Finite Group Databasebeta

← C2×#11741038 #14232343

Subgroups — C2×#11741038 #14232343

Order 1792.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#552C211yesmaximal, characteristic
2C2×#90234C211yesmaximal, characteristic
3#11741038C2116yesmaximal, direct product factor
4C2×#89835C211yesmaximal, characteristic, complemented
5C2×#89837C211yesmaximal, characteristic, complemented
6C2×#89824C211yesmaximal, characteristic, complemented
7C2×#89823C211yesmaximal, characteristic, complemented
8C2×#89816C211yesmaximal, characteristic, complemented
9C2×#89815C211yesmaximal, characteristic, complemented
10C2×#89792C211yesmaximal, characteristic, complemented
11C2×#89802C211yesmaximal, characteristic, complemented
12C2×#89783C211yesmaximal, characteristic
13C2×#89768C211yesmaximal, characteristic, complemented
14C2×#89767C211yesmaximal, characteristic, complemented
15C2×#89743C211yesmaximal, characteristic, complemented
16C22×#6382C211yesmaximal, characteristic, complemented
17C7×#552—24no—
18C7×#552C2218yes—
19C2×C7×#126—21no—
20C2×C7×#125—21no—
21C2×C7×#125C2211yescharacteristic
22C2×C7×#123—21no—
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C7×#117—21no—
28C2×C7×#117C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C22×#1144C2211yescharacteristic
31C2×D4×Dic7—21no—
32C22×C4⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C2×#6487C2211yescharacteristic
35C2×#6487C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90234—24no—
39#90234C2218yes—
40C2×#6453—21no—
41C2×#6441—21no—
42C2×#6441—21no—
43C2×#6432C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×#6409C2211yescharacteristic
46C2×#6409C2211yescharacteristic
47C2×#6409C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89837C2218yescomplemented
51#89835C2218yescomplemented
52#89824C2218yescomplemented
53#89823C2218yescomplemented
54#89816C2218yescomplemented
55#89815C2218yescomplemented
56#89802C2218yescomplemented
57#89792C2218yescomplemented
58#89783C2218yes—
59#89768C2218yescomplemented
60#89767C2218yescomplemented
61#89743C2218yescomplemented
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71C2×#6382C2218yescomplemented
72C2×#6381C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3344—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4D411yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×Dic7—21no—
84C23×Dic7—21no—
85C22×Dic14—21no—
86C22×Dic14C2311yescharacteristic
87C7×#126—28no—
88C7×#125—28no—
89C7×#125—22no—
90C7×#125C2314yes—
91C7×#123—28no—
92C7×C22⋊Q8—22no—
93C7×C22⋊Q8—22no—
94C7×C22⋊Q8C2314yes—
95C7×C22⋊Q8C2314yes—
96C4×C7×Q8—22no—
97C4×C7×Q8C2314yes—
98C4×C7×D4D414yes—
99C4×C7×D4C2314yes—
100C7×#117—22no—
101C7×#117—28no—
102C7×#117C2314yes—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—22no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4D411yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C4⋊C4C2314yes—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4D411yescharacteristic
119C2×C7×C22⋊C4D411yescharacteristic
120C2×C42×C7—21no—
121C2×C42×C7—21no—
122C2×C42×C7C2311yescharacteristic
123C2×C22⋊Dic7—21no—
124C2×C22⋊Dic7—21no—
125C2×#1144—24no—
126C2×#1144C2314yes—
127D4×Dic7—28no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7—22no—
132C2×C4⋊Dic7—22no—
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2311yescharacteristic
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2314yes—
137C2×C4⋊Dic7C2314yes—
138#6487—22no—
139#6487—22no—
140#6487C2314yes—
