Finite Group Databasebeta

← C2×#22621794 #33962365

Subgroups — C2×#22621794 #33962365

Order 18688.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989250C211yesmaximal, characteristic, complemented
2C2×#17989238C211yesmaximal, characteristic
3#22621794C2116yesmaximal, direct product factor
4C2×#17988936C211yesmaximal, characteristic, complemented
5C2×#17988919C211yesmaximal, characteristic, complemented
6C2×#17988871C211yesmaximal, characteristic, complemented
7C2×#17988818C211yesmaximal, characteristic, complemented
8C2×#17988817C211yesmaximal, characteristic, complemented
9C2×#17988791C211yesmaximal, characteristic, complemented
10C2×#17988728C211yesmaximal, characteristic, complemented
11C2×#17988727C211yesmaximal, characteristic, complemented
12C2×#17988674C211yesmaximal, characteristic, complemented
13C2×#17988650C211yesmaximal, characteristic, complemented
14C22×#14556514C211yesmaximal, characteristic, complemented
15C2×#103×D73C211yesmaximal, characteristic, complemented
16C2×#483×C73C211yesmaximal, characteristic, complemented
17C22×#11924028—21no—
18C23×Dic146C2211yescharacteristic
19C22×Q8×D73C2211yescharacteristic
20C22×#11924017C2211yescharacteristic
21C22×#11924017C2211yescharacteristic
22C22×#11924015C2211yescharacteristic
23C23×#10596831C2211yescharacteristic
24C22×C8×D73C2211yescharacteristic
25#17989250—24no—
26#17989250C2218yescomplemented
27#17989238—24no—
28#17989238C2218yes—
29C2×#14556590—21no—
30C2×#14556590C2211yescharacteristic
31C2×#14556589C2211yescharacteristic
32C2×#14556576—21no—
33C2×#14556574—21no—
34C2×#14556571C2211yescharacteristic
35C2×#14556569—21no—
36C2×#14556569—21no—
37C2×#14556568—21no—
38C2×#14556566C2211yescharacteristic
39C2×#14556565C2211yescharacteristic
40C2×#14556556C2211yescharacteristic
41C2×#14556553C2211yescharacteristic
42C2×C4×C22⋊D73C2211yescharacteristic
43C2×#14556551—21no—
44C2×C4⋊C4×D73C2211yescharacteristic
45#17988936C2218yescomplemented
46#17988919C2218yescomplemented
47#17988871C2218yescomplemented
48#17988818C2218yescomplemented
49#17988817C2218yescomplemented
50#17988791C2218yescomplemented
51#17988728C2218yescomplemented
52#17988727C2218yescomplemented
53#17988674C2218yescomplemented
54#17988650C2218yescomplemented
55C2×#14556522C2211yescharacteristic
56C2×#14556520C2211yescharacteristic
57C2×#14556516C2211yescharacteristic
58C2×#14556516C2211yescharacteristic
59C2×#14556515C2211yescharacteristic
60C2×#14556514C2211yescharacteristic
61C2×#14556514C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2218yescomplemented
65#103×D73C2218yescomplemented
66C2×#14556511C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×C22⋊Q8×C73C2211yescharacteristic
