Finite Group Databasebeta

← C2×#22622306 #33964427

Subgroups — C2×#22622306 #33964427

Order 18688.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989285C211yesmaximal, characteristic
2C2×#17989272C211yesmaximal, characteristic, complemented
3#22622306C2116yesmaximal, direct product factor
4C2×#17988987C211yesmaximal, characteristic, complemented
5C2×#17988922C211yesmaximal, characteristic, complemented
6C2×#17988931C211yesmaximal, characteristic, complemented
7C2×#17988913C211yesmaximal, characteristic, complemented
8C2×#17988900C211yesmaximal, characteristic, complemented
9C2×#17988897C211yesmaximal, characteristic, complemented
10C2×#17988886C211yesmaximal, characteristic, complemented
11C2×#17988817C211yesmaximal, characteristic, complemented
12C2×#17988816C211yesmaximal, characteristic, complemented
13C2×#17988674C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D73C211yesmaximal, characteristic, complemented
15C2×#17988622C211yesmaximal, characteristic, complemented
16C22×#106×C73C211yesmaximal, characteristic, complemented
17C22×#11924017C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19#17989285—24no—
20#17989285C2218yes—
21#17989272—24no—
22#17989272C2218yescomplemented
23C2×#14556586—21no—
24C2×#14556586—21no—
25C2×#14556582C2211yescharacteristic
26C2×#14556582C2211yescharacteristic
27C2×#14556581—21no—
28C2×#14556576—21no—
29C2×#14556574—21no—
30C2×#14556571C2211yescharacteristic
31C2×#14556570C2211yescharacteristic
32C2×#14556566C2211yescharacteristic
33C2×#14556565—21no—
34C2×#14556565C2211yescharacteristic
35C2×#14556556C2211yescharacteristic
36C2×#14556553C2211yescharacteristic
37C2×C4×C22⋊D73—21no—
38C2×C4×C22⋊D73C2211yescharacteristic
39C2×#14556550—21no—
40C2×#14556549C2211yescharacteristic
41C2×#14556549C2211yescharacteristic
42#17988987C2218yescomplemented
43#17988931C2218yescomplemented
44#17988922C2218yescomplemented
45#17988913C2218yescomplemented
46#17988900C2218yescomplemented
47#17988897C2218yescomplemented
48#17988886C2218yescomplemented
49#17988817C2218yescomplemented
50#17988816C2218yescomplemented
51#17988674C2218yescomplemented
52C8×C22⋊D73C2218yescomplemented
53#17988622C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556524C2211yescharacteristic
58C2×#14556523C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556513C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65C2×#14556511C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C23×C8×C73C2211yescharacteristic
70C22×C4⋊C4×C73C2211yescharacteristic
71C22×C4⋊C4×C73C2211yescharacteristic
72C2×#106×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×#106×C73C2211yescharacteristic
75C2×#106×C73C2211yescharacteristic
76C2×#106×C73C2218yescomplemented
77C22×Dic146C2311yescharacteristic
78C22×D292—21no—
79C22×D292C2311yescharacteristic
