Finite Group Databasebeta

← #13360263

Subgroups — #13360263

Order 1792.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3035C211yesmaximal, characteristic
2C2×#89969C211yesmaximal, characteristic, complemented
3C2×#89968C211yesmaximal, characteristic, complemented
4#11740721C211yesmaximal, characteristic, complemented
5#11739956C211yesmaximal, characteristic, complemented
6#11729841C211yesmaximal, characteristic, complemented
7#11729841C211yesmaximal, characteristic, complemented
8#11729572C211yesmaximal, characteristic, complemented
9#11729400C211yesmaximal, characteristic, complemented
10#11728228C211yesmaximal, characteristic, complemented
11#11728221C211yesmaximal, characteristic, complemented
12#11728045C211yesmaximal, characteristic, complemented
13#11728045C211yesmaximal, characteristic, complemented
14#11728044C211yesmaximal, characteristic, complemented
15#11728043C211yesmaximal, characteristic, complemented
16C2×C7×#135C2211yescharacteristic
17C2×C7×#135C2211yescharacteristic
18C7×#532C2211yescharacteristic
19C4×C7×#41C2211yescharacteristic
20C2×#6511C2211yescharacteristic
21C2×#6511C2211yescharacteristic
22C2×#6511C2211yescharacteristic
23C2×#6511C2211yescharacteristic
24C7×#464C411yescharacteristic, complemented
25C7×#464C411yescharacteristic, complemented
26C7×#463C411yescharacteristic, complemented
27C7×#463C411yescharacteristic, complemented
28C7×#462C411yescharacteristic, complemented
29C7×#461C411yescharacteristic, complemented
30C7×#460C411yescharacteristic, complemented
31C7×#459C411yescharacteristic, complemented
32C2×C7×C4⋊C8C2211yescharacteristic
33C7×#416C2211yescharacteristic
34C7×#416C2211yescharacteristic
35C2×#6411C2211yescharacteristic
36C2×#6411C2211yescharacteristic
37C2×#6411C2211yescharacteristic
38C2×#6411C2211yescharacteristic
39C2×#6411C2211yescharacteristic
40C2×#6411C2211yescharacteristic
41#90006C2211yescharacteristic
42#90006C2211yescharacteristic
43#89969—24no—
44#89968—24no—
45C2×#6393C2211yescharacteristic
46C2×#6393C2211yescharacteristic
47C2×#6389C2211yescharacteristic
48C2×C8×Dic7C2211yescharacteristic
49#89783—21no—
50#89783—21no—
51#89783—21no—
52#89783—21no—
53#89769—21no—
54#89769—21no—
55#89769C2211yescharacteristic
56#89769C2211yescharacteristic
57C4×C4⋊Dic7C2211yescharacteristic
58#89696C2211yescharacteristic
59C4×#1136—21no—
60C4×#1136C2211yescharacteristic
61C2×#6377—21no—
62C2×#6377C2211yescharacteristic
63#89347C2211yescharacteristic
64#89347C2211yescharacteristic
65#89345C2211yescharacteristic
66#89345C2211yescharacteristic
67#89327C2211yescharacteristic
68#89327C2211yescharacteristic
69#21519—71nomaximal, Sylow
70C2×C7×#41C2311yescharacteristic
71C2×C7×#41C2311yescharacteristic
72C2×C7×#41C2311yescharacteristic
73C7×#135—22no—
74C7×#135—22no—
75C7×#135—22no—
76C7×#135—22no—
77C2×C7×Q16C2×C411yescharacteristic
78C2×C7×Q16C2×C411yescharacteristic