141#6487C2314yes—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×C4×Dic7—21no—
146C2×#1136—24no—
147C2×#1136C2314yes—
148C22×C7⋊C8—24no—
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2314yes—
153C22×C7⋊C8C2311yescharacteristic
154#6453—28no—
155#6441—28no—
156#6441—28no—
157#6432—22no—
158#6432C2314yes—
159C4×Dic14—22no—
160C4×Dic14C2314yes—
161#6409C2314yes—
162#6409C2314yes—
163#6409C2314yes—
164C22⋊(C7⋊C8)C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166#6384C2314yes—
167#6384C2314yes—
168#6384C2314yes—
169#6382C2314yes—
170#6382C2314yes—
171#6382C2314yes—
172#6382C2314yes—
173#6382C2314yes—
174#6382C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178C4⋊(C7⋊C8)C2314yes—
179#6377C2314yes—
180C2×#554—71no—
181C2×#552D711yescharacteristic
182#3344—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#485—71no—
186C2×#483—71no—
187C2×#483—71no—
188C2×#479—71no—
189C2×#475—71no—
190C2×#470—71no—
191C2×#467—71no—
192C2×#441—71no—
193C2×#435—71no—
194C2×#428—71no—
195C22×#106—71no—
196C24×C7C2×D411yescharacteristic
197C24×C7C2×D411yescharacteristic
198C2×C7×Q8—21no—
199C2×C7×Q8—22no—
200C2×C7×Q8—22no—
201C2×C7×Q8C2412yes—
202C2×C7×D4—24no—
203C2×C7×D4C2×D414yes—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—24no—
213C22×C4×C7—44no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2411yescharacteristic
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—24no—
228C22×Dic7—24no—
229C22×Dic7—82no—
230C22×Dic7—82no—
231C2×Dic14—22no—
232C2×Dic14—22no—
233C2×Dic14—21no—
234C2×Dic14—24no—
235C2×Dic14—82no—
236C2×Dic14C2412yes—
237C7×C4⋊C4—21no—
238C7×C4⋊C4—21no—
239C7×C4⋊C4—24no—
240C7×C4⋊C4—24no—
241C7×C4⋊C4—24no—
242C7×C4⋊C4—24no—
243C7×C4⋊C4—24no—
244C7×C4⋊C4—24no—
245C7×C4⋊C4—21no—
246C7×C4⋊C4C2×D414yes—
247C7×C4⋊C4C2412yes—
248C7×C4⋊C4C2412yes—
249C7×C4⋊C4C2412yes—
250C7×C22⋊C4—24no—
251C7×C22⋊C4—24no—
252C7×C22⋊C4—24no—
253C7×C22⋊C4C2×D414yes—
254C7×C22⋊C4C2×D414yes—
255C42×C7—24no—
256C42×C7—24no—
257C42×C7C2×D412yes—
258C42×C7C2412yes—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261#1144—28no—
262C4⋊Dic7—21no—
263C4⋊Dic7—21no—
264C4⋊Dic7—21no—
265C4⋊Dic7—24no—
266C4⋊Dic7—24no—
267C4⋊Dic7—24no—
268C4⋊Dic7C2412yes—
269C4⋊Dic7C2412yes—
270C4⋊Dic7C2412yes—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274C4×Dic7—24no—
275#1136—28no—
276C2×C7⋊C8—22no—
277C2×C7⋊C8—22no—
278C2×C7⋊C8—22no—
279C2×C7⋊C8—28no—
280C2×C7⋊C8#4114yes—
281C2×C7⋊C8C2412yes—
282C2×C7⋊C8C2412yes—
283C2×C7⋊C8C2412yes—
284C2×C7⋊C8C2412yes—
285C22×Q16—71no—
286C22×M16—71no—
287C23×C8—71no—
288#554—78no—
289#554—144no—
290#552—24no—
291#552C2×D718yes—
292C2×C4⋊Q8—71no—
293C2×#126—21no—
294C2×#125—21no—
295C2×#125—141no—
296C2×#125C2×D711yescharacteristic
297C2×#123—21no—
298C2×C22⋊Q8—71no—
299C2×C22⋊Q8—71no—
300C2×C22⋊Q8—141no—
301C2×C22⋊Q8—141no—
302C2×C22⋊Q8C2×D711yescharacteristic
303C2×C22⋊Q8C2×D711yescharacteristic
304C2×C4×Q8—71no—
305C2×C4×Q8C2×D711yescharacteristic
306C2×C4×D4—141no—
307C2×C4×D4C2×D711yescharacteristic
308C2×#117—21no—
309C2×#117C2×D711yescharacteristic
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4C2×D711yescharacteristic
313#501—78no—
314#485—78no—
315#484—78no—
316#483—78no—
317#483—78no—
318#479—78no—
319#475—78no—
320#470—78no—
321#467—78no—
322#441—78no—
323#435—78no—
324#428—78no—
325C2×#107—71no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#106—71no—
329C2×#106—71no—
330C2×#106—71no—
331C2×#106—71no—
332C2×#106—78no—
333C2×#106—71no—
334C2×#106—71no—
335C2×C4⋊C8—71no—
