Finite Group Databasebeta

← C2×#22620815 #33956672

Subgroups — C2×#22620815 #33956672

Order 18688.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989165C211yesmaximal, characteristic
2C2×#17989158C211yesmaximal, characteristic, complemented
3#22620815C2116yesmaximal, direct product factor
4C2×#17988923C211yesmaximal, characteristic, complemented
5C2×#17988929C211yesmaximal, characteristic, complemented
6C2×#17988912C211yesmaximal, characteristic, complemented
7C2×#17988918C211yesmaximal, characteristic, complemented
8C2×#17988845C211yesmaximal, characteristic, complemented
9C2×#17988833C211yesmaximal, characteristic, complemented
10C2×#17988828C211yesmaximal, characteristic, complemented
11C2×#17988816C211yesmaximal, characteristic, complemented
12C2×#17988751C211yesmaximal, characteristic, complemented
13C2×#17988751C211yesmaximal, characteristic, complemented
14C2×#17988745C211yesmaximal, characteristic, complemented
15C2×#17988728C211yesmaximal, characteristic, complemented
16C2×#408×C73C211yesmaximal, characteristic, complemented
17C22×#11924028C2211yescharacteristic
18C23×Dic146C2211yescharacteristic
19C22×Dic292C2211yescharacteristic
20C22×Dic292C2211yescharacteristic
21C22×#11924017C2211yescharacteristic
22C22×#11924017C2211yescharacteristic
23#17989165—24no—
24#17989165C2218yes—
25#17989158—24no—
26#17989158C2218yescomplemented
27C2×#14556589—21no—
28C2×#14556578—21no—
29C2×#14556572—21no—
30C2×#14556572—21no—
31C2×#14556570C2211yescharacteristic
32C2×#14556570C2211yescharacteristic
33C2×#14556570C2211yescharacteristic
34C2×#14556570C2211yescharacteristic
35C2×#14556570C2211yescharacteristic
36C2×#14556570C2211yescharacteristic
37C2×#14556567—21no—
38C2×#14556565C2211yescharacteristic
39C2×#14556565C2211yescharacteristic
40C2×#14556563—21no—
41C2×#14556563—21no—
42C2×#14556562—21no—
43C2×#14556550C2211yescharacteristic
44C22×C4⋊Dic73C2211yescharacteristic
45#17988929C2218yescomplemented
46#17988923C2218yescomplemented
47#17988918C2218yescomplemented
48#17988912C2218yescomplemented
49#17988845C2218yescomplemented
50#17988833C2218yescomplemented
51#17988828C2218yescomplemented
52#17988816C2218yescomplemented
53#17988751C2218yescomplemented
54#17988751C2218yescomplemented
55#17988745C2218yescomplemented
56#17988728C2218yescomplemented
57C2×#14556525C2211yescharacteristic
58C2×#14556525C2211yescharacteristic
59C2×#14556523C2211yescharacteristic
60C2×#14556523C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556516C2211yescharacteristic
63C2×#14556516C2211yescharacteristic
64C2×#14556516C2211yescharacteristic
65C2×#14556516C2211yescharacteristic
66C2×#14556516C2211yescharacteristic
67C2×#14556513C2211yescharacteristic
68C2×#14556513C2211yescharacteristic
