Finite Group Databasebeta

← C2×#22622957 #33966947

Subgroups — C2×#22622957 #33966947

Order 18688.

1906 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989312C211yesmaximal, characteristic, complemented
2C2×#17989309C211yesmaximal, characteristic
3#22622957C2116yesmaximal, direct product factor
4C2×#17988980C211yesmaximal, characteristic
5C2×#17988979C211yesmaximal, characteristic
6C2×#17988965C211yesmaximal, characteristic, complemented
7C2×#17988811C211yesmaximal, characteristic
8C2×#17988810C211yesmaximal, characteristic
9C2×#17988796C211yesmaximal, characteristic, complemented
10C2×#17988795C211yesmaximal, characteristic, complemented
11C2×#17988791C211yesmaximal, characteristic
12C2×#17988716C211yesmaximal, characteristic, complemented
13C2×#17988692C211yesmaximal, characteristic, complemented
14C2×#17988691C211yesmaximal, characteristic, complemented
15C2×#17988672C211yesmaximal, characteristic
16C2×#462×C73C211yesmaximal, characteristic, complemented
17C22×Dic292C2211yescharacteristic
18C22×#11924018C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×#11924017C2211yescharacteristic
22C22×#11924015C2211yescharacteristic
23C22×#11924015C2211yescharacteristic
24#17989312—24no—
25#17989312C2218yescomplemented
26#17989309—24no—
27#17989309C2218yes—
28C2×#14556589C2211yescharacteristic
29C2×#14556589C2211yescharacteristic
30C2×#14556589C2211yescharacteristic
31C2×#14556586—21no—
32C2×#14556585—21no—
33C2×#14556582—21no—
34C2×#14556581—21no—
35C2×#14556581—21no—
36C2×#14556580C2211yescharacteristic
37C2×#14556579C2211yescharacteristic
38C2×#14556569—21no—
39C2×Q8×Dic73C2211yescharacteristic
40C2×Q8×Dic73C2211yescharacteristic
41C2×C4×Dic146C2211yescharacteristic
42C2×C4×Dic146C2211yescharacteristic
43C2×#14556556—21no—
44C2×#14556556C2211yescharacteristic
45C2×#14556553C2211yescharacteristic
46C2×#14556548—21no—
47#17988980C2218yes—
48#17988979C2218yes—
49#17988965C2218yescomplemented
50#17988811C2218yes—
51#17988810C2218yes—
52#17988796C2218yescomplemented
53#17988795C2218yescomplemented
54#17988791C2218yes—
55#17988716C2218yescomplemented
56#17988692C2218yescomplemented
57#17988691C2218yescomplemented
58#17988672C2218yes—
59C2×#14556522C2211yescharacteristic
60C2×#14556520C2211yescharacteristic
61C2×#14556520C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556513C2211yescharacteristic
66C2×#14556502C2211yescharacteristic
67C2×#14556501C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×Q16×C73C2211yescharacteristic
70C22×Q16×C73C2211yescharacteristic
71C2×C4⋊Q8×C73C2211yescharacteristic
72C2×C4×Q8×C73C2211yescharacteristic
73#462×C73C2218yescomplemented
74C2×C4⋊C8×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C22×Dic146D411yescharacteristic
78C22×Dic146C2311yescharacteristic
79C22×Dic146C2311yescharacteristic
80C22×D292C2311yescharacteristic
81C22×C4×D73—21no—
82C2×Dic292—42no—
83C2×Dic292C2314yes—
84C2×#11924018—24no—
85C2×#11924018—24no—
86C2×#11924018—42no—
87C2×#11924018C2314yes—
88C2×#11924018C2314yes—
89C2×#11924018C2314yes—
90C2×#11924017—42no—
91C2×#11924017C2314yes—
92C2×#11924015—24no—
93C2×#11924015—42no—
94C2×#11924015C2314yes—
95C2×#11924015C2314yes—
96C22×#10596831C2311yescharacteristic
97C22×#10596831C2311yescharacteristic