70C22×C4⋊C4×C73C2211yescharacteristic
71#483×C73C2218yescomplemented
72C2×#106×C73C2211yescharacteristic
73C2×#106×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C2×#11924028—28no—
78C2×#11924028—48no—
79C22×Dic146—21no—
80C22×Dic146—21no—
81C22×Dic146—24no—
82C22×Dic146—21no—
83C22×Dic146—22no—
84C22×Dic146—42no—
85C22×Dic146C2311yescharacteristic
86C22×Dic146C2314yes—
87C22×Dic146C2311yescharacteristic
88C2×Q8×D73—22no—
89C2×Q8×D73—24no—
90C2×Q8×D73—42no—
91C2×Q8×D73C2314yes—
92C22×D292—21no—
93C22×D292C2311yescharacteristic
94C22×C22⋊D73—21no—
95C22×C22⋊D73D411yescharacteristic
96C23×Dic73—21no—
97C22×C4×D73—21no—
98C22×C4×D73—21no—
99C22×C4×D73—21no—
100C22×C4×D73C2311yescharacteristic
101C2×#11924017—24no—
102C2×#11924017—42no—
103C2×#11924017C2314yes—
104C2×#11924017C2314yes—
105C2×#11924015—42no—
106C2×#11924015C2314yes—
107C22×#10596831—42no—
108C22×#10596831C2311yescharacteristic
109C22×#10596831C2311yescharacteristic
110C22×#10596831C2314yes—
111C2×C8×D73—42no—
112C2×C8×D73C2314yes—
113#14556590—28no—
114#14556590—22no—
115#14556590C2314yes—
116#14556589—22no—
117#14556589C2314yes—
118#14556576—28no—
119#14556574—28no—
120#14556571—22no—
121#14556571C2314yes—
122#14556569—28no—
123#14556569—28no—
124#14556568—28no—
125#14556566—22no—
126#14556566C2314yes—
127#14556565—22no—
128#14556565C2314yes—
129#14556556—22no—
130#14556556C2314yes—
131#14556553—22no—
132#14556553C2314yes—
133C4×C22⋊D73D414yes—
134C4×C22⋊D73C2314yes—
135#14556551—28no—
136C2×C4⋊Dic73—21no—
137C2×C4⋊Dic73C2311yescharacteristic
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×#11924007—21no—
141C2×#11924007—21no—
142C2×#11924007—21no—
143C2×#11924007D411yescharacteristic
144C4⋊C4×D73—22no—
145C4⋊C4×D73C2314yes—
146C2×C22⋊Dic73D411yescharacteristic
147C2×#11924005—21no—
148C2×#11924005—21no—
149C2×#11924005—21no—
150C2×#11924005—21no—
151C2×#11924005D411yescharacteristic
152C2×C4×Dic73—21no—
153C2×C4×Dic73C2311yescharacteristic
154#14556522C2314yes—
155#14556520C2314yes—
156#14556516C2314yes—
157#14556516C2314yes—
158#14556515C2314yes—
159#14556514C2314yes—
160#14556514C2314yes—
161#14556514C2314yes—
162#14556514C2314yes—
163#14556511C2314yes—
164#14556503C2314yes—
165C8×Dic73C2314yes—
166C22×Q8×C73C2311yescharacteristic
167C23×C4×C73—21no—
168C23×C4×C73C2311yescharacteristic
169C22×C8×C73C2311yescharacteristic
170C22×C8×C73C2311yescharacteristic
171C22⋊Q8×C73—22no—
172C22⋊Q8×C73C2314yes—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73—22no—
175C2×C4⋊C4×C73—21no—
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C4⋊C4×C73C2311yescharacteristic
179C2×C4⋊C4×C73C2314yes—
180C2×C22⋊C4×C73—21no—