79C2×C7×SD16C2×C411yescharacteristic
80C2×C7×SD16C2×C411yescharacteristic
81C2×C7×SD16C2×C411yescharacteristic
82C2×C7×SD16C2×C411yescharacteristic
83C2×C7×D8C2×C411yescharacteristic
84C2×C7×D8C2×C411yescharacteristic
85C22×C7×C8C2311yescharacteristic
86C22×C7×C8C2311yescharacteristic
87C7×C4⋊Q8C2×C411yescharacteristic
88C7×#127C2×C411yescharacteristic
89C7×#124C2×C411yescharacteristic
90C7×#124C2×C411yescharacteristic
91C7×#121—21no—
92C7×#121—21no—
93C4×C7×Q8C2×C411yescharacteristic
94C4×C7×Q8C2×C411yescharacteristic
95C4×C7×D4—21no—
96C4×C7×D4—21no—
97C4×C7×D4—21no—
98C4×C7×D4—21no—
99C4×C7×D4C2×C411yescharacteristic
100C4×C7×D4C2×C411yescharacteristic
101C7×#117—21no—
102C7×#117C2311yescharacteristic
103C2×C42×C7—21no—
104C2×C42×C7C2311yescharacteristic
105#6511—22no—
106#6511—22no—
107#6511—22no—
108#6511—22no—
109#6511—22no—
110#6511—22no—
111#6511—22no—
112#6511D414yescomplemented
113C2×C4⋊Dic7—21no—
114C2×C4×Dic7C2311yescharacteristic
115C2×C4×Dic7C2311yescharacteristic
116C2×#1136—21no—
117C2×#1136—21no—
118C2×#1136—21no—
119C2×#1136—21no—
120C2×#1136C2311yescharacteristic
121C2×#1136C2311yescharacteristic
122C2×#1136C2311yescharacteristic
123C2×#1136C2311yescharacteristic
124C22×C7⋊C8—21no—
125C22×C7⋊C8—21no—
126C22×C7⋊C8—21no—
127C22×C7⋊C8—21no—
128C22×C7⋊C8C2311yescharacteristic
129C22×C7⋊C8C2311yescharacteristic
130C7×C4⋊C8C2×C411yescharacteristic
131C7×C4⋊C8C2×C411yescharacteristic
132C7×C4⋊C8C2×C411yescharacteristic
133C7×C4⋊C8C2×C411yescharacteristic
134C7×#103C2×C411yescharacteristic
135C7×#103C2×C411yescharacteristic
136C7×#103C2×C411yescharacteristic
137C7×#103C2×C411yescharacteristic
138C7×#102C2×C411yescharacteristic
139C7×#102C2×C411yescharacteristic
140C7×#102C2×C411yescharacteristic
141C7×#102C2×C411yescharacteristic
142#6411—22no—
143#6411—22no—
144#6411—22no—
145#6411—22no—
146#6411—22no—
147#6411—22no—
148C7⋊#95—21no—
149C22⋊(C7⋊C8)—21no—
150C22⋊(C7⋊C8)—21no—
151C22⋊(C7⋊C8)—21no—
152C22⋊(C7⋊C8)—21no—
153#6393—22no—
154#6393—22no—
155#6389—22no—
156C8×Dic7—22no—
157C4⋊(C7⋊C8)—21no—
158C4⋊(C7⋊C8)—21no—
159#6377—21no—
160#6377—21no—
161#6377—21no—
162#6377D411yescharacteristic
163#6377D411yescharacteristic
164#6377D411yescharacteristic
165#6377D411yescharacteristic
166C4×C7⋊C8—21no—
167C4×C7⋊C8—21no—
168C4×C7⋊C8—21no—
169#3035D711yescharacteristic
170C2×#444—71no—
171C2×#443—71no—
172#2932—71no—
173#2875—71no—
174#1980—71no—
175#1950—71no—
176#1929—71no—
177#1929—71no—
178#1876—71no—
179#1876—71no—
180#1806—71no—
181#1771—71no—
182#1765—71no—
183#1764—71no—
184C7×#41—21no—
185C7×#41—21no—
186C7×#41—21no—
187C7×#41—21no—
188C7×#41—21no—
189C7×#41—21no—
190C7×#41—21no—
191C7×#41—21no—
192C7×#41—21no—
193C7×#41—21no—
194C7×#41C2×D412yes—
195C7×#41#4112yes—
196C2×C7×Q8C22×C411yescharacteristic
197C2×C7×Q8C22×C411yescharacteristic
198C2×C7×Q8C22×C411yescharacteristic
199C2×C7×D4—21no—