98#14556589—22no—
99#14556589—22no—
100#14556589—22no—
101#14556589C2314yes—
102#14556589C2314yes—
103#14556589C2314yes—
104#14556586—28no—
105#14556585—28no—
106#14556582—28no—
107#14556581—28no—
108#14556581—28no—
109#14556580—22no—
110#14556580C2314yes—
111#14556579—22no—
112#14556579C2314yes—
113#14556569—28no—
114Q8×Dic73—22no—
115Q8×Dic73—22no—
116Q8×Dic73C2314yes—
117Q8×Dic73C2314yes—
118C4×Dic146—22no—
119C4×Dic146D414yes—
120C4×Dic146C2314yes—
121C4×Dic146C2314yes—
122#14556556—28no—
123#14556556—22no—
124#14556556C2314yes—
125#14556553—22no—
126#14556553C2314yes—
127#14556548—28no—
128C2×C4⋊Dic73—21no—
129C2×C4⋊Dic73—21no—
130C2×C4⋊Dic73D411yescharacteristic
131C2×C4⋊Dic73C2311yescharacteristic
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×#11924007D411yescharacteristic
141C2×#11924007D411yescharacteristic
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005—21no—
145C2×#11924005—21no—
146C2×#11924005—21no—
147C2×C4×Dic73—21no—
148C2×C4×Dic73—21no—
149C2×C4×Dic73—21no—
150C2×C4×Dic73—21no—
151C2×C4×Dic73C2311yescharacteristic
152C2×C4×Dic73C2311yescharacteristic
153#14556522C2314yes—
154#14556520C2314yes—
155#14556520C2314yes—
156#14556516C2314yes—
157#14556515C2314yes—
158#14556514C2314yes—
159#14556513C2314yes—
160#14556502C2314yes—
161#14556501C2314yes—
162C8×Dic73C2314yes—
163C22×Q8×C73C2311yescharacteristic
164C22×Q8×C73C2311yescharacteristic
165C22×Q8×C73C2311yescharacteristic
166C2×Q16×C73—42no—
167C2×Q16×C73—42no—
168C2×Q16×C73C2314yes—
169C2×Q16×C73C2314yes—
170C22×C8×C73C2311yescharacteristic
171C22×C8×C73C2311yescharacteristic
172C4⋊Q8×C73—22no—
173C4⋊Q8×C73C2314yes—
174C4×Q8×C73—22no—
175C4×Q8×C73C2314yes—
176C2×C4⋊C4×C73—21no—
177C2×C4⋊C4×C73—21no—
178C2×C4⋊C4×C73—21no—
179C2×C4⋊C4×C73C2311yescharacteristic
180C2×C42×C73—21no—
181C2×C42×C73C2311yescharacteristic
182C4⋊C8×C73C2314yes—
183#103×C73C2314yes—
184#103×C73C2314yes—
185C23×D73—21no—
186C2×Dic146—24no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—22no—
191C2×Dic146—21no—
192C2×Dic146—21no—
193C2×Dic146C2×D414yes—
194C2×Dic146C2412yes—
195C2×Dic146C2412yes—
196C2×D292—22no—
197C2×D292—22no—
198C2×D292—21no—
199C2×D292C2412yes—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73C2×D411yescharacteristic
204C22×Dic73C2×D411yescharacteristic
205C22×Dic73C2×D411yescharacteristic
206C22×Dic73C2×D411yescharacteristic
207C2×C4×D73—24no—
208C2×C4×D73—44no—
209Dic292—44no—
210#11924018—28no—
211#11924018—28no—
212#11924018—44no—
213#11924017—44no—
214#11924015—28no—
215#11924015—44no—
216C2×#10596831—22no—
217C2×#10596831#4114yes—
218C2×#10596831C2412yes—
219C2×#10596831C2412yes—
220C4⋊Dic73—21no—
221C4⋊Dic73—24no—
222C4⋊Dic73—24no—
223C4⋊Dic73C2×D414yes—
224C4⋊Dic73C2412yes—
225#11924007—24no—
226#11924007—24no—
227#11924007—24no—
228#11924007—24no—
229#11924007—24no—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007C2×D414yes—
234#11924007C2×D414yes—
235#11924005—24no—
236#11924005—24no—
237#11924005—24no—
238#11924005—24no—
239#11924005—24no—
240C4×Dic73—24no—
241C4×Dic73—24no—
242C4×Dic73—24no—
243C4×Dic73—24no—
244C4×Dic73C2×D412yes—
245C4×Dic73C2×D412yes—
246C4×Dic73C2412yes—
247C4×Dic73C2412yes—
248C2×Q8×C73—21no—
249C2×Q8×C73—21no—
250C2×Q8×C73—21no—
251C2×Q8×C73—22no—
