Finite Group Databasebeta

← C73×#10394 #32919798

Subgroups — C73×#10394 #32919798

Order 18688.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2617C211yesmaximal, characteristic
2C73×#1874C211yesmaximal, characteristic, complemented
3C73×#1852C211yesmaximal, characteristic, complemented
4C2×#327×C73C211yesmaximal, characteristic, complemented
5C2×#323×C73C211yesmaximal, characteristic, complemented
6C73×#1439C211yesmaximal, characteristic, complemented
7C73×#1294C211yesmaximal, characteristic, complemented
8C2×#121×C73C2211yescharacteristic
9C2×#120×C73—21no—
10C22×C4⋊C4×C73C2211yescharacteristic
11C22×C22⋊C4×C73—21no—
12C22×C22⋊C4×C73C2211yescharacteristic
13C2×#107×C73—21no—
14C2×#102×C73—21no—
15C2×C22⋊C8×C73C2211yescharacteristic
16C2×C22⋊C8×C73C2211yescharacteristic
17#397×C73—21no—
18#394×C73—21no—
19#394×C73—21no—
20#392×C73—21no—
21#386×C73—21no—
22#380×C73C2211yescharacteristic
23C2×#95×C73—21no—
24C2×#95×C73C2211yescharacteristic
25#340×C73—21no—
26#340×C73—21no—
27#327×C73—22no—
28#323×C73—22no—
29C25×C73D411yescharacteristic
30C22×D4×C73—21no—
31C22×D4×C73—21no—
32C22×D4×C73—21no—
33C22×D4×C73D411yescharacteristic
34C23×C4×C73—21no—
35C23×C4×C73—21no—
36C23×C4×C73D411yescharacteristic
37C23×C4×C73C2311yescharacteristic
38C22×C8×C73—21no—
39C22×C8×C73—21no—
40#121×C73—21no—
41#121×C73—21no—
42#121×C73—21no—
43#121×C73—21no—
44#120×C73—42no—
45#120×C73—42no—
46C2×C4⋊C4×C73—21no—
47C2×C4⋊C4×C73—21no—
48C2×C4⋊C4×C73—42no—
49C2×C4⋊C4×C73D411yescharacteristic
50C2×C4⋊C4×C73D411yescharacteristic
51C2×C4⋊C4×C73D411yescharacteristic
52C2×C22⋊C4×C73—21no—
53C2×C22⋊C4×C73—21no—
54C2×C22⋊C4×C73—21no—
55C2×C22⋊C4×C73—21no—
56C2×C22⋊C4×C73—21no—
57C2×C22⋊C4×C73—21no—
58C2×C22⋊C4×C73—21no—
59C2×C22⋊C4×C73—21no—
60C2×C22⋊C4×C73—21no—
61C2×C22⋊C4×C73—21no—
62C2×C22⋊C4×C73—21no—
63C2×C22⋊C4×C73—21no—
64C2×C22⋊C4×C73—42no—
65C2×C22⋊C4×C73—42no—
66C2×C22⋊C4×C73—42no—
67#107×C73—42no—
68#102×C73—42no—
69C22⋊C8×C73—21no—
70C22⋊C8×C73—21no—
71C22⋊C8×C73—21no—
72C22⋊C8×C73D412yescomplemented
73#95×C73—21no—
74#95×C73—21no—
75#95×C73—21no—
76#95×C73—21no—
77#95×C73—21no—
78#95×C73—42no—
79C24×C73—21no—
80C24×C73—21no—
81C24×C73—21no—
82C24×C73—21no—
83C24×C73—21no—
84C24×C73—21no—
85C24×C73—21no—
86C24×C73—41no—
87C24×C73—41no—
88C24×C73—41no—
89C24×C73—41no—
90C24×C73D812yes—
91C24×C73C2×D411yescharacteristic
92C2×D4×C73—21no—
93C2×D4×C73—21no—
94C2×D4×C73—41no—
95C2×D4×C73—41no—
96C2×D4×C73—42no—
97C2×D4×C73—42no—
98C2×D4×C73—41no—
99C2×D4×C73—41no—
100C2×D4×C73—41no—
101C2×D4×C73—41no—
102C2×D4×C73—41no—
103C2×D4×C73—41no—
104C2×D4×C73—81no—
105C2×D4×C73—81no—
106C2×D4×C73—81no—
107C2×D4×C73—81no—
108C22×C4×C73—22no—
109C22×C4×C73—22no—
110C22×C4×C73—21no—
111C22×C4×C73—21no—
112C22×C4×C73—21no—
113C22×C4×C73—21no—
114C22×C4×C73—21no—
115C22×C4×C73—21no—
116C22×C4×C73—41no—
117C22×C4×C73—41no—
118C22×C4×C73—41no—
119C22×C4×C73—41no—
120C22×C4×C73—41no—
121C22×C4×C73—41no—
122C22×C4×C73—41no—
123C22×C4×C73—41no—
124C22×C4×C73—41no—
125C22×C4×C73—41no—
126C22×C4×C73—41no—
127C22×C4×C73—41no—
128C22×C4×C73—41no—
129C22×C4×C73—41no—
130C22×C4×C73—41no—
131C22×C4×C73—41no—
132C22×C4×C73C2×D411yescharacteristic
133C22×C4×C73C2×D411yescharacteristic
134C22×C4×C73C2×D411yescharacteristic
135C22×C4×C73#4111yescharacteristic
136C22×C4×C73#4111yescharacteristic
137C22×C4×C73#4111yescharacteristic
138C2×C8×C73—22no—
139C2×C8×C73—41no—
140C2×C8×C73—41no—
141C2×C8×C73—41no—
142C2×C8×C73—41no—
143C2×C8×C73—41no—
144C4⋊C4×C73—22no—
145C4⋊C4×C73—22no—
146C4⋊C4×C73—21no—
147C4⋊C4×C73—21no—
148C4⋊C4×C73—41no—
149C4⋊C4×C73—41no—
150C4⋊C4×C73—41no—
151C4⋊C4×C73—41no—
152C22⋊C4×C73—42no—
153C22⋊C4×C73—42no—
154C22⋊C4×C73—48no—