200C2×C7×D4—21no—
201C2×C7×D4—21no—
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4C22×C411yescharacteristic
205C2×C7×D4C22×C411yescharacteristic
206C2×C7×D4C22×C411yescharacteristic
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7#4111yescharacteristic
213C22×C4×C7#4111yescharacteristic
214C22×C4×C7C2411yescharacteristic
215C22×Dic7—21no—
216C22×Dic7—21no—
217C7×Q16—22no—
218C7×Q16—22no—
219C7×SD16—22no—
220C7×SD16—22no—
221C7×SD16—22no—
222C7×SD16—22no—
223C7×D8—22no—
224C7×D8—22no—
225C2×C7×C8—21no—
226C2×C7×C8—21no—
227C2×C7×C8—21no—
228C2×C7×C8—21no—
229C2×C7×C8C22×C411yescharacteristic
230C2×C7×C8C22×C411yescharacteristic
231C2×C7×C8C22×C411yescharacteristic
232C2×C7×C8C22×C411yescharacteristic
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4C22×C411yescharacteristic
238C7×C4⋊C4C22×C411yescharacteristic
239C7×C22⋊C4—21no—
240C7×C22⋊C4—21no—
241C7×C22⋊C4—21no—
242C7×C22⋊C4—21no—
243C7×C22⋊C4—21no—
244C7×C22⋊C4—21no—
245C7×C22⋊C4—21no—
246C42×C7—21no—
247C42×C7—21no—
248C42×C7—21no—
249C42×C7C22×C411yescharacteristic
250C42×C7C22×C411yescharacteristic
251C42×C7C2×D411yescharacteristic
252C42×C7C2×D411yescharacteristic
253C4⋊Dic7—42no—
254C4×Dic7—21no—
255C4×Dic7—21no—
256C4×Dic7—21no—
257C4×Dic7—21no—
258#1136—24no—
259#1136—21no—
260#1136—21no—
261#1136—24no—
262#1136—21no—
263#1136—21no—
264#1136—21no—
265#1136—21no—
266#1136—42no—
267#1136—42no—
268#1136C2×D412yes—
269#1136#4112yes—
270C2×C7⋊C8—24no—
271C2×C7⋊C8—21no—
272C2×C7⋊C8—21no—
273C2×C7⋊C8—21no—
274C2×C7⋊C8—21no—
275C2×C7⋊C8—24no—
276C2×C7⋊C8—21no—
277C2×C7⋊C8—21no—
278C2×C7⋊C8—42no—
279C2×C7⋊C8—42no—
280C2×C7⋊C8C2×D411yescharacteristic
281C2×C7⋊C8C2×D411yescharacteristic
282C2×C7⋊C8C2×D411yescharacteristic
283C2×C7⋊C8C2×D411yescharacteristic
284C2×C7⋊C8C2×D412yes—
285C2×C7⋊C8#4112yes—
286C2×#135C2×D711yescharacteristic
287C2×#135C2×D711yescharacteristic
288C2×#131—71no—
289C2×#131—71no—
290C2×#131—71no—
291C2×#131—71no—
292#532C2×D711yescharacteristic
293C4×#41C2×D711yescharacteristic
294#464Dic711yescharacteristic, complemented
295#464Dic711yescharacteristic, complemented
296#463Dic711yescharacteristic, complemented
297#463Dic711yescharacteristic, complemented
298#462Dic711yescharacteristic, complemented
299#461Dic711yescharacteristic, complemented
300#460Dic711yescharacteristic, complemented
301#459Dic711yescharacteristic, complemented
302#444—144no—
303#443—144no—
304#435—141no—
305#435—141no—
306#435—141no—
307#435—141no—
308C2×#108—71no—
309C2×#108—71no—
310#423—71no—
311C2×C4⋊C8C2×D711yescharacteristic
312C2×#104—71no—
313C2×#104—71no—
314C2×#104—71no—
315C2×#104—71no—
316C2×#104—71no—
317C2×#104—71no—
318#416C2×D711yescharacteristic
319#416C2×D711yescharacteristic
320#408—71no—
321#408—71no—
322#405—71no—
323#405—71no—
324#405—141no—
325#405—141no—
326C4×M16—71no—
327C4×M16—141no—
328C2×#97—71no—
329C2×#97—71no—
330C2×#97—141no—