252C2×Q8×C73—22no—
253C2×Q8×C73—22no—
254C2×Q8×C73—22no—
255C2×Q8×C73—22no—
256C2×Q8×C73—22no—
257C2×Q8×C73C2412yes—
258C2×Q8×C73C2412yes—
259C2×Q8×C73C2412yes—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2×D411yescharacteristic
266C22×C4×C73C2411yescharacteristic
267Q16×C73—44no—
268Q16×C73—44no—
269C2×C8×C73—22no—
270C2×C8×C73—22no—
271C2×C8×C73C2412yes—
272C2×C8×C73C2412yes—
273C4⋊C4×C73—24no—
274C4⋊C4×C73—24no—
275C4⋊C4×C73—24no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73C2412yes—
278C42×C73—24no—
279C42×C73C2×D412yes—
280C42×C73C2412yes—
281C23×C73C22×D411yescharacteristic
282C22×D73—22no—
283C22×D73—42no—
284C22×D73—42no—
285C22×D73—42no—
286Q8×C73—22no—
287Q8×C73—22no—
288Q8×C73—22no—
289Q8×C73—22no—
290Q8×C73—22no—
291Q8×C73—22no—
292Q8×C73—42no—
293Q8×C73—42no—
294Q8×C73—42no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—42no—
302C2×C4×C73—42no—
303C2×C4×C73—42no—
304C2×C4×C73—42no—
305C2×C4×C73C22×D412yes—
306C2×C4×C73C22×D412yes—
307C2×C4×C73C22×D411yescharacteristic
308C2×C4×C73C2×#4112yes—
309C2×C4×C73H(5,𝔽2)12yes—
310C2×C4×C73C2511yescharacteristic
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—42no—
318C2×Dic73—42no—
319C2×Dic73—42no—
320C2×Dic73#13714yes—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323C2×Dic73C22×D412yes—
324C2×Dic73C22×D412yes—
325D292—22no—
326D292—22no—
327D292—42no—
328C4×D73—48no—
329Dic146—28no—
330Dic146—22no—
331Dic146—22no—
332Dic146—22no—
333Dic146—22no—
334Dic146—42no—
335Dic146—42no—
336C8×C73—22no—
337C8×C73—22no—
338#10596831—22no—
339#10596831C2×#4114yes—
340C22×C73#55012yes—
341C22×C73C2×#13712yes—
342C22×C73#57812yes—
343C22×C73C23×D411yescharacteristic
344C2×D73—42no—
345C2×D73—42no—
346C2×D73—42no—
347C2×D73—84no—
348C4×C73—22no—
349C4×C73—22no—
350C4×C73—42no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73—42no—
354C4×C73#55012yes—
355C4×C73C22×#4111yescharacteristic
356C4×C73C2×H(5,𝔽2)11yescharacteristic
357Dic73—22no—
358Dic73—22no—
359Dic73—22no—
360Dic73—42no—
361Dic73—42no—
362Dic73—42no—
363Dic73C2×#13714yes—
364C2×#3398—731nomaximal, Sylow
365C2×C73#339814yescomplemented
366C2×C73C2×#55011yescharacteristic
367C2×C73C22×#13711yescharacteristic
368C2×C73C2×#57811yescharacteristic
369D73—82no—
370C2×#557—731no—
371C2×#556—731no—
372#3398—7316no—
373C2×#497—731no—
374C2×#497—731no—
375C2×#494—731no—
376C2×#464—731no—
377C2×#464—731no—
378C2×#462—731no—
379C2×#462—731no—
380C2×#462D7311yescharacteristic, complemented
381C2×#461—731no—
382C2×#446—731no—
383C2×#441—731no—
384C2×#441—731no—
385C2×C4×SD16—731no—
386C73C2×#339811yescharacteristic, complemented, Sylow
387C22×Q16—731no—
388C22×Q16—731no—
389C22×Q16—731no—
390C22×Q16—731no—
391C22×Q16C2×D7311yescharacteristic
392C22×Q16C2×D7311yescharacteristic
393C22×SD16—731no—
394C22×SD16—731no—
395C22×SD16—731no—
396#557—738no—
397#557—1464no—
398#556—738no—
399#556—1464no—
400C2×C4⋊Q8—731no—
401C2×C4⋊Q8—731no—
402C2×C4⋊Q8—731no—
403C2×C4⋊Q8C2×D7311yescharacteristic
404C2×#126—1461no—
405C2×#126—1461no—
406C2×#125—1461no—
407C2×#125—1461no—
408C2×#125—1461no—
409C2×#124—731no—
410C2×#124—731no—
411C2×C22⋊Q8—1461no—
412C2×C4×Q8—731no—
413C2×C4×Q8—731no—
414C2×C4×Q8—731no—
415C2×C4×Q8—731no—
416C2×C4×Q8—731no—