155C22⋊C4×C73—41no—
156C22⋊C4×C73—41no—
157C22⋊C4×C73—41no—
158C22⋊C4×C73—41no—
159C22⋊C4×C73—41no—
160C22⋊C4×C73—41no—
161C22⋊C4×C73—41no—
162C22⋊C4×C73—41no—
163C22⋊C4×C73—81no—
164C22⋊C4×C73—81no—
165C23×C73—21no—
166C23×C73—21no—
167C23×C73—21no—
168C23×C73—21no—
169C23×C73—22no—
170C23×C73—22no—
171C23×C73—22no—
172C23×C73—42no—
173C23×C73—42no—
174C23×C73—42no—
175C23×C73—42no—
176C23×C73—42no—
177C23×C73—42no—
178C23×C73—41no—
179C23×C73—41no—
180C23×C73—41no—
181C23×C73—41no—
182C23×C73—41no—
183C23×C73—41no—
184C23×C73—41no—
185C23×C73—41no—
186C23×C73—41no—
187C23×C73—41no—
188C23×C73—41no—
189C23×C73—41no—
190C23×C73—41no—
191C23×C73—41no—
192C23×C73—41no—
193C23×C73—81no—
194C23×C73—81no—
195C23×C73—81no—
196C23×C73—81no—
197C23×C73—81no—
198C23×C73—81no—
199C23×C73#12011yescharacteristic
200C23×C73#12111yescharacteristic
201C23×C73#12311yescharacteristic
202C23×C73C2×D811yescharacteristic
203C23×C73#13511yescharacteristic
204C23×C73AGL(1,ℤ/8)11yescharacteristic
205C23×C73#13711yescharacteristic
206D4×C73—42no—
207D4×C73—81no—
208D4×C73—84no—
209D4×C73—84no—
210D4×C73—81no—
211D4×C73—81no—
212D4×C73—81no—
213D4×C73—81no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—42no—
223C2×C4×C73—42no—
224C2×C4×C73—42no—
225C2×C4×C73—42no—
226C2×C4×C73—42no—
227C2×C4×C73—42no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—42no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—81no—
242C2×C4×C73—81no—
243C2×C4×C73—81no—
244C2×C4×C73—81no—
245C2×C4×C73—81no—
246C2×C4×C73—81no—
247C2×C4×C73—81no—
248C2×C4×C73—81no—
249C2×C4×C73—81no—
250C2×C4×C73#12111yescharacteristic
251C2×C4×C73#12111yescharacteristic
252C2×C4×C73#12311yescharacteristic
253C2×C4×C73#12411yescharacteristic
254C8×C73—42no—
255C8×C73—81no—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—21no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73—21no—
263C22×C73—21no—
264C22×C73—21no—
265C22×C73—21no—
266C22×C73—21no—
267C22×C73—21no—
268C22×C73—44no—
269C22×C73—42no—
270C22×C73—42no—
271C22×C73—42no—
272C22×C73—82no—
273C22×C73—82no—
274C22×C73—82no—
275C22×C73—81no—
276C22×C73—81no—
277C22×C73—81no—
278C22×C73—81no—
279C22×C73—81no—
280C22×C73—81no—
281C22×C73—81no—
282C22×C73—81no—
283C22×C73—81no—
284C22×C73—81no—
285C22×C73—81no—
286C22×C73#39411yescharacteristic
287C22×C73#44711yescharacteristic
288C22×C73#45211yescharacteristic
289C22×C73#45311yescharacteristic
290C22×C73#45511yescharacteristic
291C22×C73B(4,𝔽2)11yescharacteristic
292C22×C73#45811yescharacteristic
293C22×C73#46611yescharacteristic
294C22×C73#46811yescharacteristic
295C22×C73#48011yescharacteristic
296C22×C73#48211yescharacteristic
297C4×C73—21no—
298C4×C73—21no—
299C4×C73—21no—
300C4×C73—21no—
301C4×C73—82no—
302C4×C73—82no—
303C4×C73—81no—
304C4×C73—81no—
305C4×C73—81no—
306C4×C73—81no—
307#10394C7311yesmaximal, characteristic, direct product factor, Sylow
308C2×C73—21no—
309C2×C73—21no—
310C2×C73—21no—
311C2×C73—21no—
312C2×C73—82no—
313C2×C73—161no—
314C2×C73#159511yescharacteristic
315C2×C73#160611yescharacteristic
316C2×C73#160711yescharacteristic
317C2×C73#161811yescharacteristic
318C2×C73#203311yescharacteristic
319C2×C73#203711yescharacteristic
320C2×C73#204411yescharacteristic
321#2617C2×C7311yescharacteristic
322#1874C2×C7311yescharacteristic, complemented
323#1852C2×C7311yescharacteristic, complemented
324C2×#327C2×C7311yescharacteristic, complemented
325C2×#323C2×C7311yescharacteristic, complemented
326#1439C2×C7311yescharacteristic, complemented
327#1294C2×C7311yescharacteristic, complemented
328C73#1039411yescharacteristic, direct product factor, Sylow
329C2×#121C22×C7311yescharacteristic
330C2×#120—21no—
331C22×C4⋊C4C22×C7311yescharacteristic