80C22×C22⋊D73—21no—
81C22×C22⋊D73D411yescharacteristic
82C22×C4×D73—21no—
83C22×C4×D73C2311yescharacteristic
84C2×#11924017—24no—
85C2×#11924017C2314yes—
86C22×#10596831C2311yescharacteristic
87C22×#10596831C2311yescharacteristic
88C2×C8×D73—24no—
89C2×C8×D73C2314yes—
90#14556586—28no—
91#14556586—28no—
92#14556582—22no—
93#14556582—22no—
94#14556582C2314yes—
95#14556582C2314yes—
96#14556581—28no—
97#14556576—28no—
98#14556574—28no—
99#14556571—22no—
100#14556571C2314yes—
101#14556570—22no—
102#14556570C2314yes—
103#14556566—22no—
104#14556566C2314yes—
105#14556565—28no—
106#14556565—22no—
107#14556565C2314yes—
108#14556556—22no—
109#14556556C2314yes—
110#14556553—22no—
111#14556553C2314yes—
112C4×C22⋊D73—28no—
113C4×C22⋊D73D414yes—
114C4×C22⋊D73C2314yes—
115#14556550—28no—
116#14556549—22no—
117#14556549—22no—
118#14556549C2314yes—
119#14556549C2314yes—
120C2×C4⋊Dic73—21no—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73C2311yescharacteristic
124C2×C4⋊Dic73C2311yescharacteristic
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007D411yescharacteristic
130C2×C22⋊Dic73—21no—
131C2×C22⋊Dic73D411yescharacteristic
132C2×#11924005—21no—
133C2×#11924005—21no—
134C2×#11924005—21no—
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005D411yescharacteristic
139C2×C4×Dic73—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73C2311yescharacteristic
143#14556524C2314yes—
144#14556524C2314yes—
145#14556524C2314yes—
146#14556524C2314yes—
147#14556523C2314yes—
148#14556520C2314yes—
149#14556516C2314yes—
150#14556514C2314yes—
151#14556514C2314yes—
152#14556513C2314yes—
153#14556511C2314yes—
154#14556511C2314yes—
155C22⋊#10596831C2314yes—
156#14556503C2314yes—
157C8×Dic73C2314yes—
158C23×C4×C73—21no—
159C23×C4×C73—21no—
160C23×C4×C73C2311yescharacteristic
161C22×C8×C73—24no—
162C22×C8×C73C2314yes—
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C2×C4⋊C4×C73—22no—
166C2×C4⋊C4×C73—22no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73—21no—
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2311yescharacteristic
173C2×C4⋊C4×C73C2314yes—
174C2×C4⋊C4×C73C2314yes—
175#106×C73C2314yes—
176#106×C73C2314yes—
177#106×C73C2314yes—
178#106×C73C2314yes—
179C23×D73—21no—
180C23×D73C2×D411yescharacteristic
181C2×Dic146—22no—
182C2×Dic146—22no—
183C2×Dic146—21no—
184C2×Dic146C2412yes—
185C2×D292—22no—
186C2×D292—22no—
187C2×D292—21no—
188C2×D292—24no—
189C2×D292—82no—
190C2×D292C2412yes—
191C2×C22⋊D73—24no—
192C2×C22⋊D73—24no—
193C2×C22⋊D73—44no—
194C2×C22⋊D73C2×D414yes—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73C2×D411yescharacteristic
199C22×Dic73C2×D411yescharacteristic
200C22×Dic73C2×D411yescharacteristic
201C2×C4×D73—22no—
202C2×C4×D73—22no—
203C2×C4×D73—24no—
204C2×C4×D73—82no—
205C2×C4×D73C2×D412yes—