417C2×C4×Q8—1461no—
418C2×C4×Q8C2×D7311yescharacteristic
419C2×C4×D4—731no—
420C2×#117—1461no—
421#497—738no—
422#497—738no—
423#494—738no—
424#464—738no—
425#464—738no—
426#462—738no—
427#462—738no—
428#462C2×D7318yescomplemented
429#461—738no—
430#446—738no—
431#441—738no—
432#441—738no—
433C4×SD16—738no—
434C2×#106—731no—
435C2×C4⋊C8—731no—
436C2×C4⋊C8—731no—
437C2×C4⋊C8C2×D7311yescharacteristic
438C2×#103—731no—
439C2×#103—731no—
440C2×#103—731no—
441C2×#103C2×D7311yescharacteristic
442C2×#103C2×D7311yescharacteristic
443C2×#102—731no—
444C2×#97—731no—
445C2×#97—731no—
446C2×C4×C8—731no—
447C22×Q8—731no—
448C22×Q8—731no—
449C22×Q8—731no—
450C22×Q8C22×D7311yescharacteristic
451C22×Q8C22×D7311yescharacteristic
452C22×Q8C22×D7311yescharacteristic
453C22×D4—731no—
454C23×C4—1461no—
455C2×Q16—42no—
456C2×Q16—42no—
457C2×Q16—2922no—
458C2×Q16—2922no—
459C2×Q16—734no—
460C2×Q16—734no—
461C2×Q16—734no—
462C2×Q16—734no—
463C2×Q16—1464no—
464C2×Q16—1464no—
465C2×Q16C22×D7314yes—
466C2×Q16C22×D7314yes—
467C2×SD16—2922no—
468C2×SD16—2922no—
469C2×SD16—734no—
470C2×SD16—734no—
471C2×SD16—734no—
472C2×SD16—1464no—
473C22×C8—731no—
474C22×C8—731no—
475C22×C8C22×D7311yescharacteristic
476C22×C8C22×D7311yescharacteristic
477C4⋊Q8—22no—
478C4⋊Q8—734no—
479C4⋊Q8—734no—
480C4⋊Q8—734no—
481C4⋊Q8—1462no—
482C4⋊Q8—1462no—
483C4⋊Q8—1462no—
484C4⋊Q8C22×D7314yes—
485#126—1468no—
486#126—1468no—
487#125—1468no—
488#125—1468no—
489#125—1468no—
490#124—734no—
491#124—734no—
492#124—1462no—
493#124—1462no—
494C22⋊Q8—1468no—
495C4×Q8—22no—
496C4×Q8—734no—
497C4×Q8—734no—
498C4×Q8—734no—
499C4×Q8—734no—
500C4×Q8—734no—
501C4×Q8—734no—
502C4×Q8—1462no—
503C4×Q8—1462no—
504C4×Q8—1462no—
505C4×Q8—1468no—
506C4×Q8—1462no—
507C4×Q8C22×D7314yes—
508C4×D4—734no—
509C4×D4—1462no—
510#117—1468no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—731no—
517C2×C4⋊C4—731no—
518C2×C4⋊C4—1461no—
519C2×C4⋊C4—1461no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4—1461no—
522C2×C4⋊C4—1461no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4—1461no—
528C2×C4⋊C4C22×D7311yescharacteristic
529C2×C22⋊C4—1461no—
530C2×C22⋊C4—1461no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C42—21no—
535C2×C42—731no—
536C2×C42—731no—
537C2×C42—1461no—
538C2×C42—1461no—
539C2×C42—1461no—
540C2×C42—1461no—
541C2×C42C22×D7311yescharacteristic
542#106—734no—
543C4⋊C8—734no—
544C4⋊C8—734no—
545C4⋊C8C22×D7314yes—
546#103—734no—
547#103—734no—
548#103—734no—
549#103C22×D7314yes—
550#103C22×D7314yes—
551#102—734no—
552#97—734no—
553#97—734no—
554C4×C8—734no—
555C24—1461no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—734no—
566C2×Q8—732no—
567C2×Q8—732no—
568C2×Q8—1464no—
569C2×Q8—1462no—
570C2×Q8—1462no—
571C2×Q8—1462no—
572C2×Q8—1462no—
573C2×Q8—1461no—
574C2×Q8—1461no—
575C2×Q8C23×D7312yes—
576C2×Q8C23×D7312yes—
577C2×Q8C23×D7312yes—
578C2×D4—732no—
579C2×D4—1461no—
580C2×D4—1462no—
581C2×D4—1462no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—2924no—
587C22×C4—731no—
588C22×C4—731no—
589C22×C4—731no—
590C22×C4—731no—
591C22×C4—1464no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4D4×D7311yescharacteristic
596C22×C4D4×D7311yescharacteristic
597C22×C4C23×D7311yescharacteristic
598Q16—44no—
599Q16—44no—