331C2×C4×C8—71no—
332C4×C4⋊C4—71no—
333#341—71no—
334#341—71no—
335#339—71no—
336#339—71no—
337#336—71no—
338#336—71no—
339C23×C7—21no—
340C23×C7—21no—
341C23×C7—21no—
342C23×C7C2×#4111yescharacteristic
343C7×Q8—21no—
344C7×Q8—21no—
345C7×Q8—21no—
346C7×Q8—21no—
347C7×Q8—21no—
348C7×Q8C4×D412yes—
349C7×D4—22no—
350C7×D4—22no—
351C7×D4—21no—
352C7×D4—21no—
353C7×D4—21no—
354C7×D4—21no—
355C7×D4—21no—
356C7×D4—41no—
357C7×D4—41no—
358C7×D4—41no—
359C7×D4—41no—
360C7×D4—81no—
361C7×D4—81no—
362C7×D4C4×D412yes—
363C2×C4×C7—21no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—21no—
367C2×C4×C7—21no—
368C2×C4×C7—21no—
369C2×C4×C7—21no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—81no—
377C2×C4×C7—81no—
378C2×C4×C7C4×D411yescharacteristic
379C2×C4×C7C4×D411yescharacteristic
380C2×C4×C7C4×D411yescharacteristic
381C2×C4×C7C4×D411yescharacteristic
382C2×C4×C7C23×C411yescharacteristic
383C2×C4×C7C22×D411yescharacteristic
384C2×C4×C7C22×D411yescharacteristic
385C2×C4×C7C2×#4111yescharacteristic
386C2×C4×C7C2×#4111yescharacteristic
387C2×C4×C7C2×#4111yescharacteristic
388C2×Dic7—22no—
389C2×Dic7—41no—
390C2×Dic7—41no—
391C2×Dic7—41no—
392C2×Dic7—41no—
393C2×Dic7—41no—
394C7×C8—21no—
395C7×C8—21no—
396C7×C8—21no—
397C7×C8—21no—
398C7⋊C8—22no—
399C7⋊C8—21no—
400C7⋊C8—22no—
401C7⋊C8—21no—
402C7⋊C8—41no—
403C7⋊C8—41no—
404C7⋊C8#12112yes—
405C7⋊C8#12112yes—
406C2×#41C22×D711yescharacteristic
407C2×#41C22×D711yescharacteristic
408C2×#41C22×D711yescharacteristic
409#135—22no—
410#135—22no—
411#135—22no—
412#135—22no—
413C2×Q16C2×Dic711yescharacteristic
414C2×Q16C2×Dic711yescharacteristic
415C2×SD16C2×Dic711yescharacteristic
416C2×SD16C2×Dic711yescharacteristic
417C2×SD16C2×Dic711yescharacteristic
418C2×SD16C2×Dic711yescharacteristic
419C2×D8C2×Dic711yescharacteristic
420C2×D8C2×Dic711yescharacteristic
421#131—74no—
422#131—142no—
423#131—142no—
424#131—142no—
425#131—142no—
426#131—142no—
427#131—142no—
428#131—142no—
429C2×M16—71no—
430C2×M16—71no—
431C2×M16—71no—
432C2×M16—71no—
433C2×M16—141no—
434C2×M16—141no—
435C2×M16—141no—
436C2×M16—141no—
437C22×C8—71no—
438C22×C8—71no—
439C22×C8—141no—
440C22×C8—141no—
441C22×C8—141no—
442C22×C8—141no—
443C22×C8C22×D711yescharacteristic
444C22×C8C22×D711yescharacteristic
445C4⋊Q8C2×Dic711yescharacteristic
446#127C2×Dic711yescharacteristic
447#124C2×Dic711yescharacteristic
448#124C2×Dic711yescharacteristic
449#121—21no—
450#121—21no—
451C4×Q8C2×Dic711yescharacteristic
452C4×Q8C2×Dic711yescharacteristic
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4C2×Dic711yescharacteristic
458C4×D4C2×Dic711yescharacteristic
459#117—21no—
460#117C22×D711yescharacteristic
461C2×C4⋊C4—141no—
462C2×C42—21no—
463C2×C42—71no—
464C2×C42—71no—
465C2×C42C22×D711yescharacteristic
466#108—142no—
467#108—142no—
468C4⋊C8—141no—
469C4⋊C8—141no—
470C4⋊C8C2×Dic711yescharacteristic