206C2×C4×D73C2412yes—
207#11924017—28no—
208C2×#10596831—22no—
209C2×#10596831—22no—
210C2×#10596831C2412yes—
211C2×#10596831C2412yes—
212C8×D73—28no—
213C4⋊Dic73—21no—
214C4⋊Dic73—21no—
215C4⋊Dic73—24no—
216C4⋊Dic73—24no—
217C4⋊Dic73—24no—
218C4⋊Dic73C2412yes—
219C4⋊Dic73C2412yes—
220#11924007—24no—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007C2×D414yes—
225C22⋊Dic73—24no—
226C22⋊Dic73C2×D414yes—
227#11924005—24no—
228#11924005—24no—
229#11924005—24no—
230#11924005—24no—
231#11924005—24no—
232#11924005—24no—
233#11924005C2×D414yes—
234C4×Dic73—24no—
235C4×Dic73—24no—
236C4×Dic73—24no—
237C4×Dic73C2×D412yes—
238C4×Dic73C2412yes—
239C24×C73C2×D411yescharacteristic
240C22×C4×C73—22no—
241C22×C4×C73—22no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—24no—
247C22×C4×C73—24no—
248C22×C4×C73—44no—
249C22×C4×C73—82no—
250C22×C4×C73C2×D411yescharacteristic
251C22×C4×C73C2×D412yes—
252C22×C4×C73C2412yes—
253C22×C4×C73C2411yescharacteristic
254C2×C8×C73—22no—
255C2×C8×C73—28no—
256C2×C8×C73#4114yes—
257C2×C8×C73C2412yes—
258C2×C8×C73C2412yes—
259C4⋊C4×C73—21no—
260C4⋊C4×C73—21no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73—21no—
263C4⋊C4×C73—24no—
264C4⋊C4×C73—24no—
265C4⋊C4×C73C2412yes—
266C4⋊C4×C73C2412yes—
267C4⋊C4×C73C2412yes—
268C4⋊C4×C73C2412yes—
269C23×C73—22no—
270C23×C73—22no—
271C23×C73#13514yes—
272C23×C73C22×D412yes—
273C23×C73C22×D411yescharacteristic
274C22×D73—22no—
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—22no—
278C22×D73—42no—
279C22×D73—42no—
280C22×D73—42no—
281C22×D73C22×D412yes—
282C2×C4×C73—22no—
283C2×C4×C73—24no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—48no—
291C2×C4×C73—42no—
292C2×C4×C73—42no—
293C2×C4×C73—42no—
294C2×C4×C73—42no—
295C2×C4×C73—84no—
296C2×C4×C73C22×D412yes—
297C2×C4×C73C22×D411yescharacteristic
298C2×C4×C73C2×#4112yes—
299C2×C4×C732−1+412yes—
300C2×C4×C73C2511yescharacteristic
301C22⋊D73—28no—
302C22⋊D73—48no—
303C2×Dic73—22no—
304C2×Dic73—22no—
305C2×Dic73—22no—
306C2×Dic73—22no—
307C2×Dic73—22no—
308C2×Dic73—22no—
309C2×Dic73—42no—
310C2×Dic73—42no—
311C2×Dic73—42no—
312C2×Dic73C22×D412yes—
313C2×Dic73C22×D412yes—
314C2×Dic73C22×D412yes—
315D292—22no—
316D292—22no—
317D292—42no—
318D292—84no—
319C4×D73—24no—
320C4×D73—22no—
321C4×D73—22no—
322C4×D73—84no—
323Dic146—22no—
324Dic146—22no—
325Dic146—42no—
326C8×C73—22no—
327C8×C73C2×#4114yes—
328#10596831—22no—
329#10596831—22no—
330C22×C73—28no—
331C22×C73—22no—
332C22×C73—22no—
333C22×C73#54712yes—
334C22×C73C2×#13514yes—
335C22×C73C2×#13512yes—
336C22×C73#57712yes—
337C22×C73C23×D411yescharacteristic
338C2×D73—22no—
339C2×D73—22no—
340C2×D73—22no—
341C2×D73—44no—
342C2×D73—42no—
343C2×D73—42no—
344C2×D73—42no—
345C2×D73—84no—
346C4×C73—22no—
347C4×C73—42no—
348C4×C73—42no—
349C4×C73—42no—