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×C22⋊C8—71no—
343C2×C22⋊C8—71no—
344C2×#97—71no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7#13714yes—
351C23×C7C22×D412yes—
352C23×C7C22×D412yes—
353C23×C7C22×D411yescharacteristic
354C7×Q8—22no—
355C7×Q8—22no—
356C7×Q8—42no—
357C7×D4—28no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—24no—
363C2×C4×C7—24no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—42no—
373C2×C4×C7—48no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C2×#4112yes—
383C2×C4×C72−1+412yes—
384C2×C4×C7C2511yescharacteristic
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—84no—
394C2×Dic7—84no—
395Dic14—22no—
396Dic14—22no—
397Dic14—42no—
398Dic14—84no—
399C7⋊C8—22no—
400C7⋊C8—22no—
401C7⋊C8—22no—
402C7⋊C8C2×#4114yes—
403C22×Q8—71no—
404C22×Q8—141no—
405C22×Q8C22×D711yescharacteristic
406C22×D4C22⋊D711yescharacteristic
407C23×C4—21no—
408C23×C4—141no—
409C23×C4—141no—
410C23×C4C22×D711yescharacteristic
411C23×C4C22×D711yescharacteristic
412C2×Q16—74no—
413C2×Q16—144no—
414C2×M16—74no—
415C2×M16—144no—
416C22×C8—71no—
417C22×C8—71no—
418C22×C8—74no—
419C22×C8—71no—
420C22×C8—71no—
421C22×C8—144no—
422C4⋊Q8—74no—
423C4⋊Q8—142no—
424#126—28no—
425#125—28no—
426#125—22no—
427#125—148no—
428#125C22×D714yes—
429#123—28no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C22⋊Q8—74no—
433C22⋊Q8—74no—
434C22⋊Q8—142no—
435C22⋊Q8—142no—
436C22⋊Q8—148no—
437C22⋊Q8—148no—
438C22⋊Q8C22×D714yes—
439C22⋊Q8C22×D714yes—
440C4×Q8—22no—
441C4×Q8—74no—
442C4×Q8—142no—
443C4×Q8C22×D714yes—
444C4×D4—148no—
445C4×D4C22⋊D714yes—
446C4×D4C22×D714yes—
447#117—22no—
448#117—28no—
449#117C22×D714yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—71no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—74no—
461C2×C4⋊C4—74no—
462C2×C4⋊C4—141no—
463C2×C4⋊C4—141no—
464C2×C4⋊C4—142no—
465C2×C4⋊C4—142no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4C22⋊D711yescharacteristic
471C2×C4⋊C4C22×D711yescharacteristic
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C4⋊C4C22×D714yes—
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4C22⋊D711yescharacteristic
481C2×C22⋊C4C22⋊D711yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—141no—
485C2×C42C22×D711yescharacteristic
486#107—74no—
487#107—74no—
488#107—74no—
489#106—74no—
490#106—74no—
491#106—74no—
492#106—74no—
493#106—74no—
494#106—74no—
495C4⋊C8—74no—
496#103—74no—
497#103—74no—
498#103—74no—
499#103—74no—
500#103—74no—
501#103—74no—
502C22⋊C8—74no—
503C22⋊C8—74no—
504#97—74no—
505C22×C7—28no—
506C22×C7—22no—
507C22×C7—22no—
508C22×C7—22no—
509C22×C7—22no—
510C22×C7—22no—
511C22×C7—44no—
512C22×C7#54712yes—
513C22×C7C2×#13714yes—
514C22×C7C2×#13712yes—
515C22×C7#57712yes—
516C22×C7C23×D411yescharacteristic
517C4×C7—22no—
518C4×C7—22no—
519C4×C7—22no—
520C4×C7—22no—
521C4×C7—42no—
522C4×C7—42no—
523C4×C7—42no—
524C4×C7—42no—
525C4×C7#54712yes—
526C4×C7C22×#4111yescharacteristic
527C4×C7C2×2−1+411yescharacteristic
528Dic7—42no—
529Dic7—42no—
530Dic7—42no—
531Dic7—42no—
532C24C2×C22⋊D711yescharacteristic
533C24C2×C22⋊D711yescharacteristic
534C2×Q8—21no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—72no—
538C2×Q8—141no—
539C2×Q8—144no—
540C2×Q8—142no—
541C2×Q8—142no—
542C2×Q8—562no—
543C2×Q8C23×D712yes—
544C2×D4—24no—
545C2×D4C2×C22⋊D714yes—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—44no—
556C22×C4—141no—
557C22×C4—141no—
558C22×C4—141no—
559C22×C4—141no—
560C22×C4—144no—
561C22×C4—144no—
562C22×C4—562no—
563C22×C4—562no—
564C22×C4C2×C22⋊D712yes—