69C22×#41×C73C2211yescharacteristic
70C22×M16×C73C2211yescharacteristic
71C23×C8×C73C2211yescharacteristic
72#408×C73C2218yescomplemented
73C2×C22⋊C8×C73C2211yescharacteristic
74C2×C22⋊C8×C73C2211yescharacteristic
75C2×C22⋊C8×C73C2211yescharacteristic
76C2×C22⋊C8×C73C2211yescharacteristic
77C2×#11924028—22no—
78C2×#11924028—42no—
79C2×#11924028—42no—
80C2×#11924028C2314yes—
81C22×Dic146—21no—
82C22×Dic146—22no—
83C22×Dic146—42no—
84C22×Dic146—42no—
85C22×Dic146C2311yescharacteristic
86C22×Dic146C2311yescharacteristic
87C22×Dic146C2311yescharacteristic
88C22×Dic146C2314yes—
89C22×D292C2311yescharacteristic
90C22×C22⋊D73—21no—
91C22×C22⋊D73—21no—
92C22×C22⋊D73—21no—
93C23×Dic73—21no—
94C23×Dic73—21no—
95C22×C4×D73—21no—
96C2×Dic292—42no—
97C2×Dic292—42no—
98C2×Dic292C2314yes—
99C2×Dic292C2314yes—
100C2×#11924017—42no—
101C2×#11924017—42no—
102C2×#11924017C2314yes—
103C2×#11924017C2314yes—
104#14556589—28no—
105#14556578—28no—
106#14556572—28no—
107#14556572—28no—
108#14556570—22no—
109#14556570—22no—
110#14556570—22no—
111#14556570—22no—
112#14556570—22no—
113#14556570—22no—
114#14556570C2314yes—
115#14556570C2314yes—
116#14556570C2314yes—
117#14556570C2314yes—
118#14556570C2314yes—
119#14556570C2314yes—
120#14556567—28no—
121#14556565—22no—
122#14556565—22no—
123#14556565C2314yes—
124#14556565C2314yes—
125#14556563—28no—
126#14556563—28no—
127#14556562—28no—
128#14556550—22no—
129#14556550C2314yes—
130C2×C4⋊Dic73—22no—
131C2×C4⋊Dic73—21no—
132C2×C4⋊Dic73C2311yescharacteristic
133C2×C4⋊Dic73C2311yescharacteristic
134C2×C4⋊Dic73C2311yescharacteristic
135C2×C4⋊Dic73C2311yescharacteristic
136C2×C4⋊Dic73C2314yes—
137C2×#11924007—21no—
138C2×#11924007—21no—
139C2×#11924007—21no—
140C2×#11924007—21no—
141C2×#11924007—21no—
142C2×#11924007—21no—
143C2×C22⋊Dic73—21no—
144C2×C22⋊Dic73—21no—
145C2×C22⋊Dic73—21no—
146C2×C22⋊Dic73—21no—
147C2×C22⋊Dic73—21no—
148C2×C22⋊Dic73—21no—
149C2×C22⋊Dic73—21no—
150C2×#11924005—21no—
151C2×#11924005—21no—
152C2×C4×Dic73—21no—
153#14556525C2314yes—
154#14556525C2314yes—
155#14556523C2314yes—
156#14556523C2314yes—
157#14556516C2314yes—
158#14556516C2314yes—
159#14556516C2314yes—
160#14556516C2314yes—
161#14556516C2314yes—
162#14556516C2314yes—
163#14556513C2314yes—
164#14556513C2314yes—
165C2×#41×C73—42no—
166C2×#41×C73—42no—
167C2×#41×C73D414yes—
168C2×#41×C73C2314yes—
169C22×Q8×C73D411yescharacteristic
170C22×D4×C73D411yescharacteristic
171C22×D4×C73D411yescharacteristic
172C22×D4×C73D411yescharacteristic
173C23×C4×C73C2311yescharacteristic
174C23×C4×C73C2311yescharacteristic
175C23×C4×C73C2311yescharacteristic
176C2×M16×C73—42no—
177C2×M16×C73C2314yes—
178C22×C8×C73—42no—
179C22×C8×C73C2311yescharacteristic