332C22×C22⋊C4—21no—
333C22×C22⋊C4C22×C7311yescharacteristic
334C2×#107—21no—
335C2×#102—21no—
336C2×C22⋊C8C22×C7311yescharacteristic
337C2×C22⋊C8C22×C7311yescharacteristic
338#397—21no—
339#394—21no—
340#394—21no—
341#392—21no—
342#386—21no—
343#380C22×C7311yescharacteristic
344C2×#95—21no—
345C2×#95C22×C7311yescharacteristic
346#340—21no—
347#340—21no—
348#327—22no—
349#323—22no—
350C25D4×C7311yescharacteristic
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4D4×C7311yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4D4×C7311yescharacteristic
358C23×C4C23×C7311yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#120—42no—
366#120—42no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4D4×C7311yescharacteristic
371C2×C4⋊C4D4×C7311yescharacteristic
372C2×C4⋊C4D4×C7311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388#107—42no—
389#102—42no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8D4×C7312yescomplemented
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—42no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24D8×C7312yes—
412C24C2×D4×C7311yescharacteristic
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4—81no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C7311yescharacteristic
454C22×C4C2×D4×C7311yescharacteristic
455C22×C4C2×D4×C7311yescharacteristic
456C22×C4#41×C7311yescharacteristic
457C22×C4#41×C7311yescharacteristic
458C22×C4#41×C7311yescharacteristic
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—48no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—81no—
515C23—81no—
516C23—81no—
517C23—81no—
518C23—81no—
519C23—81no—
520C23#120×C7311yescharacteristic
521C23#121×C7311yescharacteristic
522C23#123×C7311yescharacteristic
523C23C2×D8×C7311yescharacteristic
524C23#135×C7311yescharacteristic
525C23AGL(1,ℤ/8)×C7311yescharacteristic
526C23#137×C7311yescharacteristic
527D4—42no—
528D4—81no—
529D4—84no—
530D4—84no—
531D4—81no—
532D4—81no—
533D4—81no—
534D4—81no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4#121×C7311yescharacteristic
572C2×C4#121×C7311yescharacteristic
573C2×C4#123×C7311yescharacteristic
574C2×C4#124×C7311yescharacteristic
575C8—42no—
576C8—81no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#394×C7311yescharacteristic
608C22#447×C7311yescharacteristic
609C22#452×C7311yescharacteristic
610C22#453×C7311yescharacteristic
611C22#455×C7311yescharacteristic
612C22B(4,𝔽2)×C7311yescharacteristic
613C22#458×C7311yescharacteristic
614C22#466×C7311yescharacteristic
615C22#468×C7311yescharacteristic
616C22#480×C7311yescharacteristic
617C22#482×C7311yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—82no—
623C4—81no—
624C4—81no—
625C4—82no—
626C4—81no—
627C4—81no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—161no—
634C2C73×#159511yescharacteristic
635C2C73×#160611yescharacteristic
636C2C73×#160711yescharacteristic
637C2C73×#161811yescharacteristic
638C2C73×#203311yescharacteristic
639C2C73×#203711yescharacteristic
640C2C73×#204411yescharacteristic
subgroupG/H
center, socleC23×C73#120
commutator, Frattini, cosocleC23×C4C23×C73
prime radicalC73×#2617C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#1874C2semidirect
3. C73×#1852C2semidirect
4. C2×#327×C73C2semidirect
5. C2×#323×C73C2semidirect
6. C73×#1439C2semidirect
7. C73×#1294C2semidirect
72. C22⋊C8×C73D4semidirect
307. #10394C73direct (N × H)
322. #1874C2×C73semidirect
323. #1852C2×C73semidirect
324. C2×#327C2×C73semidirect
325. C2×#323C2×C73semidirect
326. #1439C2×C73semidirect
327. #1294C2×C73semidirect
328. C73#10394direct (N × H)
393. C22⋊C8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#26172
C73×#18742
C73×#18522
C2×#327×C732
C2×#323×C732
C73×#14392
C73×#12942
#1039473