350C4×C73—42no—
351C4×C73#54712yes—
352C4×C73C22×#4111yescharacteristic
353C4×C73C2×2−1+411yescharacteristic
354Dic73—22no—
355Dic73—22no—
356Dic73—22no—
357Dic73—42no—
358Dic73—42no—
359Dic73—42no—
360C2×#3337—731nomaximal, Sylow
361C2×C73—24no—
362C2×C73#333714yescomplemented
363C2×C73C2×#54711yescharacteristic
364C2×C73C22×#13511yescharacteristic
365C2×C73C2×#57711yescharacteristic
366D73—42no—
367D73—82no—
368C2×#553—731no—
369C2×#552—731no—
370#3337—7316no—
371C2×#499—731no—
372C2×#484—731no—
373C2×#485—731no—
374C2×#482—731no—
375C2×#480—731no—
376C2×#479—731no—
377C2×#478—731no—
378C2×#465—731no—
379C2×#465—731no—
380C2×C4×SD16—731no—
381C2×C8×D4—731no—
382C2×#427—731no—
383C22×#106D7311yescharacteristic, complemented
384C73C2×#333711yescharacteristic, complemented, Sylow
385C22×SD16—731no—
386C23×C8—731no—
387C23×C8C2×D7311yescharacteristic
388#553—738no—
389#553—1464no—
390#552—738no—
391#552—1464no—
392C2×#126—1461no—
393C2×#126—1461no—
394C2×#125—731no—
395C2×#125—731no—
396C2×#125—1461no—
397C2×#123—1461no—
398C2×#123—1461no—
399C2×C22⋊Q8—731no—
400C2×C22⋊Q8—731no—
401C2×#121—731no—
402C2×#121—731no—
403C2×#121—1461no—
404C2×C4×Q8—731no—
405C2×C4×D4—731no—
406C2×C4×D4—731no—
407C2×C4×D4—1461no—
408C2×#117—731no—
409C2×#117—731no—
410C2×#117—1461no—
411C22×C4⋊C4C2×D7311yescharacteristic
412C22×C4⋊C4C2×D7311yescharacteristic
413#499—738no—
414#485—738no—
415#484—738no—
416#482—738no—
417#480—738no—
418#479—738no—
419#478—738no—
420#465—738no—
421#465—738no—
422C4×SD16—738no—
423C8×D4—738no—
424#427—738no—
425C2×#107—731no—
426C2×#107—731no—
427C2×#107—731no—
428C2×#107—731no—
429C2×#106—731no—
430C2×#106C2×D7311yescharacteristic
431C2×#106C2×D7311yescharacteristic
432C2×#106C2×D7311yescharacteristic
433C2×#106C2×D7311yescharacteristic
434C2×#106C2×D7318yescomplemented
435C2×C4⋊C8—731no—
436C2×#103—731no—
437C2×#103—731no—
438C2×#103—731no—
439C2×#102—731no—
440C2×#102—731no—
441C2×#102—731no—
442C2×C22⋊C8—731no—
443C2×C22⋊C8—731no—
444C2×C4×C8—731no—
445C22×Q8—731no—
446C22×D4—731no—
447C22×D4—731no—
448C22×D4—1461no—
449C22×D4—1461no—
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—731no—
453C23×C4—1461no—
454C23×C4C22×D7311yescharacteristic
455C2×SD16—734no—
456C2×SD16—1464no—
457C22×C8—24no—
458C22×C8—731no—
459C22×C8—731no—
460C22×C8—734no—
461C22×C8—1464no—
462C22×C8C22×D7311yescharacteristic
463C22×C8C22×D7314yes—
464C22×C8C22×D7311yescharacteristic
465#126—1468no—
466#126—1468no—
467#125—734no—
468#125—734no—
469#125—1462no—
470#125—1462no—
471#125—1468no—
472#123—1468no—
473#123—1468no—
474C22⋊Q8—734no—
475C22⋊Q8—734no—
476C22⋊Q8—1462no—
477C22⋊Q8—1462no—
478#121—734no—
479#121—734no—
480#121—1462no—
481#121—1468no—
482#121—1462no—
483C4×Q8—734no—
484C4×Q8—1462no—
485C4×D4—734no—
486C4×D4—734no—
487C4×D4—734no—
