#440×C732
C2×#312173