180C22×C8×C73C2311yescharacteristic
181C22×C8×C73C2311yescharacteristic
182C22×C8×C73C2311yescharacteristic
183C22×C8×C73C2314yes—
184C22⋊C8×C73C2314yes—
185C22⋊C8×C73C2314yes—
186C22⋊C8×C73C2314yes—
187C22⋊C8×C73C2314yes—
188C23×D73—21no—
189#11924028—44no—
190#11924028—44no—
191#11924028—48no—
192C2×Dic146—22no—
193C2×Dic146—22no—
194C2×Dic146—22no—
195C2×Dic146—22no—
196C2×Dic146—22no—
197C2×Dic146—22no—
198C2×Dic146—21no—
199C2×Dic146—21no—
200C2×Dic146—21no—
201C2×Dic146—24no—
202C2×Dic146—44no—
203C2×Dic146—44no—
204C2×Dic146—44no—
205C2×Dic146—48no—
206C2×Dic146C2412yes—
207C2×Dic146C2412yes—
208C2×Dic146C2412yes—
209C2×D292—22no—
210C2×D292—22no—
211C2×D292—21no—
212C2×D292C2412yes—
213C2×C22⋊D73—24no—
214C2×C22⋊D73—24no—
215C2×C22⋊D73—24no—
216C2×C22⋊D73—44no—
217C2×C22⋊D73—82no—
218C2×C22⋊D73—82no—
219C22×Dic73—21no—
220C22×Dic73—21no—
221C22×Dic73—21no—
222C22×Dic73—21no—
223C22×Dic73—21no—
224C22×Dic73—21no—
225C22×Dic73—21no—
226C22×Dic73—24no—
227C22×Dic73—24no—
228C22×Dic73—44no—
229C22×Dic73—82no—
230C2×C4×D73—24no—
231C2×C4×D73—44no—
232Dic292—44no—
233Dic292—44no—
234#11924017—44no—
235#11924017—44no—
236C4⋊Dic73—24no—
237C4⋊Dic73—21no—
238C4⋊Dic73—21no—
239C4⋊Dic73—21no—
240C4⋊Dic73—21no—
241C4⋊Dic73C2412yes—
242C4⋊Dic73C2412yes—
243C4⋊Dic73C2412yes—
244C4⋊Dic73C2412yes—
245#11924007—24no—
246#11924007—24no—
247#11924007—24no—
248#11924007—24no—
249#11924007—24no—
250#11924007—24no—
251C22⋊Dic73—24no—
252C22⋊Dic73—24no—
253C22⋊Dic73—24no—
254C22⋊Dic73—24no—
255C22⋊Dic73—24no—
256C22⋊Dic73—24no—
257C22⋊Dic73—24no—
258#11924005—24no—
259#11924005—24no—
260C4×Dic73—24no—
261C24×C73C2×D411yescharacteristic
262C24×C73C2×D411yescharacteristic
263C24×C73C2×D411yescharacteristic
264#41×C73—48no—
265#41×C73—44no—
266#41×C73—44no—
267C2×Q8×C73—42no—
268C2×Q8×C73C2×D414yes—
269C2×D4×C73—42no—
270C2×D4×C73—42no—
271C2×D4×C73—42no—
272C2×D4×C73C2×D414yes—
273C2×D4×C73C2×D414yes—
274C2×D4×C73C2×D414yes—
275C22×C4×C73—22no—
276C22×C4×C73—22no—
277C22×C4×C73—22no—
278C22×C4×C73—22no—
279C22×C4×C73—22no—
280C22×C4×C73—22no—
281C22×C4×C73C2×D411yescharacteristic
282C22×C4×C73C2×D411yescharacteristic
283C22×C4×C73C2×D411yescharacteristic
284C22×C4×C73C2×D412yes—
285C22×C4×C73C2×D412yes—
286C22×C4×C73C2×D412yes—
287C22×C4×C73C2412yes—
288C22×C4×C73C2412yes—
289C22×C4×C73C2412yes—
290C22×C4×C73C2411yescharacteristic
291M16×C73—44no—
292C2×C8×C73—22no—
293C2×C8×C73—22no—
294C2×C8×C73—22no—
295C2×C8×C73—22no—
296C2×C8×C73—44no—
297C2×C8×C73C2412yes—
298C2×C8×C73C2412yes—
299C2×C8×C73C2412yes—
300C2×C8×C73C2412yes—
301C23×C73—22no—
302C23×C73—22no—
303C23×C73—22no—
304C23×C73—22no—
305C23×C73—22no—
306C23×C73—22no—
307C23×C73—22no—
308C23×C73—22no—
309C23×C73—22no—
310C23×C73C22×D412yes—