488C4×D4—1462no—
489C4×D4—1468no—
490#117—734no—
491#117—734no—
492#117—1468no—
493#117—1462no—
494#117—1462no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4—1461no—
505C2×C4⋊C4—1461no—
506C2×C4⋊C4—1461no—
507C2×C4⋊C4—1461no—
508C2×C4⋊C4—1461no—
509C2×C4⋊C4C22×D7311yescharacteristic
510C2×C4⋊C4C22×D7311yescharacteristic
511C2×C4⋊C4C22×D7311yescharacteristic
512C2×C4⋊C4C22×D7311yescharacteristic
513C2×C4⋊C4C22×D7314yes—
514C2×C4⋊C4C22×D7314yes—
515C2×C22⋊C4—731no—
516C2×C22⋊C4—731no—
517C2×C22⋊C4—1461no—
518C2×C22⋊C4—1461no—
519C2×C22⋊C4—1461no—
520C2×C22⋊C4—1461no—
521C2×C22⋊C4—1461no—
522C2×C22⋊C4—1461no—
523C2×C22⋊C4—1461no—
524C2×C42—731no—
525C2×C42—1461no—
526C2×C42—1461no—
527C2×C42—1461no—
528#107—734no—
529#107—734no—
530#107—734no—
531#107—734no—
532#106—734no—
533#106C22×D7314yes—
534#106C22×D7314yes—
535#106C22×D7314yes—
536#106C22×D7314yes—
537C4⋊C8—734no—
538#103—734no—
539#103—734no—
540#103—734no—
541#102—734no—
542#102—734no—
543#102—734no—
544C22⋊C8—734no—
545C22⋊C8—734no—
546C4×C8—734no—
547C24—731no—
548C24—1461no—
549C24D4×D7311yescharacteristic
550C2×Q8—732no—
551C2×Q8—1462no—
552C2×Q8—1462no—
553C2×Q8—1461no—
554C2×D4—2924no—
555C2×D4—5842no—
556C2×D4—734no—
557C2×D4—732no—
558C2×D4—1464no—
559C2×D4—1464no—
560C2×D4—1464no—
561C2×D4—1461no—
562C2×D4—1462no—
563C2×D4—1462no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—44no—
573C22×C4—82no—
574C22×C4—5842no—
575C22×C4—731no—
576C22×C4—731no—
577C22×C4—731no—
578C22×C4—732no—
579C22×C4—732no—
580C22×C4—1464no—
581C22×C4—1461no—
582C22×C4—1461no—
583C22×C4—1461no—
584C22×C4—1462no—
585C22×C4—1462no—
586C22×C4D4×D7312yes—
587C22×C4D4×D7311yescharacteristic
588C22×C4C23×D7312yes—
589C22×C4C23×D7311yescharacteristic
590SD16—1468no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—732no—
594C2×C8—732no—
595C2×C8—1462no—
596C2×C8—1462no—
597C2×C8—1468no—
598C2×C8#1192402814yes—
599C2×C8C23×D7312yes—
600C2×C8C23×D7312yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—734no—
608C4⋊C4—732no—
609C4⋊C4—732no—
610C4⋊C4—1464no—
611C4⋊C4—1464no—
612C4⋊C4—1464no—
613C4⋊C4—1464no—
614C4⋊C4—1464no—
615C4⋊C4—1464no—
616C4⋊C4—1464no—
617C4⋊C4—1461no—
618C4⋊C4—1461no—
619C4⋊C4C23×D7312yes—
620C4⋊C4C23×D7312yes—
621C4⋊C4C23×D7312yes—
622C4⋊C4C23×D7312yes—
623C22⋊C4—734no—
624C22⋊C4—734no—
625C22⋊C4—1464no—
626C22⋊C4—1464no—
627C22⋊C4—1464no—
628C22⋊C4—1464no—
629C22⋊C4—1464no—
630C22⋊C4—1464no—
631C22⋊C4—1464no—
632C42—732no—
633C42—732no—
634C42—1464no—
635C42—1464no—
636C42—1464no—
637C23—22no—
638C23—22no—
639C23—2922no—
640C23—2922no—
641C23—2922no—
642C23—732no—
643C23—1462no—
644C23—1462no—
645C23—1462no—
646C23—1462no—
647C23#1455661214yes—
648C23C2×D4×D7312yes—
649C23C2×D4×D7311yescharacteristic
650Q8—2922no—
651Q8—1462no—
652Q8—1462no—
653D4—2928no—