471C4⋊C8C2×Dic711yescharacteristic
472C4⋊C8C2×Dic711yescharacteristic
473C4⋊C8C2×Dic711yescharacteristic
474#104—142no—
475#104—142no—
476#104—142no—
477#104—142no—
478#104—142no—
479#104—142no—
480#103C2×Dic711yescharacteristic
481#103C2×Dic711yescharacteristic
482#103C2×Dic711yescharacteristic
483#103C2×Dic711yescharacteristic
484#102C2×Dic711yescharacteristic
485#102C2×Dic711yescharacteristic
486#102C2×Dic711yescharacteristic
487#102C2×Dic711yescharacteristic
488C22⋊C8—141no—
489C22⋊C8—141no—
490C22⋊C8—141no—
491C22⋊C8—141no—
492#97—71no—
493#97—71no—
494#97—71no—
495#97—71no—
496#97—141no—
497#97—141no—
498#97—142no—
499#97—141no—
500C4×C8—141no—
501C4×C8—141no—
502C4×C8—142no—
503C4×C8—141no—
504#95—141no—
505C22×C7—21no—
506C22×C7—21no—
507C22×C7—22no—
508C22×C7—41no—
509C22×C7—41no—
510C22×C7—41no—
511C22×C7—41no—
512C22×C7—41no—
513C22×C7—41no—
514C22×C7—41no—
515C22×C7—41no—
516C22×C7C2×C4×D411yescharacteristic
517C22×C7#52911yescharacteristic
518C22×C7#53211yescharacteristic
519C4×C7—21no—
520C4×C7—21no—
521C4×C7—21no—
522C4×C7—21no—
523C4×C7—22no—
524C4×C7—41no—
525C4×C7—41no—
526C4×C7—41no—
527C4×C7—41no—
528C4×C7C2×C4×D411yescharacteristic
529C4×C7C4×#4111yescharacteristic
530C4×C7C2×#12111yescharacteristic
531C4×C7#52511yescharacteristic
532Dic7—42no—
533Dic7—81no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—21no—
541#41—21no—
542#41—21no—
543#41—21no—
544#41D4×D712yes—
545#41#115912yes—
546C2×Q8C22×Dic711yescharacteristic
547C2×Q8C22×Dic711yescharacteristic
548C2×Q8C22×Dic711yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4C22×Dic711yescharacteristic
555C2×D4C22×Dic711yescharacteristic
556C2×D4C22×Dic711yescharacteristic
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4#115911yescharacteristic
565C22×C4#115911yescharacteristic
566C22×C4C23×D711yescharacteristic
567Q16—22no—
568Q16—22no—
569SD16—22no—
570SD16—22no—
571SD16—22no—
572SD16—22no—
573D8—22no—
574D8—22no—
575M16—72no—
576M16—72no—
577M16—144no—
578M16—144no—
579M16—141no—
580M16—141no—
581M16—141no—
582M16—141no—
583M16—141no—
584M16—141no—
585M16—282no—
586M16—282no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—72no—
592C2×C8—71no—
593C2×C8—71no—
594C2×C8—72no—
595C2×C8—71no—
596C2×C8—71no—
597C2×C8—144no—
598C2×C8—144no—
599C2×C8—141no—
600C2×C8—141no—
601C2×C8—141no—
602C2×C8—141no—
603C2×C8—141no—
604C2×C8—141no—
605C2×C8—282no—
606C2×C8—282no—
607C2×C8C22×Dic711yescharacteristic
608C2×C8C22×Dic711yescharacteristic
609C2×C8C22×Dic711yescharacteristic
610C2×C8C22×Dic711yescharacteristic
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—282no—
616C4⋊C4C22×Dic711yescharacteristic
617C4⋊C4C22×Dic711yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—141no—
629C42—141no—
630C42—141no—
631C42—141no—
632C42D4×D711yescharacteristic
633C42D4×D711yescharacteristic
634C42C22×Dic711yescharacteristic
635C42C22×Dic711yescharacteristic