311C23×C73C22×D412yes—
312C23×C73C22×D412yes—
313C23×C73C22×D411yescharacteristic
314C22×D73—22no—
315C22×D73—42no—
316C22×D73—42no—
317C22×D73—42no—
318Q8×C73—44no—
319D4×C73—44no—
320D4×C73—44no—
321D4×C73—44no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—24no—
326C2×C4×C73—24no—
327C2×C4×C73—24no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73C22×D412yes—
335C2×C4×C73C22×D412yes—
336C2×C4×C73C22×D412yes—
337C2×C4×C73C22×D411yescharacteristic
338C2×C4×C73H(5,𝔽2)12yes—
339C2×C4×C73H(5,𝔽2)12yes—
340C2×C4×C73C2511yescharacteristic
341C22⋊D73—48no—
342C22⋊D73—84no—
343C22⋊D73—84no—
344C2×Dic73—22no—
345C2×Dic73—22no—
346C2×Dic73—22no—
347C2×Dic73—22no—
348C2×Dic73—22no—
349C2×Dic73—22no—
350C2×Dic73—22no—
351C2×Dic73—48no—
352C2×Dic73—42no—
353C2×Dic73—42no—
354C2×Dic73—42no—
355C2×Dic73—42no—
356C2×Dic73—42no—
357C2×Dic73—42no—
358C2×Dic73—42no—
359C2×Dic73—84no—
360D292—22no—
361D292—22no—
362D292—42no—
363C4×D73—48no—
364Dic146—22no—
365Dic146—22no—
366Dic146—22no—
367Dic146—22no—
368Dic146—22no—
369Dic146—22no—
370Dic146—48no—
371Dic146—42no—
372Dic146—42no—
373Dic146—42no—
374C8×C73—22no—
375C8×C73—22no—
376C8×C73—22no—
377C8×C73—22no—
378C22×C73—22no—
379C22×C73—22no—
380C22×C73—22no—
381C22×C73—22no—
382C22×C73—22no—
383C22×C73—22no—
384C22×C73—22no—
385C22×C73—22no—
386C22×C73—22no—
387C22×C73—44no—
388C22×C73—44no—
389C22×C73—44no—
390C22×C73#53412yes—
391C22×C73#57712yes—
392C22×C73#57812yes—
393C22×C73C23×D411yescharacteristic
394C2×D73—42no—
395C2×D73—42no—
396C2×D73—42no—
397C2×D73—84no—
398C4×C73—22no—
399C4×C73—22no—
400C4×C73—22no—
401C4×C73#53412yes—
402C4×C73C2×H(5,𝔽2)11yescharacteristic
403C4×C73C2×H(5,𝔽2)11yescharacteristic
404Dic73—42no—
405Dic73—42no—
406Dic73—42no—
407Dic73—42no—
408Dic73—42no—
409Dic73—42no—
410Dic73—42no—
411C2×#3201—731nomaximal, Sylow
412C2×C73—42no—
413C2×C73—42no—
414C2×C73—42no—
415C2×C73#320114yescomplemented
416C2×C73C2×#53411yescharacteristic
417C2×C73C2×#57711yescharacteristic
418C2×C73C2×#57811yescharacteristic
419D73—82no—
420C2×#537—731no—
421C2×#536—731no—
422#3201—7316no—
423C2×#484—731no—
424C2×#485—731no—
425C2×#482—731no—
426C2×#483—731no—
427C2×#470—731no—
428C2×#468—731no—
429C2×#467—731no—
430C2×#465—731no—
431C2×#452—731no—
432C2×#452—731no—
433C2×#451—731no—
434C2×#448—731no—
435C2×#408D7311yescharacteristic, complemented
436C73C2×#320111yescharacteristic, complemented, Sylow
437C22×#41—731no—
438C22×#41C2×D7311yescharacteristic
439C23×Q8—731no—
440C22×Q16—731no—
441C22×Q16—731no—
442C22×SD16—731no—
443C22×SD16—731no—
444C22×M16C2×D7311yescharacteristic
445C23×C8C2×D7311yescharacteristic
446#537—738no—
447#537—1464no—
448#536—738no—
449#536—1464no—
450C2×C4⋊Q8—1461no—