181#106×C73C2314yes—
182#106×C73C2314yes—
183#103×C73C2314yes—
184#103×C73C2314yes—
185C22⋊C8×C73C2314yes—
186C23×D73—21no—
187C23×D73C2×D411yescharacteristic
188#11924028—432no—
189C2×Dic146—21no—
190C2×Dic146—22no—
191C2×Dic146—22no—
192C2×Dic146—22no—
193C2×Dic146—28no—
194C2×Dic146—24no—
195C2×Dic146—21no—
196C2×Dic146—24no—
197C2×Dic146—24no—
198C2×Dic146—44no—
199C2×Dic146—48no—
200C2×Dic146—44no—
201C2×Dic146—44no—
202C2×Dic146—44no—
203C2×Dic146#4114yescomplemented
204C2×Dic146C2412yes—
205C2×Dic146C2412yes—
206Q8×D73—28no—
207Q8×D73—44no—
208Q8×D73—48no—
209C2×D292—22no—
210C2×D292—22no—
211C2×D292—24no—
212C2×D292—21no—
213C2×D292—44no—
214C2×D292C2412yes—
215C2×C22⋊D73—24no—
216C2×C22⋊D73—44no—
217C2×C22⋊D73SD1618yescomplemented
218C2×C22⋊D73C2×D414yes—
219C22×Dic73—21no—
220C22×Dic73—21no—
221C22×Dic73—21no—
222C22×Dic73—24no—
223C22×Dic73—44no—
224C22×Dic73C2×D411yescharacteristic
225C22×Dic73C2×D411yescharacteristic
226C22×Dic73C2×D411yescharacteristic
227C2×C4×D73—22no—
228C2×C4×D73—22no—
229C2×C4×D73—24no—
230C2×C4×D73—24no—
231C2×C4×D73—24no—
232C2×C4×D73—44no—
233C2×C4×D73—44no—
234C2×C4×D73—44no—
235C2×C4×D73C2×D412yes—
236C2×C4×D73C2412yes—
237#11924017—28no—
238#11924017—44no—
239#11924015—44no—
240C2×#10596831—22no—
241C2×#10596831—22no—
242C2×#10596831—44no—
243C2×#10596831C2412yes—
244C2×#10596831C2412yes—
245C8×D73—44no—
246C4⋊Dic73—21no—
247C4⋊Dic73—24no—
248C4⋊Dic73C2412yes—
249#11924007—24no—
250#11924007—24no—
251#11924007—24no—
252#11924007—24no—
253#11924007—24no—
254#11924007C2×D414yes—
255C22⋊Dic73C2×D414yes—
256#11924005—24no—
257#11924005—24no—
258#11924005—24no—
259#11924005—24no—
260#11924005C2×D414yes—
261C4×Dic73—24no—
262C4×Dic73C2×D412yes—
263C4×Dic73C2412yes—
264C24×C73C2×D411yescharacteristic
265C2×Q8×C73—21no—
266C2×Q8×C73—22no—
267C2×Q8×C73—22no—
268C2×Q8×C73C2412yes—
269C22×C4×C73—22no—
270C22×C4×C73—22no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—24no—
276C22×C4×C73—44no—
277C22×C4×C73C2×D411yescharacteristic
278C22×C4×C73C2×D412yes—
279C22×C4×C73C2412yes—
280C22×C4×C73C2411yescharacteristic
281C2×C8×C73—22no—
282C2×C8×C73—22no—
283C2×C8×C73C2412yes—
284C2×C8×C73C2412yes—
285C4⋊C4×C73—21no—
286C4⋊C4×C73—21no—
287C4⋊C4×C73—24no—
288C4⋊C4×C73—24no—
289C4⋊C4×C73—21no—
290C4⋊C4×C73C2412yes—
291C4⋊C4×C73C2412yes—
292C4⋊C4×C73C2412yes—
293C22⋊C4×C73—24no—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73C2×SD1614yes—
297C23×C73C22×D412yes—
298C23×C73C22×D411yescharacteristic
299C22×D73—22no—
300C22×D73—22no—
301C22×D73—22no—
302C22×D73—42no—
303C22×D73—42no—
304C22×D73—42no—
305C22×D73C2×SD1614yes—
306C22×D73C22×D412yes—
307Q8×C73—22no—