565C22×C4C2×C22⋊D712yes—
566C22×C4C2×C22⋊D711yescharacteristic
567C22×C4C2×C22⋊D711yescharacteristic
568C22×C4C2×C22⋊D711yescharacteristic
569C22×C4C2×C22⋊D711yescharacteristic
570C22×C4C23×D712yes—
571C22×C4C23×D712yes—
572C22×C4C23×D711yescharacteristic
573Q16—148no—
574M16—148no—
575C2×C8—74no—
576C2×C8—72no—
577C2×C8—72no—
578C2×C8—72no—
579C2×C8—72no—
580C2×C8—148no—
581C2×C8—142no—
582C2×C8—142no—
583C2×C8—142no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—72no—
594C4⋊C4—72no—
595C4⋊C4—72no—
596C4⋊C4—144no—
597C4⋊C4—144no—
598C4⋊C4—144no—
599C4⋊C4—141no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—141no—
603C4⋊C4—141no—
604C4⋊C4—144no—
605C4⋊C4C2×C22⋊D714yes—
606C4⋊C4C23×D712yes—
607C4⋊C4C23×D712yes—
608C4⋊C4C23×D712yes—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—144no—
613C22⋊C4—144no—
614C22⋊C4C2×C22⋊D714yes—
615C22⋊C4C2×C22⋊D714yes—
616C42—24no—
617C42—24no—
618C42—144no—
619C42C2×C22⋊D712yes—
620C42C23×D712yes—
621C2×C7—24no—
622C2×C7—42no—
623C2×C7#334414yescomplemented
624C2×C7C2×#54711yescharacteristic
625C2×C7C22×#13711yescharacteristic
626C2×C7C2×#57711yescharacteristic
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23#651414yes—
633C23C22×C22⋊D712yes—
634C23C22×C22⋊D712yes—
635C23C22×C22⋊D711yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—42no—
639Q8—142no—
640Q8—142no—
641Q8—282no—
642Q8—564no—
643D4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—48no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—282no—
668C2×C4—282no—
669C2×C4—282no—
670C2×C4—282no—
671C2×C4—564no—
672C2×C4—564no—
673C2×C4D7×#4112yes—
674C2×C4#655412yes—
675C2×C4C22×C22⋊D712yes—
676C2×C4C22×C22⋊D712yes—
677C2×C4C22×C22⋊D712yes—
678C2×C4C22×C22⋊D712yes—
679C2×C4C22×C22⋊D711yescharacteristic
680C2×C4C24×D711yescharacteristic
681C8—74no—
682C8—142no—
683C8—142no—
684C8—142no—
685C7C2×#334411yescharacteristic, complemented, Sylow
686C22—22no—
687C22—22no—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22C2×#651414yes—
694C22C2×#651412yes—
695C22#9051512yes—
696C22#9052812yes—
697C22C23×C22⋊D711yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—282no—
710C4#9051512yes—
711C4C2×D7×#4111yescharacteristic
712C4C2×#655411yescharacteristic
713C2—24no—
714C2—42no—
715C2#1174103814yesdirect product factor
716C2C22×#651411yescharacteristic
717C2C2×#9051511yescharacteristic
718C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#552C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
hypercenterC2×#552D7
hypocenterC7C2×#3344
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
3. #11741038C2direct (N × H)
4. C2×#89835C2semidirect
5. C2×#89837C2semidirect
6. C2×#89824C2semidirect
7. C2×#89823C2semidirect
8. C2×#89816C2semidirect
9. C2×#89815C2semidirect
10. C2×#89792C2semidirect
11. C2×#89802C2semidirect
13. C2×#89768C2semidirect
14. C2×#89767C2semidirect
15. C2×#89743C2semidirect
16. C22×#6382C2semidirect
50. #89837C22semidirect
51. #89835C22semidirect
52. #89824C22semidirect
53. #89823C22semidirect
54. #89816C22semidirect
55. #89815C22semidirect
56. #89802C22semidirect
57. #89792C22semidirect
59. #89768C22semidirect
60. #89767C22semidirect
61. #89743C22semidirect
71. C2×#6382C22semidirect
623. C2×C7#3344semidirect
685. C7C2×#3344semidirect
715. C2#11741038direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5522
C2×#902342
#117410382
C2×#898352
C2×#898372
C2×#898242
C2×#898232
C2×#898162
C2×#898152
C2×#897922
C2×#898022
C2×#897832
C2×#897682
C2×#897672
C2×#897432
C22×#63822
C2×#33447