451C2×#124—1461no—
452C2×#123—1461no—
453C2×#123—1461no—
454C2×C22⋊Q8—731no—
455C2×C22⋊Q8—731no—
456C2×C22⋊Q8—731no—
457C2×C22⋊Q8—731no—
458C2×C22⋊Q8—731no—
459C2×C22⋊Q8—731no—
460C2×C22⋊Q8—1461no—
461C2×#121—731no—
462C2×#121—731no—
463C2×#121—1461no—
464C2×#121—1461no—
465C2×#121—1461no—
466C2×#117—731no—
467C22×C4⋊C4—731no—
468#485—738no—
469#484—738no—
470#483—738no—
471#482—738no—
472#470—738no—
473#468—738no—
474#467—738no—
475#465—738no—
476#452—738no—
477#452—738no—
478#451—738no—
479#448—738no—
480C2×#107—731no—
481C2×#107—731no—
482C2×#106—731no—
483C2×#106—731no—
484C2×#103—731no—
485C2×#103—731no—
486C2×#103—731no—
487C2×#103—731no—
488C2×#103—731no—
489C2×#103—731no—
490C2×#102—731no—
491C2×#102—731no—
492#408C2×D7318yescomplemented
493C2×C22⋊C8C2×D7311yescharacteristic
494C2×C22⋊C8C2×D7311yescharacteristic
495C2×C22⋊C8C2×D7311yescharacteristic
496C2×C22⋊C8C2×D7311yescharacteristic
497C2×#41—42no—
498C2×#41—42no—
499C2×#41—2922no—
500C2×#41—2922no—
501C2×#41—734no—
502C2×#41—1462no—
503C2×#41D29214yes—
504C2×#41C22×D7314yes—
505C22×Q8—2922no—
506C22×Q8—2922no—
507C22×Q8—734no—
508C22×Q8—731no—
509C22×Q8—731no—
510C22×Q8—731no—
511C22×Q8—1461no—
512C22×Q8—1462no—
513C22×Q8D29211yescharacteristic
514C22×D4—731no—
515C22×D4—1461no—
516C22×D4—1461no—
517C22×D4—1461no—
518C22×D4D29211yescharacteristic
519C22×D4D29211yescharacteristic
520C22×D4D29211yescharacteristic
521C23×C4—1461no—
522C23×C4—1461no—
523C23×C4—1461no—
524C23×C4C22×D7311yescharacteristic
525C23×C4C22×D7311yescharacteristic
526C23×C4C22×D7311yescharacteristic
527C2×Q16—2922no—
528C2×Q16—2922no—
529C2×Q16—734no—
530C2×Q16—734no—
531C2×SD16—2922no—
532C2×SD16—2922no—
533C2×SD16—734no—
534C2×SD16—734no—
535C2×M16—42no—
536C2×M16C22×D7314yes—
537C22×C8—42no—
538C22×C8C22×D7311yescharacteristic
539C22×C8C22×D7311yescharacteristic
540C22×C8C22×D7311yescharacteristic
541C22×C8C22×D7311yescharacteristic
542C22×C8C22×D7314yes—
543C4⋊Q8—1468no—
544#124—1468no—
545#123—1468no—
546#123—1468no—
547C22⋊Q8—734no—
548C22⋊Q8—734no—
549C22⋊Q8—734no—
550C22⋊Q8—734no—
551C22⋊Q8—734no—
552C22⋊Q8—734no—
553C22⋊Q8—1468no—
554C22⋊Q8—1462no—
555C22⋊Q8—1462no—
556C22⋊Q8—1462no—
557C22⋊Q8—1462no—
558C22⋊Q8—1462no—
559C22⋊Q8—1462no—
560#121—734no—
561#121—734no—
562#121—1468no—
563#121—1468no—
564#121—1468no—
565#121—1462no—
566#121—1462no—
567#117—734no—
568#117—1462no—
569C2×C4⋊C4—731no—
570C2×C4⋊C4—731no—
571C2×C4⋊C4—734no—
572C2×C4⋊C4—731no—
573C2×C4⋊C4—731no—
574C2×C4⋊C4—1461no—
575C2×C4⋊C4—1462no—
576C2×C4⋊C4—1461no—
577C2×C4⋊C4—1461no—
578C2×C4⋊C4—1461no—
579C2×C4⋊C4—1461no—
580C2×C4⋊C4—1461no—
581C2×C4⋊C4—1461no—
582C2×C22⋊C4—1461no—
583C2×C22⋊C4—1461no—
584C2×C22⋊C4—1461no—
585C2×C22⋊C4—1461no—
586C2×C22⋊C4—1461no—