308Q8×C73—22no—
309Q8×C73—42no—
310C2×C4×C73—22no—
311C2×C4×C73—24no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—22no—
318C2×C4×C73—42no—
319C2×C4×C73—42no—
320C2×C4×C73—42no—
321C2×C4×C73—48no—
322C2×C4×C73—42no—
323C2×C4×C73C22×D412yes—
324C2×C4×C73C22×D411yescharacteristic
325C2×C4×C73C2×#4112yes—
326C2×C4×C73H(5,𝔽2)12yes—
327C2×C4×C73C2511yescharacteristic
328C22⋊D73—48no—
329C22⋊D73C2×SD16116yescomplemented
330C2×Dic73—22no—
331C2×Dic73—24no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—22no—
336C2×Dic73—48no—
337C2×Dic73—42no—
338C2×Dic73—42no—
339C2×Dic73C2×SD1614yes—
340C2×Dic73C22×D412yes—
341C2×Dic73C22×D412yes—
342C2×Dic73C22×D412yes—
343D292—22no—
344D292—22no—
345D292—48no—
346D292—42no—
347C4×D73—24no—
348C4×D73—22no—
349C4×D73—22no—
350C4×D73—48no—
351C4×D73—48no—
352C4×D73—48no—
353Dic146—24no—
354Dic146—22no—
355Dic146—22no—
356Dic146—22no—
357Dic146—48no—
358Dic146—48no—
359Dic146—42no—
360Dic146—48no—
361Dic146C2×#4114yescomplemented
362C8×C73—22no—
363C8×C73—22no—
364#10596831—22no—
365#10596831—22no—
366C22×C73—22no—
367C22×C73—28no—
368C22×C73—22no—
369C22×C73#54612yes—
370C22×C73C22×SD1614yes—
371C22×C73C22×SD1612yes—
372C22×C73#57812yes—
373C22×C73C23×D411yescharacteristic
374C2×D73—22no—
375C2×D73—28no—
376C2×D73—22no—
377C2×D73—42no—
378C2×D73—42no—
379C2×D73—42no—
380C2×D73—84no—
381C2×D73C22×SD1614yes—
382C4×C73—22no—
383C4×C73—42no—
384C4×C73—42no—
385C4×C73—42no—
386C4×C73—42no—
387C4×C73#54612yes—
388C4×C73C22×#4111yescharacteristic
389C4×C73C2×H(5,𝔽2)11yescharacteristic
390Dic73—24no—
391Dic73—22no—
392Dic73—22no—
393Dic73—42no—
394Dic73—42no—
395Dic73C22×SD1614yes—
396C2×#3298—731nomaximal, Sylow
397C2×C73—24no—
398C2×C73#329814yescomplemented
399C2×C73C2×#54611yescharacteristic
400C2×C73C23×SD1611yescharacteristic
401C2×C73C2×#57811yescharacteristic
402D73—24no—
403D73—82no—
404C2×D4×Q8—731no—
405C2×#547—731no—
406#3298—7316no—
407C2×#487—731no—
408C2×#483—731no—
409C2×#483D7311yescharacteristic, complemented
410C2×#475—731no—
411C2×#465—731no—
412C2×#465—731no—
413C2×#461—731no—
414C2×#448—731no—
415C2×#448—731no—
416C2×C4×SD16—731no—
417C2×C8×D4—731no—
418C22×#103—731no—
419C22×#103—731no—
420C73C2×#329811yescharacteristic, complemented, Sylow
421C22×#41—1461no—
422C23×Q8—731no—
423C23×Q8—731no—
424C22×SD16—731no—
425C22×SD16—731no—
426C22×SD16—731no—
427C23×C8—731no—
428C23×C8—731no—
429D4×Q8—738no—
430D4×Q8—1464no—
431#547—738no—
432#547—1464no—
433C2×C4⋊Q8—731no—
434C2×C4⋊Q8—731no—
435C2×C4⋊Q8—1461no—
436C2×#123—1461no—
437C2×#123—1461no—
438C2×C22⋊Q8—731no—
439C2×C22⋊Q8—1461no—
440C2×C22⋊Q8—1461no—
441C2×C22⋊Q8—1461no—
442C2×C22⋊Q8C2×D7311yescharacteristic
