Finite Group Databasebeta

← #33085588

Subgroups — #33085588

Order 18688.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556599C211yesmaximal, characteristic
2C2×#17988628C211yesmaximal, characteristic, complemented
3C2×#17988626C211yesmaximal, characteristic, complemented
4#22612520C211yesmaximal, characteristic
5#22612520C211yesmaximal, characteristic
6#22609964C211yesmaximal, characteristic, complemented
7#22609963C211yesmaximal, characteristic, complemented
8#22609963C211yesmaximal, characteristic, complemented
9#22609958C211yesmaximal, characteristic, complemented
10#22609957C211yesmaximal, characteristic, complemented
11#22609954C211yesmaximal, characteristic, complemented
12#22609953C211yesmaximal, characteristic, complemented
13#22609646C211yesmaximal, characteristic, complemented
14#340×D73C211yesmaximal, characteristic, complemented
15C73×#1809C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C2×#14556599—24no—
18C2×#14556599—24no—
19C2×#14556599C418yescomplemented
20C22×#11924011C2211yescharacteristic
21C22×#11924011C2211yescharacteristic
22C23×#10596831C2211yescharacteristic
23C22×C8×D73C2211yescharacteristic
24C22×C8×D73C2211yescharacteristic
25C2×#14556549C2211yescharacteristic
26C2×#14556549C2211yescharacteristic
27C2×C4⋊C4×D73C2211yescharacteristic
28C2×C4⋊C4×D73C2211yescharacteristic
29#17988628—24no—
30#17988626—24no—
31C2×#14556525C2211yescharacteristic
32C2×#14556524C2211yescharacteristic
33C2×#14556524C2211yescharacteristic
34C2×#14556523C2211yescharacteristic
35C2×#14556522C2211yescharacteristic
36C2×#14556522C2211yescharacteristic
37#17988491—21no—
38#17988491—21no—
39#17988487—21no—
40#17988487—21no—
41#17988465—21no—
42#17988465—21no—
43#17988463—21no—
44#17988463—21no—
45#17988447C2211yescharacteristic
46#17988447C2211yescharacteristic
47#17988444C2211yescharacteristic
48#17988444C2211yescharacteristic
49#17988444C2211yescharacteristic
50#17988444C2211yescharacteristic
51#17988350C2211yescharacteristic
52#17988350C2211yescharacteristic
53#17988349C2211yescharacteristic
54#17988349C2211yescharacteristic
55#17988349C2211yescharacteristic
56#17988349C2211yescharacteristic
57C22×M16×C73C2211yescharacteristic
58C2×#107×C73C2211yescharacteristic
59C2×#106×C73C2211yescharacteristic
60#380×C73C2211yescharacteristic
61#380×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63#340×C73C2211yescharacteristic
64C2×#11924028—22no—
65C2×#11924028—22no—
66C2×#11924028—22no—
67C2×#11924028—22no—
68C2×#11924028C2×C414yes—
69C2×#11924028Q814yes—
70C22×Dic146D411yescharacteristic
71C22×D292D411yescharacteristic
72C22×C22⋊D73D411yescharacteristic
73C22×C22⋊D73D411yescharacteristic
74C22×C4×D73—21no—
75C22×C4×D73—21no—
76C22×C4×D73C2311yescharacteristic
77C22×C4×D73C2311yescharacteristic
78#14556599—232no—
79C2×#11924011—22no—
80C2×#11924011—22no—
81C2×#11924011C2×C414yes—
82C2×#11924011C2×C414yescomplemented
83C2×#11924011D414yes—
84C2×#11924011D414yes—
85C22×#10596831—22no—
86C22×#10596831—22no—
87C22×#10596831C2×C414yescomplemented
88C22×#10596831C2311yescharacteristic
89C22×#10596831C2311yescharacteristic
90C2×C8×D73—22no—
91C2×C8×D73—22no—
92C2×C8×D73—22no—
93C2×C8×D73—22no—
94C2×C8×D73C2×C414yes—
95C2×C8×D73C2×C414yescomplemented
96#14556549—22no—
97#14556549—22no—
98#14556549—22no—
99#14556549—22no—