587C2×C22⋊C4—1461no—
588C2×C22⋊C4—1461no—
589C2×C22⋊C4—1461no—
590C2×C22⋊C4—1461no—
591C2×C42—1461no—
592#107—734no—
593#107—734no—
594#106—734no—
595#106—734no—
596#103—734no—
597#103—734no—
598#103—734no—
599#103—734no—
600#103—734no—
601#103—734no—
602#102—734no—
603#102—734no—
604C22⋊C8C22×D7314yes—
605C22⋊C8C22×D7314yes—
606C22⋊C8C22×D7314yes—
607C22⋊C8C22×D7314yes—
608C24—1461no—
609C24C2×D29211yescharacteristic
610C24C2×D29211yescharacteristic
611C24C2×D29211yescharacteristic
612#41—48no—
613#41—44no—
614#41—44no—
615#41—2928no—
616#41—2924no—
617#41—2924no—
618C2×Q8—42no—
619C2×Q8—2924no—
620C2×Q8—2928no—
621C2×Q8—2924no—
622C2×Q8—2924no—
623C2×Q8—732no—
624C2×Q8—732no—
625C2×Q8—732no—
626C2×Q8—1462no—
627C2×Q8—1462no—
628C2×Q8—1462no—
629C2×Q8—1462no—
630C2×Q8—1462no—
631C2×Q8—1462no—
632C2×Q8—1461no—
633C2×Q8—1461no—
634C2×Q8—1461no—
635C2×Q8—1464no—
636C2×Q8C2×D29214yes—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—2924no—
641C2×D4—5842no—
642C2×D4—5842no—
643C2×D4—732no—
644C2×D4—1464no—
645C2×D4—1464no—
646C2×D4—1464no—
647C2×D4—1461no—
648C2×D4—1462no—
649C2×D4—1462no—
650C2×D4C2×D29214yes—
651C2×D4C2×D29214yes—
652C2×D4C2×D29214yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—2924no—
660C22×C4—2924no—
661C22×C4—5842no—
662C22×C4—1464no—
663C22×C4—1461no—
664C22×C4—1461no—
665C22×C4—1461no—
666C22×C4—1461no—
667C22×C4—1461no—
668C22×C4—1461no—
669C22×C4—1461no—
670C22×C4—1464no—
671C22×C4—1464no—
672C22×C4C2×D29212yes—
673C22×C4C2×D29212yes—
674C22×C4C2×D29212yes—
675C22×C4C2×D29211yescharacteristic
676C22×C4C2×D29211yescharacteristic
677C22×C4C2×D29211yescharacteristic
678C22×C4C23×D7312yes—
679C22×C4C23×D7312yes—
680C22×C4C23×D7312yes—
681C22×C4C23×D7311yescharacteristic
682Q16—2924no—
683Q16—2924no—
684SD16—2924no—
685SD16—2924no—
686M16—44no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—44no—
692C2×C8C23×D7312yes—
693C2×C8C23×D7312yes—
694C2×C8C23×D7312yes—
695C2×C8C23×D7312yes—
696C4⋊C4—732no—
697C4⋊C4—732no—
698C4⋊C4—732no—
699C4⋊C4—732no—
700C4⋊C4—1464no—
701C4⋊C4—1464no—
702C4⋊C4—1464no—
703C4⋊C4—1464no—
704C4⋊C4—1464no—
705C4⋊C4—1464no—
706C4⋊C4—1464no—
707C4⋊C4—1461no—
708C4⋊C4—1461no—
709C4⋊C4—1461no—
710C4⋊C4—1461no—
711C22⋊C4—1464no—
712C22⋊C4—1464no—
713C22⋊C4—1464no—
714C22⋊C4—1464no—
715C22⋊C4—1464no—
716C22⋊C4—1464no—
717C22⋊C4—1464no—
718C22⋊C4—1464no—
719C22⋊C4—1464no—
720C42—1464no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—2922no—
731C23—2922no—
732C23—2922no—
733C23—1462no—
734C23C22×D29212yes—
735C23C22×D29212yes—
736C23C22×D29212yes—
737C23C22×D29211yescharacteristic
738Q8—44no—
739Q8—2928no—
740Q8—2922no—
741Q8—2922no—
742Q8—2922no—
743Q8—1462no—
744Q8—1462no—
745Q8—1462no—
746Q8—1462no—