443C2×#121—731no—
444C2×#121—731no—
445C2×C4×Q8—731no—
446C2×C4×D4—731no—
447C2×C4×D4—731no—
448C2×C4×D4—1461no—
449C22×C4⋊C4—731no—
450C22×C4⋊C4C2×D7311yescharacteristic
451#487—738no—
452#483—738no—
453#483C2×D7318yescomplemented
454#475—738no—
455#465—738no—
456#465—738no—
457#461—738no—
458#448—738no—
459#448—738no—
460C4×SD16—738no—
461C8×D4—738no—
462C2×#106—731no—
463C2×#106C2×D7311yescharacteristic
464C2×#106C2×D7311yescharacteristic
465C2×C4⋊C8—731no—
466C2×#103—731no—
467C2×#103—731no—
468C2×#103—731no—
469C2×#103—731no—
470C2×#103—731no—
471C2×#103—731no—
472C2×#103—731no—
473C2×#103—738no—
474C2×#103—738no—
475C2×#103C2×D7311yescharacteristic
476C2×#103C2×D7311yescharacteristic
477C2×#102—731no—
478C2×C22⋊C8—731no—
479C2×C22⋊C8C2×D7311yescharacteristic
480C2×C4×C8—731no—
481C2×#41—2928no—
482C2×#41—1468no—
483C22×Q8—2922no—
484C22×Q8—2922no—
485C22×Q8—734no—
486C22×Q8—734no—
487C22×Q8—731no—
488C22×Q8—731no—
489C22×Q8—1464no—
490C22×Q8—1461no—
491C22×Q8—1461no—
492C22×Q8—1464no—
493C22×Q8—1462no—
494C22×Q8—1461no—
495C22×Q8—1462no—
496C22×Q8C22×D7311yescharacteristic
497C22×D4—731no—
498C22×D4—731no—
499C22×D4—1461no—
500C22×D4—1461no—
501C23×C4—21no—
502C23×C4—731no—
503C23×C4—1461no—
504C23×C4—1461no—
505C23×C4—1461no—
506C23×C4—1461no—
507C23×C4C22×D7311yescharacteristic
508C2×SD16—2922no—
509C2×SD16—2922no—
510C2×SD16—734no—
511C2×SD16—734no—
512C2×SD16—734no—
513C2×SD16—1464no—
514C22×C8—2922no—
515C22×C8—2922no—
516C22×C8—734no—
517C22×C8—734no—
518C22×C8—731no—
519C22×C8—731no—
520C22×C8C22×D7311yescharacteristic
521C22×C8C22×D7311yescharacteristic
522C4⋊Q8—734no—
523C4⋊Q8—734no—
524C4⋊Q8—1462no—
525C4⋊Q8—1462no—
526C4⋊Q8—1468no—
527#123—1468no—
528#123—1468no—
529C22⋊Q8—22no—
530C22⋊Q8—734no—
531C22⋊Q8—1468no—
532C22⋊Q8—1468no—
533C22⋊Q8—1468no—
534C22⋊Q8—1462no—
535C22⋊Q8C22×D7314yes—
536#121—734no—
537#121—734no—
538#121—1462no—
539#121—1462no—
540C4×Q8—734no—
541C4×Q8—1462no—
542C4×D4—734no—
543C4×D4—734no—
544C4×D4—734no—
545C4×D4—1462no—
546C4×D4—1468no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—731no—
551C2×C4⋊C4—731no—
552C2×C4⋊C4—734no—
553C2×C4⋊C4—1462no—
554C2×C4⋊C4—1461no—
555C2×C4⋊C4—1461no—
556C2×C4⋊C4—1461no—
557C2×C4⋊C4—1461no—
558C2×C4⋊C4—1461no—
559C2×C4⋊C4—1461no—
560C2×C4⋊C4C22×D7311yescharacteristic
561C2×C4⋊C4C22×D7311yescharacteristic
562C2×C4⋊C4C22×D7314yes—
563C2×C4⋊C4C22×D7311yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—731no—
566C2×C22⋊C4—731no—
567C2×C22⋊C4—1461no—
568C2×C22⋊C4—1461no—
569C2×C22⋊C4—1461no—
570C2×C22⋊C4—1461no—
571C2×C42—731no—
572C2×C42—1461no—
573#106—734no—
574#106C22×D7314yes—
575#106C22×D7314yes—