636C2×C7—21no—
637C2×C7—21no—
638C2×C7—42no—
639C2×C7—81no—
640C2×C7—81no—
641C2×C7C4×#12111yescharacteristic
642C2×C7#295611yescharacteristic
643C2×C7#295711yescharacteristic
644C23—21no—
645C23—21no—
646C23—21no—
647C23C2×#115911yescharacteristic
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8D4×Dic712yes—
654D4—22no—
655D4—22no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667D4D4×Dic712yes—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—142no—
684C2×C4—281no—
685C2×C4—281no—
686C2×C4—281no—
687C2×C4—281no—
688C2×C4—281no—
689C2×C4D4×Dic711yescharacteristic
690C2×C4D4×Dic711yescharacteristic
691C2×C4D4×Dic711yescharacteristic
692C2×C4D4×Dic711yescharacteristic
693C2×C4C2×D4×D711yescharacteristic
694C2×C4C2×D4×D711yescharacteristic
695C2×C4C2×#115911yescharacteristic
696C2×C4D7×#4111yescharacteristic
697C2×C4D7×#4111yescharacteristic
698C2×C4C23×Dic711yescharacteristic
699C8—21no—
700C8—21no—
701C8—21no—
702C8—21no—
703C8—72no—
704C8—72no—
705C8—142no—
706C8—141no—
707C8—141no—
708C8—142no—
709C8—281no—
710C8—281no—
711C7#2151911yescharacteristic, complemented, Sylow
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22#9028711yescharacteristic
724C22#9029111yescharacteristic
725C22C2×D4×Dic711yescharacteristic
726C4—21no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—282no—
736C4—561no—
737C4D7×#12111yescharacteristic
738C4#9029711yescharacteristic
739C4C2×D4×Dic711yescharacteristic
740C4#41×Dic711yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—81no—
745C2—81no—
746C2Dic7×#12111yescharacteristic
747C2#1174135511yescharacteristic
748C2#1174144511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
Fitting, prime radicalC7×#3035C2
socleC22×C7C2×C4×D4
cosocleC22×C4×C7C24
hypercenter#3035D7
hypocenterC7#21519
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
2. C2×#89969C2semidirect
3. C2×#89968C2semidirect
4. #11740721C2semidirect
5. #11739956C2semidirect
6. #11729841C2semidirect
7. #11729841C2semidirect
8. #11729572C2semidirect
9. #11729400C2semidirect
10. #11728228C2semidirect
11. #11728221C2semidirect
12. #11728045C2semidirect
13. #11728045C2semidirect
14. #11728044C2semidirect
15. #11728043C2semidirect
24. C7×#464C4semidirect
25. C7×#464C4semidirect
26. C7×#463C4semidirect
27. C7×#463C4semidirect
28. C7×#462C4semidirect
29. C7×#461C4semidirect
30. C7×#460C4semidirect
31. C7×#459C4semidirect
112. #6511D4semidirect
294. #464Dic7semidirect
295. #464Dic7semidirect
296. #463Dic7semidirect
297. #463Dic7semidirect
298. #462Dic7semidirect
299. #461Dic7semidirect
300. #460Dic7semidirect
301. #459Dic7semidirect
711. C7#21519semidirect

Maximal subgroups

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

subgroupindex
C7×#30352
C2×#899692
C2×#899682
#117407212
#117399562
#117298412
#117295722
#117294002
#117282282
#117282212
#117280452
#117280442
#117280432
#215197