747Q8—1462no—
748Q8—1462no—
749D4—44no—
750D4—44no—
751D4—44no—
752D4—2928no—
753D4—2922no—
754D4—5844no—
755D4—5844no—
756D4—1462no—
757D4—1462no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—2928no—
771C2×C4—2928no—
772C2×C4—2922no—
773C2×C4—2922no—
774C2×C4—2922no—
775C2×C4—2922no—
776C2×C4—2922no—
777C2×C4—2922no—
778C2×C4—2922no—
779C2×C4—5844no—
780C2×C4—1462no—
781C2×C4—1462no—
782C2×C4—1462no—
783C2×C4—1462no—
784C2×C4—1462no—
785C2×C4—1462no—
786C2×C4—1462no—
787C2×C4C22×D29212yes—
788C2×C4C22×D29212yes—
789C2×C4C22×D29212yes—
790C2×C4C22×D29211yescharacteristic
791C2×C4#1455663612yes—
792C2×C4#1455663612yes—
793C2×C4C24×D7311yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—2922no—
811C22—2922no—
812C22—2922no—
813C22—5844no—
814C22#1798914912yes—
815C22#1798939912yes—
816C22#1798940412yes—
817C22C23×D29211yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—2922no—
822C4—2922no—
823C4—2922no—
824C4—2922no—
825C4—2922no—
826C4—2922no—
827C4—2922no—
828C4#1798914912yes—
829C4C2×#1455663611yescharacteristic
830C4C2×#1455663611yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—5842no—
835C2#2262081514yesdirect product factor
836C2C2×#1798914911yescharacteristic
837C2C2×#1798939911yescharacteristic
838C2C2×#1798940411yescharacteristic
subgroupG/H
centerC23C22×D292
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#408×C73C2
socleC23×C73C22×D4
prime radicalC2×#17989165C2
hypercenterC2×#408D73
hypocenterC73C2×#3201
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C2×#17989158C2semidirect
3. #22620815C2direct (N × H)
4. C2×#17988923C2semidirect
5. C2×#17988929C2semidirect
6. C2×#17988912C2semidirect
7. C2×#17988918C2semidirect
8. C2×#17988845C2semidirect
9. C2×#17988833C2semidirect
10. C2×#17988828C2semidirect
11. C2×#17988816C2semidirect
12. C2×#17988751C2semidirect
13. C2×#17988751C2semidirect
14. C2×#17988745C2semidirect
15. C2×#17988728C2semidirect
16. C2×#408×C73C2semidirect
26. #17989158C22semidirect
45. #17988929C22semidirect
46. #17988923C22semidirect
47. #17988918C22semidirect
48. #17988912C22semidirect
49. #17988845C22semidirect
50. #17988833C22semidirect
51. #17988828C22semidirect
52. #17988816C22semidirect
53. #17988751C22semidirect
54. #17988751C22semidirect
55. #17988745C22semidirect
56. #17988728C22semidirect
72. #408×C73C22semidirect
415. C2×C73#3201semidirect
435. C2×#408D73semidirect
436. C73C2×#3201semidirect
492. #408C2×D73semidirect
835. C2#22620815direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179891652
C2×#179891582
#226208152
C2×#179889232
C2×#179889292
C2×#179889122
C2×#179889182
C2×#179888452
C2×#179888332
C2×#179888282
C2×#179888162
C2×#179887512
C2×#179887452
C2×#179887282
C2×#408×C732
C2×#320173