600Q16—2924no—
601Q16—2924no—
602Q16—1468no—
603Q16—1468no—
604SD16—2924no—
605SD16—2924no—
606SD16—1468no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—734no—
610C2×C8—732no—
611C2×C8—732no—
612C2×C8—1462no—
613C2×C8C23×D7312yes—
614C2×C8C23×D7312yes—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—734no—
620C4⋊C4—734no—
621C4⋊C4—734no—
622C4⋊C4—732no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C4⋊C4—1464no—
626C4⋊C4—1464no—
627C4⋊C4—1464no—
628C4⋊C4—1464no—
629C4⋊C4—1464no—
630C4⋊C4—1464no—
631C4⋊C4—1464no—
632C4⋊C4—1464no—
633C4⋊C4—1461no—
634C4⋊C4C23×D7312yes—
635C22⋊C4—1464no—
636C22⋊C4—1464no—
637C22⋊C4—1464no—
638C22⋊C4—1464no—
639C22⋊C4—1464no—
640C42—24no—
641C42—732no—
642C42—732no—
643C42—732no—
644C42—732no—
645C42—1464no—
646C42—1464no—
647C42—1464no—
648C42—1464no—
649C42D4×D7312yes—
650C42C23×D7312yes—
651C23—2922no—
652C23—2922no—
653C23—2922no—
654C23—1462no—
655C23C2×D4×D7311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—2922no—
666Q8—2922no—
667Q8—1468no—
668Q8—1462no—
669Q8—1462no—
670Q8—1462no—
671Q8—1462no—
672D4—2922no—
673D4—1462no—
674D4—1462no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—2928no—
686C2×C4—2922no—
687C2×C4—2922no—
688C2×C4—2922no—
689C2×C4—734no—
690C2×C4—732no—
691C2×C4—732no—
692C2×C4—732no—
693C2×C4—732no—
694C2×C4—1462no—
695C2×C4—1462no—
696C2×C4—1462no—
697C2×C4—1462no—
698C2×C4—1462no—
699C2×C4—1462no—
700C2×C4C2×D4×D7312yes—
701C2×C4C2×D4×D7312yes—
702C2×C4C2×D4×D7311yescharacteristic
703C2×C4#41×D7312yes—
704C2×C4#1455663612yes—
705C2×C4C24×D7311yescharacteristic
706C8—22no—
707C8—22no—
708C8—734no—
709C8—1462no—
710C22—2922no—
711C22—2922no—
712C22—2922no—
713C22—5844no—
714C22#1798925512yes—
715C22#137×D7312yes—
716C22#1798940012yes—
717C22C22×D4×D7311yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—2922no—
725C4—2922no—
726C4—2922no—
727C4—734no—
728C4—1462no—
729C4—1462no—
730C4—1462no—
731C4#1798925512yes—
732C4C2×#41×D7311yescharacteristic
733C4C2×#1455663611yescharacteristic
734C2—5842no—
735C2#2262295714yesdirect product factor
736C2C2×#1798925511yescharacteristic
737C2C2×#137×D7311yescharacteristic
738C2C2×#1798940011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#462×C73C2
socleC23×C73C22×D4
prime radicalC22×D292C23
hypercenterC2×#462D73
hypocenterC73C2×#3398
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#17989312C2semidirect
3. #22622957C2direct (N × H)
6. C2×#17988965C2semidirect
9. C2×#17988796C2semidirect
10. C2×#17988795C2semidirect
12. C2×#17988716C2semidirect
13. C2×#17988692C2semidirect
14. C2×#17988691C2semidirect
16. C2×#462×C73C2semidirect
25. #17989312C22semidirect
49. #17988965C22semidirect
52. #17988796C22semidirect
53. #17988795C22semidirect
55. #17988716C22semidirect
56. #17988692C22semidirect
57. #17988691C22semidirect
73. #462×C73C22semidirect
365. C2×C73#3398semidirect
380. C2×#462D73semidirect
386. C73C2×#3398semidirect
428. #462C2×D73semidirect
735. C2#22622957direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893122
C2×#179893092
#226229572
C2×#179889802
C2×#179889792
C2×#179889652
C2×#179888112
C2×#179888102
C2×#179887962
C2×#179887952
C2×#179887912
C2×#179887162
C2×#179886922
C2×#179886912
C2×#179886722
C2×#462×C732
C2×#339873