654D4—2922no—
655D4—5844no—
656D4—1468no—
657D4—1462no—
658D4—1462no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—48no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—84no—
673C2×C4—2922no—
674C2×C4—2922no—
675C2×C4—2922no—
676C2×C4—5844no—
677C2×C4—732no—
678C2×C4—732no—
679C2×C4—732no—
680C2×C4—1462no—
681C2×C4—1462no—
682C2×C4—1462no—
683C2×C4—1462no—
684C2×C4—1462no—
685C2×C4—1462no—
686C2×C4—1462no—
687C2×C4—1462no—
688C2×C4—1464no—
689C2×C4C2×D4×D7312yes—
690C2×C4C2×D4×D7311yescharacteristic
691C2×C4C2×#1192402812yes—
692C2×C4#1455663912yes—
693C2×C4C24×D7311yescharacteristic
694C8—22no—
695C8—1462no—
696C8—1462no—
697C8C2×#1192402814yes—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—2924no—
702C22—2922no—
703C22—2922no—
704C22—2922no—
705C22—5844no—
706C22—1462no—
707C22—1462no—
708C22—1462no—
709C22#1798923812yes—
710C22C2×#1455661214yes—
711C22C2×#1455661212yes—
712C22#1798939312yes—
713C22C22×D4×D7311yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—2922no—
720C4—2922no—
721C4—2922no—
722C4—1462no—
723C4—1462no—
724C4—1462no—
725C4#1798923812yes—
726C4C22×#1192402811yescharacteristic
727C4C2×#1455663911yescharacteristic
728C2—24no—
729C2—2922no—
730C2—5842no—
731C2#2262230614yesdirect product factor
732C2C2×#1798923811yescharacteristic
733C2C22×#1455661211yescharacteristic
734C2C2×#1798939311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC22×#106×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989285C2
hypercenterC22×#106D73
hypocenterC73C2×#3337
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#17989272C2semidirect
3. #22622306C2direct (N × H)
4. C2×#17988987C2semidirect
5. C2×#17988922C2semidirect
6. C2×#17988931C2semidirect
7. C2×#17988913C2semidirect
8. C2×#17988900C2semidirect
9. C2×#17988897C2semidirect
10. C2×#17988886C2semidirect
11. C2×#17988817C2semidirect
12. C2×#17988816C2semidirect
13. C2×#17988674C2semidirect
14. C2×C8×C22⋊D73C2semidirect
15. C2×#17988622C2semidirect
16. C22×#106×C73C2semidirect
22. #17989272C22semidirect
42. #17988987C22semidirect
43. #17988931C22semidirect
44. #17988922C22semidirect
45. #17988913C22semidirect
46. #17988900C22semidirect
47. #17988897C22semidirect
48. #17988886C22semidirect
49. #17988817C22semidirect
50. #17988816C22semidirect
51. #17988674C22semidirect
52. C8×C22⋊D73C22semidirect
53. #17988622C22semidirect
76. C2×#106×C73C22semidirect
362. C2×C73#3337semidirect
383. C22×#106D73semidirect
384. C73C2×#3337semidirect
434. C2×#106C2×D73semidirect
731. C2#22622306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892852
C2×#179892722
#226223062
C2×#179889872
C2×#179889222
C2×#179889312
C2×#179889132
C2×#179889002
C2×#179888972
C2×#179888862
C2×#179888172
C2×#179888162
C2×#179886742
C2×C8×C22⋊D732
C2×#179886222
C22×#106×C732
C2×#333773