576C4⋊C8—734no—
577#103—734no—
578#103—734no—
579#103—734no—
580#103—734no—
581#103—734no—
582#103—734no—
583#103—734no—
584#103C22×D7314yes—
585#103C22×D7314yes—
586#102—734no—
587C22⋊C8—734no—
588C22⋊C8C22×D7314yes—
589C4×C8—734no—
590C24—731no—
591C24—1461no—
592C24D4×D7311yescharacteristic
593#41—29232no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—2928no—
598C2×Q8—2924no—
599C2×Q8—2924no—
600C2×Q8—2924no—
601C2×Q8—2924no—
602C2×Q8—2924no—
603C2×Q8—2928no—
604C2×Q8—734no—
605C2×Q8—732no—
606C2×Q8—732no—
607C2×Q8—1468no—
608C2×Q8—1464no—
609C2×Q8—1464no—
610C2×Q8—1468no—
611C2×Q8—1462no—
612C2×Q8—1462no—
613C2×Q8—1461no—
614C2×Q8—1464no—
615C2×Q8—1461no—
616C2×Q8—1462no—
617C2×Q8C23×D7312yes—
618C2×D4—2924no—
619C2×D4—2924no—
620C2×D4—738no—
621C2×D4—734no—
622C2×D4—732no—
623C2×D4—1464no—
624C2×D4—1464no—
625C2×D4—1461no—
626C2×D4—1462no—
627C2×D4—1462no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—44no—
636C22×C4—2924no—
637C22×C4—2924no—
638C22×C4—2924no—
639C22×C4—2924no—
640C22×C4—731no—
641C22×C4—731no—
642C22×C4—731no—
643C22×C4—732no—
644C22×C4—732no—
645C22×C4—1464no—
646C22×C4—1464no—
647C22×C4—1464no—
648C22×C4—1464no—
649C22×C4—1461no—
650C22×C4—1461no—
651C22×C4—1461no—
652C22×C4—1462no—
653C22×C4—1462no—
654C22×C4D4×D7312yes—
655C22×C4D4×D7311yescharacteristic
656C22×C4C23×D7312yes—
657C22×C4C23×D7311yescharacteristic
658SD16—2924no—
659SD16—2924no—
660SD16—1468no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—2924no—
664C2×C8—2924no—
665C2×C8—732no—
666C2×C8—732no—
667C2×C8—1462no—
668C2×C8—1462no—
669C2×C8C23×D7312yes—
670C2×C8C23×D7312yes—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—734no—
677C4⋊C4—732no—
678C4⋊C4—1464no—
679C4⋊C4—1464no—
680C4⋊C4—1464no—
681C4⋊C4—1464no—
682C4⋊C4—1464no—
683C4⋊C4—1464no—
684C4⋊C4—1461no—
685C4⋊C4C23×D7312yes—
686C4⋊C4C23×D7312yes—
687C4⋊C4C23×D7312yes—
688C22⋊C4—24no—
689C22⋊C4—734no—
690C22⋊C4—734no—
691C22⋊C4—1464no—
692C22⋊C4—1464no—
693C22⋊C4—1464no—
694C22⋊C4—1464no—
695C42—732no—
696C42—732no—
697C42—1464no—
698C23—22no—
699C23—22no—
700C23—2922no—
701C23—2922no—
702C23—2922no—
703C23—732no—
704C23—734no—
705C23—1462no—
706C23—1462no—
707C23—1462no—
708C23SD16×D7314yes—
709C23C2×D4×D7312yes—
710C23C2×D4×D7311yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—42no—
714Q8—2928no—
715Q8—2928no—
716Q8—2928no—
717Q8—2922no—
718Q8—734no—
719Q8—1462no—
720Q8—1462no—
721Q8—1462no—
722Q8—1464no—
723D4—2928no—
724D4—2928no—
725D4—2922no—
726D4—7316no—
727D4—1462no—
728D4—1462no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—48no—
742C2×C4—2928no—
743C2×C4—2928no—
744C2×C4—2928no—
745C2×C4—2922no—
746C2×C4—2922no—