100C2×C4⋊Dic73C2311yescharacteristic
101C2×C4⋊Dic73C2311yescharacteristic
102C2×C4⋊Dic73C2311yescharacteristic
103C2×C4⋊Dic73C2311yescharacteristic
104C2×#11924007—21no—
105C2×#11924007—21no—
106C4⋊C4×D73—22no—
107C4⋊C4×D73—22no—
108C4⋊C4×D73—22no—
109C4⋊C4×D73—22no—
110C2×C22⋊Dic73—21no—
111C2×C22⋊Dic73—21no—
112C2×#11924005—21no—
113C2×#11924005—21no—
114C2×#11924005—21no—
115C2×#11924005—21no—
116C2×#11924005—21no—
117C2×#11924005—21no—
118C2×C4×Dic73—21no—
119C2×C4×Dic73—21no—
120#14556525—22no—
121#14556524—22no—
122#14556524—22no—
123#14556523—22no—
124#14556522—22no—
125#14556522—22no—
126#14556498—21no—
127#14556498—21no—
128#14556498—21no—
129#14556498—21no—
130#14556498—21no—
131#14556498—21no—
132C23×C4×C73C2311yescharacteristic
133C2×M16×C73—22no—
134C2×M16×C73—22no—
135C2×M16×C73C2×C414yescomplemented
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C4⋊C4×C73C2311yescharacteristic
140C2×C4⋊C4×C73C2311yescharacteristic
141C2×C4⋊C4×C73C2311yescharacteristic
142C2×C22⋊C4×C73—21no—
143C2×C22⋊C4×C73—21no—
144#107×C73—22no—
145#106×C73—22no—
146#95×C73—21no—
147#95×C73—21no—
148C23×D73C2×D411yescharacteristic
149C23×D73C2×D411yescharacteristic
150#11924028—28no—
151#11924028—28no—
152#11924028—28no—
153#11924028—28no—
154C2×Dic146—22no—
155C2×Dic146—22no—
156C2×Dic146C4⋊C414yes—
157C2×D292—22no—
158C2×D292—22no—
159C2×D292C4⋊C414yes—
160C2×C22⋊D73—22no—
161C2×C22⋊D73—22no—
162C2×C22⋊D73—22no—
163C2×C22⋊D73—22no—
164C2×C22⋊D73C4⋊C414yes—
165C2×C22⋊D73C4⋊C414yes—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73C2×D411yescharacteristic
171C22×Dic73C2×D411yescharacteristic
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—21no—
176C2×C4×D73—42no—
177C2×C4×D73—42no—
178C2×C4×D73—81no—
179C2×C4×D73—81no—
180C2×C4×D73—81no—
181C2×C4×D73—81no—
182C2×C4×D73C22×C412yes—
183C2×C4×D73C22×C412yes—
184C2×C4×D73C2×D412yes—
185C2×C4×D73C2×D412yes—
186C2×C4×D73C2×Q812yes—
187C2×C4×D73C2×Q812yes—
188C2×C4×D73#4112yes—
189C2×C4×D73#4112yes—
190#11924011—28no—
191#11924011C22⋊C4116yescomplemented
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831—28no—
195C2×#10596831C22×C412yes—
196C2×#10596831C22×C412yes—
197C2×#10596831C2×D412yes—
198C2×#10596831C2×D412yes—
199C8×D73—28no—
200C8×D73—28no—
201C4⋊Dic73—21no—
202C4⋊Dic73—21no—
203C4⋊Dic73—21no—
204C4⋊Dic73—21no—
205C4⋊Dic73—21no—
206C4⋊Dic73—21no—
207C4⋊Dic73—21no—
208C4⋊Dic73—21no—
209#11924007—42no—
210#11924007—42no—
211C22⋊Dic73—81no—
212C22⋊Dic73—81no—
213#11924005—42no—
214#11924005—42no—
215#11924005—81no—
216#11924005—81no—
217#11924005—81no—
218#11924005—81no—
219C4×Dic73—42no—
220C4×Dic73—42no—
221C24×C73C2×D411yescharacteristic
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73C22×C412yes—
231C22×C4×C73C2×D411yescharacteristic
232C22×C4×C73C2×Q812yes—
233C22×C4×C73C2411yescharacteristic
234M16×C73—28no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73C22×C412yes—
238C2×C8×C73C22×C412yes—
239C2×C8×C73C2×D412yes—
240C2×C8×C73C2×D412yes—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C22⋊C4×C73—81no—
250C22⋊C4×C73—81no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73C2×C4⋊C412yes—
258C23×C73C22×D411yescharacteristic
259C22×D73—21no—
260C22×D73—21no—
261C22×D73—21no—
262C22×D73—21no—
263C22×D73—21no—
264C22×D73—21no—
265C22×D73—21no—
266C22×D73—21no—
267C22×D73—21no—
268C22×D73—21no—
269C22×D73C2×C4⋊C412yes—
270C22×D73C2×C4⋊C412yes—
271C22×D73#12112yes—
272C22×D73#12112yes—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73C2×C4⋊C412yes—
292C2×C4×C73C23×C411yescharacteristic
293C2×C4×C73C22×D411yescharacteristic
294C2×C4×C73C22×D411yescharacteristic
295C2×C4×C73C22×Q811yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×C4×C73C2×#4111yescharacteristic
298C22⋊D73—28no—
299C22⋊D73—28no—
300C2×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73C2×C4⋊C412yes—
315C2×Dic73C2×C4⋊C412yes—
316C2×Dic73#12112yes—
317C2×Dic73#12112yes—
318D292—28no—
319C4×D73—22no—
320C4×D73—22no—
321C4×D73—22no—
322C4×D73—22no—
323C4×D73—84no—
324C4×D73—84no—
325C4×D73C2×C22⋊C414yes—
326C4×D73#11714yes—
327C4×D73C22⋊Q814yes—
328C4×D73C22⋊Q814yes—
329Dic146—28no—
330C8×C73—22no—
331C8×C73C2×C22⋊C414yes—
332#10596831—22no—
333#10596831C2×C22⋊C414yes—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73—41no—
340C22×C73—41no—
341C22×C73C22×C4⋊C411yescharacteristic
342C22×C73C2×#12111yescharacteristic
343C22×C73C2×#12111yescharacteristic
344C22×C73#57611yescharacteristic
345C22×C73#57711yescharacteristic
346C22×C73#57711yescharacteristic
347C22×C73#57811yescharacteristic
348C2×D73—22no—
349C2×D73—22no—
350C2×D73—22no—
351C2×D73—22no—
352C2×D73—22no—
353C2×D73—22no—
354C2×D73—22no—
355C2×D73—22no—
356C2×D73—22no—
357C2×D73—41no—
358C2×D73—41no—
359C2×D73—41no—
360C2×D73—41no—
361C2×D73#38014yes—
362C4×C73—22no—
363C4×C73—81no—
364C4×C73—81no—
365C4×C73—81no—
366C4×C73—81no—
367C4×C73C22×C22⋊C411yescharacteristic
368C4×C73C2×#11711yescharacteristic
369C4×C73C2×C22⋊Q811yescharacteristic
370C4×C73C2×C22⋊Q811yescharacteristic
371Dic73—22no—
372Dic73—81no—
373Dic73—81no—
374Dic73—81no—
375Dic73—81no—
376Dic73#38014yes—
377#20664—731nomaximal, Sylow
378C2×C73—42no—
379C2×C73C2×#38011yescharacteristic
380C2×C73#291211yescharacteristic
381C2×C73#291311yescharacteristic
382C2×C73#306211yescharacteristic
383C2×C73#306211yescharacteristic
384C2×C73#306311yescharacteristic
385C2×C73#306311yescharacteristic
386D73—24no—
387D73—42no—
388C22×#131—731no—
389C2×#428—731no—
390C2×#428—731no—
391#2311—731no—
392#2311—731no—
393#1809—731no—
394#1809—731no—
395#1809—731no—
396#1809D7311yescharacteristic, complemented
397#1808—731no—
398#1808—731no—
399#1807—731no—
400#1807—731no—
401#1735—731no—
402C2×#340—731no—
403C73#2066411yescharacteristic, complemented, Sylow
404C22×#41—731no—
405C2×#131—738no—
406C2×#131—1464no—
407C2×#131—1464no—
408C22×M16—731no—
409C22×M16—731no—
410C22×M16C2×D7311yescharacteristic
411C23×C8—731no—
412C23×C8—731no—
413C23×C8—731no—
414C2×#117—731no—
415C2×#117—731no—
416C22×C4⋊C4—731no—
417C22×C4⋊C4—731no—
418#428—1464no—
419#428—1464no—
420C2×#107—731no—
421C2×#107—731no—
422C2×#107—731no—
423C2×#107C2×D7311yescharacteristic
424C2×#106—731no—
425C2×#106—731no—
426C2×#106—731no—
427C2×#106C2×D7311yescharacteristic
428#391—1461no—
429#391—1461no—
430#390—1461no—
431#390—1461no—
432#386—1461no—
433#386—1461no—
434#386—1461no—
435#386—1461no—
436#380—731no—
437#380—731no—
438#380—731no—
439#380—731no—
440#380—731no—
441#380—731no—
442#380C2×D7311yescharacteristic
443#380C2×D7311yescharacteristic
444#340—731no—
445#340—731no—
446#340—731no—
447#340—731no—
448#340—731no—