747C2×C4—2928no—
748C2×C4—732no—
749C2×C4—734no—
750C2×C4—732no—
751C2×C4—732no—
752C2×C4—1462no—
753C2×C4—1462no—
754C2×C4—1462no—
755C2×C4—1462no—
756C2×C4—1464no—
757C2×C4—1462no—
758C2×C4—1462no—
759C2×C4—1462no—
760C2×C4—1464no—
761C2×C4C2×D4×D7312yes—
762C2×C4C2×D4×D7311yescharacteristic
763C2×C4#41×D7312yes—
764C2×C4#1455663712yes—
765C2×C4C24×D7311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1462no—
769C8—1462no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—2922no—
774C22—2922no—
775C22—2922no—
776C22—5844no—
777C22—734no—
778C22—1468no—
779C22—1462no—
780C22—1462no—
781C22#1798922912yes—
782C22C2×SD16×D7314yes—
783C22C2×SD16×D7312yes—
784C22#1798940312yes—
785C22C22×D4×D7311yescharacteristic
786C4—22no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—2922no—
792C4—2922no—
793C4—734no—
794C4—1464no—
795C4—1462no—
796C4—1462no—
797C4#1798922912yes—
798C4C2×#41×D7311yescharacteristic
799C4C2×#1455663711yescharacteristic
800C2—24no—
801C2—5842no—
802C2—1464no—
803C2#2262179414yesdirect product factor
804C2C2×#1798922911yescharacteristic
805C2C22×SD16×D7311yescharacteristic
806C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#483×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989238C2
hypercenterC2×#483D73
hypocenterC73C2×#3298
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#17989250C2semidirect
3. #22621794C2direct (N × H)
4. C2×#17988936C2semidirect
5. C2×#17988919C2semidirect
6. C2×#17988871C2semidirect
7. C2×#17988818C2semidirect
8. C2×#17988817C2semidirect
9. C2×#17988791C2semidirect
10. C2×#17988728C2semidirect
11. C2×#17988727C2semidirect
12. C2×#17988674C2semidirect
13. C2×#17988650C2semidirect
14. C22×#14556514C2semidirect
15. C2×#103×D73C2semidirect
16. C2×#483×C73C2semidirect
26. #17989250C22semidirect
45. #17988936C22semidirect
46. #17988919C22semidirect
47. #17988871C22semidirect
48. #17988818C22semidirect
49. #17988817C22semidirect
50. #17988791C22semidirect
51. #17988728C22semidirect
52. #17988727C22semidirect
53. #17988674C22semidirect
54. #17988650C22semidirect
64. C2×#14556514C22semidirect
65. #103×D73C22semidirect
71. #483×C73C22semidirect
203. C2×Dic146#41semidirect
217. C2×C22⋊D73SD16semidirect
329. C22⋊D73C2×SD16semidirect
361. Dic146C2×#41semidirect
398. C2×C73#3298semidirect
409. C2×#483D73semidirect
420. C73C2×#3298semidirect
453. #483C2×D73semidirect
803. C2#22621794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892502
C2×#179892382
#226217942
C2×#179889362
C2×#179889192
C2×#179888712
C2×#179888182
C2×#179888172
C2×#179887912
C2×#179887282
C2×#179887272
C2×#179886742
C2×#179886502
C22×#145565142
C2×#103×D732
C2×#483×C732
C2×#329873