449#340—731no—
450#340C2×D7311yescharacteristic
451#340C2×D7311yescharacteristic
452C2×#41—734no—
453C2×#41—734no—
454C2×#41—1462no—
455C2×#41—1462no—
456C2×#41—1462no—
457C2×#41—1462no—
458C22×Q8—731no—
459C22×D4—731no—
460C22×D4—731no—
461C22×D4—731no—
462C23×C4—731no—
463C23×C4—731no—
464C23×C4—1461no—
465C23×C4—1461no—
466C23×C4C22×D7311yescharacteristic
467#131—14632no—
468C2×M16—22no—
469C2×M16—22no—
470C2×M16—734no—
471C2×M16—734no—
472C2×M16—734no—
473C2×M16—734no—
474C2×M16—1462no—
475C2×M16—1462no—
476C2×M16C4×D7314yescomplemented
477C22×C8—731no—
478C22×C8—734no—
479C22×C8—731no—
480C22×C8—734no—
481C22×C8—734no—
482C22×C8—1462no—
483C22×C8—1462no—
484C22×C8—1462no—
485C22×C8—1462no—
486C22×C8—1462no—
487C22×C8—1462no—
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490#117—1462no—
491#117—1462no—
492#117—1462no—
493#117—1462no—
494C2×C4⋊C4—731no—
495C2×C4⋊C4—731no—
496C2×C4⋊C4—731no—
497C2×C4⋊C4—731no—
498C2×C4⋊C4—1462no—
499C2×C4⋊C4—1462no—
500C2×C4⋊C4—1462no—
501C2×C4⋊C4—1462no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4C22×D7311yescharacteristic
505C2×C4⋊C4C22×D7311yescharacteristic
506C2×C4⋊C4C22×D7311yescharacteristic
507C2×C4⋊C4C22×D7311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1461no—
511C2×C22⋊C4—1461no—
512C2×C22⋊C4—1461no—
513C2×C22⋊C4—1461no—
514C2×C22⋊C4—1461no—
515C2×C22⋊C4—1461no—
516C2×C22⋊C4—1461no—
517C2×C22⋊C4—1461no—
518C2×C42—1461no—
519C2×C42—1461no—
520#107—22no—
521#107—1462no—
522#107—1462no—
523#107—1462no—
524#106—22no—
525#106—1462no—
526#106—1462no—
527#106—1462no—
528#95—21no—
529#95—21no—
530#95—1461no—
531#95—1461no—
532#95—1461no—
533#95—1461no—
534#95—1461no—
535#95—1461no—
536C24—731no—
537C24—731no—
538C24D4×D7311yescharacteristic
539#41—1468no—
540#41—1468no—
541#41—1468no—
542#41—1468no—
543C2×Q8—734no—
544C2×Q8—1462no—
545C2×Q8—1462no—
546C2×D4—734no—
547C2×D4—734no—
548C2×D4—734no—
549C2×D4—1462no—
550C2×D4—1462no—
551C2×D4—1462no—
552C2×D4—1462no—
553C2×D4—1462no—
554C2×D4—1462no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—2922no—
564C22×C4—2922no—
565C22×C4—5841no—
566C22×C4—5841no—
567C22×C4—5841no—
568C22×C4—5841no—
569C22×C4—731no—
570C22×C4—732no—
571C22×C4—732no—
572C22×C4—732no—
573C22×C4—732no—
574C22×C4—732no—
575C22×C4—732no—
576C22×C4—731no—
577C22×C4—732no—
578C22×C4—732no—
579C22×C4—1461no—
580C22×C4—1461no—
581C22×C4—1461no—
582C22×C4—1461no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4C2×C4×D7312yes—
588C22×C4D4×D7311yescharacteristic
589C22×C4Q8×D7312yes—
590C22×C4C23×D7311yescharacteristic
591M16—28no—
592M16—7316no—
593M16—1468no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—732no—
597C2×C8—732no—
598C2×C8—732no—
599C2×C8—732no—
600C2×C8—1468no—
601C2×C8—1468no—
602C2×C8—1461no—
603C2×C8—1461no—
604C2×C8—1468no—
605C2×C8C2×C4×D7312yes—
606C2×C8C2×C4×D7312yes—
607C2×C8D4×D7312yes—
608C2×C8D4×D7312yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—2922no—
618C4⋊C4—2922no—
619C4⋊C4—1461no—
620C4⋊C4—1461no—
621C4⋊C4—1461no—
622C4⋊C4—1461no—
623C4⋊C4—1461no—
624C4⋊C4—1461no—
625C4⋊C4—1461no—
626C4⋊C4—1461no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—2922no—
630C22⋊C4—2922no—
631C22⋊C4—5841no—
632C22⋊C4—5841no—
633C22⋊C4—5841no—
634C22⋊C4—5841no—
635C22⋊C4—5841no—
636C22⋊C4—5841no—
637C42—2922no—
638C42—2922no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—732no—
646C23—732no—
647C23—732no—
648C23—732no—
649C23—1461no—
650C23—1461no—
651C23—1461no—
652C23—1461no—
653C23—1461no—
654C23—1461no—
655C23—1461no—
656C23—1461no—
657C23—1461no—
658C23—1461no—
659C23C4⋊C4×D7312yes—
660C23C2×D4×D7311yescharacteristic
661Q8—1468no—
662D4—1468no—
663D4—1468no—
664D4—1468no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—2921no—
684C2×C4—2921no—
685C2×C4—2921no—
686C2×C4—2921no—
687C2×C4—2921no—
688C2×C4—2921no—
689C2×C4—2921no—
690C2×C4—2921no—
691C2×C4—2921no—
692C2×C4—2921no—
693C2×C4—2921no—
694C2×C4—2921no—
695C2×C4—5844no—
696C2×C4—5844no—
697C2×C4—732no—
698C2×C4—732no—
699C2×C4—732no—
700C2×C4—734no—
701C2×C4—734no—
702C2×C4—734no—
703C2×C4—734no—
704C2×C4—732no—
705C2×C4—1461no—
706C2×C4—1461no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4—1462no—
710C2×C4—1462no—
711C2×C4C4⋊C4×D7312yes—
712C2×C4C22×C4×D7311yescharacteristic
713C2×C4C2×D4×D7311yescharacteristic
714C2×C4C2×D4×D7311yescharacteristic
715C2×C4C2×Q8×D7311yescharacteristic
716C2×C4#41×D7311yescharacteristic
717C2×C4#41×D7311yescharacteristic
718C8—22no—
719C8—734no—
720C8—1462no—
721C8C22⋊C4×D7314yes—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—2921no—
730C22—2921no—
731C22—2921no—
732C22—2921no—
733C22—734no—
734C22—1462no—
735C22—1462no—
736C22—1462no—
737C22—1462no—
738C22—1462no—
739C22—1462no—
740C22—1462no—
741C22—1462no—
742C22—1462no—
743C22C2×C4⋊C4×D7311yescharacteristic
744C22#121×D7311yescharacteristic
745C22#121×D7311yescharacteristic
746C22#1798939111yescharacteristic
747C22#1798939611yescharacteristic
748C22#1798939711yescharacteristic
749C22#1798940311yescharacteristic
750C4—22no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—5841no—
756C4—5841no—
757C4—5841no—
758C4—5841no—
759C4—734no—
760C4—1462no—
761C4C2×C22⋊C4×D7311yescharacteristic
762C4#117×D7311yescharacteristic
763C4C22⋊Q8×D7311yescharacteristic
764C4C22⋊Q8×D7311yescharacteristic
765C2—42no—
766C2—2922no—
767C2—1464no—
768C2#380×D7311yescharacteristic
769C2#2261852511yescharacteristic
770C2#2261853011yescharacteristic
771C2#2261960611yescharacteristic
772C2#2261960811yescharacteristic
773C2#2261961711yescharacteristic
774C2#2261961911yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1809C2
socleC23×C73C22×D4
prime radicalC22×#11924028C22
cosocleC22×C4×C73C24
hypercenter#1809D73
hypocenterC73#20664
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#17988628C2semidirect
3. C2×#17988626C2semidirect
6. #22609964C2semidirect
7. #22609963C2semidirect
8. #22609963C2semidirect
9. #22609958C2semidirect
10. #22609957C2semidirect
11. #22609954C2semidirect
12. #22609953C2semidirect
13. #22609646C2semidirect
14. #340×D73C2semidirect
15. C73×#1809C2semidirect
19. C2×#14556599C4semidirect
82. C2×#11924011C2×C4semidirect
87. C22×#10596831C2×C4semidirect
95. C2×C8×D73C2×C4semidirect
135. C2×M16×C73C2×C4semidirect
191. #11924011C22⋊C4semidirect
396. #1809D73semidirect
403. C73#20664semidirect
476. C2×M16C4×D73semidirect

Maximal subgroups

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

subgroupindex
C22×#145565992
C2×#179886282
C2×#179886262
#226125202
#226099642
#226099632
#226099582
#226099572
#226099542
#226099532
#226096462
#340×D732
C73×#18092
#2066473